Energy and power density for ESS.
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Until recently, electric cars were only small vehicles often designed with unusual shapes, able to move almost exclusively in the city area [1, 2]. Nowadays, electric cars are available in every size and style, often derived from the corresponding petrol models, so leading to the same internal and external fittings, load capacity, and passenger transport. Over the past few years, several legislative provisions aimed at encouraging electric mobility, pushing above all the administrations to create the boundary conditions so that the switch from a traditional vehicle to a zero-emission vehicle (ZEV) occurs with reduced discomfort [3]. Indeed, regarding the environmental impact, for assigning an optimal fuel/combustion ratio, about 85% of the combustion products in internal combustion engines (ICE) is represented by: carbon dioxide (CO2), nontoxic but responsible for the greenhouse effect, carbon monoxide (CO), toxic and now constituting 2% of the air breathed, unburned hydrocarbons (HC) and nitrogen oxides (NOx), toxic and responsible for acid rain. Therefore, the emissions of pollutants produced by traditional propulsion, multiplied by the number of vehicles in circulation, have a significant impact on our survival and life quality [4, 5]. As a consequence, the e-mobility role becomes crucial in the “green revolution,” at least as much as that of the energy production from renewable sources. The transition to this new era of mobility is gradually increasing, passing through an intermediate phase, where there is also a fair presence of hybrid solutions that are progressively accustoming the user to the electric technology. After the transition period, the full electric propulsion will be destined to establish itself exclusively.
\nThis revolution is accompanied by the parallel innovation in other sectors. The electric grid, for instance, is one of the fundamental elements to promote the development of electric cars; through a capillary presence of the charging stations to compensate the weak capacity of the onboard energy storage. The future is made of renewable sources and smart grids that manage power while taking into account both consumption and distributed generation, and electric cars can become a tool to strengthen efficiency and stability of the electric grid [6]. Several countries are already going down that route, with the so-called vehicle to grid (V2G) service: an innovative service, which allows electric vehicles to return energy to the grid when they are not in use, thus generating income for their owners [7]. Moreover, the spread of electric goes well with the sharing economy: electric car sharing is becoming increasingly common in all of the world’s major cities.
\nDesigning an electric car does not just mean replacing the ICE with an electric motor. Generally, electric car has no traditional transmission, no gear, and the engine size changes significantly (it can even be fitted in the wheels), but it needs space for the batteries, which are very heavy: the frame requires a new design; also materials change, shifting from aluminum to composite materials that are resistant but lighter, in order to increase battery capacity. The electric revolution thus opens up new opportunities regarding the areas of the design and manufacturing [8].
\nThe electric drive (ED) represents the core of the electric vehicle propulsion. It is realized by different subsystems that have a single mission: to ensure the requested power/energy based on the operating condition. This chapter will show the characteristics of the individual subsystems that carry out a generic electric drive and the main architectures of electric drives suitable for ZEVs. Particular attention will be dedicated to state-of-the-art of the architectures and topologies employed for each power-subsystem in order to obtain the best performance on the market. This approach is fundamental to obtain an improving efficiency; nowadays, according to well-to-wheel (W2W) analysis [9], thermal engines have 17–19% efficiency scores, whereas the electric engine scores are at least equal to 36%.
\nIn recent years, hybrid and electric vehicles have always gained more market share [10]. These cars are equipped with an energy storage system (ESS, typically batteries), also integrating an ICE in the case of hybrid vehicle [11]. Despite the presence of an electric motor/generator and a battery, it is not possible to define a hybrid car a zero-emission vehicle. Therefore, before addressing the main issues of our topic, it is important to better define the different topologies of hybrid/electric cars, as briefly shown in Figure 1:
Plug-in hybrid electric vehicles (PHEVs): they are hybrid vehicles, that is, with double power source for propulsion, an electric and a combustion engine whose battery, normally designed for a range of a few tens of kilometers, and can be recharged from the electric grid [12]. Once the battery is discharged or as soon as it reaches a minimum charge level (20–40% of its energy), the vehicle, according to the type of system management, enters in “normal” hybrid operation, similar to that of hybrid vehicles not rechargeable. With a battery sizing suitable for delivering a range of 30 km, it may meet to “zero emissions” most of the vehicles in the city. Several cars of this type have autonomy in electric operation even over 50 km.
Range-extended electric vehicles (REEVs): they have a plug-in battery pack and electric motor, as well as an internal combustion engine. The battery, normally sized for a range around hundred kilometers or more, can be recharged from the electric grid; once discharged, comes into action an electric generator powered by the onboard internal combustion engine which provides the battery charging [13]. The difference from a plug-in hybrid is that the electric motor always drives the wheels, with the internal combustion engine acting as a generator to recharge the battery when it is depleted. The ICE of a REEV works at an optimized regime and this allows to obtain better efficiency compared to a traditional vehicle.
Bimodal vehicles: they are vehicles equipped with two completely independent engines, respectively, electric powered by a rechargeable battery from the electric grid and endothermic that can be used as an alternative to the electric one for long distances. Often, each of the engines is connected to an axis of the vehicle, which then operates with front or rear wheel drive depending on the activated motor.
Fuel cell electric vehicles (FCEVs): hydrogen fuel cell vehicles are a different topology of electric car and they have a fuel cell stack which uses hydrogen to produce energy that then powers the wheels of the vehicle [14]. The main difference between a fuel cell and a battery is the manner for supplying the source of energy. In the fuel cell, the production of the energy carries out thanks to hydrogen supply; in this way, it is not necessary to recharge in order to generate power. The products of the chemical reaction that occurs in a fuel cell are substantially heat and water; in particular, the latter is disposed of through the tailpipe. Differently from what happens for battery-powered vehicles, vehicles equipped with fuel cell can be recharged to appropriate filling stations in the same way as conventional vehicles. Charging times are comprised between 3 and 6 min. Typically, these vehicles have autonomy of about 500 km.
Zero-emission vehicles (ZEVs): full electric vehicles, otherwise known as battery electric vehicles (BEV) or pure electric vehicles (PEV), are wholly driven by an electric motor, powered by a battery that can be plugged to the grid [15]. There is no combustion engine.
Classification of the hybrid and electric vehicles.
Then, it will be evaluated and analyzed only the several solutions to realize the power train of a ZEV.
\nThe main elements on which ZEV architecture is built on are shown in Figure 2.
\nMain subsystems of the basic ZEV architecture.
Indeed, several subsystems can be identified and each of these performs a specific mission also interacting with one or more other subsystems. The main macroblocks identified are:
The energy storage system: usually the battery pack with its management system (battery management system also called BMS), which is designed to accumulate and supply energy.
DC/AC converter: it is the power interface between the storage and the electric motor. It not only has the task of adapting the power supply but it also play important control functions, as will be fully described later.
Motor: the electric motor, which can also be operated as a generator in case of the adoption of the regenerative braking, has the task of carrying out the conversion of electric energy coming from the ESS into mechanical energy to be supplied to the mechanical transmission to allow the car motion.
Charging interface: the charging interface is essential for a ZEV, as it must allow the batteries to be recharged onboard. The charging interface includes different kinds, depending on the type/types of recharge that it wants to adopt (even more types on the same vehicle).
Control layer: the supervisor and data acquisition system is dedicated to processing driving information and transforming it into references for the aforementioned power subsystems.
Auxiliary load: the auxiliary loads, which will not be analyzed in this chapter, represent all the utilities onboard that need a power supply. Typically, the power of these loads occurs at a much lower voltage of the main voltage of the DC-bus, for example, 12 V, and must be galvanically insulated, for safety reasons, since this last. The power supply of the auxiliary load, therefore, is derived from the DC-bus through a DC/DC converter with electronic transformer (e.g., flying bridge converter or isolated switch mode power supply) which ensures the request insulation condition [16].
Mechanical transmission: the mechanical transmission of an electric vehicle takes care of converting the energy coming from the electric motor into mechanical energy of movement, distributing it directly to the wheels of the car. This element has been borrowed from traditional vehicles and therefore has poor interest in carrying out its analysis here.
Next paragraphs are dedicated to the analysis of the technological solutions used and the technical characteristics regarding the main power subsystems of the power train previously indicated. In particular, we will provide the characteristics of the individual subsystems, identifying the performances achieved by the research in progress and their use/integration into the different proposed architectures.
\nThe storage system is becoming a key component in the electric vehicle. The panorama of energy storage devices can be divided into two main families: on one side electromechanical storage devices and on the other electrochemical/electrostatic devices. The first set fundamentally includes flywheels, while for the characteristics and the performances required of an electric vehicle, electrochemical systems are employed exclusively in order to guarantee the main propulsion; the classification is broader and more detailed [17], in particular, the main categories identified are:
Fuel cells: it is an electrochemical system in which electric energy is produced through an oxidation–reduction chemical reaction. The storage difficulties are the main obstacle to the diffusion of systems based on hydrogen technologies, even if at the theoretical level, there are about several types of storage systems [18].
Electrochemical batteries:
Lead-acid batteries: they are commercially mature rechargeable batteries. Generally, they are made up of lead metal and lead dioxide electrodes immersed in a sulfuric acid electrolyte (in the charged state). Lead-acid batteries generally are used in stationary energy storage applications, especially as a DC auxiliary. The energy density of lead-acid batteries is 35–40 Wh/kg, whereas the power density is 250 W/kg; the cost is (battery system only) 150–200 $/kWh [19].
Nickel metal hydride batteries: With reference to the positive electrode (cathode) of the nickel metal hydride (NiMH) batteries, it is made by nickel hydroxide (Ni(OH)2). On the other hand, the anode uses the hydrogen as absorbing negative electrode. This latter is composed by metal hydrides, typically alloys of lanthanum and rare earths that work as a solid source of reduced hydrogen, which becomes oxidized to provide protons. As a rule, the electrolyte is alkaline (e.g., potassium hydroxide). These batteries have an energy density of 70–80 Wh/kg and a typical power density of 150–200 W/kg. The cost is around 400–450 $/kWh. Their main disadvantages are high self-discharge rates and a relatively low cycling capacity. Moreover, NiMH battery deteriorates during long time storage. This problem can be solved by charging and discharging the battery several times before reuse. This reconditioning also serves to overcome the problems of the “memory” effect [20].
Sodium/metal chloride batteries: the sodium-nickel chloride battery is better known as zero-emission battery research activities (ZEBRA) battery. These batteries work at high temperature, about 300 °C; it is very similar to the sodium sulfur battery. The energy density of the considered battery is around 100–120 Wh/kg and the specific power is about 150 W/kg. The negative electrode is composed of molten sodium, while the positive electrode is nickel in the discharged state and nickel chloride in the charged state. The molten sodium salt is employed as electrolyte. Lately, there has been a growing attention in the sodium-nickel chloride batteries for EV application. These batteries are substantially being developed and manufactured by General Electric and Fiamm SoNick. NaNiCl2 batteries have a much lower self-discharge rate and better cycling capabilities than the other nickel battery variants. Like lead-acid batteries, sodium-sulfur batteries have a limited cycle life; they are able to charge and discharge a limited number of times before significantly degrading. The cost is about 600–700 $/kWh [21].
Metal-air batteries: metal-air batteries have a hypothetical energy density much higher than lithium-ion batteries and they are commonly sponsored as a solution toward next generation of ESS for electric vehicles or grid energy applications. This type of battery has a very high specific energy density; the reason is that these batteries are very performant because one of the reactants (the air) does not have to be stored in the battery. The metal-air battery is made by an exposed porous carbon electrode (called the air cathode) separated from the metal anode by an electrolyte. The exposed carbon electrode traps oxygen atoms from the air, which react with the positive metal ions from the anode. The scientific literature is investigating to substitute the nonaqueous electrolyte with solid, liquid, aqueous, and organic electrolytes but truth of facts demonstrate that the nonaqueous electrolyte is the most developed. The main advantage of this type of battery is the huge increase in energy density over more conventional batteries; it is supposed that an energy density of up to 3 kWh/kg may be achievable although the actual maximum is 350 Wh/kg [22] in lab test. This is a developing technology that promises excellent results in the near future. It promises that the cost can reach 130–160 $/kW.
Lithium polymer: lithium polymer batteries use lithium metal and a transition metal intercalation oxide (MyOz) for the negative and positive electrodes, respectively. It has a specific energy of 155 Wh/kg and operates at a nominal voltage of 3 V with specific power of the 315 W/kg. A very low self-discharge rate, equal to 0.5% per month, is the main advantages together with capability of fabrication in a variety of sizes and shapes, and safe operation thanks to reduced activity of lithium with solid electrolyte. However, it has the low performance when works at a low temperature; this aspect is linked to the temperature dependence of ionic conductivity. The cost is about 200 $/kWh, a reduction to 100 $/kWh in 2025 is expected [23].
Lithium ion batteries: lithium ion batteries are now the leading type of batteries found in electric vehicles due to their high energy density, high efficiencies, and lightweight. The positive electrode is made by graphitic carbon with a layered structure, while the negative electrode in these batteries is a lithiated metal oxide. Typically, the electrolytes consist of lithium salts dissolved in organic carbonates. Lithium ion batteries are set to be the dominant battery for the electric vehicle market, and their development for this market is driving their costs down. The lithium-ion batteries are at the heart of technological development as it is currently the most promising technology. The current trend is to develop batteries in nanoscale and with vastly increased electrode surface areas. This approach provides significant improvements in terms of power, capacity, cost, materials, and sustainability. One other issue with Li-ion batteries is the lack of a viable recycling process. This is another topic of current research. There are many types of lithium-ion batteries. Those that have commercial relevance are lithium cobalt, lithium manganese, lithium nickel manganese cobalt, and lithium iron phosphate batteries. The energy density of actual L-ION batteries is 150–190 Wh/kg, whereas the power density is 500 W/kg; the cost is (battery system only) 150–200 $/kWh [24, 25].
Supercaps: known as electric double-layer capacitor (EDLC); they are devices with a very high specific capacity when compared to the most common electrostatic capacitors. The electrochemical capacitor is characterized by a very similar construction to that of a battery; it has substantially two electrodes and an ion permeable separator, placed between the electrodes, which contains the electrolyte. The porous electrodes are immersed in an electrolytic solution and the area in which the charges are concentrated at the electrode/electrolyte interface is also called double-layer or “double layer.” The electrochemical capacitors thus store energy in the double layer, or Helmholtz layer. The use of supercap in electric vehicles is linked to a demand for power rather than energy storage, indeed the frequent stop/go operation of EVs, the discharging/charging profile of the energy storage is vastly varied. The average power that the energy storage has to provide is very lower than the peak power; indeed, the peak power is required only for short time, for example, for fast acceleration and hill climbing. The ratio between peak power and average power can overcome 10:1. The energy involved in the acceleration and deceleration transients is roughly two-thirds of the total amount of energy over the whole vehicle mission in urban driving. Since it is difficult to obtain at the same time an energy storage with high values of specific energy, specific power, and cycle life, a hybridization solution can be chased for EV/HEV applications. In particular, the energy storage can be fulfilled with combination of the high specific energy system together to high specific power system. The power source system can be recharged from the energy system during less demanding driving or regenerative braking [26].
In order to have a general overview, in Figure 3, the characteristics of the main storage technologies that can be used for the purpose are summarized.
\nRagone diagram for the main storage technologies.
Although there are different types of batteries, those with lithium ion dominate the most recent group of developing electric vehicles. This type of batteries, as known, has a high energy density and they have a low memory effect. Furthermore, in the technical comparison of the different systems, an element that plays a crucial role is certainly the stability of the system and the expected life both in terms of system availability over time and life cycles. The effective life of lithium-ion batteries can be carried out with two different criteria: calendar life and cycle life. The first one allows the estimation of the useful life span without considering the cyclical model of the battery. The other one, instead, allows evaluation of the number of charge/discharge cycles that the battery can undertake before its usable capacity falls below 80% of its nominal capacity [27]. Several research studies have investigated the degradation process of lithium-ion batteries, identifying the different factors contributing to it and parameterizing the de-rate according to the characteristics of battery use, such as charge/discharge cycles, discharge depth (DOD), state of charge (SOC), operating temperature, charge/discharge rate, end-of-charge voltage (EOCV), etc. [28]. The loss of the cell capacity depends on a nonlinear way by the retention time, with a tendency to slow down while the aging process evolves. Conversely, the reduction of the power of the cell follows a linear dependence.
\nTable 1 shows the characteristics of the main accumulators examined previously, with particular attention to the energy density and power density.
\nType | \nEnergy density (Wh/kg) | \nPower density (W/kg) | \nEfficiency (%) | \nCost ($/kWh) | \nCycling capacity | \n
---|---|---|---|---|---|
Fuel cell | \n18501 | \n— | \n50–55 | \n— | \n— | \n
Pb-A | \n35–40 | \n250 | \n75–90 | \n150–200 | \n500–2000 cycles | \n
NiMH | \n70–80 | \n150–200 | \n72–78 | \n400–450 | \n1500–3000 cycles | \n
NaNiCl2 | \n100–120 | \n150 | \n75–85 | \n600–700 | \n300–500 cycles | \n
Metal-air | \n350 | \n— | \n50 | \n130–160 | \n100–300 cycles | \n
Lithium polymer | \n155 | \n315 | \n\n | 200 | \n300–2000 cycles | \n
Li-ion | \n150–190 | \n500 | \n75–90 | \n150–200 | \n3000 cycles at 80% D.O.D. | \n
EDLC | \n5–15 | \nup to 20.000 | \n90–95 | \nup to 10.000 | \nup to 20.000.000 cycles | \n
Energy and power density for ESS.
Hydrogen tank at 700 Bar and 10 kg of H2.
The battery represents a time-varying system with a heavy nonlinear behavior due to the complex electrochemical process and to its inherent parameters: equivalent series resistance, open circuit voltage (OCV), and available capacity. The stable battery behavior in harsh environments represents a relevant issue regarding the safety and the utilization efficiency. Moreover, another objective is to increase the lifetime of the battery by suitably controlling the charging/discharging process. The latter means that it is recommended to avoid wide temperature excursion as well as a high frequency of charging cycles and/or deep discharging. Therefore, a battery management system (BMS) becomes an essential component to properly supervise the battery state [29]. The BMS represents a separate part, with its own hardware and firmware, which can usually be adapted to different battery categories by also allowing a safe battery operation. The battery state of charge (SOC) is the ratio between the available and the maximum capacity and its estimation is not very simple, because of the nonlinear nature of the battery itself. Nevertheless, a careful SOC evaluation is useful to prevent a battery fault, while also avoiding a premature aging, due to undesired undercharging/overcharging [30]. The above discussion highlights that an accurate battery model is crucial to guarantee an adequate dynamic behavior and to improve performance in terms of lifetime [31, 32, 33]. In fact, an accurate battery modeling should allow predicting the battery behavior in steady-state condition as well as during transient operation. Therefore, the main goal is to provide an accurate SOC estimation method, able to precisely track the SOC also during the charge/discharge transient operation, so that the residual vehicle autonomy is properly evaluated. In the current literature [34, 35], different approaches are proposed to model the battery behavior. The obtained models can be divided in three main categories: experimental, mathematical, and electrochemical equivalent circuit-based. The mathematical modeling is based on the evaluation of the battery voltage as a function of SOC, current and dc gain, while the equivalent circuit-based one neglects the internal electrochemical processes. The aforementioned models endorse good results in terms of accuracy and can be implemented in BMS for battery voltage prediction. Indeed, the model implementation inside the BMS is mandatory to suitably manage the energy flow both in case of charge and discharge process. Usually, in underperforming applications, one of the most used models is the simplified circuit model, which does not take into account the SOC as well as the battery dynamics: it consists of an ideal voltage source with a series resistance (i.e., internal resistance). On the other hand, an equivalent circuit, which also considers the battery dynamic behavior, consists of an OCV with voltage depending on SOC, an internal resistance and a number n of RC branches that take into account the effects of hysteresis and polarization, which occur inside the cells [36]. The model parameters are not constant but their behaviors vary with the SOC, the temperature, the lifetime, and the history (i.e., number and depth of cycles) of the cells. In order to evaluate the model parameters, it is possible to implement several series of charge/discharge cycles, monitoring the terminal voltages and currents at controlled temperature. The evaluation of the model parameters is a difficult task, since, either at the time of manufacturing or during their operation, a slightly variation of capacity occurs. In order to minimize the effects caused by cell parameter differences, it is very important to keep the cells at the same SOC. Thus, the equalization of the cell voltage and relative capacity is mandatory. Passive and active cell balancing action allows to maintain a suitable battery SOCs by monitoring individual cells in the stack. Consequently, the battery lifetime increases [37], while also assuring an extra protection against possible damage arising from deep discharging and/or overcharging. The passive balancing acts in a simple manner by dissipating the surplus of charge in a bleed resistor, so maintaining balanced SOCs. Nevertheless, this method does not extend the system run time. On the contrary, the active balancing represents a more effective method, able to equally distribute the energy among the cells both during charge and discharge cycles. This allows an increase of the available charge in the battery stack, so resulting in higher run time, while reducing the charging time and the heat generation, with respect to passive balancing.
\nIn the architecture of an EV, the presence of the DC/AC converter is fundamental both for storage management and for the operation of the electric motor. Its main goal is to promote the transfer of energy from the batteries to the engine. Compared to the first versions of electric cars, currently, the best technological solution employs as a traction motor an AC type: permanent magnet synchronous machine (PMSM) or alternatively an induction motor (IM), for the relative details, see next section. This choice requires the adoption of a converter that must convert from DC to AC to supply the traction motor. Torque and speed of the motors can be controlled accurately by converter’s control, improving the handling of the EV and maximizing the traction effort. Variable-speed, variable-frequency operations are essential features of traction drives and, therefore, electric motors and power converters are intimately connected in terms of design and performances [38, 39]. Future electric drives can improve the present state-of-the-art with an optimization of all the subsystems. Therefore, it is evident how the topology of this converter affects all the power train of an EV. It is possible to discriminate three topological configurations for the considered converter:
a single-stage DC/AC converter
a double-stage DC/AC converter
an integrated DC/AC converter
Each of the previously mentioned types has advantages and disadvantages and can be implemented with different circuit topologies, extending the realization possibilities and the achievable performances.
\nThe direct conversion from DC to AC current can be realized with converters as H-bridge and neutral point clamped (NPC) [40, 41]. The aim is to obtain an output AC, which appropriately performs the motor control consistent with the assigned reference, starting from DC in output from the batteries. However, given the dependence of the voltage of the battery pack from the SOC, it is appropriate to balance the operation just as the DC input voltage changes. This can be achieved by acting appropriately on the modulation index of the traction control. However, the performance of this solution might be affected by their state of charge. Therefore, compared to a simple construction, a reduction in weight and dimensions, the solution examined certainly has significant performance limitations and in any case variable with the SOC. For example, the classic diagram of a three-level NPC inverter is shown in Figure 4 with the correspondent voltage space vectors (18 active and 1 zero-voltage vectors). Large, medium, and small voltage magnitudes are identified by subscripts “L,” “M,” and “S” while with “Z” refers to zero-voltage vectors. The complex plane can be split in six sectors each of which up into two regions (region 1, region 2), in order to accurately modulate the reference to be followed.
\nNeutral point clamped topology with correspondent voltage vectors.
The most high-performance converters are those multilevel, who provide a large number of voltage space vectors. In fact, this allows to follow with a good degree of accuracy the reference imposed by the control logic. However, in multilevel converters, the problem of capacitor voltage balancing leads to limitations in selecting the converter output voltage vector, and suitable corrections are introduced in the control technique. The voltage balancing method is strongly linked to the converter topology used. In the literature, it is possible to find different solutions that propose complex algorithms based on analytical methods, coordinate transformation, pulse width (PWM), or space vector (SVM) modulation, among others [42]. The issue of balancing becomes even more critical when there is a direct connection to the storage system.
\nIn this case, as can be seen from the architecture shown later (Figure 12), the battery pack must be interfaced with the DC-bus through a DC/DC converter that can manage the flow of power both during charging (regenerative break) and during the discharge phase. The type of converter is bidirectional for the flow of energy [43, 44]. Its characteristics are closely linked to the voltage levels chosen for the DC-bus and the battery string. Typically, this is a buck-boost chopper that can also accommodate the option of interfacing with a fast and/or ultrafast charging system for charging the whole battery pack. Many topologies of this converter are proposed in the literature, borrowing the configuration by the application of steady storage that is already established, for example, in order to highlight the differences compared to abovementioned converter, one of the double-stage topologies consists of the interleaved DC/DC chopper [45] before the NPC, as shown in Figure 5.
\nDouble-stage converter topology: interleaved DC/DC chopper with NPC inverter.
Solutions worthy of note, instead, refer to the DC/AC topologies that are trying to integrate, in a single converter, both the battery management system and the interface toward the DC-bus [46]. Indeed, as it is shown in Figure 6, the onboard storage systems must be managed very carefully, ensuring constant balancing, in different operation conditions, in order to preserve the declared performances for lifetime. The lifetime of the batteries is strictly dependent on the use of the batteries and the management capacity. In a traditional method, all the battery cells are connected in series/parallel to reach the desired DC-bus voltage and to obtain required energy. The charge/discharge phase is carried out with the same current but, due to the different electrochemical characteristics of the batteries, different voltages and different SOCs will be obtained for each cell. Therefore, the charge/discharge phase must be stopped as soon as even one of the cells reaches its cutoff voltage. The inequality of chemical characteristics among the cells affects load current and determines an unbalanced power contribution. Unbalancing of the cells can cause premature failure of the pack over extended cycling due to the overhanging/undercharging of cells. This aspect introduces a progressive damage of battery cells and consequently reduction of their service lifetime. For this reasons, passive or active battery management systems (BMSs), as described above, are usually added to the battery pack. The BMS has the main purpose of dynamically minimizing the imbalance of the battery pack during normal operations in order to preserve the cells’ lifetime. In this traditional approach, the traction power unit is equipped with an AC converter that allows the connection with AC-motor and/or AC-grid for recharge. In some cases, it is possible to find ZEVs that host onboard another converter, which has the task of allowing the charging of the battery from the grid. More and more widespread are the solutions that integrate in one integrated DC/AC converter the features that individual converters offer separately. Different converter solutions have been considered to obtain high performance, especially from the point of view of the conversion efficiency. Among them, multilevel converter is one of the most accredited topologies to achieve good performance. The most promising one is definitely the modular multilevel converter (MMC), where each individual submodule (SM), in half- or full-bridge configuration, is directly fed by an elementary cell. Generally, this converter topology is used for high-voltage application, where the main advantages over conventional ones and the most significant features are: simple realization of redundancy, low device ratings, easy scalability and a possibility of common DC-bus configuration for multidrive applications, low THD of the output voltage, good fault-tolerance capability, and enhanced motor efficiency/performance in comparison with the traditional two-level voltage source inverter (VSI). The converter plays a double role: in fact, it can work as traction converter as well as a charger, which increases the power density and reduces the cost by combining the traction and charger converters. This solution allows to obtain both the BMS functionality and the power interface to AC utilities. However, this type of converter has also some drawbacks. The main disadvantage is substantially linked to the conversion efficiency: the presence of a high number of switching devices generates power losses that penalize the overall efficiency of the power train. Moreover, each cell delivers a current waveform not only dependent on the load active power request. The difference between the RMS and DC value of the current increases the losses of the battery cells [47].
\nModular multilevel converters power topology.
The quick growth of road electric traction applications (i.e., zero-emission electric vehicle, hybrid electric vehicle, E-motorcycle, E-bike, aerospace taxing driving, and so on) drew the attention of the world of electric machines exposing several critical issues, so far ignored for industrial applications. This aspect is strictly related to the different needs that characterize the traction chain of a road electric vehicle. Therefore, the design of an electrical drive for such applications requires an adaptation of the external characteristics of the system, especially in terms of torque vs. speed ratio in the whole speed range. In fact, the performance of the drive system (motors + power converter) is strongly limited by the current rating of the ESS. Consequently, the effective torque output of the system is heavily reduced in low-speed range with respect to the potentially available torque by the electric motor. Actually, in order to follow the constraints that a road electrical traction system has to satisfy, three-phase brushless/induction motors are generally used. These solutions require high-frequency switched power converters and suitable control strategy, in order to ensure dynamic performance in line with the expectations of the end user. In a conventional traction drive, the motor current limit vs. the motor speed is practically constant until the nominal motor speed. As a consequence, in order to increase the torque-speed ratio of the drive in the low speed range, two solutions are generally adopted:
The motor current limit is increased in the low speed range;
A different gear ratio is used in low-speed range.
In the first case, an oversizing of the power converter is needed. Of course, the employed converter will never be used at its full power capability, resulting in a worst cost/benefits ratio. In the second case, additional mechanics are required resulting in a worst system efficiency in the low speed range. Different solutions in order to overcome the previous limits are being investigated by the scientific world [48, 49, 50]. Such studies, although different in the substance, try to increase the torque-speed ratio of a given motor by modifying the stator-winding configuration of the motor in order to obtain a different behavior of the torque/speed ratio for a fixed motor current. This approach allows avoiding the oversize of the power converter and/or the need of a variable gear ratio [51, 52]. In EV automotive applications, the torque/weight ratio value for PM machines is typically less than 10 Nm/kg (Nissan Leaf 6.52 Nm/kg; Toyota Prius 7.84 Nm/kg) [53], while for induction machine, it is problematic to reach 5 Nm/kg (TeslaS).
\nIn the last few years, the use of permanent rare earth magnets has made feasible use of permanent magnet synchronous motors (PMSM) in all those applications where it was customary to use direct current or induction machines [54]. One of the fundamental characteristics of the synchronous realized with permanent magnets is that of having a high specific torque; this makes them particularly suitable in EV applications where compactness, lightness, and high mechanical shaft power are requests. The permanent rare earth magnets have a high residual induction value and a high coercive field value, in addition to the possibility of being able to work at very high temperatures (up to 350°). Compared to the induction machine, the permanent magnet synchronous loses reliability due to the magnets that can be subject to demagnetization, but it has the possibility of being built with a high number of pole pairs and it works well with single-layer and concentrated-type windings, which are preferred in traction applications as they ensure a longer lifetime. With regard to the magnets, the types of rare earth magnets used are mainly two [55]:
Neodymium-iron-boron (NdFeB) magnets: characterized by a high residual induction field (1.2–1.4 T), high value of the coercive field (higher than 1000 kA/m), maximum operating temperature without undergoing a strong decay of the magnetic characteristic of 150 °C;
Samarium-cobalt magnets (SmCo): characterized by a high residual induction field (1.0–1.2 T), high value of the coercive field (greater than 850 kA/m), maximum operating temperature without undergoing a strong decay of the magnetic characteristic, about 350 °C.
In view of the moldability of the rare earth magnets (they are generally made using powder metallurgy techniques), different types and geometric configurations of permanent magnet motors have been developed, see Figure 7.
\nClassification of permanent magnet electric motors.
As can be seen from the figure, the main classification of PMSM is made according to the direction of the magnetic flux with respect to the rotation axis: the distinction between axial motors and radial motors. In the first type of motor, the flux lines of the magnetic field to the air gap generated by the permanent magnets are parallel to the axis of the motor, while in the second case, the magnetic flux is parallel to the radial direction of the machine. Constructively, the axial flow motors have a greater radial development (they are sometimes also referred to as pancake motors), they are composed of multiple stacks (i.e., repeated parts composed of stator and rotor, or several stators and rotors assembled together) and it can be used in those applications in which the motor is thought to be integrated directly into the drive (e.g., motor wheel, or in general, for gearless applications) [56]. The axial motors are used for low-speed applications, and therefore, they are built with a high number of pole pairs (also because the high radial extension would cause problems of mechanical stress at high speeds). The radial motors are characterized by a greater axial length and they can be used both for standard applications and for special applications [57]. The two types of motors can be built with windings concentrated at the tooth or with distributed windings. For each of the types of winding, it is can think of realizing the motor with a magnetic configuration isotropic or anisotropic, that is characterized by an inductance constant magnetization in all directions or variable.
\nThe isotropic and anisotropic motors have different magnetic and constructive characteristics, which affect their operation. The isotropic motors are made with the magnets arranged on the rotor surface (the rotor can be internal or external), and can be characterized by the use of magnets of different shapes adapted to optimize the field of magnetic induction provided by the magnets themselves. The anisotropic motor consists of magnets, partially or totally, drowned in the iron, arranged perpendicular to the radial direction or rotated by a certain angle with respect to the main machine axes; the isotropic and anisotropic motors allow to obtain high specific power density with also high torque or speed. In particular, the anisotropic motor can reach higher specific power density thanks to contribution of reluctance torque component; it is usually employed in lower speed performance when the asymmetric rotor configuration is adopted or rather, when drowned magnets are used, it is generally preferred for operation in field weakening. The main electrical faults that may affect the electrical machines are divided into three main categories:
opening of a winding;
short circuit between phase and ground or between phase and phase;
short circuit at the motor terminals.
In order to minimize the occurrence of faults and their effect on mechanical performance, constructive measures are used to make the motor fault tolerant [58]. The fault tolerant characteristics of an electric machine are obtained by suitably modifying the winding [59]. Normally, in most electric machines in alternating current, a distributed multilayer winding is used, capable of generating an almost sinusoidal air gap induction field. From the constructive point of view, a multilayer winding can submit within a slot of the coil sides belonging to different phases, and therefore between the insulators of the two sides would impose a potential difference capable of creating discharges inside the insulating. Moreover, a possible short circuit that would affect a phase, besides damaging the insulator of the phase itself, could cause the failure to propagate also to the insulation of the other phase present in the same slot. To avoid this, a first fault tolerant feature is obtained by using the single-layer windings concentrated on the tooth: in this way, it is possible to avoid the overlapping of the coils of the various phases, and in each slot, there will be a single winding relative to a determined phase. The use of single-layer winding concentrated on the tooth allows to reduce the length of the heads, also bringing a considerable advantage for the machine’s overall dimensions [60, 61, 62, 63]. An innovative solution to extend the drive operating range in EV would be to use multiphase motor and to dynamically modify its torque-speed ratio by changing the stator-winding configuration. This approach would give also the multiphase motor advantages: greater fault tolerance, smaller torque ripple, less phase power rating, and so on.
\nSince many years, field-oriented control (FOC) and direct torque control (DTC) are the most popular control methodologies for AC motor drives. The FOC strategy, see Figure 8, is strictly dependent on the motor electrical parameters, requires long computation time and high switching frequency of the inverter. Instead, the DTC strategy (see Figure 9) is a more robust technique that needs very low computation time and ensures acceptable results even at low switching frequency [64]. A fast torque response can be obtained by means of DTC, due to “direct” interaction of machine electromagnetic quantities (torque and flux) and selected voltage space-vector [65]. Despite these important benefits, DTC has several drawbacks as variable switching frequency (strongly dependent on hysteresis band and motor speed) and large torque ripple in the low-speed region.
\nGeneral block diagram of the field oriented control (FOC).
General block diagram of the direct torque control (DTC).
The rapid development of multilevel converters for drive systems has strongly improved DTC performance with regards to the torque ripple especially when a high number of levels are used [66]. Applying the DTC for converters with more levels, a larger number of voltage vectors can be exploited in order to better control stator flux and torque in induction motors. In this case, the identification of the proper voltage space-vector to be applied has a number of solutions increasing with the number of inverter levels, and consequently, a more complex voltage selection criterion is needed. On the contrary, the increased freedom degrees can be exploited by minimizing the switching frequency, while keeping uniform both the conduction and switching losses of the electronic devices. These methods allow to solve problems of torque ripples, difficulty to control torque at very low speed, variable switching frequency, high values of total harmonic distortion (THD) contents in armature currents. In DTC induction drives supplied by multilevel inverters, usually not all the available converter voltage vectors are used by the selection criterion, due to the aforementioned freedom degrees. This could negatively influence steady-state and/or dynamic drive behavior.
\nThe charging infrastructure is essential to “refuel” the ESS of an electric vehicle. They are classified and configured according to the type of power supply, whether in alternating current (AC) or in direct current (DC), of the operating power and of the charging time, of the type of connection by cable (plug) between the fixed part (station) and moving part (vehicle) both for the power and signal part [67, 68, 69].
\nA first distinction between the alternating current and direct current infrastructures as well as the type of power supply is based on the position of the battery charger, i.e., the converter that manages the charge profiles required by the battery pack. The alternating ones in most cases have the battery charger onboard the vehicle. In the case of direct current charging, however, the converter is integrated into the charging station. Obviously, the management of the recharging process in the case of AC recharges is simplified compared to the DC case, because the charging infrastructure is limited to providing energy to the vehicle and to guarantee the safety requirements prescribed by the IEC 61851 standard.
\nIn the case of DC recharges, the infrastructure is called to check the current and voltage profiles supplied to the vehicle that may vary according to the battery packs onboard. Therefore, they are exchanged during the connection of the vehicle, and during the charging phase, a whole series of information with the battery management system (BMS) onboard the vehicle. The main advantage of DC charging regards to lighten the vehicle of a conversion unit, and therefore, to reduce the weights, the overall dimensions, and the costs. Furthermore, since the external converter to the vehicle, it is easy to increase the power when charging the battery if pack so permits. The charging time is strictly dependent on the energy of the battery pack and the power of the charging station. In an electric car, a “full” of energy is of the order of 20/30 kWh and requires 20–30 min to 100 kW (80% of the SOC).
\nThe possibility of reducing the charging time is therefore linked, on the one hand, to the increase in the maximum power of supply of the charging point, and on the other hand to the increase in the maximum charging current of the battery without reducing the useful life cycles [70, 71]. However, the excessive increase of the installed power in a charging point leads to an unjustified increase in the installation and maintenance costs of the plant as a function of the reduction in recharge time. Based on these preliminary remarks, the IEC 61851 classifies charging points accessible to the users:
standard power recharge point “Normal Power” (≤22 kW): this is a recharging point that allows the transfer of electric energy to an electric vehicle with a power rating of 22 kW or less, excluding devices with a power rating of less than or equal to 3.7 kW, which are installed in private homes or whose main purpose is not to recharge electric vehicles, and which are not accessible to the public. The standard power recharge is detailed in the following types:
slow = equal to or less than 7.4 kW;
quick = more than 7.4 kW and equal to or less than 22 kW;
high power recharge point “High Power” (> 22 kW): this is a recharging point that allows the transfer of electric energy to an electric vehicle with a power greater than 22 kW. The high power recharge is detailed in the following types:
fast: more than 22 kW and equal to or less than 50 kW;
ultrafast: more than 50 kW.
The standards EN 62196-2 and EN 62196-3 define the types of connectors and the “mode” to allow the charging of the vehicle from the mentioned charging stations:
Mode 1: the vehicle is connected to the AC grid with domestic connectors up to 16 A and with 30 mA differential protection type A.
Mode 2: the connection of the electric vehicle to the power supply is carried out with household or industrial connectors up to 32 A, with 30 mA differential protection type A and a control test on the cable.
Mode 3: the connection of the electric vehicle to the power supply is carried out with dedicated connectors, with 30 mA differential protection type A. The connection must also have a connecting cable with some extra conductors suitable for a maximum current of 250 A or a cable compatible with the Mode 2 suitable for a maximum current of 32 A.
Mode 4: it is a direct current (DC) connection for fast recharging. Practically, the connection of the electric vehicle to the power supply is made via an external charger to the vehicle. Control and protection functions and the vehicle charging cable are installed always in the charging station.
The sockets and plugs, for charging electric vehicles in AC, are defined and regulated by IEC 62196-2, while accessories for DC charging are regulated by the IEC 62196-3 standard.
\nIn particular, the standard defines the following types for AC charging:
Type 1: single-phase plug socket with two pilot contacts. Maximum current up to 32 A, maximum voltage 250 V, and IPXXB protection degree.
Type 2: single-phase or three-phase plug socket up to 63 A 500 V. Required degree of protection IPXXB with interlocking requirement to avoid disconnection under load.
Type 3A: for light vehicles: single-phase plug socket up to 16 A 250 V. Required degree of protection IPXXD. This standard requires that the plug can be disconnected under load.
Type 3C: for all vehicles: both three-phase and single-phase plug socket with two pilot contacts up to 63 A 500 V and IPXXD protection degree with the option of disconnecting the plug even under load up to 32 A.
With reference to the four types of charging, the standard IEC 62196-2 specifies four types of electrical connectors:
Type 1—SAE J1772-2009 (Yazaki): it is a single-phase connector with two power contacts + PE and two pilot contacts for the control, max 32 A 230 V (7.4 kW), is adopted by Japanese and American vehicles. The specifications of the connector, referred to by the previous standard. The connector is equipped with mechanical interlock.
Type 2—VDE-AR-E 2623-2-2 (Mennekes): it is a single/three-phase connector, with two pilot contacts for control, max 32 A—7.4 kW (63 A—43.5 kW), 230/400 V, is adopted on European vehicles. Initially, there was no mechanical interlocking that was introduced only from 2012.
Type 3A—EV Plug Alliance (Scame): single-phase, two power contacts + PE and one pilot contact for the control, max 16A, 230 V, is used only for light vehicles (scooters and quadricycles) and refills up to 3.7 kW.
Type 3C—EV Plug Alliance (Scame): single/three-phase, two/three power contacts + PE and two pilot contacts for control, max 32A—230/400 V, 7.4 kW/21 kW, it is scarcely widespread.
For direct current charging, the standard defines two types of connectors:
CHAdeMO: it’s connector for DC charging with additional pins for communication with the vehicle;
Combo combined charging system (CCS): it’s connector for DC charging that integrates also the Type 2 AC inside to allow both AC and DC charge through a single connector;
The CHAdeMO standard is the standard for fast charging in direct current (DC) [72]. This standard is adopted for Nissan, Mitsubishi, Peugeot, Citroen vehicles. Vehicles equipped with this standard have two connectors:
CHAdeMO for fast DC charging
Connector for AC charging (normally Type 1)
Its specifications are defined by the Japan Automobile Research Institute (JARI) G105-1993 standard and use a CAN-BUS communication protocol. With reference to the combined charging system (CCS), however, it provides a unique charging connector on the electric vehicle, which allows both the fast charge current (DC) and the slow charging alternating current (AC). The CCS is made from Type 2 connector, so the system is called Combo2. This system is now adopted by some European car manufacturers (for example, BMW and Volkswagen). Figure 10 shows the previously defined connectors.
\nStandard connectors for AC and DC charging.
With reference to the previous power classification, the “normal power” charging systems must be equipped with a Type 2 socket compliant with the IEC 62196-2 standard for each charging point dedicated to passenger cars and four-wheel commercial vehicles; a socket type 3A conforms to the IEC 62196-2 standard for each charging point dedicated to mopeds, motorcycles, and quads. The “high-power” charging systems, on the other hand, must be equipped with at least one connector of the CCS Combo 2 type and of the CHAdeMO type, according to the IEC 62196-3 standard for direct current charging; and finally, a charging connector/socket with standard Type 2, according to the IEC 62196-2 standard, for charging in alternating current. Finally, the charging systems must be connected to a control system that allows carrying out at least the following functions in real time:
verification of correct operation (availability);
verification of the employment status;
user recognition;
enabling/inhibition of the charge;
reading of the electrical parameters during charging.
In conclusion, it is possible to synthesize the main characteristics of the different charging points in Table 2.
\nClassification | \nNormal power (slow) | \nNormal power (quick) | \nHigh power (fast) | \nHigh power (ultrafast) | \n
---|---|---|---|---|
Categories | \n1 | \n2 | \n3 | \n4 | \n
Supply | \nSingle-phase AC | \nSingle-phase or three-phase AC | \nthree-phase AC | \nDC | \n
Power | \n<3.7 kW | \n3.7–22 kW | \n>22 kW | \n>50 kW | \n
Charging time | \n>6 h | \n1–3 h | \n20–60 min | \n20–30 min | \n
Connector | \nType 1 | \nType 2/Type 3 | \nType 2/Type 3 | \nChadeMO Combo | \n
Standard communication protocol | \n— | \nIEC 81851-1 PWM | \nIEC 81851-1 PWM | \nDigital communication | \n
Main characteristics of the different charging points.
However, charging via a physical connection to a charging station is not the only possibility that can be used to supply the ESS. In fact, the research is very hot to allow an inductive or wireless charging [73, 74]. The latter allows to recharge an electric vehicle without connecting it to the charging station via cables, but by exploiting the magnetic field for transferring power from a transmitter toward a receiver coil. This solution currently involves high manufacturing costs, and therefore, not to make it competitive on the market.
\nBased on the considerations made previously, it is possible to identify different architectures for a ZEV. Each of the proposed architectures differs, substantially, by the choice of the DC/AC conversion stage and by the number of motors that constitute the electric drive. In each of the proposed configurations, the adoption of any of the charging modes was assumed. It is clear that every embodiment may implement one or more of the charging modes indicated. Figure 11 shows the configuration with a single-stage converter and a single electric motor for traction. By replacing the previously described double-stage solution to the DC/AC converter, the architecture shown in Figure 12 can be obtained. An innovative solution, on the other hand, can be achieved by using a DC/AC converter that interfaces directly with the batteries; in this case, the converter can also perform the BMS function, managing the charge and discharge of the battery pack, see Figure 13.
\nElectric drive architecture for ZEV: single-stage converter/single motor.
Electric drive architecture for ZEV: double-stage converter/single motor.
Electric drive architecture for ZEV: integrate converter/single motor.
Alongside the proposed solutions, it is possible to derive new configurations depending on the use of several traction motors. The presence of multiple motors determines a change once again in the AC side converter. In this case, it is possible to adopt “dual motor” solutions where only one converter is used to supply two motors or solutions where each converter supplies its motor, see Figures 14 and 15.
\nElectric drive architecture for ZEV: single-stage converter/multiple motor.
Electric drive architecture for ZEV: multiple-stage converter/multiple motor.
In this chapter, it has been presented the main subsystems that making up the electric drives for a ZEV. In particular, analyzing each of one, it is evident that there are different solutions to carry out the assigned task in the whole system. Matching all possible alternatives for the realization of each subsystem, different architectures for the power train are obtained. In each of the architectures, the substantial difference is linked to the DC/AC converter, thanks to which it is possible to transfer energy from and/or toward the battery pack. Indeed, the identified configurations differ precisely in function of the choice of the latter: single-stage, double-stage, or integrated DC/AC converters generate the respective solutions examined. A further difference is related to employ one or more traction motors coupled with one or more inverters to produce the respective last two configurations.
\nChromatography, first employed in Russia by the Italian-born scientist Mikhail Tsvet in 1900, is a laboratory technique for the separation of a mixture. In the first decade of the twentieth century, scientists continued to work with chromatography primarily for the purpose of separating plant pigments such as chlorophyll, carotenes, and xanthophylls. Since these pigments separated showed various colors (green, orange, and yellow, respectively), they gave the technique its name. After various types of chromatography had sprung up in the 1930s and 1940s, it became useful for many separation processes. Up to now, many chromatographic techniques have been developed, and they can be classified according to different properties. Based on chromatographic bed shape techniques, they can be divided into column chromatography and planar chromatography. Also, gas chromatography and liquid chromatography are classified by the physical state of mobile phase. In addition, there are also many other categories classified by other properties (i.e. separation mechanism, special techniques); but the chromatographic classification is out of scope of this chapter.
The purpose of chromatography is to separate the components of a mixture for later use. The mixture is dissolved in a fluid called the mobile phase, which carries it through a structure holding another material called the stationary phase. The separation is based on differential partitioning between the mobile and stationary phases. Subtle differences in a compound’s partition coefficient result in differential retention on the stationary phase and thus affect the separation.
Nowadays, due to its prominent separation properties, chromatography techniques have become an indispensable tool for the routine analysis and research in pharmaceutical, biomedical, food, and environmental industries [1]. However, there are two main drawbacks needed to be solved/improved. The first one is about the sample itself; when complex matrix samples are analyzed, some proper tedious pretreatment procedures, such as extraction and purification, are necessary to remove the potential interferences contained in complex matrices. Optimizing these procedures is rather tedious and large sum of solvents’ consumption are inevitable, making this method become uneconomical and environmentally unfriendly. What’s more, in traditional chromatography analysis, when a complex sample is analyzed, the overlap between the analytes and matrix constituents is frequently observed; consequently, a long time or much more complex chromatography condition is required for the separation. In general, the elution time for each sample often costs 30–50 min, which is quite time consuming and inefficient. In the same time, some other problems such as baseline drift, changes in the shape of the peaks, incomplete extraction of the analytes, and shifts in the elution times may also decrease the quality of the final result of the analysis. Another problem with chromatography is due to its universal aspect. There are now hundreds of different chromatographic columns, which can be obtained from the market and new ones are being developed constantly [2, 3]. However, when faced with the large number of possible columns, it is hard for analysts to select which could be the most appropriate one for a given condition. Meanwhile, many laboratories and public institutions may not possess all available stationary phases and the column performance may become worse during long-term storage and/or usage in LC analysis [4]. Thus, the analysts often waste a lot of time in search of the most appropriate one from several different stationary phases for analysis. All of the above shortcomes may hinder the further development for chromatographic applications.
A current trend in quantitative analysis is to avoid tedious sample preprocessing steps and long chromatographic elution, exploiting the ability of modern data processing tools for mathematical resolution of coeluting components [5]. The combination of suitable chemometric tools along with chromatographic-spectral data or chromatographic-mass data may solve/improve the problem. With less time and solvent consumption, better quantitative results can be obtained. The multiway (second- and third-order) calibration based on “mathematical separation” is a dazzling pearl in the field of chemical analysis and can calibrate the potential interferences and resolve coeluting peaks successfully in real samples with minimum sample preparation steps. Accurately concentration profiles of individual components of interest can also be obtained. This property generally refers to the prominent “second-order advantage,” which has enormous potential in multiway analysis and becomes a recent focus of theoretical research and practical uses. Combining chromatography with multiway calibration has some distinct advantages because it can simplify the tedious multistep pretreatment and exploration of complicated chromatography separate conditions, showing the potential abilities for the analysis of various samples with different interferences at a time. Tedious pretreatment or purification procedures can be discarded by using prominent “mathematic separation” instead of tradition “physical/chemical separation.” HPLC coupled with second-order calibration methods is especially popular for it can rapidly and simultaneously determine multiple compounds in complex backgrounds with unknown interferences, resolve coeluted peaks, and remove baselines drifts [6, 7, 8, 9, 10].
So far, a lot of algorithms for decomposition of multiway data arrays have already been proposed and genuinely provided alternative tools to analytical chemists for the convenient study of the body of multiway data arrays. Several methodologies have also been expounded in “Encyclopedia of Analytical Chemistry” [11] and “Factor Analysis in Chemistry” [12] at some length. To help readers systematically and intensively understand about concerning algorithms, a detailed description including multilinear models, the multiway cyclic symmetry property, the algorithms for multiway calibration, the estimation of the chemical rank, the toolbox for multiway calibration, and other fundamental issues and applications in chromatography has been presented in this paper.
To facilitate understanding for readers when dealing with multivariate analysis on multiway data arrays, it is necessary to introduce the terminology and nomenclature used in multiway data in the following.
The relationship and difference between the concepts of “data order” and “data way” should be investigated firstly. The term “order” is the dimensions for data of a single sample and term “way” represents the data arrays stacked by all samples with similar properties. As shown in Figure 1, zeroth order corresponds to instruments producing a single response per sample, such as the reading of a pH meter or the absorbance at a single wavelength. First-order data are arranged as a vector or first-order tensor for a single sample, such as UV, fluorescence, infrared, and nuclear magnetic resonance spectra. At the same time, second-order data are formed when matrix data can be obtained for a single sample. There are two ways that second-order data can be obtained: (i) using a single instrument such as excitation-emission spectrofluorimeter (EEMs) or diode-array spectrophotometer to monitor the kinetics of a chemical reaction and (ii) using the hyphenated instruments such as high performance liquid chromatography-photodiode array detection (HPLC-DAD) or liquid chromatography-mass spectrometry (LC-MS). When the second-order data that obtained from a series of samples (calibration and prediction samples) are stacked in one direction, three-dimensional array, which is also called as three-way array can be obtained, and the corresponding data are usually known as three-way data. Hence, when a series of samples are stacked into a single, zeroth-order (a scalar), first-order (a vector), second-order (a matrix), third-order (a three-way array), and higher order tensors can yield the corresponding one-way, two-way, three-way, four-way, and N-way data sets, respectively. The zeroth-order tensor calibration is also called as univariate calibration. This method has great restraint on its application as it needs full selectivity for the signals of target analytes. Except univariate calibration for the analysis of data, others are known as multivariate calibration, the analysis of second-order tensor and higher order tensor is denoted as multiway multivariate or multicomponent calibration.
Relationships and differences between the concepts of “data order” and “data way” described with symbols.
Meanwhile, a detailed description for various sample types is also provided. Based on different functions, samples can be divided into calibration, prediction, and actual sets. Actual sets include predicted samples (the target analyte(s) is (are) unambiguously included) and/or real samples (whether the target analyte(s) is (are) included or unknown). Constituents present in the samples used for calibration and validation are regularly called “known” or “expected,” which is expected in these sets as they are expected to be existed in actual samples. The expected constituents can be further divided into “calibrated” and “uncalibrated.” The concentrations of former ones used for calibration are predesigned and known, while those of “calibrated” components in actual sets can also be available, involving the analyte(s) of interest. On the other hand, the constituents which are only included in actual sets are called “unknown” or “unexpected” and also potential interferences.
In this chapter, lowercase italics represent scalars; two-way matrices are denoted by bold capitals; underlined bold capitals designate three-way arrays, the superscript T represents the transpose of a matrix, and the superscript + is the Moore-Penrose generalized inverse of a matrix. || · ||F designates the Frobenius matrix norm. To have a better understanding about the multiway calibration, readers are advised to comprehend an inner cyclic symmetry property of trilinear decomposition proposed by our laboratory in 1996 and also called as three-way cycle symmetry. As shown in Figure 2, elements, vectors, subscripts, and physical modes in resolved matrices, sliced matrices, and unfolded matrices, together with residue and resolution formulas, all obey the principle of inner cyclic symmetry property, circumrotating along the same way. Table 1 provides the detailed information of the nomenclature mentioned. Similar to the three-way cyclic symmetry, the four-way and five-way cyclic symmetries for quadrilinear and quinquelinear decomposition can be obtained easily by simple mathematical manipulation of exchanging the symbols similar to three-way cyclic symmetry. These regularities provide useful instructions for the standardization of symbol systems in multiway data analysis, for better understanding the essence of multiway multilinear decomposition, developing new multiway calibration algorithms, and exploring multilinear algebra in mathematics.
Schematic representation for three-way cyclic symmetry property.
X | Three-way data array |
---|---|
I, J, K | The three dimensions of three modes of X |
xijk | The ijkth element of X |
AI × N, BJ × N, CK × N | The three underlying profile matrices of X with I × N, J × N, and K × N, respectively |
ain, bjn, ckn | The inth, jnth, and knth elements of the three underlying profile matrices A, B, and C, respectively |
a(i), b(j), c(k) | The ith, jth, and kth row vectors of profile matrices A, B, and C, respectively |
diag(a(i)), diag (b(j)), diag(c(k)) | Diagonal matrices with elements equal to the elements of a(i), b(j), and c(k), respectively |
Xi.., X.j., X..k | The ith horizontal, jth lateral, and kth frontal slices of X, respectively |
Ei.., E.j., E..k | The ith horizontal, jth lateral, and kth frontal slices of the three-way array residue E, respectively |
eijk | The ijkth element of the three-way residue array E |
Detailed information of the nomenclature mentioned.
According to the data type and its inner cyclic symmetry property, the multilinear models can be divided into trilinear, quadrilinear, quinquelinear, and even higher linear models. In chromatographic analysis combined with multiway calibration, the trilinear and quadrilinear models are commonly used.
Harshman [13] together with Carroll and Chang [14] first proposed the PARAFAC (PARallel FACtor analysis) model with the name of CANDECOMP in the year of 1970. In this trilinear model, each element xijk of a three-way array X (I×J×K) can be reasonably fit to the following equation:
where N represents the total number of detectable components including the component(s) of interest, uncalibrated background(s), and unknown interferences. Figure 3 illustrates the graphical representation of a trilinear model of three-way data array X. A, B, and C are the three underlying profile matrices of X with I × N, J × N, and K × N, respectively; I is the three-way diagonal core array of size N × N × N with ones on the superdiagonal and zeros elsewhere; and E is the three-way residue data array of size I × J × K. To further comprehend the mathematic meaning of the trilinear model graphically expressed, the response data array X is returned with three inverse steps as described in Figure 4.
Schematic representation of trilinear model.
The inverse procedures to return three-way data array X.
Considering a model of the real-valued four-way data array X (I × J × K × L), in which each element xijk can be expressed as [8, 15]:
where ain, bjn, ckn, and dln correspond to the underlying profile matrices AI × N, BJ × N, CK × N, and DL × N of X (I × J × K × L), respectively. The term eijkl is the element of the four-way residual array E (I × J × K × L). Then, the modeled part of xijkl is quadrilinear in the parameter sets ain, bjn, ckn, and dln. The graphical representation of a quadrilinear model of four-way data array X is shown in Figure 5.
Schematic representation of quadrilinear model.
The correctness of decomposition of a multilinear model requires that the multilinear model holds multilinearity. However, there are some nonmultilinear factors which can cause a multilinear model to deviate the multilinearity. For example, in the chromatography type of trilinear model such as HPLC-DAD and LC-MS data, the time shift and baseline problem among different runs will cause the trilinear model to deviate the trilinearity. Thus, the data arrays in multivariate calibration must need appropriate data preprocessing procedures before a multilinear decomposition. The schematic representation of entire chemometrics-assisted LC-DAD and LC-MS analytical strategy is shown in Figures 6 and 7, respectively.
Schematic representation of entire chemometrics-assisted LC-DAD analytical strategy.
Schematic representation of entire chemometrics-assisted LC-MS analytical strategy.
The ATLD algorithm is a universal second-order calibration method for decomposition of three-way data arrays. It is based on an alternating least squares principle without any constrains and an improved iterative procedure that utilizes the Moore-Penrose generalized inverse based on singular value decomposition. It has been widely used in three-way data analysis due to the advantages of being insensitive to excessive component numbers and fast convergence.
According to its cyclic symmetry property, the trilinear model can also be expressed in matrix notation as follows:
Due to the property called as cyclic symmetry of the trilinear model, the three expressions are equal to each other in mathematics. According to Eqs. (3)–(5), the loss function to be minimized is the sum of the squares of the elements of the residual matrices, which can be expressed as:
By using the loss functions abovementioned, ATLD alternately minimizes the three objective functions over C on fixed A and B, over A on fixed B and C, and then over B on fixed C and A. The updates for the three profile matrices (A, B, and C) are based on the least squares principle and can be represented as follows:
herein diagm(·) stands for a column N-vector and its elements are diagonal elements in square matrix. In every iteration cycle, A and B are normalized column-wise with unit length. With the help of the resolved profile matrices C, we can get the concentrations of analytes of interests in actual samples via regression of the appropriate column of C corresponding to each analyte against its standard concentrations.
Due to the operation based on sliced matrices with less size and two other major strategies, ATLD holds the fastest convergence. The truncated least squares method employs the tolerance to truncate the small singular values in the singular value decomposition. In addition, selecting diagonal elements makes ATLD retain trilinearity property indeed and be insensitive to the excessive estimation of component numbers. The advantages have been reviewed by Fleming and Kowalski [16]. Based on the above advantages, it is very suitable to handle second-order data obtained from hyphenated instruments, such as HPLC-DAD, LC-MS, and GC-MS.
The SWATLD algorithm, as a derivative of ATLD, is also widely employed as it can yield better results in many cases. It alternately minimizes three objective functions with intrinsic relationship and also holds the characteristics of fast convergence and being insensitive to excessive component numbers. The detail explanations of these properties have been provided by authors in the original paper [17]. Three new residues can be expressed as:
By introducing some reasonable weight terms, three new objective functions are established and can be expressed as follows:
Due to the unique optimizing strategy, this algorithm is more efficient than others. It can provide more satisfactory results than ATLD with moderate noise levels. Moreover, it can deal with the problem of moderate collinearity, but it is not so effective when data are collinear severely.
The APTLD algorithm was developed by Xia et al. [18], and it can provide some improved properties. It alternately minimizes three new least squares-based objective functions by using the constraint functions as penalty terms of the PARAFAC error. Eqs. (12)–(14) are the new objective functions, which alternately used as the constraint terms. By introducing large penalty terms and combining them with residue functions (18)–(20) to establish three objective functions, APTLD transforms these constrained problems into non-constrained ones. Then, it alternately minimizes the following three objective functions to resolve the model:
where p, q, and r represent penalty factors. The performance of APTLD depends on the choice of the penalty factor values. When the values are very small, it will lead to a lot of iterations and sensitivity to excess factors, which is close to that of PARAFAC algorithm; particularly, when p = q = r = 0, APTLD can be regarded as a variant of PARAFAC. However, this algorithm will become insensitive to excess factors and speed up convergence when larger values of p, q, and r are selected. According to the variance among different trials and computational burdens, a further increase in p, q, and r values will make APTLD perform theoretically better. Therefore, its performance can be exquisitely improved by adjusting the penalty factors p, q, and r on the basis of particular circumstances and special needs.
The APQLD algorithm [19] as an extension of APTLD for decomposition of quadrilinear data is applied to third-order calibration. Similar to APTLD, four objective functions can be obtained as:
where WA = diag(1./diagm(ATA)), WB = diag(1./diagm(BTB)), WC = diag(1./diagm(CTC)), and WD = diag(1./diagm(DTD)). APQLD algorithm decomposes the quadrilinear model by alternatively minimizing the four objective functions abovementioned. The performance of APQLD also depends on the selection of the penalty factors p, q, r, and s. Obviously, it can be considered as a variant of the four-way PARAFAC when the four penalty factors equal to 0.
APQLD retains the second-order advantage possessed by second-order calibration and holds additional advantage. By introducing a new fourth mode, it can relieve the serious problem of collinearity, which cannot be solved by three-way algorithms.
It is always an important and intractable problem to estimate chemical ranks (the number of factors or components) for the trilinear model before decomposing a three-way data array. Theoretically, it can be seemingly solved by selecting the appropriate algorithms, which are insensitive to the excessive component numbers (chemical ranks). Nevertheless, these algorithms also guarantee that the component number (chemical rank) chosen should be no fewer than the underlying one. As a matter of fact, when the component number selected is far more than the actual one, it may lead to a model fitting error and a large deviation for the predicted results. On the contrary, the performances of the algorithm on providing accurate solutions will be largely improved when the most appropriate factors are chosen in analytical system.
Based on this, a lot of methods have been developed for estimating the chemical ranks. In general, they can be roughly fallen into two main categories. The first one is on the basis of the trilinear model, which includes split-half analysis [20], Wu’s maximum rank method [21], core consistency diagnostic (CORCONDIA) [22], ADD-ONE-UP [23], and self-weighted alternating trilinear decomposition and Monte Carlo simulation (SWATLD-MCS) [24]. The core of split-half analysis concerns a relatively complex splitting skill, and hence the result depends on splitting schemes greatly. CORCONDIA and ADD-ONE-UP are two of the most commonly used methods in determining the chemical ranks. However, they are quite time consuming sometimes. Furthermore, the severe collinearity data may also lead to a heavy computation burden and even get error results. Self-weighted alternating trilinear decomposition and Monte Carlo simulation (SWATLD-MCS) operate in two main steps. First of all, Monte Carlo simulation is applied to generated one pseudo three-way data array. Sorted mean relative concentration values can then be obtained by applying SWATLD to decompose the three-way data array created by MCS. By comparing the sorted mean relative concentration value, this method can determine the chemical rank. The other ones belong to nonmodel methods such as orthogonal projection approach (OPA) [25], two-mode subspace comparison (TMSC) [26], factor indicator function (IND) [27], subspace projection of pseudo high-way array (SPPH) [28], linear transform method incorporating Monte Carlo simulation (LTMC) [29], and region based on moving windows subspace projection technique (RMWSPT) [30]. Though all of the above methods can be applied to rank estimation, it is impossible to find one among them which can guarantee the correct results under all situations. Actually, more than one method is often utilized in analysis to ensure the accuracy of the analytical results [8, 15].
The maximum rank method was firstly proposed by Wu et al. [21] to estimate the chemical rank for ATLD and ATLD’s variants, as the following form shows:
In practice, the number of factors will also be determined as follows:
where rank (.) denotes the numerical rank estimate of a matrix based on a singular value decomposition procedure with a default tolerance. This method is universal and suitable to be used in any instance and can get satisfactory results when estimating the chemical rank of the three-way data.
ADD-ONE-UP was proposed by Chen et al. in [23] for determining the chemical rank. It operates by fitting two reconstructed three-way data arrays by PARAFAC with a gradually increasing component numbers and then determines the chemical rank by examining the residual sum of squares (SSR). The method is convenient and powerful, and some nonideal experimental conditions (such as slight collinearity and unknown backgrounds) can be handled.
Unfold the obtained three-way data array X into a two-way data set XI × JK.
Decompose XI × JK by SVD, XI × JK = USVT.
Define Xc = UcScVcT, Uc and Vc consist of the first c columns of U and V, respectively; Sc is a diagonal matrix with diagonal elements equal to the first c diagonal elements of S.
Fold Xc into a three-way data array Xc, then resolve it by PARAFAC with N = c (c = 1, 2, 3,…,). The residual sum of squares is denoted by SSRc.
Repeat steps 3 and 4 until SSRc reaches its minimum or satisfies the equations below: SSRc1 < sc12 and SSRc1 + 1 > sc1 + 12 and SSRc1 + 2 > sc1 + 22 (si represents the ith diagonal element of matrix S and sc12 denotes the variance obtained by the inclusion of c1th component in the truncating step).
Unfold X in another dimension to obtain XIK × J, then perform the same steps from 2 to 5 to get c2, which meets similar relationships like c1.
The factor numbers applied in decomposing the trilinear data array X should be the smaller one between c1 and c2, i.e. F = min(c1, c2).
This method utilizes the eigenvalues of factor analysis and the residuals of trilinear decomposition. It can cope with nonideal experimental conditions like varying backgrounds and moderate collinearity. However, as it is based on the PARAFAC algorithm, ADD-ONE-UP has some drawbacks. It is rather time consuming due to the need to run PARAFAC for many times. Furthermore, this method may suffer from a heavy computational burden by reason of two-factor degeneracies and may yield inaccurate results.
The principle of CORCONDIA is to assess the similarity between the superdiagonal array T and the least squares-fitted G with a gradually increasing number of components. CORCONDIA is defined as:
where gdef stands for the element of G, tdef represents the elements of T, and N denotes the number of factors in the model.
For an ideal trilinear model, gdef is equal to tdef and the value of core consistency will be equal to 100%. Usually, the model can be regarded as “very trilinear” as the value of the core consistency above 90%, whereas a value nearly 50% will indicate a problematic model, which contains both trilinear and non-trilinear variations. A value close to zero or even negative means that the model is not valid. Although it is an effective method, it suffers from the drawbacks of PARAFAC.
Chromatographic peak alignment is a challenge in the field of complex system analysis by multiway calibration methods. Some methods for peak alignment have been developed based on the second-order instruments, which generate a matrix data for per sample. These methods [31], for example iterative target factor analysis coupled to COW (ITTFA-COW), rank minimization (RM), parallel factor analysis alignment, and other recently proposed methods based on multivariate curve resolution-alternating least squares, employ signals of two-way structure to align chromatographic peaks shifts. In theory, these methods are aimed at the alignment of local chromatographic regions and therefore satisfactory results can be obtained for the time shifts existed in the whole chromatogram. They can achieve accurate time alignment regardless of the presence of unknown interferences. Not long ago, Yu and co-workers developed a new algorithm for chromatographic peak alignment, derived from the famous rank minimization method. It aligns time shift among samples and then utilizes trilinear decomposition algorithm to interpret the overlapping chromatographic peaks to quantify target analytes [31].
Figure 8(A) depicts the graphical representation of the rank minimization method (RM). A significant advantage of this method is that alignment can be successfully carried out even when the potential interferences coeluted with the analyte of interest. To have a better view on this method, a series of fixed-size time window (rectangles) along the retention time directions is applied in Figure 8(A). In particular, the red rectangle M0 stands for the retention time range of analyte in the response of reference sample, and the retention time range between green and blue rectangles in the response of a test sample is the underlying time shift ranges of the analyte. By row-wisely moving the fixed-size time window on the test sample along the retention time direction, the rectangles from M1 to Mn, can be extracted from the response of the test sample; then, augmented matrices, which are defined as [M0 | M1],…, [M0 | Mn] [stage 2 in Figure 8(A)] in the retention time direction, can be obtained. Finally, the singular value decomposition is performed on these augmented matrices and results in a list of residual variance. Consequently, the percentage of the residual variance plotted against each chromatographic time shift will mark clearly the time shift point correction corresponding to the minimum residual variance.
Graphical illustration of RM (A) and ASSD (B).
The abstract subspace difference (ASSD) method uses abstract chromatographic profiles for alignment. Accordingly, the response matrix X can be expressed in the form of singular value decomposition (SVD) notations as follows:
herein, the column vector U represents the abstract chromatographic profiles, while the V is the abstract spectra profiles; in the strict sense, all of them are not necessarily correspond to the real ones. Suppose that two data matrices have been collected: a reference data, Xref, which includes only one analyte, and a test data, Xtest, which collects the analyte together with other unknown interferences. Hence, based on the singular value decomposition, the abstract chromatographic profiles for reference and test samples can be acquired separately:
In the ideal situation, no noise is present, and there is no time shift between reference and test samples. In this case, the mathematical rank of the augmented matrix [Uref | Utest] will be identical to that of Utest. However, in the situations where the chromatographic retention time of the analyte is not the same for the reference and test samples, the mathematical rank of the augmented matrix, [Uref | Utest], will become larger than the actual ones. Therefore, the core of ASSD method is to look for the augmented matrix with minimum mathematical rank for alignment, which is the same as the rank minimization method, except that ASSD uses the abstract chromatographic profiles for alignment instead of the underlying ones.
Figure 8(B) shows the graphical illustration of the ASSD method. In order to calculate the abstract chromatographic profiles for each of the extracted matrices M1 to Mn, an additional step, SVD, has been introduced in the Stage 1 of Figure 8(B). Additionally, this new method uses the last singular value instead of the percentage of residual variance in the last stage to represent time shift correction. In practical measurement, aligning time shift for target analyte between the reference and a test sample according to the critical criterion of the mathematical rank of the augmented matrix is impractical. However, the augmented matrix, [Uref | Utest], will become a seriously ill-conditioned matrix provided that the time shift has been successfully aligned. Hereby, chromatographic peak alignment can be transformed to find the most ill-conditioned augmented matrix among the augmented matrices as shown in the Stage 3 of Figure 8(B). As the total variance is the sum of the squared elements of the augment matrix, [Uref | Utest], it will be a steady state value and equal to the column numbers. Hence, a smaller last singular value will definitely correspond to a more ill-conditioned matrix.
Non-trilinear factors such as background drift is unavoidable sometimes in the chromatographic analysis due to the composition of gradient elution and/or nature of complicated matrices, which may lead to wrong analysis results by the aforementioned chemometric algorithms. Amigo and co-workers have summarized the intuitive graphics and mathematical models used in handling chromatographic data issues [32]. Multivariate curve resolution (MCR) methods are typical examples.
A chromatographic background drift correction strategy [33] was developed in 2007 by our group for LC × LC × DAD data. The core idea is to perform trilinear decomposition, which is based on the alternating trilinear decomposition (ATLD) algorithm for the instrumental response data. In analysis, the background drift can be eliminated by regarding it as an extra component or factor. This method uses trilinear decomposition to resolve the raw data, to extract, and subtract the background component from the raw data for acquisition of the signal of analytes with a flat baseline. A detailed schematic description on how to subtract the background drift from raw three-way chromatographic data is illustrated in Figure 9.
Schematic description on how to remove the background drift from three-dimensional instrumental data.
Recently, a method that uses orthogonal spectral signal projection (OSSP) to simultaneously solve various kinds of chromatographic background drift was studied [33]. The analytical results indicated that OSSP coupled with PARAFAC can be used for handling coelution and background drift problems in chromatographic analysis. It indicates that more accurate analysis results can be obtained, regardless of the presence of background drift and unknown interferences.
Based on the “second-order or high-order advantages” provided by chemometrics methods, some actual applications have been developed for the analysis of pharmaceuticals, biological matrices, foods, cosmetics, environmental matrices, and others. Multiway calibration algorithms have been employed to enhance the selectivity and can obtain accurate predicted concentration of analyte(s) of interest free from interference of potential interfering matrix. These applications summarized in Table 2 are reviewed in the following six aspects.
Type of data | Algorithm | Analytes | Ref. |
---|---|---|---|
Pharmaceuticals | |||
HPLC-DAD | ATLD | Puerarin, daidzin, and daidzein | [34] |
HPLC-DAD | ATLD | Costunolide and dehydrocostuslactone | [35] |
HPLC-DAD | ATLD, SWATLD, AFR | Isoniazid and pyrazinamide | [36] |
Biological matrices | |||
HPLC-DAD | ATLD | Eleven antihypertensives | [37] |
HPLC-DAD | ATLD | Four tyrosine kinase inhibitors | [38] |
LC-MS | ATLD | Ten β-blockers | [40] |
LC-MS | ATLD | Six antidiabetic agents | [48] |
HPLC-DAD | ATLD | Five vinca alkaloids | [39] |
Foods | |||
HPLC-DAD | PARAFAC, ATLD, SWATLD | Sudan I and Sudan II | [49] |
HPLC-DAD | ATLD | Six synthetic colorants | [1] |
HPLC-DAD | APTLD | Synthetic phenolic antioxidants | [9] |
HPLC-DAD | ATLD,PCA | Eight coeluted compounds in tea | [7] |
HPLC-DAD | ATLD | Eight flavonoids | [42] |
HPLC-DAD | ATLD | nine polyphenols | [43] |
HPLC-DAD | ATLD | Twelve quinolones | [44] |
HPLC-DAD | ATLD, PCA-LDA | Thirteen phenolic compounds | [45] |
HPLC-DAD | ATLD | Twelve polyphenols | [46] |
LC-MS | ATLD | Ten mycotoxins | [47] |
Environmental matrices | |||
HPLC-DAD | SWATLD | Three pre-emergence herbicides | [50] |
HPLC | ATLD | 1-Chloro-2,4-dinitrobenzene and 3,5-dinitrobenzoic acid | [51] |
HPLC | ATLD | Five dimethylphenol isomers | [53] |
HPLC | ATLD | Catechol, resorcinol and hydroquinone | [52] |
Reviewed applications.
In this field, two or three drugs have been simultaneously detected in aqueous solution or Chinese traditional medicine. The data analyzed are second-order tensors, which are obtained by high performance liquid chromatography-photodiode array detection (HPLC-DAD).
Su et al. proposed a method for simultaneously quantifying the main effective constituents such as puerarin, daidzin, and daidzein in traditional Chinese medicine kudzuvine root by using HPLC-DAD with ATLD algorithm [34].
Nowadays, traditional Chinese medicine (TCM) plays an important role in the healthcare system. Thus, considerable attention has been paid to Chinese patent medicine (CPM), which generally consists of several TCMs and other ingredients. It is significantly important to quantify the constituents of CPM and plasma for pharmacological analysis. Liu et al. determined two effective constituents, costunolide and dehydrocostuslactone, in plasma sample and Chinese patent medicine Xiang Sha Yang Wei capsule by using HPLC-DAD coupled with alternating trilinear decomposition (ATLD) algorithm [35].
Besides, Ding et al. determined isoniazid and pyrazinamide by using HPLC-DAD coupled with three different second-order calibration algorithms including ATLD, alternating fitting residue (AFR), and self-weighted alternating trilinear decomposition (SWATLD). The results showed that all the three algorithms could be used for solving overlapped chromatograms and unknown interferences successfully, and the analysis results obtained from AFR were slightly better in this situation [36].
Biological samples often contain various endogenous substances such as amino acids, hormones and neurotransmitters. Determining the concentrations of these molecules or metabolites is an integral part of clinical research and also helpful for understanding pathophysiology and mechanism of diseases. Human urine and plasma are commonly primary research systems.
High blood pressure, widely called hypertension, is a cardiac chronic disease with a symptom of sustaining rise in systemic arterial blood pressure. Zhao et al. carried out the simultaneous quantification of 11 antihypertensives, human serum, health product, and Chinese patent medicine samples by using HPLC-DAD with the aid of second-order calibration based on ATLD algorithm [37].
Tyrosine kinases are critical regulators of cell growth and differentiation growth and differentiation. The measurement of concentration of TKIs in different biofluids plays a significant role in optimizing the individual dosage regimen and reducing the risk of inapposite dosages. For the analysis of four tyrosine kinase inhibitors in different plasma samples, HPLC-DAD was utilized without absolutely chromatographic separations by resorting to ATLD algorithm. The contents of four tyrosine kinase inhibitors in different complex plasma samples can be accurately determined [38].
Liu et al. simultaneously determined vincristine, vinblastine, vindoline, catharanthine, and yohimbine in Catharanthus roseus and human serum samples utilizing ATLD algorithm to analyze the resulting three-way data array stacked by HPLC-DAD [39].
β-blockers are the first-line therapeutic agents for treating cardiovascular diseases and also a class of prohibited substances in athletic competitions. Therefore, rapid screening for multiple β-blockers in a single analysis has been of growing demand in clinical toxicology, forensic science, and antidoping control as well. Gu et al. proposed a smart strategy that combines three-way liquid chromatography-mass spectrometry (LC-MS) data with second-order calibration method based on alternating trilinear decomposition (ATLD) algorithm for simultaneous determination of 10 b-blockers in human urine and plasma samples [40]. The quantitative results were validated by the LC-MS/MS operated in multiple reaction monitoring (MRM) mode.
The applications in this field cover the analysis of contaminants, essential ingredients, and additives.
Synthetic phenolic antioxidants as food additives were successfully determined in edible vegetable oil by using HPLC-DAD and APTLD [9]. Some extraction procedures, in which the antioxidants of interest would be separated, is unnecessary and the 10 antioxidants can be eluted within 6 min.
Yin et al. proposed a smart strategy that combined HPLC-DAD with ATLD algorithm to solve varying interfering patterns from different chromatographic columns and sample matrices for the rapid simultaneous determination of six synthetic colorants in beverages with little sample pretreatment [1].
Tea is one of the most widely consumed beverages in the world. The biological functions of tea have been reported in numerous studies, such as anti-inflammation, antiatherosclerotic, antioxidant, anticarcinoma, antiobesity, and antiviral properties. These beneficial effects are related to the presence of purine alkaloids and polyphenols in tea. An attractive chemometrics-enhanced HPLC-DAD strategy was proposed by Yin et al. for simultaneous and fast determination of eight coeluted compounds including gallic acid, caffeine, and six catechins in 10 kinds of Chinese teas by using second-order calibration method based on ATLD algorithm [41]. Subsequently, based on the quantitative results, principal component analysis (PCA) was used to conduct a cluster analysis for these Chinese teas.
Propolis is a naturally occurring resinous hive product gathered by worker honeybees from buds and barks of different plant species. Sun et al. developed a fast analytical strategy by combining HPLC-DAD with ATLD algorithm for simultaneous determination of eight flavonoids in propolis capsule samples [42].
Honey is a wholesome natural food product well known for its high nutrition. The antioxidant ability of a number of honeys has been determined and found to be significantly correlated to the contents of polyphenols, which can affect the quality of honeys and their products beneficial for improving overall health and preventing some diseases. By using second-order calibration for development of HPLC-DAD method, Zhang et al. quantified nine polyphenols in five kinds of honey samples successfully [43]. Quinolones, a kind of antibacterial, which is widely used in agriculture for its high antimicrobial activity, were also detected by HPLC-DAD with ATLD algorithm in honey samples [44].
Wine phenolic compounds, as secondary metabolites and functional components, determine the important sensorial characteristics of wines, such as mouth-feel, fragrance, and color. The combination of HPLC-DAD and second-order calibration method based on ATLD has been used for the determination of 13 phenolic compounds in red wines, and linear discriminant analysis (PCA-LDA) was applied for distinguishing wines aged for years [45]. Similarly, the same strategy was carried out by Wang et al. for simultaneously quantify 12 polyphenols in different kinds of apple peel and pulp samples [46].
Mycotoxins are a class of highly carcinogenic substances often naturally occurring in the moldy foods, especially cereals. Liu et al. proposed a smart strategy that combines three-way LC-MS data with second-order calibration method based on ATLD algorithm for direct, fast, and interference-free determination of multiclass regulated mycotoxins in complex cereal samples [47]. Ten mycotoxins with different property could be fast eluted out and detected by full scanning MS with a segmented fragment program to enhance the sensitivity.
By using LC-MS in combination with second-order calibration method based on ATLD algorithm, Gu et al. simultaneously green determined six coeluted sulfonylurea-type oral antidiabetic agents in healthy herbal teas and human plasma samples [48]. The strategy proved to be a promising method for resolution and determination of coeluted multianalytes of interest in complex samples while avoiding elaborate sample pretreatment steps and complicated experimental conditions as well as more sophisticated high-cost instrumentations.
For the determination of Sudan dyes in hot chilli samples, HPLC-DAD was employed without completely chromatographic separations by using PARAFAC, ATLD, and SWATLD [49]. The low contents of Sudan I and Sudan II could be accurately determined in complex chilli mixtures.
In this field, we analyzed the analytes in aqueous solution, soil, tap water, river, and effluent water, mainly containing organic contaminants and pesticides.
Herbicides, which are chemicals often employed to kill weeds without causing injury to desirable vegetation, have been widely used. These may lead to their accumulation in the environment and cause continuous and serious pollution or even toxicity to crops and humans. Qing et al. developed a novel strategy for analysis of three pre-emergence herbicides in environment samples using HPLC-DAD with SWATLD algorithm [50].
Chemometrics-assisted HPLC-DAD strategy has a great potential in analysis of target analytes in complex environmental matrices. So far, this strategy has been utilized for determination of 1-chloro-2,4-dinitrobenzene and 3,5-dinitrobenzoic acid [51], catechol, resorcinol, and hydroquinone [52] as well as five dimethylphenol isomers [53] in environment successfully.
This chapter scientifically describes in detail the various multiway chemometrics methodologies and applications in chromatography. We have built more canonical symbol systems, noted the inner mathematical cyclic symmetry property for multilinear decomposition, introduced several multiway calibration algorithms, explored the rank estimation of multiway data array, and analyzed numerous actual systems by homemade methods. Some fundamental issues related to chromatographic analysis such as peak alignment and background drift were also discussed and solved. By combining chromatographic techniques with chemometrics based on multiway calibration methods, complicated and tedious sample pretreatment can be greatly simplified and long chromatographic elution can be avoided. All the applications abovementioned are universal, rapid, and sensitive for the determination of a variety of analytes in complex matrices.
The authors gratefully acknowledge the National Nature Science Foundation of China (Grant Nos. 21575039 and 21775039) and the Foundation for Innovative Research Groups of NSFC (Grant No. 21521063) for financial supports.
There are no conflicts to declare.
Edited by Jan Oxholm Gordeladze, ISBN 978-953-51-3020-8, Print ISBN 978-953-51-3019-2, 336 pages,
\nPublisher: IntechOpen
\nChapters published March 22, 2017 under CC BY 3.0 license
\nDOI: 10.5772/61430
\nEdited Volume
This book serves as a comprehensive survey of the impact of vitamin K2 on cellular functions and organ systems, indicating that vitamin K2 plays an important role in the differentiation/preservation of various cell phenotypes and as a stimulator and/or mediator of interorgan cross talk. Vitamin K2 binds to the transcription factor SXR/PXR, thus acting like a hormone (very much in the same manner as vitamin A and vitamin D). Therefore, vitamin K2 affects a multitude of organ systems, and it is reckoned to be one positive factor in bringing about "longevity" to the human body, e.g., supporting the functions/health of different organ systems, as well as correcting the functioning or even "curing" ailments striking several organs in our body.
\\n\\nChapter 1 Introductory Chapter: Vitamin K2 by Jan Oxholm Gordeladze
\\n\\nChapter 2 Vitamin K, SXR, and GGCX by Kotaro Azuma and Satoshi Inoue
\\n\\nChapter 3 Vitamin K2 Rich Food Products by Muhammad Yasin, Masood Sadiq Butt and Aurang Zeb
\\n\\nChapter 4 Menaquinones, Bacteria, and Foods: Vitamin K2 in the Diet by Barbara Walther and Magali Chollet
\\n\\nChapter 5 The Impact of Vitamin K2 on Energy Metabolism by Mona Møller, Serena Tonstad, Tone Bathen and Jan Oxholm Gordeladze
\\n\\nChapter 6 Vitamin K2 and Bone Health by Niels Erik Frandsen and Jan Oxholm Gordeladze
\\n\\nChapter 7 Vitamin K2 and its Impact on Tooth Epigenetics by Jan Oxholm Gordeladze, Maria A. Landin, Gaute Floer Johnsen, Håvard Jostein Haugen and Harald Osmundsen
\\n\\nChapter 8 Anti-Inflammatory Actions of Vitamin K by Stephen J. Hodges, Andrew A. Pitsillides, Lars M. Ytrebø and Robin Soper
\\n\\nChapter 9 Vitamin K2: Implications for Cardiovascular Health in the Context of Plant-Based Diets, with Applications for Prostate Health by Michael S. Donaldson
\\n\\nChapter 11 Vitamin K2 Facilitating Inter-Organ Cross-Talk by Jan O. Gordeladze, Håvard J. Haugen, Gaute Floer Johnsen and Mona Møller
\\n\\nChapter 13 Medicinal Chemistry of Vitamin K Derivatives and Metabolites by Shinya Fujii and Hiroyuki Kagechika
\\n"}]'},components:[{type:"htmlEditorComponent",content:'This book serves as a comprehensive survey of the impact of vitamin K2 on cellular functions and organ systems, indicating that vitamin K2 plays an important role in the differentiation/preservation of various cell phenotypes and as a stimulator and/or mediator of interorgan cross talk. Vitamin K2 binds to the transcription factor SXR/PXR, thus acting like a hormone (very much in the same manner as vitamin A and vitamin D). Therefore, vitamin K2 affects a multitude of organ systems, and it is reckoned to be one positive factor in bringing about "longevity" to the human body, e.g., supporting the functions/health of different organ systems, as well as correcting the functioning or even "curing" ailments striking several organs in our body.
\n\nChapter 1 Introductory Chapter: Vitamin K2 by Jan Oxholm Gordeladze
\n\nChapter 2 Vitamin K, SXR, and GGCX by Kotaro Azuma and Satoshi Inoue
\n\nChapter 3 Vitamin K2 Rich Food Products by Muhammad Yasin, Masood Sadiq Butt and Aurang Zeb
\n\nChapter 4 Menaquinones, Bacteria, and Foods: Vitamin K2 in the Diet by Barbara Walther and Magali Chollet
\n\nChapter 5 The Impact of Vitamin K2 on Energy Metabolism by Mona Møller, Serena Tonstad, Tone Bathen and Jan Oxholm Gordeladze
\n\nChapter 6 Vitamin K2 and Bone Health by Niels Erik Frandsen and Jan Oxholm Gordeladze
\n\nChapter 7 Vitamin K2 and its Impact on Tooth Epigenetics by Jan Oxholm Gordeladze, Maria A. Landin, Gaute Floer Johnsen, Håvard Jostein Haugen and Harald Osmundsen
\n\nChapter 8 Anti-Inflammatory Actions of Vitamin K by Stephen J. Hodges, Andrew A. Pitsillides, Lars M. Ytrebø and Robin Soper
\n\nChapter 9 Vitamin K2: Implications for Cardiovascular Health in the Context of Plant-Based Diets, with Applications for Prostate Health by Michael S. Donaldson
\n\nChapter 11 Vitamin K2 Facilitating Inter-Organ Cross-Talk by Jan O. Gordeladze, Håvard J. Haugen, Gaute Floer Johnsen and Mona Møller
\n\nChapter 13 Medicinal Chemistry of Vitamin K Derivatives and Metabolites by Shinya Fujii and Hiroyuki Kagechika
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