Summary of the different ST boost control methods expressions 
In a context of volatile fuel prices and rising concerns in terms of energy security of supply and climate change issues, one of the discussed technological alternatives for the transportation sector are electric based vehicles. Advanced technology vehicles such as hybrid electric vehicles (HEVs), plug-in hybrid electric vehicles (PHEVs), fuel cell hybrid electric vehicles (FCHEVs), and electric vehicles (EVs) require power electronics and electrical machines to function. These devices allow the vehicle to use energy from the battery to assist in the propulsion of the vehicle, either on their own or in combination with an engine . Therefore, many research efforts have been focused on developing new converters and inverters suitable for electric vehicles applications. One of the most promising topologies is the Z-source inverter (ZSI). The ZSI, as shown in Figure 1, is an emerging topology for power electronics DC/AC converters. It can utilize the shoot-through (ST) state to boost the input voltage, which improves the inverter reliability and enlarges its application field . In comparison with other power electronics converters, it provides an attractive single stage DC/AC conversion with buck-boost capability with reduced cost, reduced volume and higher efficiency due to a lower component number. Therefore, the ZSI is a very promising and competitive topology for vehicular applications .
As a research hotspot in power electronics converters, the ZSI topology has been greatly explored from various aspects, such as: ST control methods , -, designing of the Z-network elements , modeling of the ZSI , , feedback control strategies -, motor control algorithms - and automotive applications -.
This chapter starts by presenting a summary for ZSI operation modes and modeling. Then, a review and a comparison between four ST boost control methods, which are: simple boost control (SBC), maximum boost control (MBC), maximum constant boost control (MCBC), and modified space vector modulation (MSVM) boost control, is presented based on simulation and experimental results. Control strategies of the ZSI are important issue and several feedback control strategies have been investigated in recent publications. There are four methods for controlling the dc-link voltage of the ZSI, which are: capacitor voltage control, indirect dc-link voltage control, direct dc-link control and unified control. A review of the above mentioned control methods with their drawbacks will be presented. Two new proposed control methods, which are dual-loop capacitor voltage control and dual-loop peak dc-link voltage control, will be presented and demonstrated by simulation and experimental results. Then, this chapter presents a comparative study of the most significant control methods, which are: scalar control (V/F), indirect field oriented control (IFOC) and direct torque control (DTC), for an induction motor fed by a ZSI for automotive applications. These control techniques are implemented using PWM voltage modulation. Finally, this chapter proposes three applications of the ZSI for automotive applications.
2. ZSI Operation Modes and Modeling
To design a controller for the ZSI, a proper dynamic model for its switching operation is needed. An accurate small signal model of the ZSI gives not only a global also a detailed view of the system dynamics and provides guidelines to system controllers design since the transfer functions could be derived accordingly. Figure 1 shows the basic ZSI topology, which consists of two inductors (L1 and L2) and two capacitors (C1 and C2) connected in X shape to couple the inverter to the dc voltage source. The ZSI can produce any desired ac output voltage regardless of the dc input voltage. Because of this special structure, the ZSI has an additional switching state, when the load terminals are shorted through both the upper and lower switching devices of any phase leg, which called the shoot-through (ST) state besides the eight traditional non-shoot through (NST) states. General operation of a ZSI can be illustrated by simplifying the ac side circuit by an equivalent RL load in parallel with a switch S2 and the input diode D is represented by a switch S1, as shown in Figure 2. Where, is given by andis determined so that the time constant of the dc load is the same as the ac load . Two operation modes involving two different circuit topologies can be identified in the ZSI operation as shown in Figure 3. In Mode 1, Figure 3-a, the energy transferred from source to load is zero because the load side and source side are decoupled by the ST state and the open status of S1. In Mode 2, Figure 3-b, real energy transfer between source and load occurs.
Equations (1-4) represent: the third order small signal model, the steady state values of the state variables, the control to capacitor voltage and control to inductor current small signal transfer functions of the ZSI, where are the input voltage, the equivalent dc load resistance, the equivalent dc load inductance, and the steady state values of inductor current, capacitor voltage, load current and ST duty ratio at certain operating point, respectively, and are the Z-network inductor and capacitor, respectively.
Predicting the right half plane (RHP) zeros of the related transfer functions is one of the major advantages of the small-signal modeling. By considering the control to capacitor voltage transfer function, given by Eq. 3 as an example, the numerator is a quadratic equation. As known, for a quadratic equation, there will be two different poles α and β if the discriminant. Regarding this case, it can be acquired that and, therefore, this transfer function has two zeros: one is negative while the other is a positive one, which is called RHP zero. This identifies a non-minimum phase characteristic in the capacitor voltage response that is known to potentially introduce stability issues in the closed loop controlled system. The design of a feedback controller with an adequate phase margin becomes more difficult when RHP zeros appear in the transfer function, since it tends to destabilize the wide bandwidth feedback loops, implying high gain instability and imposing control limitations.
3. Review of PWM control methods for ZSI
3.1. Simple ST Boost Control (SBC)
The SBC method , uses two straight lines equal to or greater than the peak value of the three phase references to control the ST duty ratio in a traditional sinusoidal PWM, as shown in Figure 4. When the triangular waveform is greater than the upper line, V p , or lower than the bottom line, V n , the circuit turns into ST state. Otherwise it operates just as traditional carrier based PWM. This method is very straightforward; however, the resulting voltage stress across the switches is relatively high because some traditional zero states are not utilized.
3.2. Maximum ST Boost Control (MBC)
Reducing the voltage stress under a desired voltage gain becomes more important to control the ZSI; this can be achieved by making the ST duty ratio as large as possible. The MBC control, , turns all the traditional zero states into ST state. As shown in Figure 5, the circuit is in ST state when the triangular carrier wave is either greater than the maximum curve of the references (V a , V b and V c ) or smaller than the minimum of the references. The ST duty ratio varies at six times of the output frequency. The ripples in the ST duty ratio will result in ripple in the inductor current and the capacitor voltage. This will cause a higher requirement of the passive components when the output frequency becomes very low. Therefore, the MBC method is suitable for applications that have a fixed or relatively high output frequency.
3.3. Maximum Constant ST Boost Control (MCBC)
In order to reduce the volume and the cost, it is important always to keep the ST duty ratio constant. At the same time, a greater voltage boost for any given modulation index is desired to reduce the voltage stress across the switches. The MCBC method achieves the maximum voltage gain while always keeping the ST duty ratio constant . Figure 6 shows the sketch map of the maximum constant ST boost control with third harmonic injection. Using the third harmonic injection, only two straight lines, V p and V n , are needed to control the ST time with 1/6 of the third harmonic injected.
3.4. Modified Space Vector Modulation ST Control Method
The space vector PWM (SVPWM) techniques are widely used in industrial applications of the PWM inverter because of lower current harmonics and a higher modulation index. The SVPWM is suitable to control the ZSI. Unlike the traditional SVPWM, the modified space vector modulation (MSVM) has an additional ST time T 0 for boosting the dc-link voltage of the inverter beside the time intervals T 1 , T 2 and T z . The ST states are evenly assigned to each phase with T 0 /6 within zero voltage period T z . The zero voltage period should be diminished for generating a ST time, and the active states T 1 and T 2 are unchanged. So, the ST time does not affect the PWM control of the inverter, and it is limited to the zero state time T z . The MSVM can be applied using two patterns. The MSVM1 as shown in Figure 7-a, at this switch pattern, the ST time T 0 is limited to (3/4)T z , because the period (T z /4-2T s ) should be greater than zero. The MSVM2 as shown in Figure 7-b, where the distribution of zero state time is changed into (T z /6) and (T z /3). The maximum ST time is increased to the zero state time T z .
Table 1 shows a summary of all relations for the different ST boost control methods, where D 0 is the ST duty ratio, M is the modulation index, B is the boost factor, G is the voltage gain, and Vs is the voltage stress across the switch. Figure 8-a shows the voltage gain versus the modulation index and Figure 8-b shows the voltage stress versus the voltage gain for different ST boost control methods. At high voltage gain, the MSVPWM1 has the highest voltage stress.
Efficiency evaluation is an important task during inverter design. The losses of the inverter mainly distributed on the semiconductor devices. The semiconductor device losses mainly include conduction losses and switching losses. The efficiency of the ZSI is greatly affected by the ST control methods. Figure 9 shows the losses distribution of a 10 kW ZSI at nominal input and output power, where the input diode conduction and switching losses are included, which are neglected in most publications, the extra losses of the MSVM boost method mainly come from the switching losses of IGBTs and reverse recovery losses of the input diode which are about three times of other methods . Table 2 presents a comparison between the different four ST control methods. The comparison results show that the MCBC method seems to be the most suitable boost control method for the ZSI .
|ST boost control method||SBC||MBC||MCBC||MSVM|
|Line voltage harmonic||-||+||0||+|
|Phase current harmonic||0||0||+||-|
|DC link voltage ripples||0||-||+||0|
|Switch voltage stress||0||+||0||-|
|Inductor current ripples||0||-||+||-|
|Obtainable ac voltage||0||0||+||-|
4. ZSI DC link voltage control
The control strategy of the ZSI is an important issue and several feedback control strategies have been investigated in recent publications . There are four methods for controlling the ZSI dc-link voltage, which are: capacitor voltage control -, indirect dc-link voltage control ,, direct dc-link control , and unified control . Table 3, presents a review of the above mentioned control methods with their drawbacks.
In all the above mentioned control methods, a single-loop voltage control technique was used. However, in high power converters, a single-loop voltage control has two problems. The first problem is that, the inductor current is not regulated and can be overloaded during transient events and the limited stability limits is the second problem. Therefore, a dual-loop voltage control is preferred over a single-loop voltage control in high power converters to overcome the above mentioned problems . Two new control algorithms are proposed by the authors, which are: a dual-loop capacitor voltage control  and a dual-loop peak DC-link voltage control . These two control algorithms will be briefly presented as flows.
4.1. Capacitor voltage control
This chapter proposes a dual loop capacitor voltage control of the ZSI. The proposed control generates the ST duty ratio by controlling both the inductor current and the capacitor voltage of the ZSI as shown in Figure 10-a, where G M (s) is expressed by:
Based on the small signal transfer functions and given by Eqs (3), (4) and (5), both controller transfer functions and can be designed. In order to design these controllers, the continuous time transfers functions are first discretized using the zero order hold (ZOH). Once the discrete transfer functions of the system are available, the digital controllers are designed directly in the Z-domain using methods similar to the continuous time frequency response methods. This has the advantage that the poles and zeros of the digital controllers are located directly in the Z-domain, resulting in a better load transient response, as well as better phase margin and bandwidth for the closed loop power converter . Figure 10-b shows the entire digital closed loop control system containing the voltage loop controller, current loop controller, the zero order hold, the computational delay, the modified modulation, and the control to outputs transfer functions. In this implementation the chosen sampling scheme results in a computation delay of half the sampling period. The loop gains for inner current loop and outer voltage loop can be expressed as:
In this chapter, a digital PI controller with anti-windup is designed based on the required phase margin, and critical frequency, using the bode diagram of the system in the Z- domain, the transfer function of the digital PI controller in Z-domain is given by:
Figure 11 shows the bode plots for the current loop gain and voltage loop gain, respectively, with the system parameters listed in Table 4. The plots indicate that the current loop gain has a crossover frequency as high as 1 kHz, with a phase margin of 65° and a gain margin of 10 dB. To avoid interaction between the sub-systems, low control bandwidth is used for the voltage loop. The resulting outer voltage loop has a crossover frequency of 100 Hz and a phase margin of 59° and a gain margin of 25 dB. Figs. 12-13 compare simulation and experimental results during input voltage step down by 7.5% with the same load, load increasing and decreasing by 50% and steady state operations. It is noticeable that the experimental results match the simulation results very well, which verify the performance of the proposed dual-loop capacitor voltage control for the ZSI.
|Input voltage||200 V|
|Capacitor reference voltage||300 V|
|Inductance internal resistance||0.22 Ω|
|Capacitance internal resistance||0.9 mΩ|
|Switching frequency||10 kHz|
|AC load inductance||340 µH|
|AC load resistance||12.5 Ω|
4.2. Peak DC-link voltage control
The capacitor voltage, , is somewhat equivalent to the peak dc-link voltage, , of the inverter, but the peak dc-link voltage is non-linear function of the capacitor voltage. Thus, only controlling the capacitor voltage cannot bring the high performance due to the non-linear property of the relation. Figure 14 shows the entire dual-loop peak dc-link voltage control technique block diagram of the ZSI. Figs. 15-16 show the simulation and experimental results of the proposed dual-loop peak dc-link voltage control technique during input voltage step and load transient. As shown in Figure 15, the input voltage stepped-down by 7.5% with the rated load, the peak dc-link voltage remains constant at 300 V, the load phase current and line voltage are not affected by input voltage decreasing and the inductor current is increased to supply the same output power. Figure 16 shows the ZSI response during load increasing and decreasing by 50%. As noticeable the inductor current is doubled during the 50% load increase and the output line voltage and the peak dc-link voltage remain unchanged.
5. A comparative study of different control techniques for induction motor fed by a Z-source inverter
This section presents a comparative study of the most significant control methods (Scalar control (V/F), indirect field oriented control (IFOC) and direct torque control (DTC)) for an induction motor fed by a ZSI for automotive applications. The three control techniques are implemented using PWM voltage modulation. The comparison is based on various criteria including: basic control characteristics, dynamic performance, and implementation complexity. The study is done by MATLAB simulation of a 15 kW induction motor fed by a high performance ZSI (HP-ZSI). The simulation results indicates that, the IFOC seems to be the best control techniques suitable for controlling an induction motor fed by a ZSI for automotive applications.
5.1. Scalar control (V/F) technique
The closed loop speed control by slip regulation, which is an improvement of the open loop V/F control, is shown in Figure 17. The speed loop error generates the slip command through a proportional integral (PI) controller with a limiter. The slip is added to the feedback speed signal to generate the slip frequency command. Thus the frequency command generates the voltage command through a V/F generator, which incorporates the low frequency stator drop compensation. Although this control technique is simple, it provides limited speed accuracy especially in the low speed range and poor dynamic torque response.
5.2. Indirect Field Oriented Control (IFOC) technique
In the indirect field oriented control method, the rotating reference frame is rotating at synchronous angular velocity, . This reference frame allows the three phase currents to be viewed as two dc quantities under steady state conditions. The q-axis component is responsible for the torque producing current, , and the d-axis is responsible for the field producing current, . These two vectors are orthogonal to each other so that the field current and the torque current can be controlled independently. Figure 18 shows the block diagram of the IFOC technique for an induction motor. The q-axis component of the stator reference current, , may be computed using the reference torque, , which is the output of a PI speed controller, as:
where Ψ r is the estimated rotor flux, which is given by:
where L m , L r and τr are the magnetization inductance, the rotor inductance, and the rotor time constant, respectively. The d-axis component of the stator reference current, , may also be obtained by using the reference input flux, , which is the output of a PI flux controller, as:
By using the rotor speed, , and the slip frequency, , which is given by:
the angle of the rotor flux, , may be evaluated as:
Proportional integral controllers regulate the stator voltages, and, to achieve the calculated reference stator currents, and . The required voltage is then synthesized by the inverter using pulse width modulation (PWM). During motor operation the actual rotor resistance and inductance can vary. The resulting errors between the values used and the actual parameters cause an incomplete decoupling between the torque and the flux. In order to compensate for this incomplete decoupling, the values of compensation voltages are added to the output of the current controllers. This voltage compensation can improve the performance of the current control loops. The compensations terms are given by:
5.3. Direct Torque Control with Space Vector Modulation (DTC-SVM) technique
The conventional DTC scheme has many drawbacks, such as: variable switching frequency, high current and torque ripples, starting and low-speed operation problems, in addition to high sampling frequency needed for digital implementation of the hysteresis controllers. To overcome these drawbacks, the space vector modulation is combined with the conventional DTC scheme for induction motor drive to provide a constant inverter switching frequency. In the DTC-SVM scheme, as shown in Figure 19, the torque and flux hysteresis comparators are replaced by PI controllers to regulate the flux and torque magnitudes respectively. The motor stator flux and the motor developed torque can be estimated by:
The output of theses PI controllers generates the d and q components of the reference voltage command (and ) in the stator flux oriented coordinates. After coordinate transformation, using the stator flux angle , we get the reference voltage vectors and ) in the stationary frame. These two components, which can control stator flux and torque separately, are delivered to space vector modulator (SVM). The space vector modulator generates the inverter control signals, which ensures fixed inverter switching frequency. So the inverter switching frequency is significantly increased, and the associated torque ripple and current harmonics can be dramatically reduced, in comparison with the conventional switching table based DTC scheme.
Figure 20 shows the complete block diagram of the closed loop speed controlled IM fed by a high performance ZSI. A dual loop controller is designed to control the average value of the dc link voltage by controlling the magnitude of its peak voltage based on a small signal model of the high performance ZSI. Figure 21, shows the calculated overall system efficiency at different load torque. The three control techniques were compared on a simulated benchmark. The main results of this comparative study are summarized in Table 5.
6. Z-Source Inverter for vehicular applications
This section proposes three applications of the ZSI in the automotive field. The first application proposes the using of the bidirectional ZSI (BZSI) supplied by a battery to drive an induction motor for hybrid electric vehicle (HEV) applications, by replacing the two stages conversion. The second application proposes the using of the BZSI in plug-in hybrid electric vehicle (PHEV) applications for replacing the bidirectional battery charger, which composed of two stages conversion. By using the BSZI, the battery can be charged from the grid during night and can be discharged to the grid during peak power demand, which increase the grid stability. The third application proposes the using of the HP-ZSI for fuel cell hybrid electric vehicle (FCHEV) applications. Where the fuel cell (FC) stack and the supercapacitor (SC) module are directly connected in parallel with the HP-ZSI. The SC module is connected between the input diode and the bidirectional switch S7 of the HP-ZSI. The SC module supplies the transient and instantaneous peak power demands and absorbs the deceleration and regenerative braking energy. The indirect field oriented control (IFOC) is used to control the speed of the IM during motoring and regenerative braking operation modes in the first and the third proposed applications. While, a proportional plus resonance (PR) controller is used to control the AC current during connecting the BZSI to the grid for battery charging/discharging mode in the second proposed application.
6.1. ZSI applications in HEV
The ZSI is proposed to be used to replace the two stages conversion in HEV, The BZSI can replace the bidirectional DC/DC converter and the traditional VSI as a single stage converter, as shown in Figure 22. The IFOC is used for controlling the speed of the IM during motoring and regenerative braking operations and a dual loop capacitor voltage control algorithm is used to control the BZSI dc-link voltage.
6.2. ZSI applications in PHEV
The ZSI is proposed to be used to replace the two stage bidirectional battery charger in a PHEV. Figure 23 shows the entire block diagram of a grid connected BZSI containing: the battery, the BZSI, the capacitor voltage control algorithm and the AC grid current control algorithm during battery charging/discharging modes, where the capacitor voltage control generates the ST duty ratio and the AC grid current control generates the modulation index.
6.3. ZSI applications in FCHEV
In Figure 24, the FC system and the SC module are direct connected in parallel with the HP-ZSI. The SC module is connected between the input diode D and the bidirectional switch S7. The bidirectional switch S7 provides a path for the regenerative braking energy to be stored in the SC module during the ST state. The SC module supplies the transient and instantaneous peak power demands and absorbs the deceleration and regenerative braking energy. In addition, a dual loop control is used to control the Z-network capacitor voltage by controlling the ST duty ratio and the IFOC strategy is used to control the induction motor speed by controlling the modulation index. The proposed applications improve the vehicle efficiency and reduce its production cost due to a lower its component count, since it is a one stage converter with a reduced volume and easier control algorithm.