Over recent decades, the penetration of renewable energy sources (RES), especially photovoltaic and wind power plants, has been promoted in most countries. However, as these both alternative sources have power electronics at the grid interface (inverters), they are electrically decoupled from the grid. Subsequently, stability and reliability of power systems are compromised. Inertia in power systems has been traditionally determined by considering all the rotating masses directly connected to the grid. Thus, as the penetration of renewable units increases, the inertia of the power system decreases due to the reduction of directly connected rotating machines. As a consequence, power systems require a new set of strategies to include these renewable sources. In fact, ‘hidden inertia,’ ‘synthetic inertia’ and ‘virtual inertia’ are terms currently used to represent an artificial inertia created by inverter control strategies of such renewable sources. This chapter reviews the inertia concept and proposes a method to estimate the rotational inertia in different parts of the world. In addition, an extensive discussion on wind and photovoltaic power plants and their contribution to inertia and power system stability is presented.
- frequency control
- grid stability
- power systems
- inverter-interfaced renewable energy sources
Imbalances between generation and consumption cause frequency variations in a power system . To maintain frequency in its nominal value, power systems rely on synchronous machines connected to the grid, which store kinetic energy automatically extracted in response to a sudden power imbalance . However, due to the new environmental policies and the limited fossil fuel reserves, conventional generators are being replaced by renewable energy sources (RES)-based generators . Among the different RES available, the most promising for electrical power generation are PV and wind power installations, which are inverter-interfaced RES (II-RES) . However, the massive penetration of II-RES into the grid can involve several issues that should be taken into account . First, as they depend on weather conditions, these sources are intermittent and uncertain, placing stress on power system operation . Moreover, as they are connected to the grid through inverters which electrically decouple them from the grid , the effective inertia of the power system can be reduced . This inertia reduction affects the system reliability, compromising the frequency stability . The rotational inertia is related to both nadir (minimum frequency) and rate of change of frequency (ROCOF) . In fact, larger nadirs and faster ROCOFs are obtained in low rotational inertia power systems, subsequently making them more sensitive to frequency deviations [11, 12]. As a result, over the last decade, several frequency control techniques have been proposed to facilitate the massive penetration of wind and PV resources into the grid . In addition, recent contributions investigated the use of smart inverters with voltage and frequency support to enhance grid stability . Such solutions are commonly referred to as hidden, synthetic or virtual inertia .
This chapter focuses on the current and future inertia concept for power systems. A methodology to estimate the current rotational inertia of power systems based on their electricity generation mix is proposed. In addition, the possibilities of wind and PV power plants to contribute to inertia and participate in frequency control are also presented. The rest of the chapter is organized as follows. The inertia analysis and swing equation of generators and current and future power systems are presented in Section 2. In Section 3, the inertia constant estimation methodology is explained, comparing the results to a previous report published by the European Network of Transmission System Operators for Electricity (ENTSO-E). Section 4 reviews different frequency control techniques for PV and wind power plants. Finally, Section 5 gives the conclusion.
2. Inertia analysis in power systems
2.1 Inertial response of a synchronous generator: inertia constant
Moment of inertia is a measure of the resistance of an object to changes in its rotational motion . However, in power systems, it is common to express inertia constant instead of moment of inertia . Actually, the inertia constant of a generator determines the time interval during which an electrical generator can supply its rated power only by using the kinetic energy stored in its rotating masses. is defined following Eq. (2), being the rated power :
Work in  reviews the inertia constants of conventional power plants proposed in recent decades, which range between 2 and 10 s.
In power systems, the motion of each turbine-generator group is expressed as Eq. (3), where and are the mechanical torque of the turbine and the electromagnetic torque of the generator, respectively:
However, as and considering the initial status as :
where and . Moreover, for small variations:
and in steady state:
Furthermore, some electrical loads connected to the grid are also frequency-dependent, working as a load resource under frequency deviations (i.e., synchronous machines). In this way, the electrical power of those loads can be expressed as:
where is the power change of those loads independent from frequency deviations and is the damping factor (load-frequency response). Subsequently, by including the damping factor in Eq. (7), it is modified to Eq. (9), which is usually referred to as swing equation and represents the motion of a synchronous generator:
2.2 Aggregated swing equation: application to power systems
To apply the swing Eq. (9) to a power system, all synchronous generators are grouped in an equivalent rotating mass. This is carried out by determining the equivalent inertia constant of such generators:
where and are the inertia constant and rated power of synchronous generator , is the total number of synchronous generators connected to the grid and is the rated power of the power system.
In the same way, loads are reduced to an equivalent one with damping factor . If the power system under analysis is stable, an inaccurate value of will not have a significant impact on the study. However, under disturbance situations, the value of can be a major contribution . As variable frequency drives become more common, the equivalent damping factor is expected to decrease .
2.3 Hidden and virtual inertia emulation from RES: modified equivalent inertia constant
In recent decades, several policies have promoted the penetration of RES-based generation units, which have replaced synchronous generators directly connected to the grid . However, as some of them are II-RES (i.e., wind and PV), power systems with a high penetration of those RES require new frequency control strategies that emulate the behavior of conventional power plants under power imbalance conditions . Such techniques are commonly referred to as hidden, synthetic, emulated or virtual inertia . By including this emulation of inertia into power systems, equivalent inertia would be modified. Thus, it would have two different components: (i) synchronous rotating inertia coming from synchronous (conventional) generators and (ii) emulated/virtual inertia coming from II-RES [24, 25]. Thus, Eq. (10) would become:
where is the number of II-RES connected to the grid through emulation/virtual control methods and is the inertia constant of the emulated/virtual generation unit. This modified equivalent inertia expressed in Eq. (11) is graphically illustrated in Figure 1, based on . As can be seen, there are three different links between the generation units and the grid frequency: (i) rotational synchronous inertia from conventional generators, (ii) hidden inertia from VSWT and (iii) virtual inertia from PV. This is because modern VSWT have rotational inertia stored in their blades, drive train and electrical generator . However, due to the inverter and maximum power point tracking (MPPT) strategy, they cannot automatically provide this inertia to the grid [28, 29, 30, 31], being thus considered as ‘hidden’ from the power system point of view . In fact, VSWT have inertia constants comparable to those of conventional generators, as summarized in Figure 2. In consequence, it is considered that the inertia provided by VSWT is ‘emulated’ .
On the other hand, PV has no rotating masses . Thus, PV power plants cannot store kinetic energy and their inertia constant is . Consequently, they cannot provide inertia unless it is synthetic/virtual, thus being usually referred to as ‘emulated synthetic/virtual inertia’ provided by such PV power plants [34, 35].
Due to the repercussions of II-RES with regard to the rotating inertia of power systems , they should start providing active power support under disturbances . The specific literature includes several technologies that allow II-RES to participate in frequency control by providing additional power under disturbances [38, 39, 40].
3. Inertia estimation for power systems
Energy global statistics are provided by the International Energy Agency (IEA). Considering Eq. (10) and the electricity supply within a year presented in , it is possible to calculate the equivalent inertia in different regions of the world. According to each technology, the inertia constant of conventional units is estimated as the mean value of those presented in  (i.e., s, s, s, s, s). It is considered that II-RES are not participating in frequency control (i.e., not contributing to the system inertia).
Figure 3 depicts the generation mix change between 1996 and 2016. Over these two decades, the total electricity consumption increased by more than 80%. However, in the same time period, RES electricity generation only increased by 4%. Based on the approach previously described to estimate , Figure 4 depicts the change between the inertia constant for the different continents between 1996 and 2016. As can be seen, the inertia reduction in Asia, the USA and South America was negligible (between 2.5 and 3%), whereas in Europe it decreased by nearly 20%.
In line with the inertia reduction suffered, RES supply in Europe increased by nearly 20% (refer to Figure 5). Actually, ENTSO-E has already focused on the high RES integration-low synchronous inertia problem. In one of their published reports, ENTSO-E estimated the evolution of system inertia for different TYNDP scenarios for 2030 in Europe and certain countries (i.e., the United Kingdom, France and Germany), considering that II-RES do not contribute to inertia . In those estimations, depends on the percentage of hours in a year that II-RES are working. Thus, it is possible to compare the estimated in this chapter with the values obtained by ENTSO-E.
The transition of in a number of European countries can be seen in Figure 6. In , considering RES current generation rate: (i) of Europe is within range 3.8–4.5 s; (ii) of the United Kingdom is within range 3–4 s; (iii) of France is 5 s and (iv) of Germany is 3.5 s. Some discrepancies can be observed. The main cause of these is the values of the inertia constant of conventional plants. In fact, if the maximum value of for all conventional plants is considered (i.e., s, s, s, s, s), the results are nearly the same as those presented in .
4. II-RES frequency control strategies
To maintain frequency within an acceptable range, generation and load in the power system must be continuously balanced . In fact, frequency variations from the nominal value can cause several problems including under-/overfrequency relay operations and disconnection of some loads from the grid, among others . Thus, frequency stability is an essential issue for power systems .
With the increase in II-RES, the equivalent inertia constant of power systems is reduced, subsequently obtaining (i) larger frequency deviations after an imbalance and (ii) higher ROCOF [7, 46]. As a consequence, II-RES should start providing active power support under disturbances .
4.2 PV power plant frequency control strategies
In order to provide additional active power during imbalanced situations, PV power plants can integrate different solutions, mainly based on two principal approaches: energy storage systems (ESS) or de-loading control strategies. Moreover, the technical challenge is more severe with PV power plants than with wind generation, since PV systems cannot provide any inertial response unless special countermeasures are adopted .
With regard to ESS, different solutions have been proposed in the literature to be applied to PV systems. Although the relevant benefits of ESS to power system’s operation is widely recognized, some significant challenges can be identified: (i) the selection of a suitable technology to match the power system application requirements, (ii) an accurate evaluation of the energy storage facilities estimating both technical and economic benefits and (iii) a cost decreasing to a realistically acceptable level for deployment . Among the different ESS, the battery energy storage is considered by some authors as the oldest and most mature ESS . In work , it is concluded that the Li-Ion batteries are those that best suit frequency regulation services. Batteries are limited in power, though present a high storage ratio [51, 52, 53]; on the other hand, supercapacitors have high levels of power with low energy storage ratio. As a consequence, the battery-supercapacitor combination is proposed as an interesting ESS solution . Indeed, these technologies can help to solve the problem of the ‘intermittent’ nature of solar PV supply . Additional solutions for PV installations based on supercapacitors can be found in [56, 57]. Flywheels are another solution widely proposed as ESS, being applied from very small micro-satellites to large power systems . Work in  points out a great benefit of flywheels backing up solar PV power plants, mainly focused on the cloud passing, which can cope with the high cycles of the flywheel technologies. Indeed, flywheels excel in short duration and high cycle applications . Moreover, flywheels have a high efficiency, usually in the range between 90% and 95%, with an expected lifetime of around 15 years . Different solutions propose hybrid ESS coupled to PV power plants , such as a battery hybridization with mechanical flywheel .
PV power plants usually work at the maximum power point (MPP) according to ambient temperature and solar irradiation . However, they can work below their MPP, having thus some active power reserves (headroom) to supply in case of a frequency deviation. This approach is usually referred to as de-loading technique and is commonly proposed for PV installations [64, 65]. In this way, the PV plant is operated at , below , so that some power reserves are available [66, 67]. As can be seen in Figure 7, can be related with two different voltages: (i) over the maximum power point voltage, , and (ii) under the maximum power point voltage, . However, due to stability problems, the de-loaded voltage corresponds to the higher value . This is then added to the MPP controller reference, in order to also de-load the inverter. This controller for de-loaded PV is modified in , such that the release of the reserve is directly linked to both (i) the frequency excursion and (ii) the availability of the reserve in the PV system. This controller is also proposed in .
4.3 Wind power plant frequency control strategies
Wind power plants can also participate in frequency control by using different solutions. Apart from the use of ESS or working with the de-loading control strategy, wind turbines can provide inertial response as conventional generators due to the rotational inertia of the blades and generator .
With regard to ESS, wind power plants can also include batteries , supercapacitors  and flywheels . ESS are considered an alternative to compensate the lack of short-term frequency response ability of wind power plants . The utility-scale battery ESS helps to reduce the ROCOF, providing frequency support and improving the system frequency response . A battery ESS based on a state-machine-based coordinated control strategy is developed in  to support frequency response of wind power plants, including both primary and secondary frequency control. A real-time cooperation scheme by considering complementary characteristics between wind power and batteries is discussed in  to provide both energy and frequency regulation, considering the battery life cycle. The combination of battery and supercapacitor is considered in  as an effective alternative to improve the battery lifetime and enhance the system economy. In this way, an enhanced frequency response strategy is investigated in  to improve and regulate the wind frequency response with the integration of ultra-capacitors. With the aim of smoothing the net power injected to the grid by wind turbines (or by a wind power plant), some authors propose to use flywheels [80, 81]. Flywheels are also proposed to dynamically regulate the system equivalent inertia and damping, enhancing the frequency regulation capability of wind turbines [38, 82] and also the entire grid . A coordinated regulation response of the turbine power reserves and the flywheels while participating in primary frequency control is described in . Finally, other works include not only frequency response but also voltage control by using flywheels [85, 86].
In line with PV installations, wind turbines also work in the MPP according to the wind speed . As a consequence, the de-loading technique is considered as a solution to provide additional active power in imbalanced situations with wind turbines, by operating them in a suboptimal point through the de-loaded control mode . Wind turbines have two different possibilities to operate with the de-loading technique (refer to Figure 8) : (i) pitch angle control and (ii) overspeed control. The pitch-angle control increases the pitch angle from to for a constant ; in this way, the supplied power is below the maximum power , being thus a certain amount of power that can be supplied in case of frequency contingency (Figure 8(a)) [88, 89, 90, 91]. When this additional power is provided, the pitch angle has to be reduced from to . The overspeed control increases the rotational speed of the rotor, shifting the supplied power towards the right of the maximum power (Figure 8(b)) [87, 92, 93]. As in the pitch-angle control, is below . When the additional power is supplied, the rotor speed has to be reduced from to , releasing kinetic energy [39, 87, 92, 93].
In order to provide an inertial response, at least one supplementary loop control is introduced into the power controller to increase the generated power by the wind power plant. This additional loop is only activated under power imbalances (i.e., frequency deviations), supplying the kinetic energy stored in the blades and generator to the grid as an additional active power for a few seconds . The droop control provides an additional active power proportional to the frequency excursion (see Figure 9), as the primary frequency control of conventional power plants. The increase in the active power output then results in a decrease in the rotor speed [95, 96, 97, 98, 99]. can be estimated following Eq. (12), being the droop control setting of the wind turbine:
The hidden inertia emulation technique is based on emulating the inertial response of traditional synchronous generators. Two possibilities are found in the specific literature, as presented in Figure 10: (i) one loop, where the additional power is proportional to the ROCOF [100, 101, 102], and (ii) two loops, where the additional power is proportional to the ROCOF and the frequency deviation. The second strategy causes the frequency to return to its nominal value [103, 104, 105]. In both cases, the rotor and generator speeds are reduced to release the stored kinetic energy.
The fast power reserve approach is similar to the hidden inertia emulation technique: an additional power is initially supplied, which makes the rotor speed to decrease. However, in this technique, the additional active power has been defined as a constant value independent of the system configuration and frequency deviation [106, 107, 108, 109, 110] or variable (depending on the frequency deviation or minimum rotor speed limits) [43, 111, 112]. The rotational speed decrease is then recovered through a recovery period, which can cause a secondary frequency dip due to the sudden decrease of the power generated by the wind power plant. As a consequence, different recovery periods have been proposed in the last decade to avoid this secondary frequency drop [43, 106, 108, 109, 110, 111, 113, 114], even coordinating this period with ESS . Figure 11 shows the fast power reserve emulation control proposed in .
In this chapter, we have conducted an extensive literature review of inertia of power systems. A methodology to estimate the inertia constants of different power systems is proposed and verified with the inertia constant results of ENTSO-E. The contribution of wind and PV power plants as ‘hidden inertia’ and ‘virtual inertia,’ respectively, to participate in frequency control has also been discussed, providing significant information for their participation in frequency control.
This work was supported by the Spanish Education, Culture and Sports Ministry (FPU16/04282), Spanish Economy and Competitiveness Ministry and European Union FEDER, which supported this work under Project ENE2016-78214-C2-1-R.
Conflict of interest
The authors declare no conflict of interest.
|DFIG||double-fed induction generator|
|ESS||energy storage systems|
|ENTSO-E||European Network of Transmission System Operators for Electricity|
|FSWT||fixed-speed wind turbine|
|HAWT||horizontal axis wind turbine|
|II-RES||inverter-interfaced renewable energy sources|
|PMSG||permanent magnet synchronous generator|
|RES||renewable energy sources|
|ROCOF||rate of change of frequency|
|SCIG||squirrel cage induction generator|
|VSWT||variable speed wind turbine|
|WPP||wind power plant|