A Review of Virtual Inertia Techniques for Renewable Energy-Based Generators

2.1 Inertial response of a synchronous generator: inertia constant

Rotating masses of a synchronous generator store kinetic energy Ekinfollowing Eq. (1), where Jis the moment of inertia and ωris the rated rotational frequency of the machine [16]:

Moment of inertia Jis a measure of the resistance of an object to changes in its rotational motion [17]. However, in power systems, it is common to express inertia constant Hinstead of moment of inertia J. 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. His defined following Eq. (2), being Srthe rated power [18]:

Work in [10] reviews the inertia constants Hof 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 Tmand Teare the mechanical torque of the turbine and the electromagnetic torque of the generator, respectively:

However, as P=T⋅ωand considering the initial status as 0:

where ΔP=ΔPm−ΔPeand ΔT=ΔTm−ΔTe. Moreover, for small variations:

and in steady state:

In consequence, considering small variations around the steady state, Eq. (3) can be rewritten as in Eq. (7) [19]:

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 ΔPLis the power change of those loads independent from frequency deviations and Dis 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 Heqof such generators:

where Hiand SB,iare the inertia constant and rated power of synchronous generator i, SGis the total number of synchronous generators connected to the grid and SBis the rated power of the power system.

In the same way, loads are reduced to an equivalent one with damping factor Deq. If the power system under analysis is stable, an inaccurate value of Deqwill not have a significant impact on the study. However, under disturbance situations, the value of Deqcan be a major contribution [20]. As variable frequency drives become more common, the equivalent damping factor is expected to decrease [21].

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 [22]. 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 [23]. Such techniques are commonly referred to as hidden, synthetic, emulated or virtual inertia [15]. By including this emulation of inertia into power systems, equivalent inertia Heqwould be modified. Thus, it would have two different components: (i) synchronous rotating inertia coming from synchronous (conventional) generators HSand (ii) emulated/virtual inertia coming from II-RES HV[24, 25]. Thus, Eq. (10) would become:

where VGis the number of II-RES connected to the grid through emulation/virtual control methods and HVis 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 [26]. 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 [27]. 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 [32]. 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’ [33].

On the other hand, PV has no rotating masses [30]. Thus, PV power plants cannot store kinetic energy and their inertia constant is H≃0[31]. 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 [36], they should start providing active power support under disturbances [37]. The specific literature includes several technologies that allow II-RES to participate in frequency control by providing additional power under disturbances [38, 39, 40].

4.1 Preliminaries

To maintain frequency within an acceptable range, generation and load in the power system must be continuously balanced [43]. 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 [44]. Thus, frequency stability is an essential issue for power systems [45].

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 [37].

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 [47].

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 [48]. Among the different ESS, the battery energy storage is considered by some authors as the oldest and most mature ESS [49]. In work [50], 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 [54]. Indeed, these technologies can help to solve the problem of the ‘intermittent’ nature of solar PV supply [55]. 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 [58]. Work in [59] 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 [60]. Moreover, flywheels have a high efficiency, usually in the range between 90% and 95%, with an expected lifetime of around 15 years [61]. Different solutions propose hybrid ESS coupled to PV power plants [53], such as a battery hybridization with mechanical flywheel [62].

PV power plants usually work at the maximum power point (MPP) according to ambient temperature Tand solar irradiation G[63]. 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 Pdel, below PMPP, so that some power reserves ΔP=PMPP−Pdelare available [66, 67]. As can be seen in Figure 7, Pdelcan be related with two different voltages: (i) over the maximum power point voltage, Vdel,1>VMPP, and (ii) under the maximum power point voltage, Vdel,2<VMPP. However, due to stability problems, the de-loaded voltage corresponds to the higher value Vdel,1[68]. This Vdelis then added to the MPP controller reference, in order to also de-load the inverter. This controller for de-loaded PV is modified in [69], 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 [70].

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 [10].

With regard to ESS, wind power plants can also include batteries [71], supercapacitors [72] and flywheels [73]. ESS are considered an alternative to compensate the lack of short-term frequency response ability of wind power plants [74]. The utility-scale battery ESS helps to reduce the ROCOF, providing frequency support and improving the system frequency response [75]. A battery ESS based on a state-machine-based coordinated control strategy is developed in [76] 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 [77] to provide both energy and frequency regulation, considering the battery life cycle. The combination of battery and supercapacitor is considered in [78] 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 [79] 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 [83]. A coordinated regulation response of the turbine power reserves and the flywheels while participating in primary frequency control is described in [84]. 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 vw. 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 [87]. Wind turbines have two different possibilities to operate with the de-loading technique (refer to Figure 8) [32]: (i) pitch angle control and (ii) overspeed control. The pitch-angle control increases the pitch angle from β0to β1for a constant vw; in this way, the supplied power Pdelis below the maximum power PMPP, being thus a certain amount of power ΔPthat can be supplied in case of frequency contingency (Figure 8(a)) [88, 89, 90, 91]. When this additional power ΔPis provided, the pitch angle has to be reduced from β1to β0. The overspeed control increases the rotational speed of the rotor, shifting the supplied power Pdeltowards the right of the maximum power PMPP(Figure 8(b)) [87, 92, 93]. As in the pitch-angle control, Pdelis below PMPP[71]. When the additional power ΔPis supplied, the rotor speed has to be reduced from Ωdelto ΩMPP, 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 [94]. The droop control provides an additional active power ΔPproportional to the frequency excursion Δf(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]. ΔPcan be estimated following Eq. (12), being RWTthe 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 ΔPhas 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 [115]. Figure 11 shows the fast power reserve emulation control proposed in [106].