Abstract
This paper investigates the use of a virtual synchronous generator (VSG) to improve frequency stability in an autonomous photovoltaicdiesel microgrid with energy storage. VSG control is designed to emulate inertial response and damping power via power injection from/to the energy storage system. The effect of a VSG with constant parameters (CPVSG) on the system frequency is analyzed. Based on the case study, selftuning algorithms are used to search for optimal parameters during the operation of the VSG in order to minimize the amplitude and rate of change of the frequency variations. The performances of the proposed selftuning (ST)VSG, the frequency droop method, and the CPVSG are evaluated by comparing their effects on attenuating frequency variations under load variations. For both simulated and experimental cases, the STVSG was found to be more efficient than the other two methods in improving frequency stability.
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1 Introduction
Photovoltaicdiesel autonomous microgrids (MGs) are a good solution for electricity generation in isolated places where the solar resource is adequate. The MG is established by a diesel generator set (DGS) which is a controllable source of energy, and a solar generator is used to complement power production [1,2,3]. However, frequency variations of consequence are more likely to occur in islanded MGs than in large interconnected utility grids, because they feature a relatively small generation capacity and rapid changes in power demand, especially in the presence of stochastic renewable generators [4, 5]. In addition, if a reduced number of DGS units is not able to maintain frequency magnitude and rate of change within prescribed operational limits, tripping of renewable generators and loads can occur [6]. Therefore, the assistance of an energy storage system (ESS) is required to maintain frequency stability for the autonomous MG system.
A method that indirectly deals with dynamic frequency control is the smoothing of the output power of intermittent sources [7]. However, this method requires the measurements of the output powers, which needs a communication link to transmit the measurements. The frequency droop method can control the distributed power conversion systems (PCSs) solely by local measurements in a decentralized manner without using a communication link [8, 9]. Nevertheless, this approach is intended to support frequency regulation by using only a fixed form of frequency droop, thus it does not provide dynamic frequency support. In the virtual synchronous generator (VSG) concept, the power electronics interface of the ESS is controlled in a way to exhibit a reaction similar to that of a real synchronous generator (SG) to a change or disturbance [10,11,12,13].
Designing the CPVSG to support dynamic frequency control involves emulating the inertial response and the damping power of a SG [14, 15]. The emulation of inertial response typically entails the control of power in inverse proportion to the first time derivative of the system frequency [14]. The damping power helps to attenuate oscillations, and thus to reduce the stabilization time of the frequency [15]. However, constant parameters do not explore the use of the variable virtual inertia and damping that can change their values during operation. In this regard, the VSG with selftuning virtual inertia and damping, using the current control method (CCM), has been proposed to remove frequency oscillations [6].
Online optimization is used to calculate the inertial response and the damping power, which increases the computational burden of the digital signal processor (DSP). However, for MG applications, particularly considering the requirement for autonomous operation, the VSG is desired to operate using the voltage control method (VCM) as it can provide direct voltage and frequency support for the loads. Based on this fact, the bangbang control strategy of alternating virtual inertia for the VSG operating with VCM has been proposed to suppress frequency and power oscillations effectively [16, 17]. During each cycle of oscillations, the value of inertia is switched between a big moment of inertia and a small one for four times. Each switching may cause power oscillations. On the other hand, applying a large constant virtual inertia for bangbang control will result in a sluggish response. Besides, this method also does not explore the use of adaptive virtual damping that acts during the oscillation following a power disturbance. In order to overcome these limitations, a novel selftuning (ST)VSG based frequency control method is developed in this paper, which decreases the computational burden of the DSP and provides the selftuning virtual inertia as well as virtual damping.
This paper starts with a brief introduction to the hierarchical control structure for an autonomous MG in Sect. 2. The CPVSGbased frequency control scheme is developed and presented in Sect. 3. The proposed STVSG with selftuning virtual inertia and virtual damping is analyzed in Sect. 4. The STVSGbased method is more efficient than the frequency droop method as well as the CPVSG in attenuating frequency variations. A detailed comparison of these three methods is carried out in the simulation cases in Sect. 5. The corresponding experimental results are provided in Sect. 6. Finally, the main conclusion is highlighted in Sect. 7.
2 Proposed frequency hierarchical control structure for autonomous MG
Figure 1 shows the proposed frequency hierarchical control structure for a photovoltaicbatterydiesel hybrid MG which consists of DGS, ESS, loads, photovoltaic unit and MG central controller. In Fig. 1, the photovoltaic unit is connected to the MG by a PQcontrolled inverter. Each distributed generator (DG) is composed of a circuit breaker and a power flow controller commanded by the central controller. The circuit breaker is used to disconnect the correspondent DG to mitigate the impacts of severe disturbances through the MG. Similarly, the point of common coupling switch is used to dynamically disconnect the MG from the utility grid for maintenance purposes or when grid faults or another contingency occurs. Although the MG can operate in either the gridtied mode or islanded mode, only islanded operation will be considered in this paper.
The proposed method to improve the frequency stability of an islanded photovoltaicbatterydiesel MG is based on hierarchical control. Primary control investigates the use of a PCS to support dynamic frequency control. In particular, the STVSG method proposed to support dynamic frequency control used the PSC to implement a frequency droop controller, selftuning virtual inertia and virtual damping. However, an inherent limitation in the STVSG is the tradeoff between frequency regulation and power sharing accuracy, and this may affect the frequency stability of the autonomous MG. Secondary control is used for power quality improvement by the DGS with a conventional PID speed governor. This control level eliminates frequency steadystate error generated by the STVSG. Tertiary control is by the central controller which facilitates high level management of the MG operation by means of technical and economical functions.
Note that secondary control is for compensating the deviations of voltage amplitude and frequency within the MG by conventional DGS functions [18]. Because of space limitations, the DGS model is not discussed here, and details can be found in [19]. Note also that tertiary control is for achieving global controllability of the MG. More details about secondary and tertiary controls are available in [20,21,22]. As a result, only the primary control scheme for dynamic frequency support in the autonomous MG is presented.
3 Principle of CPVSG control strategy
The penetration of DGs in power systems is increasing rapidly. This increases the total system generation capacity, while it does not contribute to system rotational inertia. Because most DGs do not present rotational inertia, or are connected to the grid using switching converters, there may be inadequate balancing energy injection within the time frame of inertial response. The solution can be found in the control scheme of converterbased DGs. In the VSG concept, the power electronics interface of DG units is controlled in a way to emulate the inertial response and the damping power of a traditional SG.
3.1 CPVSG control strategy
With the objective of paralleling PCSs and promoting the system frequency stability, the CPVSG control strategy is introduced here. The control scheme is shown in Fig. 2, which comprises virtual inertia and damping emulators, activepowerfrequency (ωP) and reactivepowervoltage amplitude (QU) droop controllers, and a power calculation module [4].
The swing equation of the CPVSG can be written as [23]:
where P _{ref} is the reference active power, P _{e} is the measured output average active power; D _{eq} = (1/m + Dω _{0}) is the equivalent damping; m is the active power droop coefficient; ω _{0} is the nominal angular frequency; J is the virtual inertia. The virtual angular velocity ω is calculated by numerical integration and then the virtual phase angle θ is derived by passing through an integrator.
In order to extract the powers of fundamental frequency components, the instantaneous measured powers required to calculate CPVSG operation are passed through lowpass filters (LPFs) with a cutoff frequency of 2 Hz to filter noise [24]. However, the filtering delay makes the frequency of systems with CPVSG control change faster in both standalone mode and SGconnected mode [25]. Delayedsignal cancellation with multiple notch filters (DSCMNFs) is proposed for harmonic elimination to extract the fundamental active and reactive powers.
For this paper, the power calculation principles in the synchronous rotating reference frame are formulated as:
where u _{odq } and i _{odq } are the capacitor voltage and the output current, respectively; ω _{ y } represents the system harmonic frequency and y denotes the dominant harmonic orders (y = 2, 4, 6, 8, 10, 12, …); ζ is the quality factor for the DSCMNFs at the 2^{nd} harmonic frequency (it is set to ζ = 0.707 in this paper). The quality factor for the rest of harmonic frequencieccs is divided by their order.
In addition, the standard PIbased dualloop control of the voltage and current is applied in this study to achieve power sharing stability [11]. The capacitor voltage control outer loop provides close voltage regulation and generates the reference current. The inductor current inner loop shapes the voltage across the filter inductor and generates pulses for space vector pulse width modulation (SVPWM).
3.2 Effects of CPVSG on frequency transient
In order to analyze the effects of virtual inertia and virtual damping on a frequency transient, a simulation of an autonomous MG is developed according to Fig. 1. The parameters of the DGS and the CPVSG used in simulation are presented in Tables 1 and 2 respectively.
Figure 3a shows the system frequency with respect to virtual inertia J for a sudden increase of 100 kW load. It can be seen that the main effect of adding J to the system is that both the rate of change of frequency (RoCoF) and the peak frequency deviation decrease. However, a side effect of adding J is that the frequency will oscillate for a longer time before settling. Increasing the virtual damping D also produces a reduction in the peak frequency deviation, as can be seen in Fig. 3b.
Moreover, let J = 0 and D = 0, then the CPVSG is equivalent to frequency droop control [26]. As for the comparison between each case, the CPVSG is found to be more efficient than droop control in minimizing the amplitude and rate of change of the frequency variations.
4 Proposed STVSG control strategy
In this section, the frequency dynamic regulation mechanism of the CPVSG in an autonomous MG is analyzed. Based on the analysis, a STVSG with selftuning coefficients for virtual inertia and virtual damping is proposed. Moreover, the selection principle of selftuning coefficients is given by referring to a smallsignal model of the CPVSG and a statespace model of the parallel system.
4.1 Frequency regulation mechanism of CPVSG control
The swing equation of (1) can be rewritten as:
Equation (4) has three terms. The first term, P _{ref}, is the reference value of active power that is the steadystate value of the output active power. The second term, P _{D}, emulates the damping power of a SG. The third term, P _{J}, emulates the inertial response of a SG. Both P _{D} and P _{J} are effective only during a transient to provide dynamic frequency support for the autonomous MG. Note that the virtual angular velocity ω is dictated mostly by the MG angular frequency ω _{g} when the CPVSG is connected to the MG. Based on this fact, when the frequency of the MG starts to increase (dω _{g}/dt = dω/dt > 0), the CPVSG which is in charge of emulating the inertial response starts to absorb power from the MG to prevent the frequency from rising too quickly, until the frequency reaches its maximum (dω/dt = 0). Then the frequency starts to decrease (dω/dt < 0) and the CPVSG starts to inject power until steady state is achieved.
Considering (4), it is observed that the moment of J has a reverse relation to dω/dt, and the D has a reverse relation to ∆ω. For example, when frequency starts to deviate from steady state, a larger inertia would present a stronger opposition to the RoCoF, limiting its peak deviation. However, a larger inertia would no longer be required when frequency starts to return to steady state. On the other hand, the damping power is typically calculated from the ∆ω. Any deviation from steady state produces a power that attempts to bring the frequency back to steady state. Moreover, more damping would help to restore the system frequency faster.
4.2 STVSG control strategy
Despite the effectiveness of the CPVSG, it does not explore the use of variable virtual inertia and virtual damping that can change their values during operation. In this regard, the STVSG control strategy is proposed to improve frequency stability for the autonomous MG. Assuming that the first oscillation of the frequency is the most critical one in terms of maintaining the system frequency stability, it might be a better approach to have selftuning virtual inertia and virtual damping that are active only during a power disturbance.
Consider the frequency oscillation curve of Fig. 4. After a step load of 100 kW at t = 3 s in a typical 440 kW DGS, the operating point moves along the frequency curve, from point a to c and then from c to e. The selftuning process of both J and D during each phase of an oscillation cycle is summarized in Table 3. One cycle of the oscillation consists of four segments. It should be noted that the sign of ∆ω (∆ω = ω − ω _{0}) together with the sign of dω/dt defines the acceleration or deceleration of frequency during each segment. In other words, when ∆ω and dω/dt have the same signs in segments ① and ③, they are acceleration periods. Whereas, when ∆ω and dω/dt act in the opposite direction in segments ② and ④ when the frequency starts to go back to steady state, they are deceleration periods. When both ∆ω and dω/dt are equal to zero, it is a steady state period.
The objective is to damp frequency oscillations quickly by controlling the acceleration and deceleration terms. For instance, a larger J would present a stronger opposition to both the RoCoF and the frequency deviation during acceleration phases (a to b and c to d). On the other hand, a smaller J would boost the deceleration of the frequency more rapidly during deceleration phases (b to c and d to e). In addition, a larger D would attenuate the frequency amplitude of the oscillations more quickly and stabilize the system faster in all segments.
Based on the above analysis, the selftuning factors of virtual inertia and virtual damping are formulated as:
where J _{0} and D _{0} are the steady state values of J and D, respectively; k _{ j } and k _{ d } are the regulation coefficients of J and D, respectively; B is the threshold value for ∆ω. The STVSG is operating with the normal values of J _{0} and D _{0} in the case of steady state. During each cycle of oscillations, the value of J is switched four times. Each switching happens when the sign of either ∆ω or dω/dt changes.
When the disturbance occurs, the transition from a to b starts with ∆ω < 0 and dω/dt < 0. In the acceleration term, the value of J is increasing with the absolute value of dω/dt multiplied by k _{ j }. At the end of the first quartercycle, that is point b, the sign of dω/dt changes, and the value of J is set to zero in the deceleration term. At point c, the sign of ∆ω changes and J returns to a big value in the acceleration term. During the second halfcycle, the value of J is switched to zero at point d, and to a big value at the end of one cycle at point e. This procedure is repeated for each cycle of oscillation until the transients are suppressed. Considering (6), the value of D is increasing with the absolute value of ∆ω multiplied by k _{ d } during the whole cycle of oscillation. Note that the value of B is used to avoid the chattering, or rapid and unhelpful changes, of J and D during the sign changes of ∆ω and dω/dt, and is set to 0.3 rad/s in this paper.
4.3 Selection scheme for selftuning coefficients
The values of J together with D determine the stability and the dynamic response of the VSG system. Selecting proper values for them is a challenging issue and requires analysis. A smallsignal model of the CPVSG with different values of J and D is built to illustrate transient responses of output power during a loading transition.
In the control of the CPVSG for frequency stability, the sending side of the system can be drawn as a twomachine system as shown in Fig. 5. The output apparent power S of the CPVSG can be written as:
where E is the output voltage of the DGS; X is the distribution line reactance; δ _{1} is the rotor angle of the CPVSG; δ _{2} is the rotor angle of the DGS; δ =δ _{1} − δ _{2}, is the power angle of the CPVSG. Let sinδ ≈ δ, and K =UE/X which is the synchronizing power factor, so that the output active power P _{e} can be approximated as:
Knowing that δ=∫(ωω _{0})dt, (8) becomes:
The transfer function, considering the reference value of the active power P _{ref} as the input, is:
According to (11), the standard parameters for a secondorder transient response can be defined as:
where ω _{n} is the natural oscillation frequency; ξ is the damping ratio. Note that the value of the active power droop constant m is calculated according to the maximum allowable steadystate frequency deviation of 1% and to the maximum active power reserve of 100%. Here, m = 1% × 50 × 2π/100000 = 3.1e^{−5} rad/s/w for a 100 kVA PCS.
Based on (11), it is possible to calculate the step responses of output active power of the CPVSG with various parameters, and the results are shown in Fig. 6. Parameters used for both theoretical calculation and simulation are the same, as listed in Table 2. From (12) and Fig. 6, it is observed that the virtual inertia determines the oscillation of the frequency, whereas the virtual damping determines the attenuation speed of oscillations of the frequency.
The higher H, the higher the system inertia, resulting in a smaller frequency deviation after a change in active power load or supply. For typical large SGs used in power plants, H varies between 2 and 10 s. For this case, a value of 4 s has been chosen, as it is a good representation for an autonomous MG with reduced inertia, which is exactly the condition in which the CPVSG provides a solution for enhancing frequency stability. Calculating J for a CPVSG with a rated output power of 100kW using (2), results in inertia J = 2 × 4 × 100000/(100π)^{2} = 8.1 kg m^{2}. Considering an optimal secondorder quality factor of ξ = 0.707 for the DSCMNFs, and for U = 380 V, E = 380 V, X = 0.63 Ω, results in D = 6.4 p.u. according to (12).
A statespace model of the parallel system with the selected values of J and D is built to analyze its stability and dynamic response. The swing equations of the CPVSG and the DGS in Fig. 5 can be written as:
where H _{2}, D _{2}, P _{m2}, P _{e2} are the inertia constant, damping factor, mechanical power and electrical power of DGS, respectively. Linear approximation for the swing equations of CPVSG and DGS can be represented as [27]:
where M = (H + H _{2})/(HH _{2}); N = (DH _{2} − D _{2} H)/(HH _{2}); K _{ s } = Kcosδ _{0}; δ _{0} is the operating point of δ. The system stability is determined by the eigenvalues shown in (16).
The value of K _{ s } can be calculated as follows:
The output active power P _{e} of the CPVSG in Fig. 5 can be defined as P _{e} = Ksinδ _{0}. Then the value of K _{ s } can be expressed as:
Since this is very large (K = UE/X = 229.2 W, and the maximum value of P _{e} is 100 kW for the 100 kVA CPVSG), the value in the square root of (16) is negative. Thus, the second term of (16) is the imaginary part of the eigenvalues. When N > 0, i.e., D/H > D _{2}/H _{2}, the system maintains stability. Let D _{2} = 0.38 p.u. and H _{2} = 0.77 s, which are obtained according to [22] for a 440 kW DGS, and then D/H > 0.49, i.e., D > 1.96 p.u..
Therefore, the CPVSG with fixed values of J = 8 kg·m^{2} and D = 6 p.u. can ensure good stability and fast dynamic response for the autonomous MG. Consequently, selecting the values of RoCoF_{max} = 2.5 Hz/s, J _{0} = 2 kg·m^{2} and J _{max} = 8 kg m^{2}, results in k _{ j } = (82)/(2.5 × 2π) = 0.38 for the STVSG. In contrast, the values of D _{0} = 2 p.u. and k _{ d } = 4.1, are selected in this paper. This is because, when the value of the frequency deviation is 0.2 Hz, a larger damping (D = 4.1 × 0.2 × 2π + 2 = 7.1 p.u. > 6 p.u.) would present a stronger opposition to the frequency deviation, reducing the frequency oscillation and its stabilization time.
5 Simulation validation by experiment
The performances of the proposed STVSG, the frequency droop method and the CPVSG are evaluated by comparing their effects on frequency stability under load variations. The same autonomous MG is studied including a 100 kVA PCS, adjustable loads and a 440 kW DGS as shown in Fig. 1. Parameters used in simulations are summarized in Tables 1, 2 and 4. For simpler presentation, considering that this paper addresses frequency control, only active power is shown.
This test consists of a step load increase of 100 kW at t = 3 s from an initial load of 100 kW (the PCS supplies 20 kW, the DGS supplies 80 kW) while a 440 kW DGS is connected to a 100 kVA PCS with droop control. The same tests are conducted for the PCS with the CPVSG control and the STVSG control, respectively. Figure 7 shows the simulation results, where the curve labeled “Droop” is the response of the DGS plus the PCS with droop control, “CPVSG” is the response of the DGS plus the PCS with CPVSG control, and “STVSG” is the responses of the DGS plus the PCS with STVSG control.
Figure 7a shows the system frequency with respect to the PCS using different methods. It can be noted that the curve “CPVSG” presents a frequency nadir that lies between the other two curves. It means that the CPVSG is more efficient than droop control in reducing the RoCoF and the frequency deviation by providing virtual inertia and virtual damping. The curve “STVSG” presents a frequency nadir that lies above the curve “CPVSG”. Overshoot of the frequency is effectively suppressed by the STVSG. As can be noted, the selftuning virtual inertia and virtual damping provided by the STVSG increase the equivalent inertia and damping of the system, reducing the maximal frequency deviation. As a tradeoff, the PCS with the STVSG control needs to deliver more energy into the autonomous MG than the other two methods as shown in Fig 7b, which indicates that the ESS should be equipped with a larger capacity. However, with the help of the STVSG, the DGS delivers the least transient power to copy with the load mutation as can be seen in Fig. 7c. Hence, the STVSG obtains the best frequency stability for the autonomous MG, as the rotational speed of the DGS is proportional to its transient output active power.
On the other hand, Fig. 8 shows the frequency acceleration curves for the PCS using different methods. The curve labeled “Droop” is the response of the DGS plus the PCS with droop control, “CPVSG” is the response of the DGS plus the PCS with CPVSG control, and “STVSG” is the responses of the DGS plus the PCS with STVSG control. It is observed that the curve “STVSG” presents the RoCoF and the deviation of frequency with respect to the nominal value that lies inside the other two curves. This means that the STVSG is the most efficient method for attenuating the amplitude and rate of change of the frequency variations.
The simulation results for virtual inertia and virtual damping of the STVSG are shown in Fig. 9. It can be seen that STVSG control increases its virtual inertia rapidly in the acceleration terms, but makes its virtual inertia equal to 0 in the deceleration terms as shown in Fig. 9a. On the other hand, it increases its virtual damping in the whole cycle of oscillation as shown in Fig. 9b. This emphasizes that the proposed STVSG strategy entails the selftuning variations of the VSG parameters of virtual inertia and virtual damping during the operation of the VSG.
6 Experimental results
The proposed control method is verified experimentally using a laboratoryscale autonomous MG, developed according to the block diagram from Fig. 1. The MG consists of a 440 kW DGS, two 100 kVA PCS units, and two 10 kVA photovoltaic inverters as illustrated in Fig. 10. A threephase power supply rectified by a controllable bidirectional IGBT bridge is used to imitate the dc output of a ESS or a solar PV generator. The experimental setup parameters are the same for the simulation cases. A 200 kW controllable load is included to create dynamic events in the MG. Each PCS is controlled by an independent DSP TMS320F28335, which implements the proposed control schemes, as described in the previous sections.
Experiments were performed under three test cases in order to verify again the effectiveness of the proposed STVSG. In Case 1, two PCSs are operating with different methods including droop control and STVSG when the MG islanding occurs, respectively. This scenario evaluates the frequency control capability of the STVSG operating in the islanded mode. In Case 2, the parallel operation of a CPVSG and a DGS is analyzed in order to determine the effect of the virtual inertia and virtual damping on the frequency performance. In Case 3, the performances of the STVSG, the droop method and the CPVSG are evaluated by comparing their effects on minimizing the amplitude and rate of change of the frequency variations under load variations. In all cases the transitory regime is created by switching the load on after an interval of steadystate operation.

1)
Case 1
This scenario is characterized by switching in an additional 100 kW load. The test results for the system frequency f and the output currents (i _{o1} and i _{o2}) of the two 100 kVA PCSs are shown in Fig. 11.
Note that the droop control as well as the STVSG obtains a fast dynamic performance to respond to the load variations and achieves a good current sharing capability. It can be seen that the STVSG is more efficient than the droop control in attenuating the RoCoF due to the provided virtual inertia.
Figure 12 shows the output active powers (P _{e1} and P _{e2}) of the two 100 kVA STVSG units when the additional 100 kW load is connected. Observe that the proposed power filter method can effectively improve the dynamic performance of the system, given that the response time ranges from about 44 ms when using the LPF method to 12 ms when using the DSCMNF method.

2)
Case 2
Section 3.2 described the two parameters that the CPVSG has which can influence the frequency performance: the virtual inertial J and the virtual damping D. To analyze the influence of these parameters, Case 2 consists of a step load increase of 100 kW from an initial load of 100 kW (the CPVSG supplies 20 kW and the DGS supplies 80 kW) while the DGS is connected to the 100 kVA CPVSG unit.
Figure 13a shows the experimental results for different values of virtual inertia (J = 0, 2, 4 kg m^{2}) without any damping. As can be seen, the virtual inertia has a great impact on reducing the RoCoF as well as the peak frequency deviation. However, a side effect of adding virtual inertia is that the frequency will oscillate for a longer time before returning to its steady state.
Virtual damping was also tested. In this case, different values of virtual damping (D = 0, 2, 6 p.u.) were tested without any inertia. Fig. 13b concords with Fig. 3b. That is, increasing the virtual damping produces a reduction in the peak deviation as well as the amplitude of the frequency variations. It implies that more damping would help to stabilize the system frequency faster. These statements are similar to those found in Sect. 3.2.

3)
Case 3
This test consists of a step load increase of 100 kW at t = 2 s from an initial load of 100 kW (the PCS supplies 20 kW, the DGS supplies 80 kW) while the 440 kW DGS is connected to one of the 100 kVA PCSs. Figure 14 shows the experimental results, where the curve labeled “Droop” is the response of the DGS plus the PCS with droop control, “CPVSG” is the response of DGS plus the PCS with CPVSG control, and “STVSG” is the response of DGS plus the PCS with STVSG control.
From Fig 14a, it is observed that the curve “STVSG” presents a frequency nadir that lies above the other two curves and the frequency overshoot is suppressed effectively. This is because the STVSG makes its virtual inertia increase in the acceleration phase, but makes its virtual inertia equal to zero in the deceleration phase according to (10). The virtual damping is selftuning to keep a larger value in the whole cycle of oscillation according to (11). As a result, the average active power injected into the system by the STVSG is much more than either the CPVSG or the droop method, as can be seen from Fig. 14b. From Fig. 14c, it is observed that with the help of the STVSG, the DGS presents the lowest average output active power under the step load condition. Hence, the highest frequency stability for the autonomous MG is achieved by the STVSG, as the transient output active power of the DGS is proportional to the RoCoF and the peak frequency deviation.
The frequencyacceleration trajectories of the PCS with different control methods are shown in Fig. 15. The curve “Droop” refers to the PCS with the droop control and without any virtual inertia and damping, and the maximal absolute values of the RoCoF and frequency deviation are 5.42 Hz/s and 0.6 Hz, respectively. Whereas the curve “CPVSG” refers to the PCS with CPVSG control, and the maximal absolute values of the RoCoF and frequency deviation are reduced to 3.43 Hz/s and 0.44 Hz, respectively. It can be seen that the area enclosed by the trajectory is decreased because of the virtual inertia and virtual damping provided by the CPVSG reduce the RoCoF as well as the peak frequency deviation. The frequencyacceleration curve of the PCS with STVSG control is marked with “STVSG”. It is observed that the trajectory is forced to converge even faster by varying the acceleration or deceleration magnitude by using the selftuning virtual inertia and virtual damping in each section of an oscillation cycle.
On the other hand, Fig. 16 shows the test results for variations for virtual inertia and virtual damping of the STVSG. It can be seen that the STVSG makes its virtual inertia equal to zero in the deceleration phases as shown in Fig. 16a, and increases its virtual damping during the whole cycle of oscillation as shown in Fig. 16b. The maximal absolute values of the RoCoF and the frequency deviation (as shown in Fig. 15) are reduced to 2.5 Hz/s and 0.31 Hz, respectively. Therefore, it can be said that the STVSG achieved a better performance in improving the frequency stability than either the CPVSG or the droop method.
7 Conclusion
In this paper, the novel strategy of an STVSG was elaborated. This selftuning method allows a VSG to increase and reduce its virtual inertia and virtual damping according to its virtual angular velocity and acceleration/ deceleration in each phase of frequency oscillation. By selecting an increased virtual inertia during acceleration, the RoCoF is mitigated, and on the other hand, during deceleration, a zero virtual inertia is adopted to increase the deceleration effect. In addition, by using increased virtual damping during the whole cycle of oscillation, both the deviation and the overshoot of system frequency are reduced effectively.
The performances of the droop method, the CPVSG and the STVSG were evaluated by comparing, in simulation and by experiment, their dynamic frequency responses for different scenarios of load variation in an autonomous MG. The main results obtained in the simulation as well as the laboratory test results are presented. These results illustrate that the major advantages of the proposed STVSG are the reductions of the initial RoCoF and the maximum frequency deviation, these being the important issues for the stability of system frequency.
The performance and capability of the control strategy presented in this work directly depend on the ESS, i.e., the energy storage device and the power electronic converter. It is important to bear in mind that, depending on the type of load variation, the operation of the proposed STVSG results in a greater discharge of the ESS when compared to the droop method or CPVSG. This suggests that future work should be directed at obtaining some guidelines in order to specify the ESS according the selftuning virtual inertia and virtual damping. On the other hand, it could be also useful to coordinate the state of charge of the ESS in the STVSG control strategy.
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Acknowledgements
This work was supported by National High Technology Research and Development Program of China (863 Program) (No. 2015AA050607), the National key Research and Development Program of China (No. 2016YFB0900300) and the Science and Technology project of SGCC (No. NYB17201700151).
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SHI, R., ZHANG, X., HU, C. et al. Selftuning virtual synchronous generator control for improving frequency stability in autonomous photovoltaicdiesel microgrids. J. Mod. Power Syst. Clean Energy 6, 482–494 (2018). https://doi.org/10.1007/s4056501703473
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DOI: https://doi.org/10.1007/s4056501703473