Simulation Analysis of Issues with Grid Disturbance for a Photovoltaic Powered Virtual Synchronous Machine

Abstract

The increase in inverter-based resources associated with the increased installation of PV sources is a concern because it reduces the inertia of the power system during peak PV generation periods. As a countermeasure to reduce grid inertia, the addition of pseudo-inertia using virtual synchronous machines can be selected, and PV generation can cooperatively contribute to the stable operation of the power system by using the suppressed output as reserve power. However, few studies have analyzed VSMs that do not use batteries and use PV as a resource (PV-VSM) in simulations, including grid interconnection and solar radiation fluctuations, and it is necessary to clarify the issues and discuss countermeasures. In this study, electromagnetic transient response analysis was applied to a VSM connected to a two-generator system, simulations were performed, and the following findings were reported and countermeasure methods for the problem were proposed. When the PV capacity is insufficient for the output required by the VSM inverter, the PV-VSM control system may become unstable. This is caused by a drop in the capacitor voltage of the DC/DC converter due to insufficient PV output. The limiter control system is designed to address this problem by combining the headroom estimation system with the current limiting algorithm. The proposed limiter control system is validated on solar radiation ramp fluctuations as a test case and found that the system was effective in supressing PV-VSM instability. In our simulation case, the PV-VSM with our limiter control can continue to operate stably even if the PV available power is 0.03 [p.u.] short of the inverter’s reference power by the solar power ramp fluctuation, as long as the inverter installation rate is less than 50%.

1. Introduction

With the entry into force of the Paris Agreement in November 2016, many countries are accelerating their decarbonization efforts based on international agreements. On the other hand, the Intergovernmental Panel on Climate Change (IPCC) special report in 2018 pointed out that, in order to keep global warming below 1.5 $°$C, CO${}_2$ emissions need to be significantly lower than the original target and achieve carbon neutrality in 2050–2060 [1], which has led to further efforts to decarbonize the power sector in many countries. For instance, the Glasgow Climate Pact at the 26th session of the Conference of the Parties (COP26) to the United Nations Framework Convention on Climate Change in November 2021 calls for all parties to work towards a transition to a low emission energy system, “including accelerating efforts towards the phasedown of unabated coal power” [2].

The 2050 Net Zero Scenario released by the International Energy Agency (IEA) in 2021 states that, in addition to the elimination of inefficient coal-fired power generation by 2040, renewable energy sources must be expanded to 90% of the electricity generated (including 70% from solar and wind) for the achievement of the scenario [3]. To realize sustainable development while reducing a carbon footprint, renewable energy moreover becomes important. In particular, Japan’s Sixth Strategic Energy Plan calls for PV capacity to play an important role as a low-carbon power source in the future power system, as PV capacity accounts for a large percentage of VRE in Japan’s power supply mix planned for 2030 [4]. (PV accounts for 14–16% within 36–38% of renewable energy sources as shown in Figure 1).

However, PV is an inverter-based resource (IBR), and there is a concern about the reduction of grid inertia (deterioration of frequency stability against contingency) with the increase of their installation rate [6,7,8]. For example, in a system with a large number of synchronized inertia, the Rate of Frequency Change (RoCoF) is suppressed, which means that there is sufficient time before generators supply the governor response. On the other hand, in a power system with little inertia, the large RoCoF may cause the system to deviate from the allowed range of frequency change before the injection from generators, and in the worst case, IBRs and synchronous generators may dissociate one after another, resulting in a blackout.

In order to ensure the frequency stability of power systems with high IBR implementation rates, the following major approaches exist:

• Adding inertia such as a synchronous condenser;
• Increasing the allowable range of frequency fluctuation in the system;
• Providing fast frequency control (FFC) ancillary service from IBRs.

Introducing additional inertia with a synchronous condenser is considered to be a simple and effective approach but has the disadvantage of high equipment cost. The second approach corresponds to the sophistication of the fault ride through (FRT) function of IBRs, but this approach alone has its limitations. To deal with significant frequency fluctuations with FRTs, the hardware must be designed to withstand overcurrents, which can be very costly. With regard to the third approach, operating IBRs as a regulating power source is considered to be one of the effective ways to offset their disadvantages, as IBRs are characterized by their ability to provide very fast output regulation compared to the governor’s conventional frequency response while reducing grid inertia. For example, Hoke et al. showed that the fast frequency compensation by the inverter systems with PV is effective in stabilizing the grid frequency in the low-inertia system on Oahu. [9]. In addition, the IEA has also organized the grid interconnection requirements for distributed energy resources (DERs) with classifying four stages according to their penetration, and they assume that the technical requirement for DERs includes the low power operation for supplying reserve power and autonomous adjustment function for system frequency and voltage in a third-fourth stage with high penetration [10].

As an FFC by IBRs, in addition to the frequency droop control, recent researchers have focused on the implementation of pseudo-inertia to suppress RoCoF. IBRs with this function, called Virtual Synchronous Machine (VSM) or Virtual Synchronous Generator (VSG), are expected to contribute to resolving the technical constraint of the inverter penetration (referred to as VSMs in this paper).

Some approaches have been proposed to implement the pseudo-inertia function of the VSM. One is to impose a first order lead–lag unit on the droop control [11], and another is to emulate a synchronous generator with the controller of the IBR [12]. The latter approach is unique in that a virtual rotor frequency is stored and used as an internal signal in the control system, where various topologies have been proposed, including KHI topology [13], synchronverter topology [14,15], ISE Lab topology [16,17], VISMA topology [18,19,20], universal VSM topology [21], etc. (Refs. [22,23,24] are detailed as recent reviews.) However, pseudo-inertia by VSM is a function reproduced in software, and in order for the emulated pseudo-inertia to trigger the actual output compensation (in particular, the operation of increasing output against frequency decrease), energy resources which correspond to the kinetic energy of the synchronous generator must be reserved by the IBR side.

Such alternative energy can be guaranteed by the following options:

• Use of kinetic energy inside IBRs, such as turbine blades;
• Use of fast-responding energy storage systems (ESSs) such as batteries and capacitor banks;
• Reserve capacity from the IBR source’s headroom.

In the case of wind power, the turbine blades function as inertial bodies, making them a practical option as a virtual inertial energy resource with VSM. However, this approach cannot be adopted for PV, which is one of VRE’s main forms of power generation. The second approach of harnessing Energy Storage is one of the effective approaches, but it is burdened by additional costs. As for the third approach, particularly during peak times of PV output in low-load periods (e.g., consecutive holidays), it is necessary to curtail PV output due to the system’s inertial constraints; setting reserve power in the curtailment (headroom) could translate the opportunity loss of PV generation into system value.

The provision of reserve power through PV headroom was examined by CAISO, First Solar, and the National Renewable Energy Laboratory in 2016 at a mega solar facility in California, and its effectiveness is demonstrated [25]. When utilizing headroom, two points are important: the design of the control system and determination of reserve capacity. As a review, Dreidy et al. [26] gave a comprehensive review of frequency control of the PV system utilizing headroom. Most of them are achieved by operating PV at a voltage higher than the voltage of maximum power point (MPP) and adjusting the PV operating voltage according to the frequency deviation. (This approach is sometimes referred to as ‘de-loading’.) In addition, determining the appropriate reserve capacity is also important to achieve both grid stability and PV generation revenue, and machine learning-based methods such as neural network and random forest were recently proposed [27,28].

Regarding the study of PV-powered VSMs (hereafter referred to as PV-VSMs), those supported by ESSs are vigorously researched by many researchers [29,30]. (Recent works of them are referred to in [31,32].) On the other hand, several studies focus on the headroom-based VSMs. Ding et al. proposed a voltage limiting method and adaptive tuning of simulated inertia parameters for stable PV-VSM operation without ESS [33]; Feldmann and de Oliveira proposed an adaptively controlled PV-VSM for supporting a black start with utilizing headroom [34]; Zhang et al. proposed the headroom-based PV-VSM control method with multiple PV inverters’ cooperative control [35]; Yan et al. proposed the methodology of the adaptive switching control between maximum power point tracking mode and VSM mode according to the remaining capacity from PV maximum power [36]; Jietan et al. proposed synthetic inertia and droop controller with shifting the operating point from MPP [37].

The provision of pseudo-inertia by PV power sources is an important option for future power systems, and therefore it is important to analyze the operational feasibility of PV-VSM with headroom as virtual inertial energy. However, to the authors’ knowledge, there are few studies that have analyzed PV-VSM in power systems with high IBR ratios in a detailed model (through such as an electromagnetic transient program), including the interaction with the system, except for [34]. It should be noted that, although a detailed analysis based on a 60th order model was performed in [34] for a PV-VSM connected to the grid with a 50% IBR installation rate, their study simulated a black start situation and did not include the contingency and solar radiation ramp variations during grid operation.

In this paper, a circuit analysis by PSCAD/EMTDC (one of the tools for electro-magnetic transients program) with a two-generator system model was carried out with the aim of extracting the issues involved in a PV-VSM with headroom control, and the following findings were obtained:

• If the headroom of the PV-VSM is insufficient for the required FFR output, PV-VSMs without adequate control of the upper output limit (output limiter) will become unstable in operation. Note that insufficient headroom can be caused by solar radiation fluctuations as well as frequency fluctuations.
• The introduction of output limiters to PV-VSMs with maximum power estimation can prevent PV-VSM instability due to a lack of headroom or solar radiation fluctuations.
• However, in case the PV-VSMs’ planned generation is high for their headroom, there is a risk of grid instability due to reduced solar radiation. The instability is caused by PV-VSMs being in output-specified control mode (Grid Follow) due to reduced headroom; that is, estimated PV-VSMs’ virtual energy disappears and causes more imbalance. Consequently, insufficient Primary Frequency Response (PFR) from the synchronous machine becomes impossible to compensate rapid frequency reduction by insufficient grid inertia. Therefore, care must be taken to cope with reduced solar radiation during operation of the reserve power supply by the headroom.

This paper is organized as follows: Section 1 describes the background of the study. Section 2 describes the simulation model used in the analysis of this paper. In Section 3, we simulate the case of insufficient headroom in the FFR of the PV-VSM, and discuss the VSM control problems caused by the absence of inertial energy and how to solve them by using a power limiter. In Section 4, we describe the PV-VSM with output limiting control based on headroom estimation, simulate the system under the assumption of solar irradiance ramp fluctuation and load step-changing, and discuss the issues to be addressed when operating the PV-VSM in the grid. Section 5 summarizes the conclusions.

2. Simulation Model

2.1. Photovoltaic Powered Virtual Synchronous Machine

The circuit diagram of the PV-VSM with a two-stage configuration is shown in Figure 2. In this circuit, the PV source is stepped up by the boost converter, and a three-phase AC current is output to the grid through the VSM-controlled inverter. Note that, in our PV-VSM model, the boost converter and the VSM are independently controlled; the boost converter uses the measurement signals on the DC side of the inverter and the VSM uses the measurement signals on the AC side of the inverter. In addition, the rated capacity of the VSM is 100 [kVA], and two PV source models with different capacities were used: large capacity module (PVL) and small capacity module (PVS). PVL enables outputting about 98% of the VSM’s rated capacity, and PVS’s maximum power is given as about 65% of the VSM’s rated capacity under conditions of 1000 [W/m${}^2$] of solar irradiance and 298 [K] of temperature. The parameters of the PV-VSM circuit are shown in

Table 1. Circuit parameters of the two-stage PV-VSM.

Boost converter
Primary side capacitor	$C_1$	$1.0\times {10}^4\left[\mathsf{\mu }\mathrm{F}\right]$
Secondary side capacitor	$C_2$	$1.0\times {10}^4\left[\mathsf{\mu }\mathrm{F}\right]$
Inductor	L	250 $\left[\mathsf{\mu }\mathrm{H}\right]$
Primary side voltage	$V_{C1}$	340 $\left[\mathrm{V}\right]$ (Rated voltage)
Secondary side voltage	$V_{C2}$	680 $\left[\mathrm{V}\right]$ (Rated voltage)
PV Source
Series resistance per cell	$R_{\mathrm{s}}$	0.02$[\Omega ]$
Shunt resistance per cell	$R_{\mathrm{sh}}$	1000$[\Omega ]$
Number of cell connected in series	$N_{\mathrm{s}}$	PV-L : 455	PV-S : 495
Number of cell connected in parallel	$N_{\mathrm{p}}$	PV-L : 136	PV-S : 83
Maximum power	$P_{\max }$	PV-L : 98.2 [kW]	PV-S : 65.5 [kW]
Voltage at maximum power point	$V_{\mathrm{mpp}}$	PV-L : 316 [V]	PV-S : 337 [V]
Short circuit current	$I_{\mathrm{sc}}$	PV-L : 340 [A]	PV-S : 207 [A]
Open circuit voltage	$V_{\mathrm{op}}$	PV-L : 380 [V]	PV-S : 413 [V]

.

The control scheme of the VSM algorithm is shown in Figure 3. As the VSM controller in this work, we adopt the phasor-based VSM implementation, which includes the current feedback loop and the auto voltage regulation (AVR) model. In Figure 3, ${•}^{*}$ means the reference signal. This VSM controller simulates the rotor state using a simple swing equation expressed as the following equations:

$$\begin{array}{cc}\hfill M\frac{\mathrm{d}}{\mathrm{d}t}\left({\omega }_{\mathrm{vir}}-{\omega }^{*}\right)& =-K\left({\omega }_{\mathrm{vir}}-{\omega }^{*}\right)+P^{*}-P,\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill M& =\frac{2H_{\mathrm{vir}}}{{\omega }^{*}}\hfill \end{array}$$

(2)

where $H_{\mathrm{vir}}$ is the virtual normalized inertia constant, K is the gain parameter of the virtual governor, ${\omega }_{\mathrm{vir}}$ is the angle speed of the virtual rotor, ${\omega }^{*}$ corresponds to the frequency reference signal, which is the constant, and $P^{*}$ and P correspond to the mechanical power and the electrical power in the virtual rotor. That is, virtual rotor speed is given by the following equation from the signals:

$$\begin{array}{c}\hfill {\widehat{\omega }}_{\mathrm{vir}}-{\widehat{\omega }}^{*}=\frac{1}{Ms+K}\left({\widehat{P}}^{*}-\widehat{P}\right),\end{array}$$

(3)

where s is the Laplace operator, and $\widehat{•}$ is the Laplace transform. VSM is the unique control system in that it uses ${\omega }_{\mathrm{vir}}$ as an internal signal to simulate the response from pseudo inertia.

The control strategy on the the DC side of the inverter may take the following three approaches:

(1)

Maximum power point tracking (MPPT);

(2)

Constant voltage control for the primary side of the converter;

(3)

Constant voltage control for the secondary side of the converter.

They commonly adjust the duty ratio of the pulse width modulation signal as a control input to adjust the respective target signal. MPPT control is generally performed by a hill climbing algorithm, which obtains maximum output by updating the operating point in the direction of more output while measuring the PV output; primary and secondary side constant voltage control measures the respective voltages and adjusts the control input based on the difference between the reference value and the measured value using a PI compensator or other means.

Table 2. Stability of PV-VSM for each DC-side control strategy. ∘ means stable result and × means unstable result.

MPPT Control	Constant Voltage Control
	Primary Side	Secondary Side
×	×	∘

shows the operational stability of the PV-VSM with each control strategy mounted on a DC/DC converter when connected to the grid model described in the next subsection. MPPT and primary side constant voltage control results in unstable operation of the PV-VSM with the structure represented in Figure 2. These approaches correspond to the direct specification of the PV output by the DC-side controller, and, therefore, an imbalance in the input/output when the VSM control automatically adjusts the AC-side output results unstable operation; it is not appropriate to use these approaches for DC-side control of the PV-VSM unless the VSM cooperates with the DC/DC converter. On the other hand, the PV-VSM operates stably under the secondary-side constant voltage control case. In this case, the DC/DC converter does not directly specify the PV output, but operates to adjust the charge of the secondary-side capacitor: the control system adjusts the PV operating point by compensating for the capacitor voltage that changes in accordance with the VSM output, and therefore this DC/DC converter follows the VSM for contributing to the stable operation of the power conversion system.

From the above, the secondary side constant voltage control is adopted as the DC side control of the PV-VSM in this study and used for simulation. (the Control Scheme of it is shown in Figure 4). In this paper, a simple PI controller is used to generate the reference signal to the PWM. On the other hand, optimally tuning a PID-type controller is also an option, and several studies on tuning the control system of DC/DC converters using meta-heuristic algorithms have been done in recent years [38,39].

2.2. Two-Generator System Model

To simulate the interaction of the PV-VSM with the grid, a simple two-generator system, represented in Figure 5, is used in the simulation, where the base frequency is given by 50 [Hz]. The system consists of two generator nodes with transformers, a constant power load, and four PI section lines, with G1 as the synchronous generator and G2 representing $N_{\mathrm{INV}}$ PV-VSMs connected in parallel to the grid connection point in an aggregated form. The total capacity of the generators is fixed at 2000 MVA, and the capacity of G2 is adjusted to analyze the scenario given different IBRs’ penetration. The capacity of G2 is adjusted by changing the parallel number of the PV-VSMs (100 [kVA/unit]), which is described in the previous subsection ($S_{\mathrm{G}2}\left[\mathrm{MVA}\right]=N_{\mathrm{INV}}\left[\mathrm{unit}\right]\times 0.1[\mathrm{MVA}/\mathrm{unit}]$). The model is configured to simulate disturbances in the system by adding and removing constant power loads by switches in the model, thereby causing a step change in the effective power to the load. The list of grid parameters is shown in

Table 3. Parameters of the two-generator system model.

Synchronous generator (G1)
Rated line voltage	$V_{\mathrm{LG}1}$	100 [kV]
Base power (Rated power)	$S_{\mathrm{G}1}$	Variable [MVA]
Inertia constant	$H_{\mathrm{G}1}$	3.5 [s]
Governor gain	$D_{\mathrm{G}1}$	25 [p.u.]
Synchronous reactance (d-axis)	$X_{\mathrm{dG}1}$	1.72 [p.u.]
Synchronous reactance (q-axis)	$X_{\mathrm{qG}1}$	1.66 [p.u.]
Initial power output	$P_{0\mathrm{G}1}$	Variable [p.u.]
Transmission line
Rated line voltage	$V_{\mathrm{LTL}}$	500 [kV]
Base power	$S_{\mathrm{TL}}$	1000 [MVA]
Resistance of $\mathrm{\Pi }$-section lines	$R_{\mathrm{TL}}$	$2.52\times {10}^{-3}$ [p.u.]
Reactance of $\mathrm{\Pi }$-section lines	$X_{\mathrm{TL}}$	$7.56\times {10}^{-2}$ [p.u.]
Susceptance of $\mathrm{\Pi }$-section lines	$B_{\mathrm{TL}}$	$7.32\times {10}^{-2}$ [p.u.]
Inverter base resources (G2)
Rated line voltage	$V_{\mathrm{LG}2}$	100 [kV]
Base power	$S_{\mathrm{G}2}$	Variable [MVA]
Virtual inertia constant	$H_{\mathrm{G}2}$	25 [s]
Virtual governor gain	$D_{\mathrm{G}2}$	100 [p.u.]
Virtual synchronous reactance	$X_{\mathrm{sG}2}$	$1.36\times {10}^{-1}$ [p.u.]
Initial power output	$P_{0\mathrm{G}2}$	Variable [p.u.]
Load
Rated line voltage	$V_{\mathrm{LL}}$	500 [kV]
Base power	$S_{\mathrm{L}}$	2000 [MVA]
Initial power consumption	$P_{0\mathrm{L}}$	0.6 [p.u.]
Load power fluctuation	$\Delta P_{\mathrm{L}}$	Variable [p.u.]

. In this table, the parameters marked ‘Variable’ are those that will be changed for each case in the subsequent simulations. In the synchronous generator model (G1), the dynamic characteristics of the turbine and governor are simulated by the LPT1 model of the Central Research Institute of Electric Power Industry (CRIEPI) [40] as shown in Figure 6 with the parameters in Table 3. Note that the PV-VSMs’ virtual governors do not mimic a detailed model as G1’s turbin&governor; it is simply described by 1st order transfer function $1/\left(2H_{\mathrm{G}2}s+D_{\mathrm{G}2}\right)$. The two-generator model can simulate generator dropout accidents (load spikes), and its simple structure allows for analysis of the behavior of the VSM during accidents with limited effects on the grid side.

With the above mentioned grid model and PV-VSM, the following two situations will be analyzed by simulation:

• Step changing load power fluctuation for the PV-VSM with insufficient headroom;
• Ramp changing irradiance fluctuation for the PV-VSM.

3. Simulation of the Step Changing Load Power Fluctuation

In order to verify the behavior of the PV-VSM in situations where the headroom is insufficient for the required regulation of the power supply due to grid disturbances, simulations are performed by connecting two different modules (PV-L, PV-S) with varying PV capacities in each case shown in

Table 4. Simulation parameters of the step changing load power fluctuation cases. The cases increasing load power can be regarded as simulating contingency. For each case, two simulation patterns with different PV module capacities are performed.

	${\mathit{S}}_{\mathbf{G}1}$[MVA]	${\mathit{P}}_{0\mathbf{G}1}$[p.u.]	${\mathit{S}}_{\mathbf{G}2}$ [MVA]	${\mathit{P}}_{0\mathbf{G}2}$ [p.u.]	$\mathbf{\Delta }{\mathit{P}}_{\mathbf{L}}$ [p.u.]
Case1	1500	0.6	500	0.6	$+0.01$
Case2	1500	0.6	500	0.6	$-0.01$
Case3	1000	0.6	1000	0.6	$+0.01$
Case4	1000	0.6	1000	0.6	$-0.01$
Case5	500	0.6	1500	0.6	$+0.01$
Case6	500	0.6	1500	0.6	$-0.01$

(12 patterns in total). Each case corresponds to a situation where 1.7% of the load active power at a given time (1% of the base power of the load) increases or decreases in steps on a grid with IBR penetration set at 25%, 50%, and 75%.

The results of the simulations are shown in Figure 7, Figure 8, Figure 9 and Figure 10. In each figure, the time axis represents the elapsed time after the step change in load active power.

In Figure 7, it can be seen that, in the case of decreasing load active power (Case2, Case4, Case6), the PV- VSM operates to suppress the active power output to eliminate the imbalance between generation and supply in the grid, regardless of the PV capacity. As the penetration of the PV-VSM increases, the oscillation of the effective power tends to subside in a shorter time, and the frequency of the synchronous generator also represented in Figure 7 shows that the oscillation of the frequency can be suppressed in a shorter time, regardless of the decrease in inertia. The same tends to be true for the upward output power regulation if the PV source has sufficient capacity. In the simple 1st order transfer function from the swing equation, the time constant is given by $2H/D$, which corresponds to 0.28 and 0.5 for the synchronous generator and PV-VSM, respectively. At first glance, the time constant of the synchronous generator may appear to be smaller than that of the PV-VSM, but, because the synchronous generator is driven by the turbine, mechanical constraints require a longer time to adjust the output by the governor. IBRs are not subject to these constraints, which allows for fast output adjustment, and thus the increase in IBR penetration allows frequency oscillations to be suppressed in a shorter period of time.

For the cases where the headroom (maximum power) of the PV source is insufficient for the required regulating power (Case1:PVS, Case3:PVS and Case5:PVS), it was confirmed that the system became unstable along with the instability of the PV-VSM operation. From Figure 8 and Figure 9, it can be seen that the secondary voltage of the DC/DC converter (the DC side voltage of the inverter) decreases with the imbalance of the input and output power to the capacitor in the destabilized cases. In the control algorithm of PV-VSM, the output voltage command value to the PWM controller is adjusted to increase or decrease the output current in response to changes in the electric angular frequency at the point of interconnection regardless of the PV source capacity. Therefore, the reason for the instability of the operation of the PV-VSM is that the PV-side output power is insufficient to maintain the DC-side capacitor voltage, while the inverter output power has increased due to the decrease in the frequency at the point of interconnection. In addition, it can be seen from Figure 10 that, in the destabilization case, the operating point of the PV power supply moves to the short circuit side after moving to the maximum power point. This means that, if the PV-VSM is operated without a sufficient margin for the maximum output power of PV, there is a possibility of losing the power supplied by the PV-VSM to the grid when contingency occurs. Therefore, to prevent such unstable operation of the PV-VSM, it is necessary to ensure an appropriate margin for the maximum power or to introduce a limiter in the control system.

Ref. [36] has exemplified a few simulation results for which the lack of maximum power of the source makes the VSM unstable. This simulation reinforces their result, which is an important issue for PV-VSMs.

In the next section, the impact of solar radiation fluctuations and load fluctuation on the grid is analyzed in the situation where measures to add limiters are implemented in the PV-VSM.

4. Photovoltaic Powered Virtual Synchronous Machine with a Limiter Control System

4.1. Scheme of the Limiter Control System

The necessity to introduce limiters in VSMs is often discussed as overcurrent protection for inverters, not limited to power source side restrictions. This is because the switching semiconductors in inverters have a short thermal time constant, and, from the standpoint of damage prevention, it is necessary to protect against the high currents that could occur when mimicking a synchronous generator; synchronous generators could support about 7 [p.u.] overcurrent, while the inverters could only support less than 0.4 [p.u.] overcurrent [41].

A detailed review is reported in [32] on methods to address the VSM overcurrent issue. There are two broad categories: when an overcurrent threat occurs, switching the VSM to current source mode (Grid-following mode [GFL]) temporarily or keeping it controlled as a voltage source mode (Grid-forming mode [GFM]) by changing the virtual impedance.

An example of the former implementation is upper limit control by a current saturator or current saturation algorithm [42,43]. In this approach, a threshold value is set for the d-/q-axis currents, and overcurrents are prevented by substituting a certain saturation value for the current command value that exceeds the threshold value. Adding a current saturation algorithm to the VSM is one effective approach with low implementation cost because it does not necessarily require an additional PLL, but the possibility that it could lead to instable operation due to windup has been pointed out [44,45]. To cope with this problem, Orihara proposed a modification technique of the virtual internal induced voltage of the VSM by adding an anti-windup mechanism to the current saturation algorithm, and evaluated its effect on the frequency response performance [46].

Figure 11 shows the block diagram of the PV-VSM control algorithm with output power limiter in this study, where anti-windup gains are set at $K_{\mathrm{aw}1}=2$ and $K_{\mathrm{aw}2}=1$. As the power limiting strategy, the anti-windup mechanism and saturators are applied to the virtual load angle and virtual field voltage of the PV-VSM. This control system limits output power by using a d-axis current saturator. The virtual load angle and virtual field voltage are held and limited when current saturation is detected. An anti-windup mechanism is used to compensate for the integrator that calculates the virtual rotor angle and Integral-control of the auto voltage regulator. By adjusting the upper limit of the command d-axis current $i_{d\mathrm{limit}}^{*}$ according to the solar irradiance, it is possible to prevent unstable operation of the PV-VSM when the VSM requires the power over the headroom. That is, the objective can be achieved by adjusting the parameter by the following equation:

$$i_{d\mathrm{limit}}^{*}=\frac{P_{\max }-i_q{E}_q}{E_d},$$

(4)

where $P_{\max }$ is the maximum power output of PV source, $i_{d\mathrm{limit}}^{*}$ is the limit of the d-axis current, $i_q$ is the q-axis current, and $E_d$ and $E_q$ are the d-axis and the q-axis virtual internal voltage. Note that these are the parameters expressed in the phasor diagram with the terminal voltage at the grid connection point as the starting point.

While the above system enables control of the PV-VSM upper limit, issues remain regarding the appropriate method of determining the available power; the maximum power point needs to be properly estimated for the active power reserve. Literature reviews of the available power determination (headroom estimation) are reported in [47,48], and the PV-VSM controller may choose an option from the following approaches: sensors based approach [49,50]; entering MPPT mode periodically [51]; coordinate control by master&slave inverters [35,52]; and estimating PV characteristic by a curve fitting [53,54,55].

The PV-VSM upper limit control of this study is shown in Figure 12. The mechanism to estimate the maximum power based on solar irradiance measures or forecasts was adopted. The advantage of this method is that it does not use MPPT control, thus it does not require the coordination of the DC/DC converter and VSM, and the algorithm is easier to implement than the curve fitting method. However, this method is not necessarily optimal when sensor implementation costs and estimation accuracy and delay are considered. In this study, for the initial investigation, this control scheme was applied to the PV-VSM.

4.2. Simulation Results for Solar Power Fluctuation

When available power is estimated for PV- VSM as an operational condition of the grid, it is necessary to make a decision on what percentage of the available power should be reserved as reserve supply power. In other words, in the fixed demand case, changing the output ratio of synchronous generators and PV-VSMs is a situation that simulates different cases of supply and demand planning. In order to check the impact of the ramp variation of solar radiation on the grid in such a situation, simulations are performed according to the parameters shown in

Table 5. Simulation parameters of the ramp changing solar irradiance fluctuation with the limiter control system.

	${\mathit{S}}_{\mathbf{G}1}$ [MVA]	${\mathit{P}}_{0\mathbf{G}1}$ [p.u.]	${\mathit{S}}_{\mathbf{G}2}$ [MVA]	${\mathit{P}}_{0\mathbf{G}2}$ [p.u.]	$\mathbf{\Delta }{\mathit{P}}_{\mathbf{L}}$ [p.u.]
Case a	1500	0.53	500	0.8	0
Case b	1500	0.6	500	0.6	0
Case c	1500	0.7	500	0.3	0
Case d	1000	0.4	1000	0.8	0
Case e	1000	0.6	1000	0.6	0
Case f	1000	0.9	1000	0.3	0
Case g	500	0.6	1500	0.6	0

. Here, the solar radiation is varied from 1000 [W/m${}^2$ ] to 680 [W/m${}^2$ ] in 1 [s] in the situation where the initial cross section is formed.

Each simulation setting corresponds to a situation where the PV-VSM is operated with its initial output set to 80%, 60%, and 30% of capacity when the PV-VSM has 25%, 50%, and 75% of capacity relative to the total system capacity. (Note that combinations that are not possible as a system setup are excluded.) The PV source is PVL, and the maximum power decreases with solar radiation changes: the available power of the PV-VSM shrinks from 0.98 [p.u.] to 0.57 [p.u.] relative to the base power. Figure 13 shows the change in available power and inverter output before and after the ramp change. Even if the PV-VSM plans an operation with a margin range (headroom) before the solar irradiance fluctuation, a large fluctuation will result in a negative margin, which implies a deficiency imbalance from the planned PV generation.

The results for the grid stability under solar radiation fluctuations for each operating condition are represented in Figure 14, Figure 15 and Figure 16 showing the transient response of the grid’s active power flow and the generator frequency. Here, the areas of parameters that cannot be set as initial settings are shaded. (i.e., parameter areas where the rated output of the synchronous machine is exceeded [$P_{0\mathrm{G}1}\ge 1.0[\mathrm{p}.\mathrm{u}.]$] or stopped [$P_{0\mathrm{G}1}\le 0.0[\mathrm{p}.\mathrm{u}.]$]). The vertical axis of each figure represents the margin after solar radiation fluctuation, and the negative value corresponds to the fall from the initial operating output.

In the case of the PV-VSM with limiter control, it can be confirmed that the grid can be operated stably even if the available power falls short of the initial operating state by about 0.05 [p.u.] due to solar radiation fluctuations in the cases where IBR penetration is lower than 75% (Case b and Case e). On the other hand, in cases where the decrease in available power is significantly large, the system cannot be operated stably even if a limiter control mechanism is used. Even if the unstable operation of the PV-VSM can be eliminated by the limiter control measures, the power supplied to the grid will decrease due to solar radiation fluctuations. Therefore, in an operation plan with a high PV-VSM output ratio, the synchronous generator cannot compensate in time for the power shortage imbalance caused by solar radiation fluctuations; and the grid becomes unstable by the fast frequency descending due to the small system inertia. The above results suggest that, in PV-VSM operation, it is important not only to improve the control algorithm of the inverter itself, but also to manage risk in terms of supply-demand planning and appropriate sizing of the available power reserve.

4.3. Simulation Results for Load Fluctuation

In order to confirm the effectiveness of the limiter control against step variations in load, additional simulations were performed under the conditions shown in

Table 6. Simulation parameters of the load fluctuation with the limiter control system.

	${\mathit{S}}_{\mathbf{G}1}$ [MVA]	${\mathit{P}}_{0\mathbf{G}1}$ [p.u.]	${\mathit{S}}_{\mathbf{G}2}$ [MVA]	${\mathit{P}}_{0\mathbf{G}2}$ [p.u.]	$\mathbf{\Delta }{\mathit{P}}_{\mathbf{L}}$ [p.u.]
Case a1	1500	0.53	500	0.8	$+0.01$
Case a2	1500	0.53	500	0.8	$+0.02$
Case a3	1500	0.53	500	0.8	$+0.03$
Case d1	1000	0.4	1000	0.8	$+0.01$
Case d2	1000	0.4	1000	0.8	$+0.02$
Case d3	1000	0.4	1000	0.8	$+0.03$

; in order to evaluate the security performance of the limiter in the event of a grid accident, we shall additionally simulate a generator dropout (load surge) for the case of high initial output of IBRs in the previous subsection, where the variation of solar radiation is ignored and load fluctuation is added. The Nadir Frequency and RoCoF were evaluated as indicators to measure the impact of load variations.

The simulation results are shown in Figure 17. As shown in Figure 17 in the system without limiter control, the system becomes unstable in some cases, making it impossible to evaluate frequency stability. In addition, the two indices did not deteriorate with or without the limiter control, and no disadvantages of implementing the proposed method could be confirmed.

5. Conclusions

In this study, the issues for the operation of grid-connected PV-VSMs through simulations using EMT analysis with a two-generator system are investigated. Simulations were performed under conditions of rapid changes in load active power and rapid changes in solar radiation. In the simulations of the load changes, it is confirmed that the PV-VSM with insufficient headroom may experience unstable operation, partly because the capacitor voltage of the DC/DC converter drops due to input–output imbalance when the required output of the VSM exceeds the maximum power of the PV. A possible solution to this issue is to add a system that combines an overcurrent protection mechanism and estimation of available power to the PV-VSM. The results of using the PV-VSM with the countermeasure algorithm in the grid for the solar radiation fluctuation case showed that the grid can be operated stably even if the PV available power drops by about 5% relative to the base capacity. Furthermore, when Nadir frequency and RoCoF for load variations were evaluated, both indicators were not worsened by the proposed algorithm, and no disadvantages were identified from the introduction of the countermeasure algorithm. However, grid instability still remains if the PV-VSM is operated at a high planned output and the synchronous generator does not provide sufficient compensation when the PV available power drops due to reduced solar radiation. In PV-VSM operation, risk management of supply-demand planning including advanced forecasting and appropriate sizing of available power reserve are also important and not limited to control technology of the inverter alone.