Virtual Synchronous Machine Control of RES Plants in Isolated Power Systems

Because of the increase in renewable energy sources (RESs) share, new control strategies of isolated power systems have been developed to improve the frequency and voltage stability of inverter-interfaced RESs. A voltage source converter (VSC) with a virtual synchronous machine (VSM) is among the most promising control schemes. This paper demonstrates how VSM control of inverter-interfaced RES can be efficiently used to improve the dynamic stability in small isolated power systems. In the proposed analysis, the RESs of a Mediterranean island are assumed interfaced to the grid by VSCs with a swing controller and a vector-current controller (VCC) with two different options for the reference current (RC) to regulate the voltage at the point of common coupling (PCC) and the real power output. The system is modelled in a PSCAD environment, and the behavior of the control is tested in the case of a phase-to-phase fault. The results of the simulations for different scenarios and values for the control parameters show the effectiveness of the control in small isolated grids. Finally, the level of grid power quality is verified via harmonic analysis of the PCC voltage.


Problem Statement
Worldwide, the higher cost of electricity from diesel and the targets for reducing greenhouse gas emissions have led to incentivize using renewable energy sources (RES) on small islands not supplied by the main transmission grid [1,2]. To achieve the same level of performance as traditional synchronous generators (SG), grid control must be substantially modified to accommodate this transformation of the small island generation system [3,4].
With recent advancements in the development of virtual synchronous machine (VSM) technologies, VSM has gained prominence in isolated power systems because of its characteristics of improving performance, flexibility, efficiency, stability, and reliability [2][3][4][5][6].
Nevertheless, voltage source converters (VSC) with VSM must be suitably controlled to avoid this, in the presence of short-circuits, while keeping the power system stable, as the electronic devices of the converter are subjected to currents capable of damaging them. In this context, one of the most dangerous events for VSCs is a phase-to-phase fault, as it produces to short-circuit currents that can rise to almost the 87% of the three-phase short-circuit current at the point of common coupling (PCC).

Literature Review
VSM topologies and schemes have attracted the interest of many researchers and several papers have been published on this promising topic [5][6][7][8][9][10]. The authors of [5] presented a literature review on VSM. In addition, this review paper introduces a detailed discussion on modern control techniques for VSM. The authors of [6] provided a comprehensive review of the state-of-the-art VSM topologies along with a discussion on some of the challenges that will stem from the integration of RES. The authors of [7] presented an overview of different topologies to virtual inertia along with a detailed representation of the VSM structure. In addition, this review explained VSM control, which defines active and reactive power control and voltage and frequency control. U. Tamrakar et al. [8] presented a review of the virtual inertia implementation techniques. The major virtual inertia strategies are also compared and classified in this review paper. In [9], the authors discussed the use of electric vehicle chargers for providing virtual inertia while being operated as VSM. Finally, the authors of [10] proposed a VSM application for battery/supercapacitor hybrid energy storage systems to handle the stochastic power output of photovoltaic (PV), based on a new evolutionary algorithm called the backtracking search optimized algorithm for real-time tuning of the VSM parameters.
In light of the above literature review, Table 1 summarizes the key features and weaknesses of commonly used VSM control strategies. Therefore, new control strategies have been developed to improve the frequency and voltage stability of inverter-interfaced RES generators, considering both active and reactive power generation [11][12][13][14][15]. Among the mentioned strategies, those implemented for contrasting the natural reduction of the system inertia due to the increase in RES share [14][15][16][17][18] have a crucial role in the secure management of isolated power systems. In the technical literature, droop control coupled with virtual inertia is the most common grid-supporting method, but other solutions have recently been proposed.

Proposed Solution
VSC with VSM control is one of the most promising control schemes for imitating the dynamic response of a SG [19]. Through VSM control, it is possible to achieve a behavior similar to that of a SG, but the converter is not guarded against overcurrent. Thus, the converter input current needs to be limited by a vector-current controller (VCC) [20,21]. In this paper, the VSM control combined with a vector-current controller is applied to the converters that are assumed to be installed in the small island of Pantelleria.
Initially, the hourly generation and demand of the island (data provided by the local utility SMEDE) are analyzed during typical winter and summer days. For both seasons, hour-by-hour power system inertia is calculated, and the most critical situations based on a reduced inertial response are identified. Subsequently, an equivalent single-bus model of the power system is created in the PSCAD environment. RES plants are represented as a unique VSC, and the conventional SGs is represented as a unique equivalent SG. The internal control model of the equivalent VSC considers the grid impedance and two different options for calculating the reference current, starting from a steady-state condition and evaluating the effects due to a phase-to-phase short-circuit simulated at the PCC. Simulations are done for different values of the control parameters, energy scenarios, system inertia and provided virtual inertia, and for two values of the short circuit ratio (SCR) to represent both a strong and a weak grid [22].
The rest of the paper is organized as follows: Section 2 presents the structure of the system under study and the mathematical representation of VSM with VCC. Section 3 reports the initial data for the simulations. Section 4 provides the results of the simulations and, finally, Section 5 reports the conclusions of the study.

Structure of the System and Proposed Converter Topology
The power system of a small island not supplied by the main transmission grid can be represented, for the aim of this study, as shown in Figure 1. The island's generation system is characterized by a central diesel power plant, represented in Figure 1 as an equivalent SG identified as a "GRID" and connected in series to the grid impedance denoted as "Grid-Z". All VSCs are represented by an equivalent VSC with an internal VSM-structure with VCC and an RL filter.  The virtual damping coefficient of the VSC The details of the proposed topology for the VSC are described in this section, and Table 2 reports a description of all of the symbols used in the following equations.  Based on the swing equation, the VSC model shows a power balance synchronization mechanism [23]: Based on the aforementioned equations, a small-signal analysis of the system yields the following expression.
Studying the controller response based on Equations (1) and (6) provides a relationship between the variation in output power ∆P vsm and the variation in reference power ∆P re f . Hence, the linear model of the system can be expressed as follows: Considering the Laplace Transform for Equations (3)- (7), the following equation is obtained: Appl. Sci. 2022, 12, 5920

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Based on the aforementioned transfer function, the active power controller poles can be determined as follows: The VSM control guarantees the VSC has behavior similar to SG, but does not guarantee the protection of the converter from overcurrent in the presence of a short-circuit in the grid. A solution to this problem is to limit the converter current using the VCC. The VCC is one of the most common methods used for VSCs because of its simple implementation and robust performance in ideal-grid conditions. Figure 2 represents the block diagram of VSM with VCC with the reference current (RC). Seven blocks are visible:

•
A measurement block at the PCC, taking the measurements of P g , I g , and V g , which are the input of the RC block and the abc/dq block; • The abc/dq and dq/abc blocks, using θ vsm for the transformations of voltages and currents; • A damping controller denominated as DC used to improve the response in the active power of the VSC; • A VCC used to protect the converter from overcurrent; • An RC used to obtain the converter input of the current control and coordinate of the abc/dq and dq/abc transformations; P re f and T vsm are the reference variables, while L f and ω 0 are the complementary variables. VCC is defined by Equation (10).
In this paper, the input reference current * appearing in Equation (10) is calculated using two different methods: In this method, by combining Equations (10) and (11), it is easy to notice that the reference current is provided to the control system in order to obtain the reference value for the VSC voltage equal to that of the grid voltage and, at the same time, to limit the current to values not dangerous for the converter, thanks to the current limiter (transfer function CL).
In this method, the reference current is provided in a way that takes into account the variation in the grid voltage and the consequent variations in the grid current. In addition, in this case, the transfer function CL demonstrates the presence of a block limiting the VCC is defined by Equation (10).
In this paper, the input reference current I dq * f appearing in Equation (10) is calculated using two different methods:

1.
Option I (RC-1): In this method, by combining Equations (10) and (11), it is easy to notice that the reference current is provided to the control system in order to obtain the reference value for the VSC voltage equal to that of the grid voltage and, at the same time, to limit the current to values not dangerous for the converter, thanks to the current limiter (transfer function CL).

2.
Option II (RC-2): In this method, the reference current is provided in a way that takes into account the variation in the grid voltage and the consequent variations in the grid current. In addition, in this case, the transfer function CL demonstrates the presence of a block limiting the current to values that are not dangerous for the converter.

V dq * vsc
The reference signal for VSC voltage in dq coordinates The grid voltage in dq coordinates The current output of the VSC in dq coordinates The reference current of the VSC in dq coordinates

PI
The transfer function of the PI controller with proportional gain The sum of the VSC filter inductance L f and of the estimated grid inductance L g R t The sum of the filter resistance R f and of the estimated grid resistance R g R v The virtual resistance taking into account active damping for dealing with system parameter variations and disturbances It is worth mentioning that the CL is necessary for blocking the overcurrents during the transients, and LP is required for avoiding spiky transients and miscalculations before sending the calculated references to the current controller.

Case Study
The case study considers the 10 kV isolated power system of the island of Pantelleria in the case of the high share of RES generation. The current central power plant of the island consists of eight SGs for a total rated power of 24.5 MVA. The detailed specifications for this system are described and documented in [24,25]. The system is modelled as in Figure 1 using the control topology in Figure 2.
Based on the data provided by the local utility and considering a renewable energy mix of 1 MW photovoltaic and 1 MW wind power, the daily power profiles in typical summer and winter days are depicted in Figure 3. Appl. Sci. 2022, 12, x FOR PEER REVIEW 8 of 17 The worst case, defined as the working condition presenting the least inertia, is defined in Table 4 for both summer (scenario A) and winter (scenario B). In Table 4, NSPL refers to the non-synchronous penetration level. VSPL can be defined as the rate between the total power generated by RESs and the total power generated at a given hour [27]. The load at the PCC is modelled as a fixed impedance, where the real power and the reactive power are evaluated as follows: where  is the frequency variation; is the rated voltage, and are the active and reactive power of the load at the rated voltage and frequency, respectively; and , , , and are the indexes expressing the dependence of active and reactive power from the actual values of the voltage and frequency [20].
The grid has been simulated in the case of a phase-to-phase fault. The flowchart in Figure 4 represents the methodology of the proposed control strategy. The proposed methodology has the ability to deal with fault conditions and to check the VSM behavior in normal and fault operations. In particular, the dashed line is the daily power profile generated by the VSC, which represents the energy mix composed of wind and photovoltaic plants. According to the power profiles in Figure 3, the inertia T S of the isolated power system in each instant is evaluated as follows [26]: where T i is the inertia and A n,i is the rated apparent power of the i-th synchronous generator connected to the grid, and P load is the total active power requested by the load at each instant.
The worst case, defined as the working condition presenting the least inertia, is defined in Table 4 for both summer (scenario A) and winter (scenario B). In Table 4, NSPL refers to the non-synchronous penetration level. VSPL can be defined as the rate between the total power generated by RESs and the total power generated at a given hour [27]. The load at the PCC is modelled as a fixed impedance, where the real power P load and the reactive power Q load are evaluated as follows: where ∆ is the frequency variation; V n is the rated voltage, P load−0 and Q load−0 are the active and reactive power of the load at the rated voltage and frequency, respectively; and NP, K PF , NQ, and K QF are the indexes expressing the dependence of active and reactive power from the actual values of the voltage and frequency [20]. The grid has been simulated in the case of a phase-to-phase fault. The flowchart in Figure 4 represents the methodology of the proposed control strategy. The proposed methodology has the ability to deal with fault conditions and to check the VSM behavior in normal and fault operations. Appl. Sci. 2022, 12, x FOR PEER REVIEW 9 of 17

Results and Discussion
In the simulations, the following parameters were considered: = 0.707; = 10; ∝ 0.12π ; =5 kHz. The system was simulated for two different values equal to 8 s and 0.01 s.
Four scenarios were considered: two for winter and two for summer. For sake of simplicity, the scenarios were indicated as A1, A2, B1, and B2, where A was used for winter, B for summer, 1 for option I of RC, and 2 for option II of RC.
The system was tested in the presence of a double-phase fault applied at t = 45 s. To investigate the performance of the VSM control in two extreme fault conditions, two different values of the short-circuit resistance were considered: 0.5 Ω and 0.5 kΩ. Moreover, with the aim to allow for compensating for the delay introduced by PWM using synchronous sampling [20], VCC was examined by considering two angle options for the dq-frame transformation: Finally, two values of SCR were considered: SCR = 10 and SCR = 3, representing the hypotheses of a strong and weak grid, respectively.

Strong Grid: SCR = 10
The trends of the active power obtained in the simulation for this case are reported in Appendix A Figure A1. The main results of the simulations are summarized below:

Results and Discussion
In the simulations, the following parameters were considered: ζ = 0.707; ω n = 10; ∝ cc < 0.1·2·π· f s ; f s = 5 kHz. The system was simulated for two different T vsm values equal to 8 s and 0.01 s.
Four scenarios were considered: two for winter and two for summer. For sake of simplicity, the scenarios were indicated as A1, A2, B1, and B2, where A was used for winter, B for summer, 1 for option I of RC, and 2 for option II of RC.
The system was tested in the presence of a double-phase fault applied at t = 45 s. To investigate the performance of the VSM control in two extreme fault conditions, two different values of the short-circuit resistance R sc were considered: 0.5 Ω and 0.5 kΩ.
Moreover, with the aim to allow for compensating for the delay introduced by PWM using synchronous sampling [20], VCC was examined by considering two angle options for the dq-frame transformation: Finally, two values of SCR were considered: SCR = 10 and SCR = 3, representing the hypotheses of a strong and weak grid, respectively.

Strong Grid: SCR = 10
The trends of the active power obtained in the simulation for this case are reported in Appendix A Figure A1. The main results of the simulations are summarized below: • Throughout all of the simulations, a typical trend in grid stability was observed after the fault, with a loss of load, depending on the unbalance between SG and RES. However, because of the action of the speed regulators on the SG and of the internal controllers of the VSC, the active power returned to the previous steady-state values as soon as the fault was removed. • When the contribution of RES was greater than 60% of the load (Scenarios B1 and B2), and when R sc assumed its lowest value, the active power showed more significant oscillations. On the other hand, the grid stability improved when angle compensation was used and T vsm was raised.

•
In Scenario A1, the system had a positive behavior; this feature was due to the contribution of both SG and the control option chosen for the VSC (RC-1) during the fault. These choices ensured that scenario A1 did not present unstable situations even in the case of a low T vsm and R sc .

•
In Scenario A2 with a low value of R sc , the system became unstable when RC-2 was chosen, regardless the value of T vsm .

•
In the steady-state operation, RC-2 showed a better performance than RC-1, and when using this control option, the system stabilized quickly, as shown in the results for scenarios A2 and B2. However, in the presence of faults, this control option was not able to maintain the desired power.

Weak Grid: SCR = 3
The successful cases obtained for the strong grid (case with option RC-1) were also examined for the case of a weak grid. The trends of the active power obtained in the simulation for this case are reported in Appendix A Figure A2. The main results of the simulations are summarized below:

•
In Scenario A1, no alterations were seen in the power generation from the SG: traditional generators delivered the desired power to the load. On the other hand, in Scenario B1, the power production was reduced to 66% and this created a deficit in power generation.

•
The lower the SCR (and so, the higher the grid reactance, X g ), the closer the power contribution of VSC to that of SG. Mathematically, this could be seen by calculating the SCR = S sc /S, where S is the VSC rated power and S sc = V 2 /X g is the grid short-circuit power; • The behavior of VSC during the fault did not vary.
The PCC voltage was significantly affected by the SCR value, as shown in Figure 5, where: • the voltage variation during the fault was shown for both the robust and the weak grid; • there was a variation in the PCC voltage when the power system operated at different transfer power conditions; • Scenario A1 was less affected by the SCR value; • Scenario B1 with SCR = 3 did not meet the minimum standard established for the voltage value.
Finally, a harmonic analysis of the PCC voltage until the 15th harmonic was carried out, as shown in Figure 6. The dominant harmonic components were found to be the 2nd to the 4th. Figure 6 shows that correct sizing of the VSC filter permitted maintaining an acceptable level of grid power quality. The THD of the PCC voltage did not exceed the limit of 1%. The results of the simulations in Scenario B1 showed the 2nd, 3rd, 10th and 15th harmonics were more or less triple with respect to Scenario A1, and the harmonics from the 4th to the 9th were double.  Finally, a harmonic analysis of the PCC voltage until the 15th harmonic was carried out, as shown in Figure 6. The dominant harmonic components were found to be the 2nd to the 4th. Figure 6 shows that correct sizing of the VSC filter permitted maintaining an acceptable level of grid power quality. The THD of the PCC voltage did not exceed the limit of 1%. The results of the simulations in Scenario B1 showed the 2nd, 3rd, 10th and 15th harmonics were more or less triple with respect to Scenario A1, and the harmonics from the 4th to the 9th were double.

Conclusions
Using VSC with a swing controller and VCC with two different options for the RC on RES-based generators has been demonstrated to have mutual advantages in normal and faulty operation for small isolated power systems. The proposed VSM model allows for the implementation of virtual inertia and damping in the isolated grid, also improving

Conclusions
Using VSC with a swing controller and VCC with two different options for the RC on RES-based generators has been demonstrated to have mutual advantages in normal and faulty operation for small isolated power systems. The proposed VSM model allows for the implementation of virtual inertia and damping in the isolated grid, also improving grid stability in the presence of extremely severe fault situations such as those represented by the phase-to-phase fault. In the simulations performed for the Island of Pantelleria in the Mediterranean Sea, the transients of the active power output of the VSC and of the voltage at the PCC have been observed. The study shows how the value of the SCR can influence the behavior of the VSC. Moreover, the acceptable level of grid power quality has been ensured via harmonic analysis of the PCC voltage. The precise design of different stages of the proposed model is required to maximize the benefits gained in both the static and dynamic behavior of the isolated grids.
The performed study is useful for setting the parameters of the VSM control of VSCs in small islands not supplied by the main power transmission grid; however, this is only a first step of a more complex process for fostering the penetration of RESs in small islands.
Indeed, some other aspects must be considered before transformation towards a 100% RES-based generation system can be achieved. For example, there is still a lack of research in the determination of the required amount of power from VSC with VSM control that can be installed without creating a stability issue in the grid due to the interactions between converters. This study has been already started and is partially presented in [11], and will be the next important step in the current research on VSM application to small island power systems.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A
The graphs of Figure A1 represent the load and RES active power in the case of a strong grid (SCR = 10).

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A
The graphs of Figure A1 represent the load and RES active power in the case of a strong grid (SCR = 10).       The graphs in Figure A2 represent the load and RES active power in the case of a weak grid (SCR = 3).   The graphs in Figure A2 represent the load and RES active power in the case of a weak grid (SCR = 3). The graphs in Figure A2 represent the load and RES active power in the case of a weak grid (SCR = 3).