Distributed Virtual Synchronous Generator approach versus Singular Virtual Synchronous Generator approach: A dynamic stability evaluation

Abstract

This paper reports the modeling and dynamic performance of a wind penetrated multi-area power system incorporating a Singular Virtual Synchronous Generator (SVSG)/Distributed Virtual Synchronous Generator (DVSG). The active and reactive power controls are achieved by using Superconducting Magnetic Energy Storage (SMES) as Virtual Synchronous Generator (VSG). SMES based VSG control parameters are tuned offline using genetic algorithm (GA). Two topologies of VSGs are considered in this paper: SVSG at lowest inertia generator bus (SVSGGENBUS), SVSG at load bus (SVSGLOADBUS) and DVSG of comparatively smaller rating at three lowest inertia generator buses. A modified 18 machine, 70-bus power system is simulated in MATLAB/Simulink environment. System performance is assessed for two different types of disturbances: step wind disturbance and three-phase fault. The simulation results show that rate of change of frequency (ROCOF), deviations in frequency and voltage are minimized with DVSG. Transient stability measured in terms of critical clearing time (CCT) verifies that CCT is increased by DVSG topology.

Keywords

Virtual Synchronous Generator Superconducting Magnetic Energy Storage frequency faults wind disturbance critical clearing time

Introduction

The large-scale integration of renewable energy sources (RESs) such as wind, solar, geothermal, and biomass to power systems has become unavoidable due to two universally recognized challenges: the dependency on fossil-fuel and the need to reduce environmental impact of massive increase in energy. China has an installed capacity of 221 GW and is the leader in wind energy followed by USA with 96.4 GW. In other countries like Germany, India and Spain significant amount of power from renewable energy sources is planned to be connected to their power systems upto next two decades.

In conventional power plants, the alternators provide inertia to the grid through their rotating parts. This inertia helps to regulate grid frequency by avoiding frequency deviation from the regular frequency operation. But, these power plants are responsible for greenhouse gas emissions. To reduce the greenhouse emissions, integration of RESs is encouraged. However, these RESs have either small or no rotating part. Therefore, they reduce the inertia of the grid dramatically leading to frequency/voltage instability as compared to the system using sysnchronous generators (Aouini et al., 2014; Bevrani et al., 2014; Hartmann et al., 2019). The CCT reduces because of reduction in effective network inertia due to asynchronous generation (Naik et al., 2016). The most significant challenge for the integration of RESs is frequency regulation.

To imitate the behavior of traditional alternator, virtual synchronous generator is used. The concept of VSG aims to emulate the behavior of Synchronous Generator (SG) in order to stabilize the power system (Driesen and Visscher, 2008; Syed and Mufti, 2018). VSG consists of combination of energy storage, inverter and a control mechanism. Energy storage can be ultrabattery, supercapacitor, flywheel, SMES or a battery. Among these, SMES is a fast acting storage device with almost zero power loss. SMES has high efficiency and large number of charge and discharge cycles (Iqbal et al., 2009).

The reference output power command of SMES-VSG is given by:

P_{VSG} = k_{I} \frac{d Δ ω}{dt} + k_{D} Δ ω + k_{C} (I_{sm}^{0} - I_{sm})

(1)

where

$Δ ω = ω - ω_{0}$ , $ω_{0}$ is the nominal frequency of the system.

The first term in equation (1) emulates the power which is absorbed/released by positive or negative frequency deviation rate $(\frac{d Δ ω}{dt})$ (Morren et al., 2006). $K_{I}$ is the inertia emulating coefficient and determines response to high ROCOF values. Power will be exchanged only during transients because change in frequency is zero in steady state. After a disturbance if the frequency of the system decreases, SMES-VSG starts to supply power till $(\frac{d Δ ω}{dt}) = 0$ .

If on the other hand, the frequency of the system increases, SMES-VSG starts to absorb power till $(\frac{d Δ ω}{dt}) = 0$ . The second term emulates the damper winding effect of SG and helps to restrain maximum frequency deviation. The values of $K_{D}$ and $K_{I}$ are defined as (Karapanos et al., 2015):

\begin{matrix} K_{D} = \frac{P_{VSG - Nom}}{2 \cdot 5 Hz} \\ K_{I} = \frac{P_{VSG - Nom}}{1 Hz / s} \end{matrix}

The value of $K_{C}$ is properly chosen. The large value of $K_{C}$ will make SMES-VSG unit ineffective in reducing the frequency deviations. On the other hand a very small value of $K_{C}$ will not allow the SMES coil to return to its nominal value (Zargar et al., 2017). The values of $K_{D}$ , $K_{I}$ , and $K_{C}$ used in this manuscript are given in Appendix.

Improvement of transient stability of power system including wind generator by using SMES has been carried in Sheikh and Nasiruzzaman (2009), but effect of wind speed was not considered. The role of high wind variability in wind generation based power system with stabilizer potential from energy storage unit has been discussed in Ali et al. (2009). The improvement of frequency regulation by using kinetic energy of variable speed wind turbine and DC capacitor of VSC-HVDC has been carried in Guo et al. (2020). In Kerdphol et al. (2019), frequency improvement using SMES based virtual inertia control over traditional ESS-based virtual inertia control in a microgrid has been shown. The concept of VSG has been applied in microgrids to control distributed generation sources (Alipoor et al., 2015; Wang et al., 2015). Model predictive control has been applied to emulate virtual inertia into microgrid, thus stabilizing microgrid frequency during high penetration of RESs (Kerdphol et al., 2017). In Li et al. (2017), a self-adaptive inertia and damping combination control method to improve the frequency stability with an interleaving control technique has been discussed. As per the literature, most of the studies have only focused on the impact of VSG on microgrid and no previous work has reported the impact of distributed virtual synchronous generator on wind-penetrated interconnected power system. The present paper aims at filling this gap and provides extensive study on impact of DVSG on stability of large interconnected power system.

The main contributions of this paper are manifold, viz.

An elaborate description on modeling and integration of SVSG and DVSG for a multi-machine, multi-bus, wind penetrated power system.

The tuning of Superconducting Magnetic Energy Storage based Virtual Synchronous Generator using Genetic Algorithm.

Superior performance of DVSG in terms of ROCOF, deviations in frequency and voltage by DVSG has been validated over SVSG and absence of VSG.

Improvement in transient stability measured in terms of CCT by DVSG has been validated over SVSG and absence of VSG.

This paper aims to make a comprehensive comparison of DVSG with SVSGGENBUS and SVSGLOADBUS.

Test system configuration and mathematical modeling

Modified wind farm fed 16 machine 68 bus system

The 68-bus system consists of five areas with 16 synchronous generators. New England Test System (NETS) and New York Power System (NYPS) are represented by a group of generators, while area 3, area 4, and area 5 are represented by group of generators (Figure 1). Generator 13 also represents a small sub-area. Bus 69 is connected to bus 22 through a transformer. Bus 70 is connected to bus 17 through another transformer. The value of transformer reactance is taken as j0.01. At bus 69 and 70 two DFIG based wind farms each of capacity 87 MW are connected. Bus data, line data and alternator data can be found in Pal and Chaudhuri (2006).

Figure 1.

Single line diagram (SLD) of 18 machine 70-bus system.

SMES units operating in VSG mode are connected at various buses (Figure 1). Two approaches of genetic algorithm tuned SMES based VSGs are tested. The first approach is called as singular VSG approach. In singular VSG approach, VSG is connected at a generator bus (SVSGGENBUS) or a load bus (SVSGLOADBUS). In the second approach, VSG connected at low inertia nodes of NETS (bus 8, bus 5, and bus 7) is known as distributed VSG (DVSG). The optimal location of VSGs is decided on the basis of difference in inertia. Three medium sized SMES-VSGs are connected at above said buses in DVSG approach. In case of singular VSG model, a single SMES of large capacity operating in VSG mode is allocated at lowest alternator inertia bus, that is, bus 8 in one topology and a load bus (bus 68) in second topology.

Modeling of synchronous generator and excitation system

Taking in consideration, the constraints on data availability and study of large systems, the synchronous generators are represented by model 1.1, which neglects stator transients. This model consists of a field coil on d-axis and a damper winding on q-axis. The turbine governor transients are neglected resulting in constant mechanical input torque $T_{m}$ . The individual machine stator, rotor and electromechanical equations are given by:

Stator algebraic equations:

\begin{matrix} v_{q} = E'_{q} + x'_{d} i_{d} - R_{a} i_{q} \\ v_{d} = E'_{d} - x'_{q} i_{q} - R_{a} i_{d} \end{matrix}

(2)

Rotor differential equations:

\begin{matrix} \frac{d (E'_{q})}{dt} = \frac{1}{T'_{d 0}} [- E'_{q} + E_{fd} + (x_{d} - x'_{d}) i_{d}] \\ \frac{d (E'_{d})}{dt} = \frac{1}{T'_{q 0}} [- E'_{d} + (x_{q} - x'_{q}) i_{q}] \end{matrix}

(3)

Electromechanical equations:

\begin{matrix} \frac{d δ}{dt} = ω_{B} (ω - w_{0}) \\ \frac{d ω}{dt} = \frac{1}{2 H} [T_{m} - T_{e} - D (ω - ω_{0})] \end{matrix}

(4)

Electrical torque:

\begin{matrix} T_{e} = E'_{d} i_{d} + E'_{q} i_{q} + (x'_{d} - x'_{q}) i_{d} i_{q} \end{matrix}

(5)

The excitation system comprises of an exciter, an automatic voltage regulator (AVR), and a power system stabilizer (PSS). The generator voltage is regulated to its set point by AVR and the small signal stability is ensured by PSS. In this article, standard static exciter (ST1A) has been considered. The PSS is taken as typical speed-feedback controller which is based on three stage lead-lag compensators and one high pass washout filter. Modeling nomenclature can be referred to Kundur et al. (1994) and Padiyar et al. (1996).

Modeling of Wind Energy Conversion System (WECS)

A wind farm model typically consists of three components: wind turbine, a doubly-fed induction generator (DFIG) and a back-to-back converter. The wind turbine converts aerodynamic power to mechanical power which is converted into electrical power by DFIG. DFIG has been used because of its meritorious options like variable speed operation, maximum power extraction and robust construction.

Two wind farms based on doubly fed induction generators each of capacity 87 MW operating in maximum power point tracking (MPPT) mode are connected at bus 69 and bus 70 (Figure 1). The modeling of DFIG is performed in a synchronously rotating reference frame by a set of differential state equations. DQ voltages in per unit for stator as well as rotor circuits are represented by a set of dynamic equations given by Ahsan and Mufti (2019):

V_{Qs} = - R_{s} I_{Qs} - ω_{s} ψ_{Ds} + \frac{1}{ω_{b}} \frac{d ψ_{Qs}}{dt}

V_{Ds} = - R_{s} I_{Ds} + ω_{s} ψ_{Qs} + \frac{1}{ω_{b}} \frac{d ψ_{Ds}}{dt}

V_{Qr} = R_{r} I_{Qr} - s ω_{s} ψ_{Dr} + \frac{1}{ω_{b}} \frac{d ψ_{Qr}}{dt}

V_{Dr} = R_{r} I_{Dr} + s ω_{s} ψ_{Qr} + \frac{1}{ω_{b}} \frac{d ψ_{Dr}}{dt}

Per unit flux for stator and rotor circuits are represented by a set of dynamic equations given by:

ψ_{Qs} = - L_{ss} I_{Qs} + L_{m} I_{Qr}, ψ_{Ds} = - L_{ss} I_{Ds} + L_{m} I_{Dr}

ψ_{Qr} = L_{rr} I_{Qr} - L_{m} I_{Qs}, ψ_{Dr} = L_{rr} I_{Dr} - L_{m} I_{Ds}

The DQ current contributions and total current of the DFIG is given as under:

I_{Qdfig} = I_{Q_{s}} + I_{Q_{Gs}}, I_{Ddfig} = I_{D_{s}} + I_{D_{Gs}}

I_{dfig} = I_{Qdfig} + j * I_{Ddfig}

Modeling of SMES

SMES is modeled as a controllable current source having the capability of exchanging active power with the system. The active power modulation of SMES is made by means of a chopper shown in Figure 2(a). In Figure 2(a), $S_{1}$ and $S_{2}$ represent IGBT switches and $D_{1}$ and $D_{2}$ represent the diodes. Figure 2(a) shows the interface between SMES and AC grid. A power electronic interface called the Power Conditioning System (PCS) connects the SMES unit to the grid. The PCS includes a voltage-sourced converter (VSC) together with DC-DC chopper, a DC link capacitor and a coupling transformer.

Figure 2.

Superconducting magnetic energy storage: (a) integration scheme at bus, (b) control model for reactive power modulation, and (c) control model for active power modulation.

The SMES output is controlled through a DC-DC 2-Q chopper. A bi-directional power converter (AC/DC) connects the unit to the AC grid. This converter is generally a three-phase bridge made of semiconductor switches functioning as a voltage source inverter (VSI). The converter used is either a conventional 6-pulse type or a 12-pulse type. The control of power flow from the SMES unit to the AC system and vice versa is achieved by issuance of firing pulses based on controllable parameter deviations. The DC bus voltage builds up to its nominal value once suitable gating signals are issued to the semiconductor switches (usually insulated-gate bipolar transistors (IGBTs) are used) and this voltage remains constant thereafter. Adjusting the duty cycle of the 2-Q chopper changes the polarity and magnitude of the voltage applied to the SMES coil. This in turn enables charging and discharging of the SMES. Three regions of operation are possible for the chopper depending on the value of duty cycle D (7) shown in Figure 3.

Figure 3.

Details about the ON positions of various switching devices of the chopper for different range of values for the duty cycle.

Power is controlled by controlling the duty cycle of chopper. For D = 0.5, SMES is said to be in floating state (no excahnge of power). For D > 0.5, the power flows from system to SMES. For D < 0.5, the power flows from SMES to system.

In this article, average model of SMES is considered. The SMES coil current and DC link voltage are related by

I_{sm} = {\frac{1}{L}}_{sm} \int V_{dc} (2 D - 1) dt

(6)

The reactive power modulation is based on bus voltage error, which occurs when a disturbance hits the system 2b. The block diagram representation for active power modulation is shown in Figure 2(c). The active power regulation of SMES is based on frequency control technique. SMES power is taken as feedback. This model makes use of proportional and integral controllers as shown in Figure 2(c). The controller parameters are tuned offline to make the SMES unit behave like a first order system with a small time constant of 0.002 s. The grid side converter (GSC) is a pulse width modulated voltage source converter. The tuning of SMES by GA is discussed in next section.

Once $P_{grid}$ (Figure 2(c)) and $Q_{grid}$ (Figure 2(b)) are calculated, the D-Q components of SMES current are calculated using the equation given below:

[\begin{matrix} I_{Qsmes} \\ I_{Dsmes} \end{matrix}] = \frac{1}{v_{D}^{2} + v_{Q}^{2}} [\begin{matrix} v_{Q} & v_{D} \\ v_{D} & - v_{Q} \end{matrix}] [\begin{matrix} P_{grid} \\ Q_{grid} \end{matrix}]

(7)

The total current from the SMES is given by $I_{smes} = I_{Qsmes} + j * I_{Dsmes}$ . SMES parameters used in this article can be found in Appendix.

Control of SMES-VSG

Power exchange of SMES-VSG with power system is possible by means of VSC together with DC-DC chopper and DC link capacitor. For D > 0.5 power should flow from power system to SMES-VSG through DC link which results in reduction in DC link voltage. VSC tries to maintain the DC link voltage constant and to do so, it absorbs power from the system. Similarly, for D < 0.5 power should flow from SMES-VSG to power system through DC link which results in increase in DC link voltage. VSC tries to maintain the DC link voltage constant and to do so, it pumps power to the system. Not only SMES, but other energy storage systems like battery, flywheel communicate with the system using VSC and DC link.

Design optimization of control schemes

The ISE prediction scheme used in this paper is shown in Figure 4(a). r(t) in Figure 4(a) represents a random signal which is selected to check the tracking performance of GA tuned SMES. The different controller gains are defined in the following chromosome:

chromosome = [ $K_{p}$ , $K_{i}$ ], where $K_{p}$ , $K_{i}$ are the propotional and integral gains of controller. The tracking performance of GA tuned SMES is compared with that of the reference system in Figure 4(b). It can be observed that the GA tuned SMES exactly follows the reference model.

A cost function is framed to estimate the optimal gains ( $K_{p}$ and $K_{i}$ ) which is based on deviation in frequency. $K_{p}$ and $K_{i}$ are obtained by minimizing the cost function subject to constraint bounds. The fitness function is created as:

C_{f} (k_{p}, k_{i}) = \underset{0}{\int^{t_{sim}}} {(Δ f)}^{2} dt

(8)

subject to k_{P}^{\min} ⩽ k_{p} ⩽ k_{p}^{\max} and k_{i}^{\min} ⩽ k_{i} ⩽ k_{i}^{\max}

where $t_{sim}$ represents the simulation time.

Figure 4.

(a) ISE prediction scheme, (b) tracking performance of GA tuned SMES-VSG unit for random variable function, and (c) genetic algorithm flowchart for optimization of gain parameters of SMES-VSG.

GA’s have been widely used for solving the optimization problems of electrical power systems. The heuristic search of GA’s is based on the principle of survival of the fittest (Hasanien et al., 2012). By minimizing the objective function using GA Toolbox in MATLAB, the chromosomes (controller gains) are tuned. The flowchart depicting the procedure for timing of controller gains is shown in Figure 4(c). The values of $K_{p}$ and $K_{i}$ calculated by GA for SVSG and DVSG models are given in Appendix.

Generation of power command for SMES-VSG

The reference input to the SMES when it is operating as VSG is calculated using equation (1). $Δ ω$ is the frequency deviation and $ω$ is calculated using the concept of centre of inertia (Milano and Ortega, 2017). For NETS $ω_{COI}$ is calculated as

ω_{COINETS} = \frac{Σ_{i = 1}^{9} ω_{i} H_{i}}{Σ_{i = 1}^{9} H_{i}}

where $ω_{i}$ is the $i^{th}$ generator speed and $H_{i}$ is the inertia constant of $i^{th}$ generator.

Network integration

The generators are modeled as current sources in individual reference frame. To perform system studies all generators have to be connected to network. Hence, $v_{q}$ and $v_{d}$ for each generator have to be transformed into a common frame of reference. The relation between individual reference frame (d-q) and common reference frame (D-Q) is given below:

[\begin{matrix} F_{q} \\ F_{d} \end{matrix}] = [\begin{matrix} \cos δ & \sin δ \\ - \sin δ & \cos δ \end{matrix}] [\begin{matrix} F_{Q} \\ F_{D} \end{matrix}]

F represents voltages or currents. Equations (2) is solved and $i_{q}$ and $i_{d}$ are obtained which are given by

[\begin{matrix} I_{q} \\ I_{d} \end{matrix}] = \frac{1}{R_{a}^{2} + x'_{d} x'_{q}} [\begin{matrix} R_{a} & x'_{d} \\ - x'_{q} & R_{a} \end{matrix}] [\begin{matrix} E'_{q} - v_{q} \\ E'_{d} - v_{d} \end{matrix}]

(9)

In common reference frame, $I_{Q}$ and $I_{D}$ are given by equation (10)

\begin{matrix} [\begin{matrix} I_{Q} \\ I_{D} \end{matrix}] = \frac{1}{R_{a}^{2} + x'_{d} x'_{q}} [\begin{matrix} \cos δ & - \sin δ \\ \sin δ & \cos δ \end{matrix}] [\begin{matrix} R_{a} & x'_{d} \\ - x'_{q} & R_{a} \end{matrix}] \\ [\begin{matrix} \cos δ & \sin δ \\ - \sin δ & \cos δ \end{matrix}] [\begin{matrix} E'_{Q} - v_{Q} \\ E'_{Q} - v_{D} \end{matrix}] \end{matrix}

(10)

Equation (10) is a time varying algebraic equation, which increases computational complexity. Hence, dummy coil approach is used and stator equations are rewritten as follows:

v_{q} = E'_{q} + x'_{d} i_{d} - R_{a} i_{q}

v_{d} = E'_{d} - x'_{q} i_{q} - R_{a} i_{d} + E'_{dc}

$E'_{dc}$ is a state variable and is represented by the differential equation given below

\frac{dE'_{dc}}{dt} = \frac{1}{T_{c}} [- E'_{dc} - (x'_{q} - x'_{d}) i_{q}]

Loads are modeled as constant shunt impedences and are clubbed into admittance matrix $(Y_{load})$ . The network is represented by network bus admittance matrix $(Y_{network})$ . The admittance matrix of the generator is given by diag $(Y_{gen 1}, Y_{gen 2}, \dots ., Y_{gen 16})$ where

(Y_{geni}) = \frac{1}{R_{ai} + jx'_{di}}

Complete admittance matrix is given by $Y_{total} = Y_{load} + Y_{network} + Y_{gen}$ . Overall system algebraic equation is given by $I^{-} = Y_{total} V^{-}$

where $V^{-}$ is the vector of bus voltages, $I^{-}$ is the vector of complex current injections and is given by equation (11) when SMES-VSG is connected at bus 8 (SVSGGENBUS):

\begin{matrix} I^{-} = [I_{gen 1} I_{gen 2} \dots (I_{gen 8} + I_{smes 8}) (I_{gen 10}) \\ I_{gen 11} \dots I_{gen 16} 0 \dots 0 \dots . I_{dfig 69} I_{dfig 70}]^{T} \end{matrix}

(11)

Performance evaluation

The test system used in this article is a modified 18 machine, 70-bus system (Figure 1). Two wind farms based on doubly fed induction generators operating in maximum power point tracking (MPPT) mode have been used. The performance of singular and distributed approaches of SMES as virtual synchronous generator is validated. Two cases are discussed: a step wind disturbance and a three phase fault at various buses.

Scenario 1: The wind turbines connected to DFIGs at bus 69 and 70 were simultaneously subjected to a step wind disturbance of type shown in Figure 5. The frequency deviation of NETS and NYPS is shown in Figure 6.

Figure 5.

Step wind disturbance.

Figure 6.

Frequency response under wind disturbance: (a) NETS and (b) NYPS.

The voltages at bus 8, bus 7 and bus 5 are shown in Figure 7 and the following conclusions are drawn:

The improvement in frequency deviation by using distributed approach of VSG (DVSG) is significant in both the areas. Maximum frequency deviation in both areas is 0.009 Hz with DVSG which is very less as compared to frequency deviation of 0.012 Hz which occurs with singular VSG at generator bus (SVSGGENBUS) and singular VSG at load bus (SVSGLOADBUS) and 0.02 Hz which occurs when no VSG is connected. The slope is least with DSVG which indicates ROCOF is minimum with DVSG topology.

The steady state error in NETS and NYPS reduces to 0.006 p.u in case of DVSG, while as it is 0.007 p.u with SVSGGENBUS and SVSGLOADBUS. The steady state error is 0.01 p.u with no VSG.

The improvement in voltage at bus 8, bus 5 and bus 7 with DVSG is clearly visible in Figure 7(a)–(c) respectively. The voltage deviation is comparatively lesser with DVSG than SVSGGENBUS and SVSGLOADBUS. The voltage deviation is maximum when no VSG is connected. Also the peak overshoot at the above mentioned buses after 20 s is significantly reduced with DVSG.

Figure 7.

Voltage (p.u) under wind disturbance: (a) Bus 8, (b) Bus 5, and (c) Bus 7.

Scenario 2: The test system shown in Figure 1 is subjected to three phase fault at various buses.

(a) Three phase fault at bus 20 for 200 ms

An imbalance of electrical power ( $P_{e}$ ) and mechanical power ( $P_{m}$ ) during a fault results in an increase in relative rotor angle $(δ_{ij})$ of synchronous generator. If the increase in relative rotor angle is large, the generator may lose synchronism. During charging SMES draws power from the system to charge SMES coil, as a result of which overall system load increases (Mitra and Chatterjee, 2017). As a result, the accelerating power decreases and then $(δ_{ij})$ also decreases. The overall transient stability of the system increases.

Figure 8(a) and (b) shows the frequency deviation of NETS and NYPS respectively for three phase fault at bus 20.

Figure 8.

Frequency response with three phase fault at bus 20 with fault clearing time of 200 ms: (a) NETS and

It is clear that frequency regulation is significant with DVSG in both areas. The average frequency deviation reduction using DVSG amounts to 85%–90% in NETS and 90%–95% in NYPS in comparison with no VSG.

(b) Three phase fault at bus 25 for 313 ms

Figure 9(a) shows the rotor angle of alternator 8 when three phase fault is simulated at bus 25 which is close to generator 8 for fault clearing time of 313 ms. Generator

Figure 9.

Rotor angle of alternator: (a) 8 with three phase fault at bus 25 for 313 ms, (b) 5 with three phase fault at bus 20 for 371 ms, and (c) 7 with three phase fault at bus 23 for 270 ms.

8 loses synchronism when no VSG is connected, when single VSG is connected at bus 8 (SVSGGENBUS) and single VSG is connected at bus 68 (SVSGLOADBUS). The generator maintains its sysnchronism only when distributed VSG approach is implemented.

Figure 9(b) shows the rotor angle of alternator 5 when three phase fault is simulated at bus 20 which is close to generator 5 for fault clearing time of 371 ms. Generator 5 loses synchronism with all other topologies of VSG except distributed VSG (DVSG) approach.

(d) Three phase fault at bus 23 for 270 ms

Figure 9(c) shows the rotor angle of alternator 7 when three phase fault is simulated at bus 23 which is close to generator 7 for fault clearing time of 270 ms. Generator 7 loses synchronism when no VSG is connected, when single VSG is connected at bus 8 (SVSGGENBUS) and single VSG is connected at bus 68 (SVSGLOADBUS). The generator maintains its sysnchronism only when distributed VSG approach is implemented.

From the cases of faults discussed above, the CCTs of generators 8, 5, and 7 are calculated and shown in the form of bar chart in Figure 10. Figure 10 depicts the comparison of CCTs of generators 8, 5, and 7 for different scenarios of VSG. The CCT of generator 8 increases with DVSG topology by 96 ms as compared with the system with no VSG. The CCT of generator 5 increases with DVSG topology by 140 ms as compared with the system with no VSG. The CCT of generator 7 increases with DVSG topology by 63 ms compared with the system with no VSG. The transient stability measured in terms of CCT improves due to emulation of virtual inertia.

Figure 10.

Variation of CCTs of alternators 8, 5, and 7 for different scenarios of VSG.

Conclusion

In this paper, a comparison is documented on impact and comparison of SVSG and DVSG on a modified 18 machine, 70-bus system. Two wind farms each of capacity 87 MW are connected at bus 69 and bus 70. The inherent dynamic loop of SMES is represented by a first order system. Firstly, a step wind disturbance is considered to verify the impact of SVSG and DVSG on transient stability. Next, a three phase fault is simulated to investigate impact of SVSG and DVSG on transient stability of power system by controlling the active and reactive power. The results show that deviations in frequency and voltage are reduced significantly with distributed Virtual Synchronous Generator approach. Also, the rate of change of frequency is reduced with distributed Virtual Synchronous Generator approach. Moreover, the critical clearing time increases comprehensively by DVSG topology, allowing more time for protection system to respond. The study has been carried out in MATLAB/Simulink platform.

Footnotes

Appendix

SVSG: $L_{sm} = 4 H, I_{sm}^{0} = 20 kA$ , $K_{p} = 7.11$ , $K_{i} = 19.23$ , $K_{I} = 20 MWH z^{- 2}$ , $K_{D} = 8 MWH z^{- 1}$

DVSG: $L_{sm} = 8 H, I_{sm}^{0} = 6 kA$ , $K_{p} = 0.26$ , $K_{i} = 1.30$ , $K_{I} = 6 MWH z^{- 2}$ , $K_{D} = 2.5 MWH z^{- 1}$

$T_{g} = 0.01$ , $K_{C} = 0.001$

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Abdul Waheed Kumar

References

Ahsan

Mufti

(2019) Modelling and stability investigations of an aggregate wind farm – fed multi-machine system. Wind Engineering 44(6): 596–609.

Ali

Park

, et al. (2009) Improvement of wind generator stability by fuzzy logiccontrolled smes. IEEE Transactions on Industry Applications 45(3): 1045–1051.

Alipoor

Miura

Ise

(2015) Power system stabilization using virtual synchronous generator with alternating moment of inertia. IEEE Journal of Emerging and Selected Topics in Power Electronics 3(2): 451–458.

Aouini

Ben Kilani

Marinescu

, et al. (2014) Virtual synchronous generators dynamic performances. In: 2014 International conference on electrical sciences and technologies in Maghreb, CISTEM, Tunisia, 3–6 November 2014, pp.1–6. Tunisia: IEEE.

Bevrani

Ise

Miura

(2014) Virtual synchronous generators: A survey and new perspectives. International Journal of Electrical Power and Energy Systems 54: 244–254.

Driesen

Visscher

(2008) Virtual synchronous generators. In: IEEE power and energy society 2008 general meeting: conversion and delivery of electrical energy in the 21st century, PES, 24–24 July 2008, pp.1–3. Pittsburgh, PA: IEEE.

Guo

Yan

, et al. (2020) Control of vsc-hvdc connected wind farms for system frequency support. International Transactions on Electrical Energy Systems 30(5): e12352.

Hartmann

Vokony

Taczi

(2019) Effects of decreasing synchronous inertia on power system dynamics – Overview of recent experiences and marketisation of services. International Transactions on Electrical Energy Systems 29(12): e12128.

Hasanien

Member

Muyeen

, et al. (2012) Design optimization of controller parameters used in variable speed wind energy conversion system by genetic algorithms. IEEE Transactions on Sustainable Energy 3(2): 200–208.

10.

Iqbal

Mufti

Lone

, et al. (2009) Intelligently controlled superconducting magnetic energy storage forimproved load frequency control. International Journal of Power and Energy Systems 29(4): 241–254.

11.

Karapanos

de Haan

SWH

Zwetsloot

(2015) Testing a virtual synchronous generator in a real time simulated power system. In: International conference on power systems transients (IPST2011), 14–17 June 2011. Available at: https://www.researchgate.net/profile/SWH_Haan/publication/265281706_Testing_a_Virtual_Synchronous_Generator_in_a_Real_Time_Simulated_Power_System/links/54e763000cf2cd2e0293f13d/Testing-a-Virtual-Synchronous-Generator-in-a-Real-Time-Simulated-Power-System.pdf.

12.

Kerdphol

Rahman

Mitani

, et al. (2017) Virtual inertia control-based model predictive control for microgrid frequency stabilization considering high renewable energy integration. Sustainability 9(5): 773.

13.

Kerdphol

Watanabe

Mitani

, et al. (2019) Applying virtual inertia control topology to SMES system for frequency stability improvement of low-inertia microgrids driven by high renewables. Energies 12(20): 3902.

14.

Kundur

Balu

Lauby

(1994) Power System Stability and Control. New York: McGraw-Hill.

15.

Zhu

Lin

, et al. (2017) A self-adaptive inertia and damping combination control of VSG to support frequency stability. IEEE Transactions on Energy Conversion 32(1): 397–398.

16.

Milano

Ortega

(2017) Frequency divider. IEEE Transactions on Power Systems 32(2): 1493–1501.

17.

Mitra

Chatterjee

(2014) Stability enhancement of wind farm connected power system using superconducting magnetic energy storage unit. In: Eighteenth national power system conference, NPSC, 18–20 December 2014, Guwahati, India: IEEE.

18.

Morren

de Haan

Kling

(2006) Wind turbines emulating inertia and supporting primary frequency control. IEEE Transactions on Power Systems 21(1): 433–434.

19.

Naik

Nair

NKC

Swain

(2016) Impact of reduced inertia on transient stability of networks with asynchronous generation. International Transactions on Electrical Energy Systems 26(1): 175–191.

20.

Padiyar

. (1996) Power System Dynamics: Stability and Control. New York: John Wiley.

21.

Pal

Chaudhuri

(2006) Robust Control in Power Systems. London: Springer Science and Business Media.

22.

Sheikh

MRI

Nasiruzzaman

ABM

(2009) Transient stability enhancement of wind generator by PWM voltage source converter and chopper controlled SMES unit. Journal of Scientific Research 1(2): 226–235.

23.

Syed

Mufti

(2018) Automatic generation control of a wind embedded two-area power system, interconnected through AC/DC transmission system. International Journal of Industrial Electronics and Drives 4(4): 189.

24.

Wang

Meng

Zhang

, et al. (2015) Control of PMSG-based wind turbines for system inertial response and power oscillation damping. IEEE Transactions on Sustainable Energy 6(2): 565–574.

25.

Zargar

Mufti

Lone

(2017) Adaptive predictive control of a small capacity SMES unit for improved frequency control of a wind-diesel power system. IET Renewable Power Generation 11(14): 1832–1840.