Steady‐state operating points of islanded virtual synchronous machine microgrid

Before starting stability analysis of the multivirtual synchronous machine (n‐VISMA) power system, it is necessary to obtain the steady‐state operating points (SSOPs) of all dynamic nodes in the network. Modified traditional iterative schemes using the concept of droop bus technique in an islanded microgrid are not feasible for load flow analysis of VISMA microgrid incorporating non‐control dynamics. This paper proposes closed‐form steady‐state, fundamental‐frequency models for islanded VISMA microgrids using the concept of virtual swing buses. In this technique, the virtual internal buses of all VISMAs in the network are governed by the swing equation. The voltage at all buses is variable except the virtual buses in which the pole wheel voltages are prespecified. The algorithm was extended by a droop control localized to each VISMA. The suitability of the proposed algorithm to obtaining SSOPs of VISMA was tested on IEEE‐9 bus system with VISMA replacing electromechanical synchronous machines and also on a low‐voltage distribution system. To validate the applicability of the proposed algorithm and prove its accuracy, the case study systems were also modeled in the SIMULINK environment for detailed time domain analysis. The algorithm was found to be computationally effective for a load flow analysis of the VISMA microgrid. The results also reveal that the addition of external droop control improves the frequency stability of the system.


| INTRODUCTION
The conventional electromechanical synchronous machine (ESM) has been at the forefront of electrical power generation, and they are characterized by the ability to provide excellent inertia and damping responses, which guarantees stability of the grid frequency and regulate the power imbalance in the system. 1 In recent years, there has been a rapid penetration level of distributed generation (DG) into the power system and this has led to the evolution of microgrid.Microgrid can operate in either stiff or islanded mode.When the grid is stiff, slack bus is able to keep the system frequency constant by appropriately injecting or absorbing active power needed into or from the system, whereas, in islanded mode, stability of the network frequency is not ascertained due to the absence of the slack bus.In any of these modes, the objective is to ensure the stability of the power system. 2 Decentralized droop control of DGs is widely used in inverter-based autonomous microgrid to regulate the power flow according to the local information with no need of communication.An ideal droop control should be able to provide fast and accurate power sharing without affecting voltage and frequency at the point of common coupling (PCC). 3,4The inaccuracy of power sharing is a classic problem associated with droop control when an islanded AC microgrid suffers from high loads and line impedance differences.It degrades system performance and even destroys system stability. 5,6][9][10] When the network is perturbed due to events such as load variations, generation dispatch changes or regulator switching, the system frequency might change sharply, exceeding the df/dt threshold and resulting in the tripping of generation or unnecessary load shedding.To improve the stability of the system frequency, Virtual Synchronous Machine (VISMA) was proposed. 11VISMA have the capability to reproduce the static and dynamic properties of conventional ESM on a power electronic interface in a more rapid way.
From 2007 to now, different topologies of VISMA technology also called Virtual Synchronous Generator 12 have been proposed in literature.Some of these implementations are: Simplified VISMA configuration based on the current-voltage (voltage-current) model of ESM, 2 Synchronverter, 13,14 OSAKA, 8,15 Kawasaki Heavy Industry, 16,17 VSYNC, 18 Cascaded Virtual Synchronous Machine, 19,20 and Synchronous Power Controller. 21,22mong all these suggested models, the simplified voltage-current abc VISMA (SVI-VISMA) model stands out as it is highly stable on the grid network, uses a simple hysteresis current controller, reduced computation and implementation effort on the process computer, and synchronizes well with the grid without the need to employ the services of nonlinear phase locked loop and is thus the model of consideration in this article.
The introduction of VISMA and droop control schemes in Inverter-Based Generation (IBG) brings along some technical and analytical challenges in the formulation of power flow solutions for islanded microgrid (IM).Power flow studies play an important role in the planning, expansion and optimal operation of power systems. 23It is useful in obtaining the steady-state operating points (SSOPs) of all buses in the multimachine power system. 24However, the conventional means of iterative solution like Gauss-Siedel and Newton-Raphson are not suitable for load flow analysis of an islanded microgrid because of the absence of slack buses.The line reactance is not constant but varies with the system frequency. 25,26Quite a number of analytical models have been developed to study the power flow characteristics of IM.Load flow analysis in IM was formulated in Kamh and Iravani 27 and Nikkhajoei and Iravani 28 using the traditional iterative method.The authors failed to consider the operational behavior of IM with decentralized droop control but rather considered the DG bus with maximum capacity as the swing bus and the other buses as either power voltage (PV) or PQ buses.This assumption is not practicable as the DG units are generally of micro sources and none have the capability to act as an infinite bus to hold the network frequency and its local voltage constant.0][31] These methods have high computational efficiency and good solution accuracy, but they are only suitable for radial distribution and weakly meshed systems with singular power sources and could be subjected to convergence issues when used in multisource microgrids. 3This method also considers a slack node and other nodes as PQ nodes which is an invalid assumption in IM.As mentioned in Mumtaz et al., 32 their application is limited to grid-connected systems and cannot be directly applied to DG with droop characteristics.
Droop bus technique was introduced (see Figure 1A) in addition to the conventional PV and PQ buses 3,23,26,32,33 for load flow solution of an IM taking into account the droop characteristics of the DGs.In Abdelaziz et al., 3 a generalized 3 − φ power flow algorithm for IM using globally convergent Newton trust method was suggested.This algorithm solves sets of nonlinear equations and requires the calculation of the Hessian matrix in addition to the Jacobian matrix and this makes the computation very complex.This method in Abdelaziz et al. 3 is highly sensitive to the initial settings of problem variables. 34An improved modified Newton-Raphson method for load flow was suggested in Hesaroor and Das. 33It proposes to extend the traditional Newton-Raphson technique to the IM case with complex loads.A number of models have also been developed from the angle of evolutionary algorithms that are unconstrained with the initial values of the problem variables.Elrayyah et al. suggested a power flow technique for droop-based IM using the concept of particle swarm optimization (PSO) to select the voltage droop parameters that optimizes reactive power sharing among the DGs for all loading conditions. 35Though the model of Elrayyah is effective and allows for stability testing of the microgrid, it does fail to calculate active power sharing among the DGs.Guaranteed convergence PSO with Gaussian mutation was proposed in Esmaeli et al. 34 However, the performance of metaheuristic techniques depends on the selection of parameters.Homotopy-based method to provide solution to load flow of droop-controlled IM is presented in Lima-Silva et al. 36 The droop bus models discussed in the last paragraph are only valid for DGs that incorporate droop control schemes and cannot provide complete SSOPs of the SVI-VISMA model especially when in its natural state.SVI-VISMA in its natural state does not implement a governor and hence does not actuate a primary frequency control but nevertheless, an external droop controller can be added.This variant of VISMA is implemented using the electromechanical model of conventional ESM and it was developed by the same research institute (i.e IEE TU Clausthal) that invented the maiden two-axis VISMA model which completely emulates the behavior of ESM. 37SVI-VISMA has an inherent droop characteristic and possesses the capability to maintain network synchronization without externally added droop control.
This paper proposes a novel virtual bus technique based on the principle of swing equation to obtain the SSOP of all dynamic nodes in the IM with 100% SVI-VISMA (see Figure 1B).This proposed concept employs the use of constant amplitude of virtual excitation and virtual torque localized to each VISMA unlike the droop bus approach that uses active and reactive power coefficients as major constant control parameters.
The proposed load flow technique for VISMA microgrid further considers the following conditions: 1.The steady operating points of buses are independent of the characteristics of the interface power electronic converter, distributed energy resources and network filter.2. There is no slack bus, so any bus on the islanded (SVI-VISMA) microgrid system could serve as a reference bus.The voltage at all buses is variable except the virtual buses in which the pole wheel voltages are prespecified.The system frequency is global and also a variable.3.All (SVI-VISMA) buses are governed by swing equation.Either the terminal bus or the internal bus could act as the "virtual swing bus."Note that the designated virtual swing bus here does not have the capability to maintain system frequency.If the internal bus is taken as the virtual swing bus, then the active and reactive power at the terminal bus is determined by considering the active and reactive losses in the virtual stator.4. VISMA internal bus cannot be classified as slack, PV, or PQ buses since the parameters are not prespecified, though the pole wheel voltage is known but the active power P, Q, and pole-wheel angle on the bus is not known but to be determined via iterative scheme.
The obtained load flow solution is useful in the steady stability analysis of this variant of VISMA.The usual question about whether IBG can effectively replace the traditional generation scheme is also answered in this research work.The effectiveness of the proposed algorithm is validated by comparing the results obtained with that obtained from time domain analysis using SIMULINK.
The organization of this paper is as follows: Microgrid system modeling is presented in Section 2. In Section 3, the problem formulation and the proposed power flow method are presented.Validation results are provided in Section 4 to show the effectiveness and accuracy of the proposed method.Conclusions are drawn in Section 5.
F I G U R E 1 Steady-state operating points models for islanded microgrid.(A) Existing droop bus technique 3,23,26,32,33 and (B) proposed virtual swing bus model.PCC, point of common coupling.MODELING

| Static load modeling
A static load model describes the behavior of loads at any point in time as algebraic functions of system frequency and load bus voltage at that instant.The active power P and reactive power Q delivered to the load are represented independently by the following frequencydependent load model 38,39 : where ∆w is the angular frequency deviation w w ( − ) o , P Lo i , and Q Lo i , are the active and reactive power at initial SSOPs, U o is the nominal voltage, K K and pf qf are frequency sensitivity parameters, and, respectively, ranges between 0-3.0 and −2.0 to 0, respectively. 3The exponent values for different categories of loads are given in Mumtaz et al. 23

| Network modeling
In an IM, Y bus is the network admittance matrix and is not constant because the system frequency is also not fixed.Therefore, for a system with N buses (virtual buses inclusive), Y bus is defined as follows: VISMA is a class of grid-forming inverter that mimics the behavior of ESM on the grid.As a result of the energy storage connected to the DC side of the VISMA, it can be made to work in a full fourquadrant mode and its alternating voltage side thus corresponds to the stator output of ESM shown in Figure 2.
The machine electrical equations are as defined below; where E I U ⃗ , ⃗ , and ⃗ t are VISMA virtual internal node voltage vector, vitual stator current space vector and stator terminal voltage space vector, respectively, and are expressed as follows: VISMA terminal voltage.The per phase reference voltage is determined based on (6) as follows: ) e p is the amplitude of the pole wheel voltage.The resistance R and inductance L matrices for the virtual stator are given by (7): where r s and L s are the per phase resistance and per phase inductance, respectively.In the Laplace domain, (4) can further be expressed as follows: F I G U R E 2 Per phase equivalent circuit of VISMA stator.VISMA, virtual synchronous machine.
KAMILU and BECK where Y s ⃗ ( ) is the virtual admittance matrix and is defined in (9): The complex power delivered to the internal bus i of VISMA shown in Figure 2 is given as 40,41 where P G i , and Q G i , are the active and reactive power delivered to the internal virtual bus of VISMA i. P G i , and , are obtained as follows 42 : where δ δ δ = − ij i j is the power angle difference between the virtual bus and its corresponding terminal bus, i* i is the conjugate of the stator current from VISMA i, while Z ij and φ i are the magnitude and the phase of the virtual stator impedance, respectively.Using 43 Equations (11) and ( 12) are transformed to ( 13) and ( 14) as follows: Equations ( 13) and ( 14) are also reduced to ( 15) and ( 16) as follows: Independent control of P G and Q G is possible if we assume the virtual stator is purely inductive, so that  R 0 ij .If δ ij is small, then we can assume that δ δ sin = ij ij and cos δ = 1 ij so that, ( 15) and ( 16) become where x d ij , is the virtual reactance.It is clear from (17) that active power injected into the VISMA bus is dependent on the power angle while reactive power is dependent on the voltage amplitude difference.Since the stator is purely inductive, it implies that there is no active power drop between the internal bus and the terminal of the VISMA but there exists reactive loss.

P G i
, and Q G i , injected at the terminal bus can be proved in a similar way and in that case the complex power injected at the VISMA terminal bus 2 of Figure 2 would be From the solution of ( 10) and ( 18), the reactive loss in the virtual stator can be derived as 24,44 ( )

| Mechanical characteristics
Swing equation describes the rotor dynamics of VISMA and it is central to obtaining SSOP.Any unbalanced torque acting on the virtual rotor will result in the acceleration or deceleration of the rotor depending on whether load is reduced or added to the network.Aside using swing equation for power balancing in the network, VISMA also uses it to mimic the inertia response of ESM.The complete equation of motion for the virtual mechanical part of the VISMA with the virtual angular rotor position measured with respect to synchronously rotating reference frame per unit 20,45,46 is described as follows: Figure 3 is the block diagram representation of VISMA without excitation control and governor dynamics.The virtual bus is designated with a red line in Figure 3.

| PROBLEM FORMULATION
Generally, DGs are modeled as PV or PQ buses in the grid grid-connected system but is impossible in IM to operate all DGs in PQ or PV mode because of the absence of a slack bus.In an IM, DGs are modeled in three modes, that is, PV, PQ, and droop. 3,23,33,47However, there is an exemption as it is not all DG buses that can be modeled as droop buses.VISMA has an inherent natural droop characteristic and can work without externally added droop.The load flow analysis of the VISMA microgrid in this paper is however based on this natural droop which is later extended to accommodate the artificial droop control.It is assumed in this work that all the DGs are VISMAs.The formulation of the proposed algorithm involves two steps, first solving the load flow like the conventional Gauss-Siedel.The system frequency is initialized as 1.0 pu, and is recalculated in each step of the iteration.The voltage at all buses are also initialized to 1.0 pu.It is worth nothing that an arbitrary reference bus is selected with zero reference angle.The voltage U i at bus i can be determined by using the following iterative voltage equation. 48,49 For PV buses, net injected reactive power is evaluated based on the iterative voltages U ⃗ i k+1 and using the following expression: where is the new value of the iterated voltage at bus i, U  and j, respectively, Y ⃗ ij is the admittance between buses i, and j, P i and Q i are the scheduled active and reactive power at bus i and Y ⃗ ii is the self-admittance at bus i.For PV buses, Q is determined from (24) while the angle is determined from the complex voltage in (23).For VISMA internal bus, bus voltage is prespecified as the amplitude of the pole wheel voltage e p , in this case the pole wheel angle is determined by keeping the iterative angle in (23) and discarding the iterative voltage.The VISMA internal buses are variable frequency dependent, so P and Q injections are obtained iteratively using the following expressions: Figure 4 depicts a functional flowchart for the proposed algorithm.If there are m VISMAs in the network of system frequency, w then the total number of variable vectors X to be determined is given by Network frequency is global and an important parameter that is required in each step of the iteration until program convergence is achieved.At steady state, there is no acceleration of the virtual rotor, so from (20)  and the active expression in (17), the rotor angles are obtained as follows: The total active power generated at steady state is thus For N bus systems, the total active (P loss ) and reactive (Q loss ) losses are calculated as follows 32,50 : The total active power (P total ) and reactive power (Q total ) injected by the VISMAs at the virtual buses are defined as follows 32,45 : + , total load loss total load loss (31)   where P load is the total active power load demand and Q load the total reactive power load demand.
The classical model sometimes refers to the one in which damping is ignored (i.e., K d pu i , , = 0), but here we consider F I G U R E 4 Functional flowchart for virtual swing bus algorithm.
damping effects explicitly, as they can have a nonnegligible effect on the stability of steady-state power grid operation and can potentially be used as tunable parameters for optimizing the stability and most valuably updating the system frequency. 51In an electrical power system, frequency is a global variable, and hence all VISMAs in the network are expected to inject active power at the same angular frequency.By eliminating, P total in ( 31) and ( 29), the following iterative expression can be derived.

| Model extension with externally added droop
Equation ( 17) reveals that angle δ can be controlled by regulating P, and VISMA virtual bus voltage E is controlled by regulating Q.Control of the w dynamically controls the power angle and, thus, the active power flow.By adjusting P and Q independently, frequency and amplitude of the grid voltage are determined.Equation ( 17) forms the basis for the following conventional droop equation 52,53 : where P mo and P* m are the set and adjusted operating points of the virtual mechanical power input to the VISMA.E c , Q o i , , K p , and K q are the controlled virtual bus voltage, reactive power set point, active, and reactive droop coefficients, respectively.
Considering the steady operation of VISMA, ( 33) and ( 20) are combined to obtain the following iterative expression for the rotor angle of the VISMAs: Frequency update and virtual excitation voltage with external droop addition in the form of an iterative scheme are obtained as follows: ( ) 35) and (36), then ( 28) and ( 32) are, respectively, obtained.Also, if K = 0 qi in (37), then E E = ci .This substitution means that the VISMA microgrid model without power and excitation control dynamics is easily obtainable from that with external droop extension.The load flow solution is completed when the difference between the new estimate and the previous estimates falls within an acceptable limit F I G U R E 5 IEEE-9 bus VISMA microgrid with extended virtual buses.IEEE, Institute of Electrical and Electronics Engineers; VISMA, virtual synchronous machine.PROPOSED ALGORITHM To validate the applicability of the proposed algorithm and prove its accuracy, two case systems have been considered.These systems were also modeled in a SIMULINK environment for detailed time domain analysis.To effectively analyze VISMA operations on these networks, additional virtual buses are introduced.These buses are equivalent to the internal nodes of the conventional ESM on the network.With respect to inverters, right amount of active power at the PCC necessary for frequency stability depends on the composition of loads on the network, and as such constant power load (CPL) and constant impedance load (CZL) have been considered for the analysis.
Case study 1: The first system is an IEEE-9 bus standard network designed to operate as an island microgrid.For the purpose of the analysis, the buses are labeled as shown in Figure 5, that is, each bus number is shifted up by 3 when compared with the standard IEEE-9 bus system.The virtual buses of VISMA 1, VISMA 2, and VISMA 3 are numbered 1, 2, and 3, respectively.The parameters for the VISMAs in Figure 5 are given in Table 1 while the line and load bus parameters are obtainable in Vittal et al. 54 The validation here is in two categories.In the first category, the algorithm is used with constant excitation and constant T A B L E 1 VISMA parameters for the IEEE-9 bus system.T A B L E 2 Voltage and angle profile of IEEE-9 bus VISMA microgrid with CPL and no external droop control.

Bus
No.

Bus description
Original IEEE (grid tied) Voltage, V Voltage, V torque.Table 2 shows the performance of the proposed algorithm with that of the time domain simulation, and the generic standard grid-tied method obtained in Vittal et al. 54 for a CPL at all load buses.Table 3 shows the load flow results when all the load buses are of CZL.The average valued error of the voltage magnitude and phase angle of the proposed algorithm with respect to the time domain method are, respectively, 0.00083% and 0.005% for CPL and 0.0% and 0.00083% for CZL (see Table 12).These results demonstrate an excellent performance of the proposed load flow algorithm for islanded mode operation of microgrids based on a virtual swing bus.The steady-state frequency obtained by the proposed algorithm is shown in the respective table of results.Table 4 shows the values of active and reactive power generated by the VISMAs.
In the second category, the algorithm is used with an added external droop control.Equal values of static droop coefficients have been used for all VISMAs, that is, K = 0.03 p and K = 0.02 q .Tables 5 and 6, respectively, illustrate the performance of the algorithm for CPL and CZL in comparison with time domain values.The average valued error of the voltage magnitude and phase angle of the proposed algorithm with respect to the time domain method are, respectively, 0.0033% and 0.00083% for CPL and 0.0025% and 0.01% for CZL.These results reveal a good performance of the proposed algorithm for an IM.The active and reactive power generated by VISMAs are presented in Table 7.The total power generated by the VISMAs and the total load demand and losses of the system for both categories of case study 1 are shown in Table 8.According to Table 8, when the frequency deviation is the same among units, that VISMA with a high capacity can produce more power to microgrid. 34Tables 7 and 8  of relationships between frequency deviation and active power sharing among VISMAs.
Figure 6 demonstrates that minimal losses occur on the IEEE-9 bus VISMA microgrid when external droop control is added.The benefit of external droop is corroborated by the result shown in Figure 7 which show that frequency stability of the system improves when local droop control is added external to each VISMA.Figure 8 illustrate the voltage profile for both categories of system case study.CPL_droop and CZL droop, respectively, define CPL and CZL when external droop control is added to natural VISMA.
Figure 8 is the schematic voltage profile representation at the VISMA for different load types and controls.The plot shows that voltage at the system buses is negatively impacted when external droop control is added.The level of impact may however be reduced by using lower size of droop coefficients. 55igure 9 demonstrates the synchronization of the three VISMAs on the grid at a unified system frequency.The transient and steady-state behaviors of the VISMAs are also illustrated, respectively, in Figures 10 and 11 for active and reactive power injections at the virtual buses.Case study 2: The second system is a low-voltage (LV) distribution system (Figure 13).The base power and base line voltage are, respectively, 1000 W and 220-V LL .The parameters for the VISMAs and the lines are as given in Table 9. Proportionate equal static droop coefficients used are given in Table 9.To simplify the analysis, only CLZ type was considered at the load bus.Table 10 gives the voltage and angle profile in each bus.Values of the generated power as well as the power demands and losses of system are presented in Table 11 for the algorithm with and without external droop control.The   F I G U R E 10 Active power injection at the virtual buses.VISMA, virtual synchronous machine.
F I G U R E 11 Reactive power injection at the virtual buses.VISMA, virtual synchronous machine.
steady-state frequency obtained by the proposed algorithm for without control is 0.9999 pu and with control is 0.999953 pu which also consolidate on the capability of external droop to enhancing system frequency stability.The average valued error of the voltage magnitude and phase angle of the proposed algorithm with respect to the time domain method are given in Table 12.According to Table 12, the average valued error in IEEE-9 bus system is quite lesser compared to those obtained in the LV system.This is simply because IEEE-9 bus system is highly inductive as compared to the LV system with low X/R ratio.When X/R is high, both the active power and reactive power are efficiently decoupled.

| CONCLUSION
This paper presents a new SSOPs algorithm for an islanded VISMA microgrid using the concept of a virtual swing bus.Since the network admittance matrix is not constant due to the absence of a slack bus, grid frequency is calculated in each step of the iteration.The proposed concept employs the use of constant amplitude of virtual excitation and virtual torque localized to each VISMA for load flow formulation.The proposed algorithm has been tested on the IEEE-9 bus system with all the ESM replaced with VISMA equivalents and also on the LV system for performance authentication.The algorithm was extended with an external power controller to allow for full flexibility of operation.The average value error of the proposed algorithm with respect to the time domain simulation (shown in Table 12) demonstrates an excellent performance of the proposed load flow where H = equivalent moment of inertia of rotating mass in second, M = mech pu , virtual shaft torque input to VISMA in pu, K = d pu , virtual damping torque constant in pu, w = r pu , angular frequency in mechanical rad/s, θ = m rotor mechanical angular position in rad, w = s pu , synchronous speed in pu, w = b base speed in electrical rad/s, δ = rotor angular position measured with respect to synchronous axis in rad.
⃗ i k and U ⃗ j k are the magnitudes of voltages at buses i, F I G U R E 3 Block diagram representation of VISMA.VISMA, virtual synchronous machine.
highlight the importance KAMILU and BECK | 2229

Figure 12 demonstrates
Figure 12 demonstrates the stationary operating points of the rotor angle for the VISMAs.Case study 2: The second system is a low-voltage (LV) distribution system (Figure13).The base power and base line voltage are, respectively, 1000 W and 220-V LL .The parameters for the VISMAs and the lines are as given in Table9.Proportionate equal static droop coefficients

F I G U R E 7
System frequency for IEEE-9 bus VISMA microgrid for different load type.CPL, constant power load; CZL, constant impedance load; IEEE, Institute of Electrical and Electronics Engineers; VISMA, virtual synchronous machine.

F I G U R E 8
Voltage profile for different load types and controls.CPL, constant power load; CZL, constant impedance load.

F I G U R E 9
System frequency.VISMA, virtual synchronous machine.

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I G U R E 12 Rotor angle stationary operating points.VISMA, virtual synchronous machine.

F
I G U R E 13 Two VISMA low-voltage models.VISMA, virtual synchronous machine.

T A B L E 9
Parameters for the two-system low-voltage model.
Voltage and angle profile of IEEE-9 bus VISMA microgrid with CZL and no external droop control.Power generated by the VISMA in IEEE-9 bus VISMA microgrid for constant excitation and constant torque.Voltage and angle for IEEE-9 bus VISMA microgrid with CPL and external droop.
Abbreviations: CPL, constant power load; IEEE, Institute of Electrical and Electronics Engineers; VISMA, virtual synchronous machine.T A B L E 3Abbreviations: CZL, constant impedance load; IEEE, Institute of Electrical and Electronics Engineers; VISMA, virtual synchronous machine.T A B L E 4 T A B L E 6 Voltage and angle for IEEE-9 bus VISMA microgrid with CZL and external droop.
Abbreviations: CZL, constant impedance load; IEEE, Institute of Electrical and Electronics Engineers; VISMA, virtual synchronous machine.T A B L E 7 Power generated by the VISMAs in IEEE-9 bus VISMA microgrid with droop control.Abbreviations: CPL, constant power load; CZL, constant impedance load; IEEE, Institute of Electrical and Electronics Engineers; VISMA, virtual synchronous machine.T A B L E 8 Total terminal power generated, demands and losses for IEEE-9 bus VISMA microgrid.Abbreviations: CPL, constant power load; CZL, constant impedance load; IEEE, Institute of Electrical and Electronics Engineers; VISMA, virtual synchronous machine.F I G U R E 6 Losses on the IEEE-9 bus VISMA microgrid for different load type and control.CPL, constant power load; CZL, constant impedance load; IEEE, Institute of Electrical and Electronics Engineers; VISMA, virtual synchronous machine.