Multi-Objective Optimal Planning of Virtual Synchronous Generators in Microgrids With Integrated Renewable Energy Sources

Appropriate renewable distributed generation (RDG) placement is one of the most significant issues for the efficient operation of current power systems. Since the inverter-interfaced RDG lacks rotating mass to sustain the system’s inertia, microgrids have low total system inertia, which impairs frequency stability and can yield significant frequency and voltage instability in severe disruptions. The virtual synchronous generator (VSG), which uses concepts that regulate the inverter to simulate a conventional synchronous generator, is one of the most promising solutions to address these challenges. Hence, this research proposes a unique technique of simultaneous optimal solution for RDG and VSG sizing and placement in distribution networks using a recent metaheuristic technique called the Multi-objective Salp Swarm Optimization Algorithm (MOSSA). The objective function was to minimize the frequency deviation and maximize the total annual energy savings and operational costs of the RDG and VSG units. This study assesses IEEE 33 bus, 69 bus distribution network, and practical Masirah network as the test systems. Moreover, the MOSSA Pareto fronts are superior to two recent metaheuristics employed in this research domain: Multi-objective Particle Swarm Optimization (MOPSO) and Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The results demonstrate that the MOSSA Pareto fronts satisfied the frequency and energy-saving objectives. In addition, all Pareto fronts accurately prevented voltage limit infringements, and the overall energy losses were significantly reduced.


I. INTRODUCTION
Due to the rising adoption of renewable energy sources (RES), the energy distribution architecture is gradually transitioning from consolidated conventional power generation to distributed energy production. Recent years have seen a significant increase in integrating distributed power production units based on RES [1], [2]. The optimum utilization of renewable energy sources is facilitated by digitally controlled power electric converters or inverters that enhance the power systems' flexibility by offering a swift transient performance.
In contrast to conventional power generating units, where synchronous generators (SG) use their rotational momentum to offer frequency support during disturbances, renewable systems can assist in frequency support by contributing virtual inertia via electronic inverters [3]. Nevertheless, RDGs electronically connected to the grid or power systems exhibit different traits from traditional power-producing units. Electronic inverters control the power generated at interfaced RDGs; however, they cannot provide the necessary inertia and damping to the power grid. Inverter-based distributed generation is often controlled via grid-connected current control. However, this approach has a variety of drawbacks, including the inability to operate independently and frequency instability that inhibits the expansion of RES penetration [4]. The solution to this challenge, however, is devised by applying appropriate control techniques to the grid-connected inverter and managing its switching pattern such that it operates as an SG by replicating the behavior of a conventional SG. In this context, VSGs are introduced, known as grid-connected inverters that imitate the steady-state and transient properties of SG [5], [6], [7]. VSGintegrated systems are expected to represent the future of power system networks. Therefore, it is critical to analyze and enhance the transient stability of VSG-based power systems.
Numerous studies have been conducted in recent years to investigate the potential benefits and drawbacks of VSG implementation on microgrids. For example, the droop control [8] approach was developed to modulate real and reactive power using a paradigm comparable to the parallel operation of synchronous machines; however, it was unable to completely address the problems of low inertia and frequency stability of microgrids. The virtual synchronous generator (VSG), which uses concepts that regulate the inverter to simulate a conventional SG, is one of the most promising solutions in this research domain [9]. A thorough explanation of the VSG structure was offered in the works of [10], along with an overview of several topologies for virtual inertia and VSG control, including active power allocation, reactive power allocation, voltage control, and frequency regulation. The issues with VSG and potential avenues for future study were also explored, including centralized control, stability improvement, and interfacing for VSG.
Furthermore, several studies have used optimization techniques to investigate the potential benefits and restrictions of implementing VSG on electrical grids. For example, in the works of [11], the dynamic stability of several grid-connected voltage source converters controlled by VSG was investigated with active power control. Besides, the design approaches for a multi-VSG damping controller based on a hybrid particle swarm optimization technique and residue index were considered. Numerous simulations and test cases of the multi-VSG grid-connected system were conducted to demonstrate the efficiency of the damping controller design method. Furthermore, in [12], the authors proposed a self-adaptive VSG active power control strategy using fuzzy logic-based genetic algorithms to create specific fuzzy rules with the allocation of distributed generation units and frequency deviation as input parameters. The results show minimal frequency deviation based on constant inertia parameters. Besides, the study in [13] used two objective function functions to create an ideal VSG active power control scheme using particle swarm optimization (PSO). The first objective was to minimize the integral time absolute error, and the second objective considered the frequency deviation of the grid. In the works of [14], PSO is used to investigate how VSG affects reducing voltage drop and power fluctuations and restricting the maximum fault current of distribution lines. Moreover, in the works of [15], a novel trustworthy metaheuristic optimization method known as the artificial hummingbird algorithm (AHA) is used to fine-tune the parameters of the proposed VSG controller by constructing the load frequency control based on a two-area linked power system, the suggested AHA is superior to other potent optimization strategies as the marine predators' algorithm, grey wolf optimizer, and artificial bee colony optimization. Moreover, in the works of [16], the authors utilized a proportional-integral (PI) controller that had been ideally built using the manta ray foraging optimization algorithm as the foundation for controlling the virtual inertia control loop. The effectiveness of the MRFO-based PI controller was examined in light of various operating situations and contrasted with that of conventional PI controllers based on evolutionary optimization algorithms. Moreover, by improving the settings of the virtual inertia controller while taking into account VSG dynamics and the uncertainties of system inertia, a whale optimization technique is utilized to improve the virtual inertia control loop [17]. Furthermore, to fine-tune the settings of the aforementioned VSG controller, a unique sine augmented scaled arithmetic optimization approach is suggested in the works of [18]. Using simulation results, the usefulness of the suggested technique is verified, and the effects of a few common tactics, such as a change in system boundaries and different stages of RESs penetration, are also demonstrated. Likewise, the authors of the work [19] developed the combined whale and the ant lion algorithm. The study aimed to improve the grid voltage and frequency affected by the variations of inertia.
Moreover, achieving the global minimum of an RDG placement and sizing function is much more complex, and numerical solution methodologies often allude to substantial problems; the researchers employed a variety of multi-objective frameworks. For example, a multi-objective optimization approach was created by the authors of the study [20] in order to maximize the use of RESs while minimizing the cost of energy and the likelihood of an energy supply breakdown. Moreover, MOPSO was utilized for three different energy system designs in works of [21] with the objectives of cost minimization and voltage stability maximization. Furthermore, a multi-objective algorithm was created in the works of [22] to determine the optimal placement of RDG units for Turkey by considering financial, environmental, and technical characteristics. Besides, the study cited in [23] investigated the size and position of wind turbine (WT) and photovoltaic (PV) units in distribution networks using chaotic sequence spotted the hyena optimizer technique to reduce loss and improve the voltage profile and stability index. Furthermore, the study in [24] proposed a novel metaheuristic approach employing the AHA technique to find the proper locations and sizes of biomass-based RDGs in radial distribution networks by reducing the switching frequency and total system energy loss. Besides, the authors of the paper [25] presented symbiotic microorganism exploration algorithm for RDG placement in microgrids for different test systems. Moreover, the work in [26] guaranteed the homogeneity of the Pareto fronts and advocated an improved NSGA II. Furthermore, the work in [27] suggests a multi-objective equilibrium optimizer-based technique that includes several objectives, including reducing the operation and investment costs, energy pricing, power loss penalties, and carbon emissions penalties for the integrated units.
The researchers have contributed by developing the multi-objective model for the ideal size, placement, and type of RDG units utilizing various heuristic or stochastic methods. However, the solutions found cannot be guaranteed to be globally optimum. For example, to maximize the real power loss and the yearly expenses of system components, the multi-objective slime mould algorithm was utilized in [28]. Similarly, the work in [29] suggested a unique chaos pupil sociology and anthropology optimization algorithm for locating RDG units considering the stochastic generation pattern. Furthermore, to upgrade the RDG-based storage systems, the authors of [30] employed a thorough evaluation of RDGs using a linear modeled optimization algorithm. Additionally, to expand the penetration of RDG systems, the study's authors created a hybrid system model based on a grid-connected discrete harmony search algorithm [31]. Similarly, the research in [32] offered a multi-temporal optimal power flow approach that guaranteed accurate and optimal solutions with higher performance utilizing the convex power flow method. Moreover, the study in [33] suggested a combination model using a binary programming-based optimization approach to enhance RDG penetration. Likewise, the study in [34] developed the multi-objective multi-verse approach for the RDG allocation challenge in microgrids to enhance voltage profiles and reduce yearly expenses. Furthermore, in [35], optimal allocation issues of RDGs were resolved using a meta-heuristic algorithm coupled with a stochastic model known as monte carlo simulation. Besides, a planning strategy for the best RDG size and control was developed in [36] to reduce the curtailment from RDGs. Additionally, to estimate the ideal size of RDGs for a residential house, the authors of [37] suggested a stochastic optimization problem using mixed-integer linear programming. Moreover, [38] examined the ideal sizing and positioning of RDGs for an area in Jordan by performing a feasibility analysis utilizing the HOMER software program. VOLUME 11, 2023 65445 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.

A. MOTIVATION
The literature review and current research initiatives highlight the necessity for additional attention to formulating and resolving problems related to the optimum RDG and VSG integration into different distribution systems. The previous researches show that the set value of the active power output from the VSG is a crucial consideration when implementing VSG. In order to restore the frequency of microgrids to the permitted limits, the quantity of active power allocated during regular operation needs to be carefully controlled. Additionally, incorporating RDG units in microgrids necessitates extensive planning and design to meet the electric network's performance criteria, such as voltage stability, power quality, total active power loss reduction, and economic efficiency. Moreover, numerous metaheuristic algorithms have been utilized in prior studies to address these issues, but none of the techniques guarantees the optimal global solution. The research gaps from the literature review section are identified below: • Prior research mostly overlooked the simultaneous optimum implementation and design of VSG units with various RDG types.
• Including several objectives in optimization increases the challenge and needs decision support.
• No preceding study can vouch for the techniques' global superiority.
• Heuristic approaches are desirable for solving non-linear optimization problems when there are a variety of control variables. This study area exhibits multi-objective scenarios with unknown Pareto optimum solutions and needs to be investigated by recent heuristic algorithms.
• The recommended methodologies' techno-economic assessment in various distribution systems was primarily neglected in earlier studies.

B. MAIN CONTRIBUTIONS
To address the research gaps, this research suggests a novel method for identifying Pareto solutions for simultaneous RDG and VSG unit placement and sizing. Moreover, the proposed framework of this study is depicted in Fig. 1. The main contributions of this research work are identified as follows: • To improve microgrids' voltage and frequency stability, the conventional RDG allocation problem is combined with VSG's optimal active power distribution.
• The Multi-objective Salp Swarm Optimization Algorithm (MOSSA) [39], a recently developed technique, is used to identify the solution with the greatest exploitative aspect and exploration competency.
• Oman's meteorological information is incorporated in the RDG and VSG placement simulation.   • Frequency deviation minimization and total annual energy saving minimization are considered as the objectives.

II. VIRTUAL SYNCHRONOUS GENERATORS
As demonstrated in Fig.2 VSG comprises three essential components -inverter, energy storage, and a virtual inertia control mechanism. An inverter controlled by the VSG concept connects a distributed resource to the primary power grid. Moreover, virtual inertia control, another crucial component of VSG, represents the SG's swing equation as expressed in Eq.1 [10].
here, P denotes VSG input power per unit, P out represents measured grid power output, H is the virtual inertia constant. The virtual angular rotor speed (ω r ) per unit can expressed as Eq. 2: where ω g is the per-unit angular rotor speed of the measuring point, and K d represents the VSG's virtual damping coefficient per unit. Fig.3 demonstrates the control diagram of VSGs. Moreover, the VSG Governor represented in Fig.4 is an ω − P droop controller. Furthermore, ω 0 represents the system's nominal angular frequency, P denotes the active power set value, K p means the droop coefficient per unit equal to 1/δ, and δ represents the speed regulation factor.

III. MULTI-OBJECTIVE SALP SWARM OPTIMIZATION ALGORITHM (MOSSA)
In order to achieve rapid convergence and accomplish high variation while coordinating many objectives, MOSSA focuses on a set of solutions. It takes its cues from the swarm behavior of salps in seas and employs the salp chain for the exploration and extraction processes. Fig.5 illustrates the stages of the MOSSA approach. The salp chain is composed of the leader and followers. The first chain's leader points the blooms differently, and the others obediently imitate. MOSSA describes the salps position as a search space whose dimension relies on the number of variables. To preserve the orientation, 2-dimensional matrices are employed. The leader position and food supply are changed with each optimization cycle. The steps of the leader's position are expressed in Eq. 3: Here, X 1 j denotes the position of the leader, F j represents the position of the food source F in j dimension, H and L means the maximum and minimum Bounds, C 2 and C 3 are random numbers between 0 and 1. The following equation describes C 1 , which is crucial during the exploration and exploitation phases.
Here, T is the current iteration, and the maximum number of iterations is T MAX .

A. PENALTY-BASED BOUNDARY INTERSECTION (PBI)
The PBI method is used to scalarize two nonlinear dimensional objectives in conflict. This can be stated as: here, θ means penalty parameter of (θ ≥ 0), W denotes direction vector and z * represents the optimal point.

B. NON-SCALE APPROACH (NS)
Non-scale approach converts the two competing objectives into a mono-objective function by weighting and aggregating them and can be expressed as: here, OF Max i (X ) and OF Min i (X ) represents the upper and lower boundaries of i individual objective function and W i denotes the weight coefficients (0 > W i < 1).

C. NON-DOMINATED ROULETTE WHEEL METHOD
A distinct case arises when one identical non-dominated solution of the repository's inhabitants is discarded in contrast to the solutions in the repository, and the salp is not dominant. Using a roulette wheel, the solution is to identify non-dominated solutions utilizing the populous neighborhood by counting the number of neighborhood solutions with the greatest distance. The distance vector expressed in Eq. 7 is expressed as:

IV. SIMULATION MODELING
In order to ensure that the system can survive in the case of a substantial interruption that isolates the microgrid from the utility grid, MOSSA is utilized in this study to distribute active power output from VSG and apparent power from RDG units. The fitness function used in this study aims to determine the appropriate location and size of RDGs and VSGs to minimize total frequency deviation and annual energy-saving cost while complying with the constraints mentioned in [40].    In this study, a fixed RDG was installed in the test systems shaping it into a microgrid to examine the frequency deviation value before and after optimization. The utility grid was then disconnected from the grid in order to operate in islanded mode with only one RDG. Following this, the optimization problem was solved to determine the optimal VSG and RDG unit placement.

A. OPERATIONAL CONSTRAINTS
Certain operational constraints should be considered during the optimization procedure, which are demonstrated below: i. Power balance: The total electricity production must equal the sum of the total losses, as well as the load demand.
Qr loss (14) ii. Voltage constraint: Voltage levels on each bus (Vm bus ) are restricted to a suitable range. 0.9 p.u ≤ Vm bus ≤ 1.1 p.u (15) iii. Branch loading: The apparent load transmitted in branch l should not exceed the branch's thermal limit.
S l ≤ S l−max (16) v. RDG and VSG Capacity Constraints: In this study, the minimum (P min RDG , Q min RDG ) and maximum rating (P max RDG , Q max RDG ) of RDG has been considered as 0.1 MVA to 2.3 MVA with a constant power factor of 0.9 per unit (p.u). Furthermore, the minimum (P min VSG ) and maximum (P max VSG ) rating of VSG is considered as 0.1 MW and 6 MW [24].
The following procedure outlines the structure of the proposed MOSSA algorithm for determining ideal VSG and RDG locations and sizes, as well as their operating methods: Step 1: Supply the initial parameters that include the maximum quantity of RDGs and VSGs, size and positional constraints, population size, RDG and VSG modeling, and the load demand curve. Step 2: Create the initial population set based on algorithmic factors such as population size (40). A vector composed of the positions and capacities of VSG and RDG units is employed to demonstrate a population.
Step 3: Population variable ranges are randomly dispersed within bounds, as the RDG locations, types, sizes, and VSG operation technique.
Step 4: Conduct load flow calculations for each population.
Step 5: Employing the MOSSA exploitation approach, formulate the locations to reflect the favored candidate.

(Subsection III)
Step 6: Check if the solutions fall within the parameters specified in Subsection. IV-A.
Step 7: Steps 5 and 6 should be repeated until the permitted number of repetitions is achieved. The stopping threshold for all algorithms in this study was set at 20 iterations.
Step 8: Provide the Pareto solution.

C. TEST SYSTEMS AND DATA
The ROCOF, frequency deviation, and the power losses for the test systems without RDG and VSG placement are depicted in Table 2. To find out the ROCOF mentioned VOLUME 11, 2023 in Table 2, an RDG with 50% of the total generation was attached to the grids at random locations on the base case islanded networks. The IEEE 33 bus test system [42], 69 bus system [43], and Masirah network [44] are assessed in this study ( Fig. 6 and Fig. 7). Furthermore, Masirah Island's solar radiation and wind speed are obtained from [45] and [46]. To accommodate for weather-related variability in the load and RDG outputs, a simulation time of 72 hours (3 typical days for each season with average hourly outputs) was adopted. The one-year wind, solar, and load data are depicted in Fig. 8.

V. RESULTS ANALYSIS
Using the suggested MOSSA applied to the aforementioned test systems (IEEE 33, IEEE 69, and Masirah Island), the following simulated cases are taken into consideration. Moreover, the obtained results by the MOSSA are compared with the other algorithms, such as MOPSO and NSGA-II.

A. SIMULTANEOUS RDG AND VSG PLACEMENT
The following sections demonstrate the results obtained for the case of simultaneous VSG and RDG placement case for the three test systems using MOSSA based technique:  Table 3. As the islanded microgrid has the optimal RDG size and placement paired with active power allocation from VSG at the suitable location, the frequency  deviation value is decreased by 99.7% for the IEEE 33 test systems. Furthermore, the VSG provides 8.9241 MJ/MVA inertia to the grid. The results also reveal that MOSSA's PSCs decrease test system variance in voltage and provide an adequate trade-off between the objectives. Furthermore, a comparison of the network voltage profile before and after the simulation is shown in Fig. 10. The findings show that a minimum voltage of 0.9134 pu at bus 18, during the summer, at 5 p.m., was increased to 0.944 pu. Additionally, Fig. 11 shows how real power losses have decreased for each branch and hour compared to base case scenarios. The voltage profile adjustments additionally resulted in a decreased active power loss value. Compared to the base scenario, the PSC decreases total energy losses by 53.2% (8.1 MWh to 3.79 MWh). Moreover, the results suggest substantial loss reductions are achieved during the peak load hours, which makes the network more efficient in terms of power quality.   Table 4. The frequency deviation value is reduced by 99.7% for the IEEE 69 bus test systems because the islanded microgrid has the ideal RDG size and placement and active power allocation from VSG at the appropriate location. Fig. 13 depicts the voltage profile contrasts for the PSC and base case. The minimum voltage magnitude rises from 0.9102 pu in the base case to 0.927 pu in the PSC. Furthermore, Fig. 14 Table 5 depicts the RDG and VSG locations and capacity obtained by MOSSA. Fig. 16          VSG placement is inferior as a solution to simultaneous RDG and VSG placement scenarios since the low inertia problem is not completely alleviated.  graph depicts the test systems' hourly average ROCOF values. The results show that the ROCOF values for only RDG placement instances are significantly higher due to the lack of inertia support. Besides, in the cases of only VSG placement and simultaneous VSG and RDG deployment, coupled active power allocation and inertia support from VSGs reduce the ROCOF value and so constitute an improved stable system.

E. RESULTS COMPARISON
As the searching performances of multi-objective algorithms are more sophisticated than those of single-objective algorithms, the results of each approach are compared using a S-index and a C metric [41], [47]. The definitions for these metrics are provided in the subsections that follow.

1) S-INDEX
The neighboring residual fitness function values alleviate the selection of evenly distributed Pareto solution sets. The NDS This normalized minimum distance may be used with the spacing metric Eq. V-E1: As a result, the normal Euclidean distance is mathematically described by the following Eq. 22.
Low S values indicate that Pareto solutions are evenly distributed, indicating superior solutions for specific concerns. The boxplot median in Fig. 19 can be used to measure the effectiveness of an algorithm. MOSSA is superior as it offers the smallest value with a constrained interval.

2) C
Consider the two PSCs O 1 and O 2 generated by the two different methods. The expression O 1,2 can be expressed as: Table 8 shows the C values for the abovementioned methods. The top row of the C index data shows that, on average, 87.3% of the results found by MOSSA outnumber those identified by MOPSO. Similar findings for the other rows demonstrate that MOSSA solutions perform better than MOPSO and NSGA-II solutions in terms of C index performance. Consequently, the C and S metric results show that MOSSA produces better Pareto front solutions than other methods.

VI. CONCLUSION
A unique MOSSA approach for simultaneous RDG and VSG size and placement in distribution networks is provided to improve frequency stability and minimize yearly energy-saving expenses. To account for Oman's weatherrelated fluctuation in RDG output, the simulation duration was adjusted to 72 hours for three seasons. Based on the findings, the following conclusions have been drawn: • The best Pareto fronts satisfied the frequency stability and cost minimization.
• The hourly power losses and total energy losses were greatly reduced during the optimization period.
• The proposed multi-objective optimization strategy, which used seasonal load variance and Oman's stochastic RDG output powers, successfully improved the voltage profile of the networks. Furthermore, all of the Pareto front solutions avoided system voltage violations.
• Two performance measures were used to evaluate PSC sets of the MOSSA method with two multi-objective benchmark algorithms, notably the MOPSO and NSGA-II algorithms. The comparisons showed that the Pareto solutions generated by the MOSSA algorithm were more robust than those generated by the other two methods.
According to the results, this study can offer recommendations for improving the operating efficiency of current RDG-VSG integrated microgrid systems. The effects of installing renewable distributed generation with VSG on realistic networks might be explored in future studies. Furthermore, future development might involve techno-economic analysis and energy storage technologies combined with VSG and RDG units. The suggested system may also deal with real-time operational circumstances, provided the load and RDG output estimation is integrated.