Microgrid Management Strategies for Economic Dispatch of Electricity Using Model Predictive Control Techniques: A Review

Abstract

In recent years, microgrid (MG) deployment has significantly increased, utilizing various technologies. MGs are essential for integrating distributed generation into electric power systems. These systems’ economic dispatch (ED) aims to minimize generation costs within a specific time interval while meeting power generation constraints. By employing ED in electric MGs, the utilization of distributed energy resources becomes more flexible, enhancing energy system efficiency. Additionally, it enables the anticipation and proper utilization of operational limitations and encourages the active involvement of prosumers in the electricity market. However, implementing controllers and algorithms for optimizing ED requires the independent handling of constraints. Numerous algorithms and solutions have been proposed for the ED of MGs. These contributions suggest utilizing techniques such as particle swarm optimization (PSO), mixed-integer linear programming (MILP), CPLEX, and MATLAB. This paper presents an investigation of the use of model predictive control (MPC) as an optimal management tool for MGs. MPC has proven effective in ED by allowing the prediction of environmental or dynamic models within the system. This study aims to review MGs’ management strategies, specifically focusing on MPC techniques. It analyzes how MPC has been applied to optimize ED while considering MGs’ unique characteristics and requirements. This review aims to enhance the understanding of MPC’s role in efficient MG management, guiding future research and applications in this field.

1. Introduction

The implementation of ED and the closure of less efficient power plants are crucial strategies being considered by developed countries to facilitate the transition toward clean electricity generation [1]. This approach has sparked increasing interest in developing nations as it recognizes the importance of greater involvement of MGs with renewable energy sources.

The IEEE 2030.7 standard [2] has been introduced to provide a better understanding of the subject. This standard defines MGs as a collection of functional modes that outline the operations of an MG controller. These operational modes serve as a convenient means of specifying the entire functioning of an MG. An MG can be operated isolated or interconnected to the main network. Within these topologies, it has the possibility of assuming two types of operation modes and four possible operation transition states.

These modes and transition operations are as follows:

Mode 1: Steady-state grid work connection:

• Energy storage smooths out fluctuations in renewable energy production and supports grid stability.
• The microgrid provides auxiliary services to the main grid, such as frequency regulation and reactive power support.

Mode 2: Stable island mode; this mode requires an ongoing balance between loads and local generation/storage capabilities:

• The microgrid operates independently, balancing local demand and energy generation/storage.
• Energy storage bridges the gap between varying energy production and load demands. During periods of high energy production, surplus energy is stored in energy storage systems (e.g., batteries) for later use when renewable energy generation is low or when the demand is higher than the available generation.
• Transition 1: Transition from network connection to steady-state island mode (planned). This transition occurs when the MG’s operator deliberately decides to operate the MG in islanded mode even though the main grid is available. There could be various reasons for this, such as conducting maintenance, testing on the main grid, or improving the MG’s resilience during periods of potential grid instability.
• Transition 2: Grid connection in steady-state island mode (unplanned). When the main grid experiences a failure, the microgrid seamlessly disconnects and forms an independent power system (an island) while continuing to supply loads. Energy stored in batteries or other storage systems ensures an uninterrupted power supply during the critical period of grid failure, until a stable island operation is established.
• Transition 3: Reconnection of steady-state island mode to the grid. After operating in islanded mode, there may come a time when the main grid is restored, and the MG is ready to reconnect to it. This can assist in regulating the power flow during the reconnection process, ensuring a smooth and stable reintegration with the main grid.
• Transition 4: Black starts in steady-state island mode. The main grid experiences a complete blackout, and the MG needs to start up in islanded mode without any external support. The energy storage operation can provide the initial power required to operate essential equipment and initiate the startup sequence of local generation sources.

According to [3], ED is an optimization problem that aims to minimize the power system’s operating cost while satisfying regime constraints, such as electrical, operational, and environmental constraints. ED encompasses two distinct facets: static ED (SED) and dynamic ED (DED). While SED focuses solely on the ED problem within a single period, DED considers the interconnection of multiple periods.

Various techniques exist for effectively managing an MG, among which MPC stands out. MPC is a control technique renowned for handling dynamic systems with utmost reliability [4]. In [5], MPC was employed for ED, autonomous operation, and frequency control, encompassing essential control functions such as system forecasting, incorporation of environmental or dynamic models, and feedback capabilities, being well suited to online and real-time applications.

In [6], the penetration of DERs in MGs and efficient energy consumption were remarkable factors in mitigating carbon dioxide (CO₂) emissions [6,7,8]. This paper presents a comprehensive review of relevant studies published in recent years. The data presented in

Table 1. A summary of the contributions made by the authors of the reviewed articles related to economic dispatch in MGs with MPC application during the last five years.

References	Contribution
[9]	It provides insight into problems in the regular, reliable, and efficient operation of power systems to solve ED incorporating RESs via PSO.
[10]	It examines the influences of communication problems, market mechanisms, and administrative measures on the application of vehicles in the network (V2G) in ED.
[11]	It studies the path to the development of an ED program, which is suggested as a future trend. It studies battery energy storage system (BESS) applications in inverter-based MGs.
[12]	It studies the optimization methods for MGs and MG clusters (MGCs). It provides an overview of advanced optimization algorithms to optimize MG and MGC operation.
[13]	It verifies the implementation of economic MPC (EMPC) for optimization, including prediction modeling objectives, operating constraints, and cost-function design.
[14]	It discusses conditions for the application of optimization in MGs and MGCs, such as modeling methods, consensus control, energy coordination, and ED.
[15]	It offers an overview of optimization techniques, forecasting, economic/environmental dispatch, and metaheuristic algorithms, such as (PSO), to improve the use of renewable resources.
[16]	It identifies the optimal operation for the size of an MG through the PSO algorithm. It investigates various functions, such as EMS, unit commitment (UC), ED, optimal power flow (OPF), and cost optimization of operations.
[17]	It analyzes the optimization methods applicable to MGs and MGCs. It provides an overview of advanced optimization algorithms to optimize MG and MGC operation.
[18]	It provides an effective strategy for the flexible dispatch of distributed energy resources on the user side.
[19]	It analyzes and summarizes the state of the art using the adaptive dynamic programming (ADP) algorithm and its application to the ED problem.
[20]	It identifies MG control structures, and the optimal control methods used in optimization. It analyzes the use of the MPC algorithm in MGs online.

, extracted from recent ED reviews, demonstrate commonalities regarding the optimization methodology, integration of energy storage components, predictions, constraints, and, notably, the utilization of the PSO algorithm as an optimization method for ED across diverse MG topologies [9,10,11,12,13,14,15,16,17].

Table 2 presents a summary of the contributions made in the MPC review papers related to MGs, which include:

• A review of power converter control;
• A review of optimization methods applicable to MGs and MG clusters (MGCs);
• A review of MPC applications at the secondary and tertiary control levels of MGs;
• Improvement of power quality;
• Inertia emulation of a virtual synchronous generator;
• Improvement of voltage quality;
• Power flows in multi-MG systems;
• Uncertainty management;
• Better coordination at the three levels of hierarchical control of MGs.

These topics represent the key aspects researchers have addressed in peer-reviewed studies on MPC in MGs [21,22,23,24,25,26,27,28,29].

Table 2. A summary of the contributions made by the authors of the reviewed articles related to the use of MPC in microgrids during the last five years.

References	Contribution
[21]	It reviews MPC at the converter level and MPC at the network level, and discusses MPC strategies in the three layers of hierarchical MG control.
[22]	It provides an in-depth review of MPC-controlled converters in wind and photovoltaic power systems.
[26]	It provides an overview of model-free MPC (MFPC) in power converters, electric drives, power systems, and MGs. In addition, it discusses the several types of MPC in non-model approaches.
[27]	It provides a comparative study of uncertainty modeling techniques controlled by MPC in MGs. It considers the various uncertainties, voltage profile improvement, and power quality improvement.
[28]	It presents a study of MPC applications at the secondary and tertiary control levels of MGs, as well as MPC classifications for centralized, decentralized, and distributed MG topologies. It reviews MPC techniques used in multi-MG systems’ energy management and power-flow control.
[29]	It reviews recent FCS-MPC algorithms, addressing different topics related to power converter control in MG applications.
[30]	It reviews recent FCS-MPC algorithms, addressing different topics related to power converter control in MG applications.
[31]	It reviews the application of predictive control in MG, considering the most relevant contributions in recent years.

Table 2. A summary of the contributions made by the authors of the reviewed articles related to the use of MPC in microgrids during the last five years.

References	Contribution
[21]	It reviews MPC at the converter level and MPC at the network level, and discusses MPC strategies in the three layers of hierarchical MG control.
[22]	It provides an in-depth review of MPC-controlled converters in wind and photovoltaic power systems.
[26]	It provides an overview of model-free MPC (MFPC) in power converters, electric drives, power systems, and MGs. In addition, it discusses the several types of MPC in non-model approaches.
[27]	It provides a comparative study of uncertainty modeling techniques controlled by MPC in MGs. It considers the various uncertainties, voltage profile improvement, and power quality improvement.
[28]	It presents a study of MPC applications at the secondary and tertiary control levels of MGs, as well as MPC classifications for centralized, decentralized, and distributed MG topologies. It reviews MPC techniques used in multi-MG systems’ energy management and power-flow control.
[29]	It reviews recent FCS-MPC algorithms, addressing different topics related to power converter control in MG applications.
[30]	It reviews recent FCS-MPC algorithms, addressing different topics related to power converter control in MG applications.
[31]	It reviews the application of predictive control in MG, considering the most relevant contributions in recent years.

The trajectory depicted in the flowchart in Figure 1 emerged after reviewing these documents. It succinctly outlines the process of conducting a thorough search, careful selection, effective filtering, and necessary exclusions of the most pertinent literature related to MGs, MPC, and ED. These crucial concepts, systems, and designs significantly influence the development of renewable energy technologies.

Figure 2 provides a synoptic scheme outlining the key information that will be covered in this literature review. This paper aims to delve into these aspects to present a comprehensive analysis and understanding of the subject matter.

This review is organized as follows: Section 2 analyzes the types of MPC used by researchers in MGs with AC, DC, and hybrid topologies, in which the results obtained are presented; Section 3 presents a review of articles related to ED elaborated in the last 5 years; Section 4 presents a discussion of the present research; and, finally, Section 5 presents a general conclusion concerning the topics covered, emphasizing the future challenges or trends encountered, weaknesses found that may be feasible to overcome in further research, and potential areas of development for MPC and ED.

2. Model Predictive Control (MPC)

According to the study conducted in [28], it has been determined that MPC offers superior dynamics and performance compared to conventional methods in the secondary and tertiary control of MGs. MPC can be divided into two main categories: continuous control set MPC (CCS-MPC) and finite control set MPC (FCS-MPC). CCS-MPC, described in [32], uses a modulator to generate switching signals based on a continuous output of the predictive control. Instead, FCS-MPC takes advantage of the direct control of the converter without needing an additional modulation step, which decreases the computational load required for its implementation.

2.1. MPC in AC MGs

A methodology has been developed to address the primary frequency response (PFR) in MGs using MPC, as described in [33]. This methodology is based on combining energy storage systems and photovoltaic (PV) generation, taking advantage of the V2G and B2G concepts. In [34], a specific methodology is presented to address the primary frequency response in an MG through MPC, using the FCS-MPC approach, together with the frequency and voltage droop control applied to the grid-side converter (GSC) of a double-fed induction generator (DFIG).

Figure 3 shows a visual representation of this system, where the MPC uses the current and voltage measurements of the network in the alpha–beta (αβ) reference frame and, through a system model, makes predictions of the currents for the next sampling period. This methodology, with the MPC focusing on the primary frequency response of an MG, demonstrates MPC’s ability to effectively anticipate and control variations in frequency and voltage, providing a promising solution to the management and stability of MGs.

Using a strategy based on FCS-MPC, a proposal was presented in [35] to improve the voltage regulation performance of a voltage source converter (VSC) used for MG applications. Cooperative MPC (CMPC) was implemented in [36] for urban districts comprising multiple MGs to share the DERs. Furthermore, in [37], multiple MGs (MMGs) were operated in real time, using daily stochastic optimization programming and a real-time sliding window MPC. A consensus strategy for ED and frequency restoration was proposed in [38] to operate isolated MGs; the experimental results demonstrated that the distributed controller was resistant to load variations and communication problems.

An MG can operate in islanded mode and grid-connected mode. In islanded mode, the device-level controller, consisting of a droop mechanism and model-predictive voltage and current control (MPVIC), coordinates with a PSO-based system-level power optimization scheme for proper load sharing and voltage stabilization. Meanwhile, in grid-connected mode, the device-level controller containing model-predictive power control (MPPC) is incorporated into a PSO-based system-level power optimization scheme for economic power dispatch [39]. Decentralized primary control based on a CPM strategy was developed in [40] to address operational constraints. The experimental results of an MPC-MILP control scheme were presented in [41] to optimize MG operations economically; the cost was addressed in formulating the problem to take advantage of the economic benefits of the DERs. In [42], a method for optimizing the energy management of an MG in a high-tech park was proposed. The process divides the global optimization problem into subproblems and is implemented under a distributed framework, facilitating an increase in computational speed.

Based on daily robust and continuous optimization, a method was designed in [43] for economical programming of multiple time scales. To further optimize the control units and ensure energy stability, a robust MPC MMG with electric vehicles (EVs) was proposed in [44], adding a linear quadratic regulator (LQR). Through MPC application, a more advanced control strategy was proposed in [45] for an ultra-capacitor (UC), which provided a smoother active-power decrease and improved the frequency response of the system to minimize the rate of change of frequency (ROCF). In [46], a virtual inertia control (VIC) framework was developed for an MG. To improve the coupling of an MG with the primary grid and control and minimize the harmonic content, modulated MPC (M2PC) was implemented in [47], which uses the fixed switching frequency using a three-phase voltage source inverter (VSI). The data presented in Table 3 have been analyzed, and it is possible to observe the following findings:

• The essential participation of the input variables in the minimum-cost ED is presented, such as frequency regulation and reduction in total harmonic distortion (THD). This indicates that these aspects have been considered and optimized in the reviewed studies.
• The most used programs to solve the optimization problem are MATLAB/Simulink and CPLEX. These tools are widely recognized and used in optimization, allowing researchers to find optimal or near-optimal solutions for ED in MGs.
• Regarding the control technique, it is observed that MPC is the most used. In addition, specific variants such as FCS-MPC (MPC based on future cost-scheduling) and DMP are used. These control techniques are primarily oriented towards a centralized approach, with a centralized control system that operates in an energy management system (EMS).
• The coupling of the MG to the primary grid is accomplished by coupling the distribution network. The above implies that the MG is connected and can exchange energy with the primary grid through the existing distribution infrastructure. In addition, this implementation can be applied in any MG, indicating that coupling through the distribution network is a versatile option and adaptable to different MG configurations.

Table 3. Most important characteristics of AC MGs using the MPC strategy.

Refs.	Model	Input Variable	Output Variable	Technique/ Solver	Control Type	MG Type	Grid PCC	EMS	DSM
[33]	MPC	ED	PV	MATLAB 9.10	C	Is/int	DNS		X
[34]	FCS-MPC	Frequency regulation	Wind	FCS-MPC Droop control	C	Int	DNS		X
			ESS
[35]	FCS-MPC	THD	Wind		-	Is	-		X
		reduction	BESS, PV
[36]	CMPC	Minimal	BESS	MILP	C	MMG/ Int	DNS	X
		cost	DG	CPLEX 12.7	D
				Gurobi 7.5.2
[37]	MPC	ED	PV	MILP	C	MMG Int	DNS	X
		CO2	ESS, DG	CPLEX 12.10	D
		reduction		Gurobi 9.0.1
[38]	DMPC	ED	DG	QPKWIK Mpcqp 9.10	D	Is	-	X
		Frequency regulation
[39]	MPPC MPVIC	ED	Wind	PSO 1.0.4	C	Is/Int	DNS	X
			PV
[40]	MPC	Minimal cost	-	LQG LTR/ MATLAB 9.10	C	Is/Int	DNS	X
[41]	MPC	Minimal	BESS	MATLAB 8.4	C	Int	DNS
		cost	PV	ILOG	D
				CPLEX 12.6
[42]	DMPC	Minimal cost Emission reduction	PV	C-DMPC/HC-DMPC	D De	Int	DNS	x
[43]	DDMPC, CMPC	Minimal	PV	Lagrange	C	Int	DNS	X
		cost	Wind	Multiplier MATLAB 9.10	D
[44]	RO-MPC	ED	PV	MATLAB 9.11	D	Int	DNS	X
			Wind	PSO 1.1
[45]	RMPC	Minimal	Wind	MATLAB	D	Is/MMG		X
		cost		Simulink 9.11
		Frequency regulation
[46]	MPC	Minimal	PV	MATLAB	C	Int	DNS	X
		cost	ESS	Simulink 9.10	D
		Frequency regulation
[47]	CMPC	Current	PV	MATLAB	C	Int	TNS	X
	DMPC	frequency	BESS	Simulink 9.14

Table 3. Most important characteristics of AC MGs using the MPC strategy.

Refs.	Model	Input Variable	Output Variable	Technique/ Solver	Control Type	MG Type	Grid PCC	EMS	DSM
[33]	MPC	ED	PV	MATLAB 9.10	C	Is/int	DNS		X
[34]	FCS-MPC	Frequency regulation	Wind	FCS-MPC Droop control	C	Int	DNS		X
			ESS
[35]	FCS-MPC	THD	Wind		-	Is	-		X
		reduction	BESS, PV
[36]	CMPC	Minimal	BESS	MILP	C	MMG/ Int	DNS	X
		cost	DG	CPLEX 12.7	D
				Gurobi 7.5.2
[37]	MPC	ED	PV	MILP	C	MMG Int	DNS	X
		CO2	ESS, DG	CPLEX 12.10	D
		reduction		Gurobi 9.0.1
[38]	DMPC	ED	DG	QPKWIK Mpcqp 9.10	D	Is	-	X
		Frequency regulation
[39]	MPPC MPVIC	ED	Wind	PSO 1.0.4	C	Is/Int	DNS	X
			PV
[40]	MPC	Minimal cost	-	LQG LTR/ MATLAB 9.10	C	Is/Int	DNS	X
[41]	MPC	Minimal	BESS	MATLAB 8.4	C	Int	DNS
		cost	PV	ILOG	D
				CPLEX 12.6
[42]	DMPC	Minimal cost Emission reduction	PV	C-DMPC/HC-DMPC	D De	Int	DNS	x
[43]	DDMPC, CMPC	Minimal	PV	Lagrange	C	Int	DNS	X
		cost	Wind	Multiplier MATLAB 9.10	D
[44]	RO-MPC	ED	PV	MATLAB 9.11	D	Int	DNS	X
			Wind	PSO 1.1
[45]	RMPC	Minimal	Wind	MATLAB	D	Is/MMG		X
		cost		Simulink 9.11
		Frequency regulation
[46]	MPC	Minimal	PV	MATLAB	C	Int	DNS	X
		cost	ESS	Simulink 9.10	D
		Frequency regulation
[47]	CMPC	Current	PV	MATLAB	C	Int	TNS	X
	DMPC	frequency	BESS	Simulink 9.14

2.2. MPC in DC MGs

This section discusses different authors’ proposals for DC MG management. To optimize the performance of an MG, MPC was proposed in [48], considering the stochasticity of wind and load forecasts. One of the most severe problems in an MG is the THD. MPC reduced this in [49] when applied at several hierarchical levels, using packed U-cell converters (PUCs). Moreover, in [50], a strategy of convex MPC was applied for dynamic energy exchange between ESSs distributed in an AC MG, which allowed for solving the OPF as a convex optimization problem. The operational efficiency of an MG, and the reduction in the degradation rate of an ESS were improved using heuristic-based MPC in [51]. To improve the management of MGs, an MPC was implemented in [52], whose main objective is to reduce the number of changes in the manipulated variables, reduce the degradation of storage devices, and obtain a better performance of the cost function.

In [53], by using multi-scenario MPC (MS-MPC), tree-based MPC (TB-MPC), and probability constraints (CC-MPC), it was possible to manage the uncertainty of the energy demand and power generation, showing these methods’ effectiveness in energy management under economic and optimal criteria, with a low computational load. To perform voltage regulation and energy allocation between a battery and an ultra-capacitor (UC), MPC was designed in [54] to control three-level bidirectional DC/DC converters for a hybrid energy storage system (HESS). In [55], with the use of an MPC algorithm for Gaussian process regression forecasting in an interconnected MG, it was possible to improve the load and energy supply forecasts. In [56], hybrid control based on MPC and iterative learning control (ILC) was designed to be implemented in the hybrid energy storage system (HESS) of isolated MGs.

MPC for a residential MG has been developed to maximize the economic benefits and minimize the degradation of solar panels [57]. Figure 4 shows how this type of MPC is implemented, which is developed through three manipulated variables that manage the system, the energy exchange with the primary grid P_grid, and the energy of the lithium-ion battery (PBli), where P_loads denotes the electrical energy that satisfies the residential demand Pdem. The MPC controller also maintains the desired outputs around a certain level of stored energy, preventing fluctuations in the ESS against the state of charge (SOC) of the batteries, avoiding deep discharging and overcharging.

In [58], a two-level hierarchical MPC (HMPC), enhanced by two data-driven modules, was proposed to increase MG performance. A hybrid wind/solar/battery power system was designed using high-efficiency distributed hierarchical MPC [59]; this allowed the top layer of the HDMPC to be used to coordinate power allocation, while in the lower layer, supervisor MPC was designed based on the dynamic performance model. The data presented in

Table 4. Most important characteristics of DC MGs using the MPC strategy.

References	Model	Input Variables	Output Variables	Technique/Solver	Control Type	MG Type	Grid PCC	EMS	DSM
[48]	SMPC	ED	Wind ESS	MATLAB	De	Is	-
				Yalmip Gurobi 6.0.4
[49]	MPC (PUC)	Minimal	PV	MATLAB	C	Int	DNS	X
		cost		Simulink 9.12
[50]	MPC (NLP)	Minimize	BESS	QCQP	C	Is	-	X
		Lost	PV	MATLAB 9.5
[51]	MPC	Max./min	PV	MIQP	C	Is		X
		Degradation ESS		Gurobi 9.1.0
[52]	SSMPC	Minimal cost	BESS	Simulink 9.8	C	Int	DNS		X
[53]	MS-MPC	Minimal	PV	Multi-SS	C	Is/Int	DNS	X	X
		cost		Programming MATLAB 9.2
[54]	MPC DC/DC	Minimal cost	PV	-	C	Is/Int	DNS	X
[55]	MPC	Minimal cost	PV	MATLAB 9.10	D	Int/MMG	DNS	X
[56]	HDMPC	Minimal	Wind	MATLAB 9.11	D	Is		X
		cost	PV
		Emissions
[57]	MPC-ILC	ED	PV	Quadratic programming MATLAB 9.8	D	Is	-
[58]	MPC	Minimal	PV	MATLAB	C	Is/Int	DNS		X
		cost	Wind	Simulink 9.11
[59]	HMPC EMPC	Minimal		MILP	H	Int	DNS	X
		cost		CPLEX 12.10

show that the interconnection of MGs with the primary grid is conducted through the PCC of the DNS. In addition, it is remarkable that the most used control system is of the centralized type, and the predominant control technique is MPC, with its different variants, to achieve ED of MG operations.

Regarding the resolution of the model, it was found that the most used tool is MATLAB/Simulink. This software platform is widely used to solve equation approaches in MGs.

2.3. MPC in Hybrid MGs

In [60], dual-mode distributed economic MPC, implemented for a non-linear battery-photovoltaic-wind (WPB-MPS) MG power system, allowed the total demand to be met, optimized the SOC of the battery, and reduced the fluctuations in the energy exchange with the grid. A distributed energy management strategy has been established to reduce the operating cost of MGs through MPC [61]. Similarly, based on FCS-MPC technology in [62], a control strategy was implemented for a hybrid island MG, which could predict the future states of the hybrid MG and decide the optimal control actions before the switching signals were sent. A fault-tolerant control (FTC) scheme strategy for an AC/DC pulse-width modulation (PWM) converter was presented in [63], in an MG framework. Figure 5 shows this fuzzy logic (FL)-based MPC technique, which uses MATLAB/Simulink for its solution.

The data presented in

Table 5. Most important characteristics of hybrid MGs using the MPC strategy.

References	Model	Input Variables	Output Variables	Technique/ Solver	Control Type	MG Type	Grid PCC	EMS	DSM
[60]	EMPC	ED	Wind	EMPC	De	Int	DNS		X
			PV	Lyapunov
[61]	DMPC	ED	PV	MATLAB	D	Int			X
			BESS	Simulink 9.6
[62]	FCS-MPC	Minimal cost	PV	PSCAD	De	Is	DNS
			ESS	EMTDC MATLAB 9.4
[63]	MPC	Minimal	PV	MATLAB	C	Is/Int	DNS
		cost	Wind	Simulink 9.8
[64]	MPCP MPVP	Minimal	PV	MATLAB	C	Is/Int	DNS	X
		cost	Wind	Simulink 9.6
[65]	FCS-MPC	Minimal cost	PV	MATLAB	C	Int	DNS	X
			Wind	Simulink 9.11
[66]	CMPC	Current, frequency	PV	MATLAB	C	Int	TNS	X
	DMPC			Simulink 9.4	De
				PSO 1.0.0.0
[67]	FSTP MPDPC	Energy	-	MATLAB 9.4	H	-	-	-
		active and
		reactive
[68]	MPC	Minimal		MATLAB 9.6	-	Is/Int	DNS	-
		cost		PSCAD
				EMTDC
[69]	MPC	ED	BESS	MATLAB 8.5	D	Is/Int	DNS	X
			Wind
[70]	DDMPC CMPC	Minimal cost	PV	Lagrange	C	Int	DNS	X
			Wind	Multiplier/ MATLAB 9.4	D

show that the predominant interconnection of the MG with the main grid is through the DNS. As for the control system, a centralized approach is used, although, to a lesser extent, the distributed approach is used. The most used control technique is MPC, with some specific variants, such as DMPC and CMPC. These variants allow for obtaining the minimum-cost ED in the operations of MGs. To solve the problem statements, it was found that the creators mainly use MATLAB as an analysis and simulation tool. MATLAB is widely used in MGs to solve and analyze models of electrical systems due to its computational and simulation capabilities.

In [64], to smooth renewable energy outputs, the use of the FCS-MPC control scheme was coordinated between a DC/DC converter and an AC/DC converter. In [65], DC voltage regulation, the injection of active and reactive power into the primary grid in a single cost function, was obtained. In [66], CMPC was used to achieve coordinated control of plug-in hybrid electric vehicles (PHEVs), PV, and ESSs to suppress frequency fluctuations and minimize surplus photovoltaics in an MG.

To reduce harmonic currents and power fluctuations in MGs, finite-state direct power MPC (MPDPC) has been designed [67]. In [68], it was proven that the use of different topologies of matrix converters, such as AC, DC, and hybrid MGs, with MPC was beneficial electrically when sensitive loads were connected close to the generation sources. A market-oriented energy management system (EMS) was presented in [69] for a hybrid power system, which could extend the service life of the BESS by applying typical and practical constraints. In contrast, MPC extends the daily number of cycles (DNCs) and depth of discharge (DOD) of the BESS. A method to find the optimal power outputs of the generators and satisfy the dynamic load was proposed in [70] for distributed dispatch with MPC, allowing it to minimize the system’s operating costs in a distributed manner.

3. Economic Dispatch (ED)

ED is an optimization problem that aims to minimize the operating cost of the power system while satisfying various constraints. ED can be divided into static ED (SED) and dynamic ED (DED). SED only considers the problem of ED with a single period; in contrast, DED considers the related coupling of different periods [3]. A robust MPC-based ED strategy (RMPC) was designed in [8], assuming a low carbon cost to reduce the adverse effects of uncertainties. Similarly, in [71], three-stage online ED was implemented, which coordinated the charging behaviors of EVs within an AC/DC MG in the presence of uncertainties. In [72], a multi-stage energy management solution for MGs (MEMG) was proposed, considering its participation in the electricity market, based on daily scheduling and real-time dispatch.

3.1. ED in MGs

In [73], using an adaptive dynamic programming (ADP) algorithm, distributed MPC was implemented to solve the ED problem, which allowed for managing the forecast and operating intervals of generators and ESSs. An [74] approach to obtaining the optimal ED of combined heat-power (CHP) MGs was presented in [75]. Two types of techniques, namely dual decomposition MPC (DDMPC) and distributed MPC (DMPC) [76], were applied to the problem of ED per hour and the ultrashort-term in real time. One way to evaluate the optimization of the long-term programming of a grid-connected MG with hybrid energy storage involves the use of MPC [75].

It has been proven that variations in generation schedules can be reduced by using an intra-time ED by designing a closed-loop DMPC [77]. In [78], a comprehensive micro-energy (MEG) system of distributed resources, based on MPC, was proposed to minimize costs and reduce load uncertainties. To solve a robust multi-objective ED problem to program several resources of an MG with controllable distributed generators [79], a model capable of describing uncertainty in a flexible but more elaborate way has been implemented.

Another way to handle load demand uncertainties, namely PV with wind turbines (WTs), has been developed using the RS-MPC approach [80] for the online dispatch problem. In [8], an ED strategy based on RMPC was designed, considering a low carbon cost to reduce the adverse effects of uncertainties. Three-stage online ED has been designed to coordinate EV charging behaviors within an AC/DC MG in the presence of uncertainties. In [74], a solution for the multi-stage energy management of an MG (MEMG) was proposed, considering its participation in the electricity market, based on daily programming and dispatch in real time. In [81], considering the problem of the optimal control of dynamic systems, an ED design for an MG with hybrid renewable energy systems was developed.

Based on the data collected in Table 6, the following results are found:

• The power capacity generated by MGs varies widely, from small to large values in megawatts (MW).
• The predominant topology is interconnected/isolated, which implies that some MGs are connected to the main grid while others operate in isolation.
• The most used optimization technique is MPC, including its variants, such as DMPC and other methods, which are used to a lesser extent.
• The choice of technique or solver to solve the ED equations is wide and varied. The above findings indicate that researchers employ different approaches and optimization tools to address the problem of ED in MGs.
• The primary objective function is focused on minimizing costs, which involves finding the optimal configuration that reduces operating expenses. However, it is also found that some options exist to address energy storage and maximize the economic benefits, in addition to the cost target. As a result, the minimization of emissions in a multi-objective manner indicates that researchers seek to find economically viable solutions and be respectful towards the environment.

Table 6. Optimization techniques for solutions to ED in MGs.

				Strategies
Refs.	Technique of Optimization	Solver	MG Type	Cap. (MW)	Emissions CO2	Minimum Cost	Maximize Profit	ESS
[73]	MPC	ADP	Is/Int	19.75	X	X
[74]	ROMPC	MILP CPLEX 12.9	I/Int	10	X	X
[76]	DMPC DDMPC	ACA	Is	3		X
[75]	MPC	MIQP MATLAB 8.2	Is	0.45			X	X
[77]	DMPC	Consensus Algorithm	Is	26			X
[78]	MPC	MPC Optimization/MATLAB 9.10	Is	2.8		X
[79]	ROMPC	PPO/ MATLAB 9.13	Is/Int	112	X	X
[80]	RSMPC	SAM/MATLAB 9.8	Is	0.183		X		X
[8]	RMPC	C&CG	Is	8	X	X
[71]	SMPC	MILP CPLEX 20.1	Is	0.08		X		X
[72]	Rolling MPC	Gurobi 9.1	Is/Int	3.8	X	X
[81]	MPC	SQP/MATLAB 9.4	Is	0.07		X
[82]	MPC	MOSEK Optimization/ MATLAB 9.2	I/Int	1.5		X
[83]	RMPC	CPLEX 12.8 MATLAB 9.4	Is	0.6		X
[84]	DMPC	MATLAB 9.8	Is	-		X

Table 6. Optimization techniques for solutions to ED in MGs.

				Strategies
Refs.	Technique of Optimization	Solver	MG Type	Cap. (MW)	Emissions CO2	Minimum Cost	Maximize Profit	ESS
[73]	MPC	ADP	Is/Int	19.75	X	X
[74]	ROMPC	MILP CPLEX 12.9	I/Int	10	X	X
[76]	DMPC DDMPC	ACA	Is	3		X
[75]	MPC	MIQP MATLAB 8.2	Is	0.45			X	X
[77]	DMPC	Consensus Algorithm	Is	26			X
[78]	MPC	MPC Optimization/MATLAB 9.10	Is	2.8		X
[79]	ROMPC	PPO/ MATLAB 9.13	Is/Int	112	X	X
[80]	RSMPC	SAM/MATLAB 9.8	Is	0.183		X		X
[8]	RMPC	C&CG	Is	8	X	X
[71]	SMPC	MILP CPLEX 20.1	Is	0.08		X		X
[72]	Rolling MPC	Gurobi 9.1	Is/Int	3.8	X	X
[81]	MPC	SQP/MATLAB 9.4	Is	0.07		X
[82]	MPC	MOSEK Optimization/ MATLAB 9.2	I/Int	1.5		X
[83]	RMPC	CPLEX 12.8 MATLAB 9.4	Is	0.6		X
[84]	DMPC	MATLAB 9.8	Is	-		X

An ED design was established in [82], where the hourly schedule is constantly optimized according to the current state of the system and forecast information. Using an optimization approach based on two-stage RMPC, in [83], it was proposed to minimize the cost of operation and, in the second stage, to minimize the cost of adjustment. Similarly, in [84], an ED design was proposed for an MG, where the hourly schedule is constantly optimized according to the current state of the system and the most recent forecast information. In [85], a planning model was created for integrated electricity and natural gas systems (IEGSs), which operates on a two-tier system. Its purpose is to minimize investment costs, particularly regarding wind farms and natural gas storage units, and to reduce operating costs over the long-term planning period.

3.2. Uncertainties in Renewable Technologies for ED

Renewable and load demands pose inevitable challenges for MG online load dispatch. In [86], the abovementioned problems were addressed, and closed-loop strategies based on MPC were proposed, operating based on expected forecasts of renewable sources [87]. Some authors, as mentioned in [88], consider MPC a suitable solution for ED, despite the high uncertainty in the energy production of renewable generation units. In [89], it was stated that deterministic formulations of MPC can systematically address the uncertainties associated with renewable and electricity demands in some instances. In addition, in [90], an integrated uncertainty optimization framework was proposed, which considers the probability distribution of predictions. In [91], it was established that, through the PSO algorithm, high yields can be obtained in managing the uncertainties of photovoltaic, wind, and electricity generation.

According to [92], a daily scheduling tool for robust isolated MGs against unexpected component failures can be developed. Using a stochastic formulation, information gap decision theory (IGDT) can be used for uncertainty modeling. In [93], an optimization strategy for an MG was designed to enable it to participate in the daily market operations, considering the responses of the demand, where the uncertainties of the generation of distributed renewable energy, the electrical load, and the prices of the daily market are considered. Moreover, in [94], a two-tier power management system for an MMG system was implemented to exploit EVs being used between neighboring MGs. Simultaneous EV scheduling and demand response programs (DRPs) were proposed to minimize the costs and reduce the peaks of the MMG system, considering the uncertainty of the EV fleet, loads, and renewable generation.

3.3. Objective Function (Operational Costs) for ED

Stochastic optimization is used in various approaches to minimize the cost of operating the system, as stated in [76]. In that sense, some authors, as mentioned in [95], have applied MPC to optimize a desired objective function that defines the cost behavior in the energy management of MGs. Moreover, [96] proposed a multi-objective mixed-integer linear programming model that reduces both the daily operating cost and the total CO2 emissions of the MG. Other researchers in [97] proposed an approximate dynamic programming algorithm for ED (AD-PED) that enables the stochastic optimization of the MG. In addition, [98] presented a proposal based on the optimal coordinated dispatch method, which can provide benefits in the design and operation of networks, and potentially further reduce the net operating costs of the system.

3.4. Virtual Inertia

Frequency regulation in an MG with high penetration levels from renewable sources poses a challenge that can be addressed by installing storage systems with virtual inertia controllers [99]. Inertia is critical in stabilizing a power system, helping to smooth transient variations and limit maximum frequency deviations, such as deviations in the nadir frequency (FN) [11]. In [100], it is mentioned that virtual inertia control can be implemented in energy storage systems (ESSs). In the case of an isolated MG, robust MPC (RMPC) can be used.

Likewise, in [101], a stochastic anticipated energy dispatch model with frequency restrictions (FCS-LAPD) was proposed, which allows for optimizing the power programming and reserves of all units, as well as assigning the virtual inertia and the coefficient of fall of renewable sources and storage systems. Finally, in [102], a local power management strategy with virtual inertia was adopted to mitigate voltage disturbances at the alternating current (AC) bar and smooth the output power in the primary control layer.

3.5. Frequency Regulation

Large-scale renewable energy generation, such as wind and photovoltaic, and the imbalance between supply and demand can significantly impact the frequency regulation of an MG, as discussed in [103]. To address this challenge, the ESS proposed in [104] offers upstream and downstream control by injecting or absorbing energy according to grid requirements, contributing to primary frequency regulation. In situations of uncertainty due to the switching on and off of plug-in hybrid electric vehicles (PHEVs), as discussed in [66], implementing an MPC controller can reduce frequency deviations in the system. This MPC system also ensures the restoration of the voltage and frequency in case of contingencies, without the need for direct communication between energy sources, as mentioned in [105].

Compared to frequency control based on a PI controller, frequency regulation in an MPC-based MG, as described in [106], presents a faster response time, especially in scenarios with high penetration of wind generation. Furthermore, in [107], the predominant use of hydropower as a source of frequency regulation in an island system with multiple energy sources, such as hydroelectric, photovoltaic, and wind, was highlighted. In the case of an isolated MG with photovoltaic generation and an MPC controller, as mentioned in [97], the BESS acts as a damper to compensate for power and improve the frequency regulation performance.

3.6. Voltage Regulation

In a DC MG, DMPC is implemented at the secondary level for power control and voltage regulation, as mentioned in [108]. To optimize the total operating cost and improve the resilience of a DC MG, a voltage control strategy based on MPC was proposed in [109]. The voltage regulation reported in [110] reflects the main characteristics of MMG systems, where various devices are used to limit the transmission of information between MGs.

The DMPC strategies in [111,112] are concerned with restoring the frequency and voltage to the nominal values, and proportionally distributing the active and reactive power. In [113], a reactive power optimization model at multiple time scales based on DMPC was developed to harness the voltage regulation capacity of dynamic reactive power. Finally, in [114], droop control was used to establish voltage and frequency levels based on changes in the reactive and active power, respectively.

3.7. Optimization Functions

The optimization of intermittent energy sources and the limitations associated with active and reactive energy pose a few problems. In this context, the MPC-based optimization algorithm with sampling (SBMPC) is used in these cases, as mentioned in [115]. In [116], a holistic solution to optimally controlling the cross-sectoral energy flow between interconnected MGs was presented. The results showed that the applied interconnection line for MGs compared to the separated operation mode can decrease the system’s total costs. The model is raised with GAMS and solved with CPLEX. In [117], an EMS that can minimize the daily operating cost of an MG was presented. In the upper layer of this EMS, a convex optimization technique is used to solve the optimization problem. In the lower control layer, a rolling horizon predictive controller and MPC are used to achieve its target.

Furthermore, in [118], a bi-level EMS was considered for an isolated structure of networked MG (NMG), in which the MG contained cyber–physical connections for data communication and power exchange. The outer level of the EMS was used to exchange the required information and power support between the interconnected MGs.

In the case of [119], a bi-level energy optimization model was proposed. The lower-level model considers the real-time electricity price of distribution networks (DNs). The upper level constructs an MMG optimization model. The Dijkstra algorithm executes the solution. In the same way, [120] presented a bi-level, two-stage robust optimal scheduling (BTROS) model for an AC/DC hybrid multi MG (MMGs). In [121], a bi-level coordinated robust ED model for distribution systems (DSs) was executed, and MGs were formulated. In the upper level, a two-stage robust ED model for DSs is built. In the lower level, each MG optimizes its dispatch based on the received distribution locational marginal price (DLMP) and uncertainty distribution locational marginal price (ULMP), and the column and constraint generation (C&CG) algorithm is used.

Additionally, in [122], a bi-level coordinated control model was proposed for operation and energy management optimization. The consensus algorithm is applied in the upper-level model; in the lower-level model, MPC rolling optimization is utilized. In [123], an EMS which converts an infinite number of MMGs into an efficient system was designed, with each MG being able to achieve its goals and perspectives. A convolutional neural network (CNN) was proposed to execute the one-step estimation. In [124], the proposal consisted of a two-layer EMS for networked MGs. In the lower layer, each MG solves its own ED problem through a DMPC approach. In the upper layer, the MG decides how to optimally trade the energy based on the marginal cost information from the lower layer. A consensus-based algorithm and the replicator dynamics algorithm are applied. In [125], a two-layer system was created to enable peer-to-peer electricity sharing, where the first layer corresponds to a multi-agent coalition mechanism that allows for electricity trading negotiations, and the second layer consists of a blockchain-based mechanism that ensures the transactions established in the first layer. The Lagrangian relaxation and solver sub-gradient methods solve this model.

Furthermore, some authors, such as [126], have proposed a two-stage multi-objective optimization framework for the optimal energy management of MMG systems, using hybrid lexicography-compromise programming (HLCP). In [127], a transactive-based energy management framework was proposed for the operation of MMG distribution systems. The alternating direction method of multipliers (ADMM) is considered to develop an operational framework that copes with the distributed nature of MMG systems.

In Figure 6, the diagram illustrates that every distribution network agent (DGA) has the task of sending signals to the transactive energy (TE) coordinator assigned to its corresponding MG coordinator agent (MCA). The MCA’s role is to manage the scheduling of resources within the MG. If there is congestion in the core network, the DGAs modify the TE signals while employing the ADMM algorithm to utilize the flexibility of resources available in the MG.

In [128], a DMPC strategy is proposed to optimize the energy management of island MMG systems. The design of this strategy is based on non-cooperative game theory with a two-way auction. In the same way, in [129], a multi-objective optimal scheduling model of grid-connected MGs was proposed for minimizing the operating costs and improving the user experience based on chance-constrained programming (CCP).

3.8. CO₂ Emissions

In [130], minimizing CO₂ emissions in an MG was possible by implementing a robust approach of opportunity-constrained programming (OCP). Furthermore, in [7], the maximization of energy benefits and CO₂ reduction were addressed, integrating them into a multi-objective MPC optimization problem through a weighting factor that promotes sustainable technologies. As mentioned in [131], the integration of renewable energy sources and CO₂ emission reduction can be accomplished in one MG. Likewise, in [132], an optimal MPC control strategy was used in the target function to minimize the energy bill, meet the demand, and reduce CO₂ emissions. The importance of having exogenous variables to predict perturbations in the prediction horizon was highlighted in [133,134]. In addition, the need to have penalty signals from grid operators, such as dynamic electricity prices and CO₂ emissions, was mentioned. These elements are relevant to achieving efficient and sustainable management of MGs.

4. Discussion

The analysis of recent studies conducted by prominent authors in the field of MGs, specifically focusing on ED using MPC, brings a sense of contentment as it reveals the efficient and productive utilization of both human and economic resources for the betterment of society. This discussion aims to showcase the key insights obtained from the literature review, shedding light on the advancements and achievements in this area.

• This study presents data on electric vehicles’ participation in ED, displaying their functionality as intermittent storage resources. Further research must explore their role in MGs’ ED, especially in developing countries.
• Continual studies that enhance optimization methods for MGs are crucial to increasing their participation in the electricity market and reducing the impact of conventional energy generation expansion.
• Progress in implementing new high-capacity MGs is evident from the results obtained in ED.
• The utilization of multi-MGs in energy clusters demonstrates their reliability, resulting in significant cost savings and reductions in CO₂ emissions.

Regarding the techniques used with the diverse types of MPC, notable improvements can be observed in operability, encompassing variable control, optimization, and ED management:

• Combining DMPC and DDMPC, as seen in a recent article cited in this review, offers promising advancements in MGs.
• The use of renewable energy sources (RESs) in MGs has increased, but the uncertainty factor of energy generation has also risen. Recent articles employed more sophisticated algorithms to improve the certainty of uncertainty predictions.
• Energy storage management systems have played an increasingly significant role in MG management, extending the life and enhancing the efficiency of energy storage devices through MPC programs.
• Solar panel degradation has notably improved in terms of cell quality and efficiency.
• Bi-level optimization problems were analyzed, providing valuable insights into the complexities and challenges of optimizing MG operations. Moreover, the discussion on uncertainty modeling highlighted its importance in enhancing the robustness and adaptability of MG systems. By addressing these topics, this article contributes to a deeper understanding of MGs’ optimization and uncertainty aspects, paving the way for future, more effective and reliable energy management strategies.

Finally, the expansion of MGs worldwide, especially in developing countries, presents both challenges and opportunities, as highlighted by these studies’ results. Efforts to optimize MGs’ performance, incorporate renewable energy sources, and enhance energy storage solutions will shape the future landscape of sustainable energy systems.

5. Conclusions and Future Challenges of MPC Applied to ED

Due to the significant challenges in energy management, developing an effective operational strategy for MGs is increasingly necessary. This article provides a perspective on MG management strategies for an ED environment using MPC techniques. Below is a summary of the main themes identified during the review of the articles.

The following are future research directions or trends for further study:

• Modifying the gain value of the droop control or placing constraints directly on the control allows wind generation systems to adjust more quickly to changes in electrical systems.
• When considerable constraints of power sources are considered, the PSO algorithm can improve the design.
• Built-in MPC can be developed with the device-level droop method to achieve load-sharing, and flexible power dispatch among distributed energy resources.
• MG operations face increasing uncertainties; it has been proposed to integrate DDMPC with DMPC under a common framework based on stochastic optimization.
• Energy flow restrictions have been considered a complex task in ED.

The following are weaknesses that have been found that may be feasible to overcome in further research:

• The computational intensity of FCS-MPC is a significant drawback because power electronics applications are characterized by small sampling times.
• The primary frequency response of an MG via FSC-MPC must be performed with the fall control implemented in DFIG, with the GSC and BESS connected to the DC link.
• Recent articles provide valuable insights into examining the economic operation approach of MMGs and exploring the integration of various distributed generation sources. Furthermore, it is essential to investigate the economic operation of islanded MMGs by considering these aspects. A comprehensive understanding of economic optimization and the impact of different generation types on MG performance can be achieved, facilitating the development of more efficient and cost-effective MG management strategies.

To enhance the proposed methods presented by multiple authors, reinforcement learning can be employed to develop a closed-loop control policy for optimizing ESS operations. This approach will also address scenarios involving faults, such as short circuits, in an MG, ensuring the system remains efficient and responsive even during its initial setup.

• In the dispatch of a multi-objective load, the imbalance caused by the fluctuations in renewable energies is enormous, which merits a quick response time; a proposal must be sought to improve these times.

• In robust multi-objective cargo dispatch in MGs, cargo-clearance objectives impose considerable challenges on cost minimization.

Potential areas of development for MPC and ED:

• Improve VIC by minimizing DFIGs using wind generators;
• For frequency regulation and ED, controllers must be able to maintain frequency regulation and ED simultaneously;
• The development of predictive control strategies for power distribution control of MGs based on energy converters should continue to spread;
• Continue to drive the daily scheduling of MMG systems concerning safety constraints, to reduce operating costs and system emissions;
• Deepening the studies on fixed switching frequency MPC schemes for power converters helps to improve the harmonic spectrum at a single frequency, avoiding coupling problems between the different control levels.