Microgrids with Model Predictive Control: A Critical Review

Abstract

Microgrids face significant challenges due to the unpredictability of distributed generation (DG) technologies and fluctuating load demands. These challenges result in complex power management systems characterised by voltage/frequency variations and intricate interactions with the utility grid. Model predictive control (MPC) has emerged as a powerful technique to effectively address these challenges. By applying a receding horizon control strategy, MPC offers promising solutions for optimising constraints and enhancing microgrid operations. The purpose of this review paper is to comprehensively analyse the application of MPC in microgrids, covering various levels of the hierarchical control structure. Furthermore, this paper explores the emerging trend of employing MPC across microgrid applications, ranging from converter control levels for power quality to overarching energy management systems. It also investigates the future research perspectives by considering the challenges associated with establishing MPC-based microgrid control. The key conclusion derived from this review paper is that the implementation of MPC techniques in microgrid operations can greatly improve their overall performance, efficiency, and resilience. This paper thoroughly examines the various challenges faced in MPC-based microgrid operations, underscoring the significance of conducting research in advanced artificial intelligence (AI)-based MPC methods. It highlights how these cutting-edge AI techniques can bring about economic benefits in microgrid operations, addressing the complex demands of efficient energy management in a rapidly evolving landscape. The presented insights strive to enhance the comprehension and adoption of MPC techniques in microgrid settings, actively contributing to the ongoing improvement of their operational processes. By shedding light on key aspects and offering valuable guidance, this work aims to propel the advancement and effective utilisation of MPC methodologies in microgrids, ultimately leading to optimised performance and enhanced overall operations.

1. Introduction

According to the Government of India (Central Electricity Authority under Ministry of Power), the total electric power installed capacity [1] is 386.888 GW (as of 31 July 2021), and the maximum load demand until now is about 200 GW [2]. This indicates that approximately 50% of the generation capacity is still underutilised and that it seems unable to be further exploited in order to meet additional load demands. The problem is not with the electricity generation capacity but with the out-of-state centralised large-scale production and the intermittent nature of renewable energy resources. The primary motivation for this review paper stems from the issue of under-utilisation of generation capacity within the electricity sector. This drives the need to address these obstacles and to find solutions to effectively utilise the existing generation capacity to meet the growing demand for electricity. Consequently, this paper aims to propose solutions for large-scale centralised electricity generation at remote locations as a means to address this problem. Centralised generation, such as coal, gas, and nuclear power stations, refers to a large-scale system of electricity generation situated away from the load centres. It necessitates the use of high-voltage transmission lines and distribution systems to deliver electricity to end-users. On the other hand, distributed generation (DG) entails small-scale onsite generation, where electricity is produced closer to the load centres [3,4,5]. Several studies define DG and its two different technology implementations: integration into a utility distribution network or as a standalone structure at the consumer level [6,7]. Figure 1 provides a visualisation of these two DG technologies. Table 1 compares different DG technologies based on their respective capabilities. DGs, when combined with energy storage systems (ESSs), collectively form what is known as distributed energy resources (DER).

The popularity of growing DG technologies comes from the associated benefits. The benefits include: (i) Environmentally friendly: As these DG technologies are a mix of renewable energy resources such as solar and wind energy, it can be noted that DG technologies are more environmentally beneficial. (ii) Energy supply security: Thermal-electricity-producing resources are being depleted at a faster rate than they can be replenished. This requires the need for alternating energy resources provided by DG technologies. (iii) Increases energy mix: The DG electricity-producing technologies are a higher mix of renewable energy resources and a lower mix of carbon-generated electricity-producing resources. (v) Peak shaving: Higher cost of electricity generation at peak load time can be confronted by generating power using dispatchable DGs (like gas and microturbine based DGs) at peak times. (vi) Reliable to sensitive loads: Sensitive loads in the distribution system can use the advantage of quick start up of DGs to obtain immediate power supply. (vii) Electricity and heat production: Some of the DG resources (such as gas and microturbine-based DGs) generate heat that acts as additional benefits as it is near to load centres for its efficient usage. (viii) Commercial benefits: Benefits related to the self-consumption of electricity generated at the point of consumption, resulting in reduced electricity bills. Commercial profit may also be connected to the surplus power generated that can be sold to the distribution system utility, resulting in revenue generation [3,5].

These benefits associated with the DG technologies are achievable only when there is a seamless integration between the main utility grid and the end-users (loads). This confers the microgrid concept [8], which acts as the system’s brain required for the smooth operation of DER systems within the distribution level. The microgrid can be considered as an active distribution network for incorporating DGs, energy storage systems (ESS), and controllable loads at the distribution level [9]. It has a point-of-common-coupling (PCC) breaker for connecting/disconnecting it to/from the main grid. Based on that, it has two modes of operation, namely grid-tied and islanding mode [10]. The fundamental problems related to the power sector are mainly associated with growing expenses of energy, stability, outages, power quality and old infrastructure. The widespread acceptance of DGs backed by microgrid systems could be a potential answer to such problems. Figure 2 shows the forecast application market and market growth of a microgrid. The functionalities of these grid-connected microgrids (shown in Figure 2a) are given in [11]. The education institutes cover the maximum usage of a microgrid application followed by defence and other commercial sectors. Figure 2b shows a global forecast microgrid market growth of approximately 21–23 GW in 2022 compared to about 3–5 GW in 2011–2012 [12].

Table 1. Comparison of different DGs based on various abilities [13].

	Gas Turbine	Microturbine	Fuel Cell	Wind	Solar Cell
Peak Shaving	Yes	Yes	No	No	No
Environmentally Friendly	No	No	No	Yes	Yes
Economic Fuel	No (Except for biomass)	No (Except for biomass)	No (Except hydrogen is produced using solar and wind)	Yes	Yes
Highly Reliable	Yes	Yes	Yes	No	No
Dispatchable	Yes	Yes	Yes	No	No
Requires Energy Storage	No	No	No	Yes	Yes

Table 1. Comparison of different DGs based on various abilities [13].

	Gas Turbine	Microturbine	Fuel Cell	Wind	Solar Cell
Peak Shaving	Yes	Yes	No	No	No
Environmentally Friendly	No	No	No	Yes	Yes
Economic Fuel	No (Except for biomass)	No (Except for biomass)	No (Except hydrogen is produced using solar and wind)	Yes	Yes
Highly Reliable	Yes	Yes	Yes	No	No
Dispatchable	Yes	Yes	Yes	No	No
Requires Energy Storage	No	No	No	Yes	Yes

A microgrid is a viable way to deliver energy dependability and resiliency while having a lower environmental effect and cheaper energy costs [14]. The basic structure of a microgrid is shown in Figure 3, which includes DGs (PV, wind generators, fuel cells), loads and batteries that are connected to the bus through converters (acting as the interface between the utility grid and DGs). The microsource controller (MC) and load controller (LC) are both controlled by the main controller, i.e., the microgrid central controller (MGCC) [15].

Depending upon the load demand, the energy from the DGs should be controlled (through a proper control scheme under a microgrid) to regulate the power through the DGs accordingly. The microgrid serves as the brain to seamlessly integrate the DER systems between the main utility grid and the loads [16]. Nevertheless, microgrid operations encounter a series of challenges stemming from the dynamic nature of distribution networks, intricate power electronics converters, the diverse attributes of DG technologies in terms of generating both AC and DC power, as well as the need to manage two distinct modes of operations, namely grid-tied and islanding. Addressing these complexities in MG infrastructure necessitates the development of a robust control architecture for microgrids, which serves as the fundamental motivation behind this research. The control architecture of the microgrid based on a hierarchical control structure of a microgrid is later discussed with its three layers of control, i.e., primary or local, secondary and central, or tertiary control layers [17,18,19]. Expanding upon this research, the present literature explores the microgrid control structure by applying model predictive control (MPC) techniques, aiming to enhance its operational efficiency.

Figure 3. Basic structure of a microgrid [15].

Figure 3. Basic structure of a microgrid [15].

Model predictive control (MPC) is an optimisation technique that is preponderant in process industries, especially in the petrochemical and oil industries [20]. It is introduced formally in [21] as a heuristic technique with successful work performed related to industrial process applications. After that, MPC continued to penetrate commercially by making a solid theoretical and practical base. The previous 15 years show a significant shift in the MPC application approach, i.e., moving from industrial applications to mechanical [22,23,24,25,26,27,28] and electronic systems [29,30,31,32,33,34]. Now, the MPC technique is expanding its range of applications, i.e., becoming a more widespread application in power electronics [35]. The vast availability of powerful microprocessors with the ability to respond faster makes MPC a major source of attraction for its application in power electronics systems. The MPC method is a powerful optimisation strategy for feedback control that uses a system model to predict the future actions of the control variable. The future behaviour is based on the optimal selection of actuating action (from the forward forecast outcomes within a predefined time horizon) by considering the minimisation of a cost function. Compared to conventional closed-loop controllers (such as PID controllers), the MPC is an advanced feedback controller. The benefits associated with MPC include MIMO (multiple input, multiple output) system handling capabilities, better management of multiple constraints, compensation of dead times, better implementation of model nonlinearities, and robust control with excellent dynamic performance. The drawbacks of this strategy are related to the greater volume of mathematical calculations required, as well as to the necessity for its most accurate system model design to obtain the highest accuracy from the controller output. The various benefits and limitations of the MPC method are shown in

Table 2. Benefits and limitations of the MPC method.

Benefits	Limitations
Capability of controlling complex systems, including uncertainties and nonlinearities	Requires most accurate and complete model of the plant system
Makes use of complete dynamics of plant models	Complex deduction compared to classical controllers
Better handling and control of multivariable systems [36,37]	Difficulties related to solving optimisation problems at sampling time
Robust to disturbances [36,38]	More computational requirements
Improves steady-state responses (offsets error reduction) [39,40]	Complexity of having a larger number of controls
Predictive to both forthcoming disturbances and the required control	Expensive installation [41]

.

The technical motivation behind this work is driven by the diverse range of control challenges that arise in microgrid operations. Efficient operation of a microgrid requires addressing these challenges effectively. Some of the key control challenges include voltage and current control of DG units to accurately track reference values, regulation of supply voltage and frequency in both grid-connected and islanded modes, maintaining a balance between load and generation, and managing the load from the demand side to meet microgrid requirements [42,43]. Additionally, there are challenges related to grid resynchronisation, optimising operational costs through power-sharing between DGs and energy storage systems (ESSs), and coordinating power flow between microgrids and the main grid. Overcoming these technical challenges is essential to ensure the reliable and optimal performance of a microgrid, leading to improved energy management, grid stability, and cost-effectiveness. To tackle energy management in microgrids, researchers have employed algorithms based on heuristic approaches [44]. Another method applied in microgrids for energy management is the hysteresis band control (HBC) method [45,46,47,48]. However, model predictive control (MPC) has emerged as a promising technique for microgrid control. MPC utilises an optimisation-based problem-solving approach at each sampling time, aiming to minimise operational costs while meeting the load demands. Some studies have focused on utilising MPC for energy management in microgrids associated with electric vehicle charging stations [49,50,51]. The advantages of MPC make it a favourable choice for microgrid control. Firstly, it effectively handles disturbances and uncertainties through the incorporation of a feedback mechanism. Secondly, MPC has the capability to manage physical constraints, such as the slew-rate power limit of generators and storage capacity. Thirdly, it can forecast both the demand and generated power, enabling proactive decision making. Lastly, MPC is structured to anticipate and account for future system actions, making it particularly well suited for systems relying on renewable power generation. The MPC technique has substantial potential in resolving numerous operational and control issues in microgrids. While alternative methods exist, MPC offers a comprehensive framework to address the challenges associated with better control of a microgrid.

Table 3. MPC Methods in Microgrid: A summary based on research area and techniques.

Area of Research	References	Technique	Achievements/Contribution
Energy management	[52,53,54,55,56,57,58,59,60,61]	A two-layer stochastic MPC (sMPC) method [52]	Reduced discrepancies and nominal power production profile considering the unpredictable exchange of energy leading to optimal management of energy economically
		MPC with MLD (mixed logic dynamics) constraints [53]	Optimises issues of the ESS in microgrid operation, non-dispatchable to dispatchable generation, and enhances the lifetime of the ESS
		MPC-MILP (mixed-integer linear programming) control scheme [54]	Economic operation of a microgrid with cost minimalisation over intraday basis to meet the predicted load demand
		Supervisory MPC method for hydrogen-based microgrid [55]	Hydrogen-based microgrid with smooth operation of its equipment by preventing severe usage of fuel cell, battery and electrolysers
		Multi-scenario MPC (MS-MPC), tree-based MPC (TB- MPC), and chance-constrained MPC (CC-MPC) [56]	The three MPC-based controllers (MS-MPC, TB-MPC and CC-MPC) are compared based on the overall cost, calculations, power demand issues, and battery lifetime
		MPC strategy for power to heat and hydrogen (P2HH)- based microgrid [57]	Proposed P2HH-based microgrid with MPC controller shows better economic results by effective scheduling of various energy resources and higher efficiency by exploiting the waste heat of the electrolyser
		Hydrogen-based microgrids with hybrid storage using MPC [58]	MPC method is used for developing and solving the energy optimisation problem in a renewable energy-based microgrid with various ESSs presenting the optimal economical schedule
		Hybrid MPC (H-MPC) and Lyapunov-based hybrid MPC (LH-MPC) [59]	Comparison of proposed H-MPC and LH-MPC methods related to feasibility, closed-loop stability and receding horizon length to deal with the problems associated with energy management in microgrids
		Two-layer MPC with discrete dynamic programming (DDP) [60]	Lower running cost of operation and robust to uncertainties in microgrid are achieved using a nonlinear mixed-integer optimisation problem (MINLP)-based two-layer MPC controller
		Economic model predictive control (EMPC) for smart microgrid [61]	Compared to standard MPC for microgrid operational control, the proposed EMPC shows better economics by taking care of the cost related to production and distribution
Power Quality Improvement	[62,63,64,65,66,67,68,69,70,71]	Fourier-analysis-based MPC [62]	Compared to classical PI based controller, the proposed controller for voltage control of voltage source inverter shows speedy and improved transient response
		Finite-control-set MPC (FCS-MPC) as primary control [63]	Seamless transition between both modes of operation (grid-tied and islanding) in microgrid is achieved using overcurrent-limiting technique. The FCS-MPC method shows reduced transient compared to PI controller
		Two MPC-based controllers for primary and secondary control in islanded microgrid [64]	In islanded mode operation, the set points for primary control come from MPC-based tertiary and secondary control by solving the optimisation problem. The results are obtained from a real test facility of the University of Genova Smart Polygeration Microgrid (SPM)
		Distributed MPC (DMPC)-based secondary voltage control [65]	Distributed approach rejects the need of supervisory central control in autonomous microgrid; condescending achievement with voltage recovery using DMPC-based secondary voltage control
		Primary and secondary control-based FCS-MPC and state space predictor method [66]	Compared to conventional hierarchical control, the proposed method operates an islanded AC microgrid with enhanced output power quality having efficient tracking of the voltage reference
		Model predictive voltage control (MPVC) scheme and model predictive power control (MPPC) [67]	Reduction in renewable-energy-based fluctuating outputs by using MPPC method with ESS in AC microgrid, while efficient power sharing and stable voltage output are achieved by using MPVC and droop method to control inverters connected in parallel.
		FCS-MPC with single-step prediction horizon [68]	Rapid transient with enhanced steady-state response by using the FCS-MPC method for voltage regulation of a single voltage source converter (or multiple voltage source converters with FCS- MPC) with LC filter
		MPC-based load frequency controller (LFC) [69]	LFC-based models for multi-microgrids (grid-connected) applied with the MPC mechanism show enhanced control (compared to PI controllers) to maintain the stability of microgrid frequency; the effect of communication delays was also studied on system frequency
		Fuzzy MPC [70]	Compared to standard MPC, the fuzzy-adaptive-based MPC in microgrid application shows improved and rapid control of load frequency
		Multi-stage H-infinity (H∞) controller with harmony search (HS) optimisation [71]	For an islanded mode microgrid, the proposed work compared the multi-stage H∞ controller with HS optimisation (for secondary and tertiary layer control of hierarchical microgrid control architecture) and MPC-based controller. The multi-stage H∞ controller with the HS controller shows better results compared to MPC in terms of reducing state variables, reduced THD and improved frequency deviations
Electric Vehicle (EV) Integration	[72,73,74,75,76]	Charging operation of EV using MPC mechanism [72]	The proposed MPC-based control for EV charging operations leads to the EV users taking part in management of demand-side programs; this will enable the EV users to help in enhancing the efficiency and stability of the smart grid
		Multiple model predictive control (MMPC) for plug-in hybrid EV (PHEV) [73]	Compared to MPC and PID controllers, the proposed MMPC mechanism for PHEV charging/discharging provides better state of charge (SoC) with reduced frequency deviations and robust behaviour to uncertainties within the microgrid system
		MPC for LFC in microgrid with EVs [74]	The Proposed MPC mechanism for the load frequency control problem in the microgrid with EVs shows zero frequency deviations while addressing the constraints related to EVs and DGs
		MPC for three-level buck/boost converter [75]	Implemented the integration of an EV charging station (within dc microgrid) by proposing a controller based on a bidirectional three-level buck/boost converter with MPC; the mitigation of imbalance in voltage as well as issues related to voltage regulation in a bipolar DC microgrid are dealt with for the proposed controller with faster response
		MPC and adaptive droop control for ESS and EVs [76]	The frequency deviation problem in an isolated microgrid, caused by renewable integration or sudden load demand variations, is dealt with using MPC and adaptive droop control for ESS and EVs; the proposed controller with better performance is compared with PI as well as with a fuzzy-logic-based PI controller

provides an overview of significant research studies that have incorporated MPC in microgrid control operations, highlighting their contributions to this field.

This paper makes significant theoretical contributions that enhance its originality. These contributions can be summarised as follows:

• Microgrid systems: This paper explores the concept of microgrid systems, highlighting the relevance and challenges associated with distributed energy resource systems in electric power systems. It also discusses the hierarchical control structure employed in microgrid operations.
• Model predictive control (MPC): This paper introduces the concept of MPC, a powerful optimisation method that utilises a receding horizon strategy. This provides a foundation for the subsequent discussions on applying MPC in microgrid operations.
• MPC-based microgrid control: This paper delves into the application of MPC at different control levels in microgrid operations, including primary, secondary, and central control. This comprehensive analysis sheds light on the role of MPC in optimising microgrid performance.
• Microgrid advancements with MPC: This paper explores the advancements enabled by artificial intelligence (AI)-based intelligent MPC approaches in microgrid operations. It also includes economic analysis and discusses the challenges associated with implementing MPC in microgrid systems.

Overall, this work offers an extensive review of the use of MPC at different control levels in microgrid system operations. It not only enhances the understanding of MPC in microgrid research but also expands the scope for future research in related fields.

The organisation of this paper is as follows, as depicted in Figure 4: Section 2 offers a brief discussion on the primary, secondary, and central control layers of the hierarchical microgrid control structure. In Section 3, the fundamental principles of MPC are presented, along with its implementation in the hierarchical structure of a microgrid control. Section 4 reviews the intelligent MPC techniques and economic aspects of MPC-based microgrid operations and highlights key challenges in this domain. Finally, Section 5 concludes this paper followed by future research directions and opportunities in MPC-based microgrid control.

2. Hierarchical Control Structure of a Microgrid

Over the last two decades, microgrids have provided dependable, stable, secure, and cost-effective operations (both in grid-tied and islanding modes) that require many efforts linked to their protection system design and control structure. A higher level of the build-up for microgrid systems with conventional systems is based on its improved potential due to the advancements in microgrid control. Developments in the microgrid are required to cope with the challenges associated with its control [19,77], and these challenges include low inertia, uncertainties, bidirectional power flow, dynamic modelling, and stability issues. Such challenges require a hierarchical control structure [78,79] of a microgrid based on a timescale where system frequency and voltage variations should be rapidly controlled (less than a second) and should have a longer time frame (minutes to hours) for managing other aspects such as unit commitment, energy trade, economics, and demand optimisation. The hierarchical control structure is divided into three control levels, i.e., local (primary), secondary and central control.

Table 4. Control levels in hierarchical control structure of a microgrid [19].

Control Levels	Time Response	Functions
Local/primary control	Milliseconds to seconds	Active and reactive power sharing
		Voltage and frequency control
		Detection of island mode
		Makes use of droop control method
Secondary control	Seconds to minutes	Compensate voltage and frequency deviations caused by load deviation and load control action
		Smooth transition between grid-tied and islanding mode of operations
		Power quality control
Central control	Minutes to hours	Operates energy management system
		Maintains power flow between microgrids, neighbouring grids, and main grid
		Ancillary services, economics and coordination among other microgrids and main grid

shows the control levels, which are based on their different time responses and functions performed [19].

2.1. Primary Control Level

The local/primary control layer handles power sharing and internal control of DG units [80,81]. It comprises DG’s internal current and voltage control loops, which use the droop control method and mimic the droop characteristics of high-inertia synchronous generators to meet variable load demands [82]. The DG units use voltage source inverters that track the reference voltage signal generated using droop control [83]. This control layer has a fast time response (milliseconds to seconds) to meet its primary goal of compensating for any sudden differences in power demand and generation. The droop control in the primary layer generates reference voltage signals required by controllers to produce actuating signals for the voltage source inverter. The actuating signal for the voltage source inverter (connected to the DG unit) directs the voltage of DG units to track the reference, which keeps changing along with the mismatch in demand and generation. The microgrid is a low voltage grid with high resistance to the reactance ratio. This indicates that active power controls the voltage and that reactive power is coupled with frequency. Droop control in such cases shows limitations, especially in the case of nonlinear loads, where the harmonic currents come to play during active and reactive power balancing, while in another case, the droop control in the primary control level shows the drawbacks of variations in voltage amplitude and frequency that are dealt with in the secondary control level.

2.2. Secondary Control Level

Based on central/tertiary control planning, the secondary control layer aims to manage the sharing of load between all the DGs and ESS accordingly [84]. The secondary control layer eliminates the voltage and frequency deviations caused by the load variations and primary control actions [85]. The frequency and amplitude variations of the voltage are measured and compared with their respective reference values [86,87]. The comparison gives error signals indicating the deviations in frequency and voltage amplitude [88]. Such deviations are corrected in the secondary control layer by sending the corrective signals to the controller [89]. The synchronisation of a microgrid along with the main grid is also conducted under secondary control layer [90]. The primary and secondary control action based on the load variations is shown in Figure 5, where the load demand varies from $P^{*}$ to $P_m$ and from $Q^{*}$ to $Q_m$, corresponding to their respective voltage and frequency deviations. Following the droop control, the frequency varies from $w^{*}$ to $w_1$, and voltage amplitude varies from $V^{*}$ to $V_1$. The values $P^{*}$ and $Q^{*}$ are the reference values of active and reactive powers corresponding to the rated values of bus frequency ($w^{*}$) and voltage ($V^{*}$). The secondary controller will restore these variations in voltage and frequency by adding and shifting the droop curve to initial characteristics. Equations (1) and (2) follow the droop characteristics of active power–frequency and reactive power–voltage curves to follow the varying load demands [83].

$$w_1=w^{*}-k_p(P_m-P^{*})$$

(1)

$$V_1=V^{*}-k_q(Q_m-Q^{*})$$

(2)

where $w_1$ and $V_1$ are the values of frequency and voltage corresponding to the load $P_m$ and $Q_m$. In addition, $k_p$ and $k_q$ represent the active and reactive power droop coefficients.

Based on these values of $w_1$ and $V_1$, a reference voltage signal is generated. This signal is compared with PI-based cascaded controllers (voltage and current control feedback loops) to control the output of the inverter connected to the DG unit according to the load variations [91].

2.3. Central Control Level

The central control layer handles the supervisory activities related to monitoring primary and secondary control levels and addresses the mitigation issues in the event of a critical contingency. Any technology that advances on its predecessor must always consider the economic benefits, and these considerations are incorporated into this control layer [92]. This control level acts as an energy management system (EMS) with economic aspects for proper power flow control within the microgrid, neighbouring grid, and the main grid [93]. This control layer constructs the schedule for dispatch of generation and storage of power that includes advanced algorithms for its control, taking care of the economy, environment and its proper management of power flow within a single and interconnected microgrid system [94]. The MPC mechanism is an advanced control method that can deal with the optimisation issues related to the economics, power quality, management of power flow and degradation of ESS in microgrid systems [64].

In a microgrid, together with neighbouring microgrids and the main utility grid, the overall hierarchical control system allows for coordination of DG units with appropriate load sharing, voltage–frequency regulation, smooth grid synchronisation, optimal operating cost, and power flow control [82].

3. Model Predictive Control

The MPC can be considered a methodology capable of solving complex multivariable control problems [95]. Figure 6 shows the block diagram for the basic system of MPC. The process model outputs are compared with the actual outputs. The actual and model outputs come from the actual process and its process model. The compared result from the outputs of the process and its model is then forwarded to the prediction block as a feedback signal. The MPC calculations (set-points and control) are performed at each sampling instant using the predicted outputs from the prediction block. These MPC calculations lead to the formation of new inputs (control moves at each sampling instant) in such a way to make the predicted responses track the set-points optimally. The set-points use optimisation of control objectives (cost functions) for their calculations in the controller. The basic idea following the MPC concept lies within factors such as the model of the system, the cost function that signifies the expected behaviour of the system, and minimising the cost function to achieve optimal actuation actions [96]. MPC is more likely mentioned by a set of control methods instead of referring to a particular control approach. It takes comprehensive benefits from the model of the system by minimising the predefined targeted objectives (cost functions) and by obtaining optimal control commands to predict the future behaviour (over a finite time horizon) of state variables [97,98].

The calculations in MPC are associated with the current measurements and predictions of upcoming values of the outputs. These calculations must follow a sequence of control actions (manipulated inputs or control moves) to optimally predict the response to follow the set points. Figure 7 shows the basic concept of MPC with k denoted as the present sampling instant, y as past output, $\tilde{y}$ as predicted output, and u as control (manipulated) input. As shown in Figure 7, for the present sampling instant k, the MPC method calculates a set of N input values $u(k+i$-$1),i=1,2\dots ..N$. The input is maintained constant after N control actions, and these N values of inputs comprise one current and N-1 future values of inputs. These manipulated input values are required to calculate the predicted values of future outputs $\tilde{y}(k+i),i=1,2\dots ..P$ to meet the desired set-point optimally. The predicted output values (i.e., P) and control moves (i.e., N) are called prediction and control horizons. These calculations of control actions are based on the plant model and minimisation of the cost function, i.e., optimisation of control objectives. A predictive output value (prediction horizon) sequence of N inputs (control actions) is calculated for each sampling time. The MPC method only instigates the first control action (i.e., first input calculated) to predict the next output. Further, the next sampling time is shifted to the present sampling time, and a new sequence of control moves is calculated. This procedure is repeated at each sampling time, making MPC a receding horizon control approach [100]. In this receding horizon approach, out of N control moves, only the first one is implemented to use the most recent measurements $y\left(k\right)$ for every shifted sampling instant containing a new sequence of control moves. Without this receding horizon approach, it would be difficult to deal with the presence of unmeasured disturbances with the old information-based control actions and predictions.

3.1. MPC-Based Microgrid Control

MPC is very important for handling the nonlinearities and variety of constraints corresponding to the operation of a microgrid under different conditions [101]. Implementing MPC in microgrid control operations enhances the fast dynamic response related to control voltage, frequency, and power [102]. There are two levels suitable for implementing MPC-based microgrid control. These two levels can be termed inverter-level and grid-level MPC. If compared with their basic control structure, both inverter- and grid-level MPC approaches are similar. Both the approaches are centred on the most appropriate plant model and optimisation of cost functions. Based on the predicted plant model and the values of state variables, the MPC optimises the cost functions (i.e., solves the control objectives using algorithms) for optimal tracking of reference together with minimum error produced. Inverter-level MPC is related to the control of inverter’s switching signals, while power dispatch commandments for DERs are determined under grid-level MPC.

Continuous control set MPC (CCS-MPC) and FCS-MPC are two sets of MPC-based control at the converter level [103,104]. For controlling the converter output, the continuous signals are generated by CCS-MPC for the PWM regulator; contrarily, FCS-MPC is based on discrete signals, which remove the usage of any PWM modulator [34]. The comparison based on several attributes is shown in

Table 5. Comparison between continuous-control-set MPC (CCS-MPC) and finite-control-set MPC (FCS-MPC) [34].

Parameters	CCS-MPC	FCS-MPC
Output Control Signal	Control signals are received as continuous-time signals	Possible control actions are finite discrete signals
Modulator	Requires a modulator for its operation and therefore comes with constant switching frequency	Generally, it does not require any modulator and comes with variable switching frequency
Optimisation Problem	For unconstrained CCS-MPC, an analytical solution of an optimisation problem is obtained by making the derivative of the cost function equal to zero (if constraints are involved, then a quadratic programming (QP) is required to be solved)	At each sampling instant, a set of acceptable switching sequences are obtained with the evaluation of their cost functions; the optimisation problem is solved by selecting the switching sequence with the minimum value of its cost function
Horizon Length	A long horizon can be employed, as it provides an analytical solution for solving an optimisation problem	Short horizon length is preferable, as it is too exhaustive to evaluate the cost functions of the switching sequences
Computational Cost	In case of constrained CCS-MPC, the online optimisation is required; therefore, its computing cost is higher in this case as compared to FCS-MPC [107].	It is generally used with short horizons (usually one or two steps) and does not include fast dynamics performance with its algorithm for optimisation; hence, computing cost in this case is usually lower compared to CCS-MPC [108]

. For the short horizon, FCS-MPC is more instinctive and relatively simple as compared to CCS-MPC [105]. Figure 8 shows the basic working of MPC to control the microgrid for inverter- and grid-level operations. In inverter-level MPC [106], the predicted plant model predicts the values of its output (predicted plant’s output ($\widehat{x}$) ) based on the values of the present measured parameters (x). Further, the reference set values (x*) and predicted values ($\widehat{x}$) are taken into consideration by the optimiser to optimise the control objectives for generating the required actuating signals (i.e., switching signals) for the inverter control action. The present measured parameters (x) and the reference set output values (x*) refer to the values of voltage, frequency, or current. On the other hand, grid-level MPC is based on controlling operational issues such as ESS capacity and power flow in a microgrid among the neighbouring microgrids. The predicted or forecast states (e.g., power cost, load demands, wind and solar generations, etc.) of the system builds the predicted model required. This predicted model, based on present and past states, develops the predictions of future states depending on the optimisation of cost functions while considering all the constraints (i.e., constraints involving power lines, DGs, converters, and other components of grid operations).

3.2. Primary Control Incorporating MPC

The microgrid with the hierarchical control structure is formulated using three control levels as explained in Section 2. The primary control level is centred around the frequency, and the amplitude management of the supply voltage is delivered by each inverter using inner control loops (for islanded mode). With grid-tied mode, the focus of control changes to power flow regulation (as voltage and frequency are fixed by the grid), and it includes power flow as the cost function in MPC. The droop control method, which uses traditional PI controllers in the inner loops of each inverter, has been widely used in the primary control level of a microgrid [91]. Such an approach leads to drawbacks such as a poor transient response, high harmonics in supply voltage and coupling of active and reactive powers. It requires advanced control methods (such as MPC-based control) to eliminate the drawbacks of using the inner cascaded loops (PI-based droop control) for each inverter in the microgrid system.

For the MPC in the primary control level, the overall effort required to enhance the primary control mainly focuses on using MPC instead of the inner cascaded loops (current and voltage loops). It requires a cost function to include voltage formulations in the MPC technique necessary for stable voltage supply, especially in the islanding mode of a microgrid operation. The optimal control set is provided by the cost function (i.e., control objectives) optimisation. Figure 9 shows the implementation of MPC with the primary control of the microgrid together with the attained virtual impedance through the droop control and power calculations required for the primary control [102]. In [63], the primary controller based on FCS-MPC regulates the DG’s output power. The set-points for primary control (in islanded microgrid mode) come from MPC-based secondary and tertiary control by solving the optimisation problem, and the results are obtained from a real test facility, as shown in [64]. Compared to conventional hierarchical control, the proposed method (in [66]) operates an islanded AC microgrid with enhanced output power quality (i.e., reduced error voltage), having efficient tracking of the voltage reference. Implementation of MPC compensates for the output power fluctuations that come because of the intermittent nature of renewable energy sources [109].

3.3. Secondary Control Incorporating MPC

Droop control, extensively used in the primary control layer of hierarchical microgrid control structures, causes voltage and frequency fluctuations in steady state, which is a significant problem related to power quality issues in microgrid operations. It can lead to distorted power supply, equipment failure, and other stability issues. The fluctuation in voltage/frequency emerges due to the primary control level operations and is dealt with using secondary control in the hierarchical control structure of the microgrid. The secondary controller is implemented to compensate for the fluctuating voltage and frequency by adding a corrective term and by shifting the droop function to its initial characteristics. Alternatively, the MPC-based secondary control compensates for the changes in frequency and voltage by considering the frequency and voltage measurements in the cost function. The predictive model is developed based on a local system-based mathematical relationship between present and previous states. In [110], a Smith-predictor-based enhanced PI controller was used, showing faster response for frequency renewal with lesser oscillations. Robust secondary control is achieved by utilising MPC in a distributed way with a model based on local and neighbouring data for predicting future values [65,111]. In [64], MPC with optimisation problems is defined and solved at the secondary control level for the islanded microgrids. These problems are multi-objective optimisation problems where the MPC-based secondary level controller has to regulate the frequency and track the reference from the central level control in the islanded microgrid. The problem associated with frequency and voltage compensation in secondary control introduces time delays affecting data reliability and signal updates. Such problems arise, as the communication networks are required to deliver the signals from local and neighbouring systems where the MPC is considered to be very effective with its fast transient response in secondary control level operations together with maintaining the robustness to severe disturbances [69,110,112].

3.4. Central Control Incorporating MPC

At the apex of the hierarchical control structure within a microgrid lies the central control, which plays a pivotal role in orchestrating various aspects of the system. It encompasses the EMS and power flow optimisation, focusing on achieving economic operations. This entails the determination of active and reactive power allocations for each DG unit. The MPC method, with its versatile and optimal control characteristics, is well suited for central control in microgrid operations. By leveraging its MIMO capabilities and robust handling of constraints, MPC emerges as an attractive choice for efficient and effective management at the central control level [30,113]. The predictive model for central control requires all the mathematical formulations of the state variables required in microgrid operations. Maximum power output, optimal power flow, and microgrid operation costs are the main critical factors for designing the cost function. The main objectives of MPC-based central control in a microgrid are shown in Figure 10. Economic optimisation is a critical factor in interconnected microgrids, with the aim of minimising costs while fulfilling operational requirements. Conversely, power management constraints play a pivotal role in grid-connected microgrids, ensuring dependable and efficient operation. These constraints specifically concentrate on power flow management, system stability maintenance, and compliance with grid regulations. The study referenced in [61] focuses on developing a predictive model for a microgrid, specifically utilising an ESS and considering the power output demand of the system. By incorporating the ESS into the model, researchers aim to accurately forecast and optimise the power output required by the microgrid. In [64], the MPC mechanism was used at the central control level to formalise and solve optimisation problems, which include operating cost with implementation of constraints related to active/reactive power balance and state of charge of the storage system. The solutions to such problems at the tertiary level are obtained, forming the reference provided to secondary level control. Consideration of financial and eco-friendly aspects is crucial in constructing the cost function for MPC in a microgrid’s central control operations. Financial considerations optimise parameters such as energy prices and revenue generation, while eco-friendly objectives focus on sustainability metrics. Integrating these aspects ensures a balance between economic efficiency and environmental sustainability, promoting greener and more sustainable power-management strategies within microgrids [114]. This approach ensures that power-management strategies within microgrids not only optimise financial resources but also promote environmentally responsible practices for a greener and more sustainable energy future.

4. Advancements in Microgrids with MPC

The implementation of MPC in a microgrid hierarchical control structure was discussed in Section 3. MPC-based microgrid control techniques have limitations in dealing with grid effects, including diverse topologies, high PV penetration, and switching techniques. Intelligent approaches are needed for addressing these challenges at both basic and higher power flow regulation levels. DC microgrids face network delays in sensor, controller, and actuator communication, hindering MPC-based control [115]. Introducing compensatory schemes such as network delay compensators can enhance controller robustness. Moreover, complications arise from nonlinearities, model uncertainties, and divergence between the converter controller and plant in microgrid operations. Soft computing methods such as fuzzy logic, genetic algorithms, and neural networks are employed to enhance MPC-based microgrid control [70,116]. While these methods can enhance control effectiveness, they may introduce complexities and increased computational requirements. Automatic selection of weighing parameters for cost functions in MPC control of power converters is another challenge. AI techniques, such as combining artificial neural networks with particle swarm optimisation, have been proposed for optimising control objectives [116]. However, determining the optimal weighing parameters remains challenging.

Overcoming these limitations is vital for ensuring robust and effective microgrid operation. Ongoing research focuses on developing intelligent approaches, exploring economic analysis, and resolving associated challenges in MPC-based microgrid control. By leveraging soft computing methods, advancing communication technologies, and refining control strategies, researchers aim to mitigate these challenges and enhance overall performance. This section presents novel intelligent approaches to enhance the MPC method, along with an economic analysis and the challenges associated with MPC-based microgrid control.

4.1. Intelligent MPC Approaches

Microgrid operations are based on the application of power electronics and a power system. The MPC-based microgrid control technique still comprises some gaps related to the grid effects on the regulation of converters, its topologies with high PV penetration, and switching techniques. Therefore, it requires an intelligent approach for better operation to deal with such problems on basic levels of converter control and higher levels of power flow. Soft computing methods are incorporated with MPC-based microgrid control to add more smoothness and intelligence to microgrid operations with MPC. In [70], a fuzzy adaptive MPC approach was used to control the load frequency in a grid-forming microgrid. The cost function with its tuning parameters was fuzzified based on the proposed fuzzy MPC approach with a controller based on the fuzzy rule, showing faster and adaptable responses under different conditions. Implementing the Takagi–Sugeno (TS) fuzzy-model-based MPC can deal with the delays due to networked communication between sensors, controllers, and actuators in DC microgrids [115]. In [115], the paper implemented two network delay compensators to make the controller more robust with minimal computational weights. The delays in networked systems with nonlinearities can also be dealt with by implementing the proposed scheme presented in [115]. Other soft computing technologies, such as genetic algorithms and neural networks, are used with MPC to improve its control goals. A temperature-regulating system based on the implementation of MPC and genetic algorithms was developed for residential structures in [117]. According to the simulation results in [117], residents will have higher comfort at a lower cost and with reduced energy consumption. Dealing with the uncertainties of models and divergence between the converter controller and plant leads to complications in microgrid operations. In [118], an outlier–robust extreme learning machine (OR-ELM) algorithm was combined with DMPC to provide a framework that comprises a robust data-predictive control strategy for lowering operating costs and dealing with the volatility of the electricity retail pricing market. A model-free MPC scheme for a three-phase converter based on the recurrent neural network method (state-space neural network) was proposed in [119] to mitigate these consequences. Compared to conventional MPC, the proposed neural-network-based model-free predictive-control method shows more robustness under different scenarios. The control of power converters with finite-set MPC deals with the challenges of the automatic selection of the cost function’s weighing parameters. In [116], an artificial neural network (ANN)-based approach along with particle swarm optimisation (PSO) technique was proposed for powerful and fast optimisation of the control objectives in MPC. Soft computing methods such as fuzzy logic and ANN are being used with MPC control to provide more flexibility and intelligence for MPC approaches with microgrid applications.

4.2. Microgrid Economic Analysis with MPC

Microgrid design requires DG installations, leading to the high capital cost of energy produced by it. Due to the changing nature of equipment cost and the continual development in renewable energy technologies, it also shows variations in per kW installed for renewable DG installation. Compared to central generation systems, the high capital cost of installed power is a critical disadvantage of DG technologies (in microgrid systems). The economic operation of DG units in microgrid applications has been dealt with by including compensation mechanisms with policies and regulation systems [120,121]. The new research studies on MPC-based microgrid control minimise the acquired system operational costs and make the most out of economic profitability. Many research studies show that the predictive model-based approaches in microgrid operations lead to cost minimisation with a lower running cost of operations and optimal economic schedule [52,58,60]. In [54], the MPC-MILP control scheme was tested on an experimental microgrid (located in Athens, Greece), and the outcomes of the experiment with the MPC-MILP control scheme were more cost-effective (compared to the original practice of the experimental microgrid) for microgrid operations. The intermittent nature of non-dispatchable renewable energy resources has difficulty achieving a committed generation schedule, leading to economic penalty charges imposed by the electricity markets. MPC with an objective function, including energy prices, plant state, weather forecast, and penalty cost estimation, is beneficial for obtain profit from microgrid operations [122]. The photovoltaic-based combined heat and power (CHP) home microgrid with an electrical and thermal energy storage (TES) system has problems related to the uncertainties of CHP systems and the uncontrolled charging of the TES system. In such cases, MPC methods are beneficial for optimum usage of storage systems, which leads to smaller storage systems with lower investment costs of both the storage system based on TES and batteries [123]. The MPC method proves to be a highly effective instrument in achieving optimal EMS in microgrid operations. By employing the MPC approach, numerous advantages can be harnessed, such as advanced forecasting techniques, effective constraint management, multivariable control capabilities, and the ability to address uncertainties [124]. These factors collectively contribute to the development of a highly efficient EMS, resulting in more cost-effective and economically viable microgrid operations.

4.3. Challenges with MPC-Based Microgrids

After being implemented in process industries, the MPC has proven immensely beneficial in power electronics and power systems in microgrid control operation. Certain aspects require improvements in dealing with the restrictions and challenges for optimal performance in microgrid control operations. These challenges mainly include more accurate predictive model design, MPC-based microgrid operation stability analysis, and cost functions considering various parameters. One of the critical issues with MPC-based microgrid operations is the exchange between processing time, performance level, and financial costs. It is challenging to maintain the performance of system operations while minimising the costs and calculation time. In MPC, developing an accurate predictive plant model of high quality is essential and challenging to achieve. The complex calculation for designing an accurate predictive model can be complicated and remains a significant challenge [71,125,126] that requires a fast and powerful processor. The stability analysis of a microgrid operation with MPC-based converter control is still in its initial phase compared to droop control with conventional closed-loop PI controllers. Hence, a comprehensive stability study for MPC-based microgrids still requires a large number of authentications [101,126]. To deal with all the aspects of control targets in MPC-based microgrid control, the design of the cost function is a significant limitation. It becomes problematic to achieve stability with large numbers of variables associated with the cost function. These variables begin with power quality and control issues and progress to include economic management challenges of microgrid operations. Implementing such a large number of control parameters is incredibly challenging, and certain operations are still hypothetical. Given the challenges of adopting MPC in microgrid control operations, it has become an exceptionally motivating and appealing research topic.

5. Concluding Remarks and Research Directions

In this paper, the authors discussed the application of MPC in microgrid control operations and its potential for enhancing power quality, stability, and energy management. The emergence of cheap microprocessors has facilitated the adoption of MPC techniques in solving control problems, particularly in industrial processes. Over the past decade, MPC has gained traction as an effective control method for microgrids, with extensive studies conducted in power electronics and electrical power systems. The seamless integration of DGs with a higher mix of renewable energy resources at the distribution level necessitates smart microgrid control methods such as MPC. As a result, adopting MPC in microgrid operations has become an attractive research option for exploring its applications and improving control approaches in microgrids.

Based on our analysis, we outline several future research directions and opportunities in MPC-based microgrid control:

• Comprehensive stability analysis: The MPC-based microgrid is still in its nascent stage compared to conventional microgrid control methods. Further exploration is required to conduct a comprehensive stability analysis using contemporary techniques.
• Artificial intelligence (AI) techniques: The integration of intelligent techniques such as deep learning, fuzzy logic, artificial neural networks (ANN), and machine learning with MPC controllers holds great promise for the future. This integration would enhance the intelligence of MPC in the hierarchical control structure of a microgrid. AI techniques, such as deep learning, offer distinct advantages over model-based approaches such as model predictive control (MPC). Nevertheless, AI predictions rely on historical data and demonstrate an exceptional capacity to analyse extensive datasets, extracting valuable insights without being constrained by pre-existing models. This characteristic grants AI a notable advantage, positioning it as a compelling choice for the future. AI not only offers enhanced capabilities but also opens up new possibilities beyond the constraints of conventional model-based techniques.
• Integration of MPC with combined heat and power (CHP) systems: A comprehensive study on integrating MPC with CHP systems for microgrid applications is needed. Leveraging waste heat through CHP system implementation can lead to more efficient microgrid operations.
• MPC in DC microgrids: With the increasing interest in DC microgrids due to their advantages in reliability and efficacy, researchers are exploring their development in modern power systems [127,128]. Implementing MPC methods in DC microgrids has become an emerging trend that requires further investigation.
• Performance degradation analysis: While reducing costs and computational time, there are concerns regarding performance degradation in MPC-based microgrid operations. Research is needed to address these aspects and to optimise MPC controller applications.
• MPC-based microgrid with Internet of things (IoT): The Internet of things (IoT) has revolutionised digital communication. There is a wide range of research opportunities that remain unexplored in investigating the integration of MPC-based microgrids with IoT as a communication channel.

In conclusion, this paper emphasised the necessity of seamless integration of DERs into existing power systems through microgrids. The hierarchical control levels of a microgrid differ from conventional power systems in terms of power flow, synchronous generator inertia, transmission line characteristics, and system configuration. The control aspects of a microgrid, including power quality, stability, and energy management, still present research gaps. MPC-based microgrid control offers promising characteristics to address these gaps effectively. The authors have provided a comprehensive understanding of MPC implementation at various levels of a microgrid hierarchical control structure. The significance of MPC-based microgrid control was discussed, highlighting its advantages over conventional control methods. Additionally, the authors explored advancements in intelligent MPC approaches, economic analysis, and associated challenges.

The outlined future research directions will contribute to the further development and implementation of MPC-based microgrid control. By addressing the challenges and exploring these research opportunities, we can enhance the overall performance and reliability of a microgrid, paving the way for a sustainable and efficient power system.