Optimizing microgrid performance a multi-objective strategy for integrated energy management with hybrid sources and demand response

Abstract

This study tackles a key challenge in modern energy management: how to optimize energy distribution when expanding the network is not economically or practically feasible. It explores the integration of hybrid renewable energy sources into a microgrid (MG) and proposes an energy dispatch strategy for MGs operating in both grid-connected and standalone modes. The study incorporates various energy sources, including solar panels (PV), wind turbines (WT), fuel cells (FC), microturbines (MT), diesel generators (DG), and energy storage systems (ESS). Unlike many existing studies that focus only on reducing operating costs, this research also considers energy losses, environmental impacts, and demand response—a vital but often overlooked factor. The research introduces a new method using a mixed-integer linear programming approach to solve the microgrid energy management (MGEM) problem. This method provides a multi-objective solution that includes demand response scheduling and optimizes factors such as PV and WT capacities, energy storage strategies, battery usage, power exchange with the grid, and overall costs and environmental impacts. When compared to leading optimization algorithms, the proposed approach showed better performance. The study also highlights the benefits of demand response programs in improving MG operations. For instance, using a Real-Time Pricing (RTP)-based demand response program reduced operating costs by 3.31%, emission penalties by 2.61%, and power losses by 0.62%. Similarly, a Direct Load Control (DLC)-based program achieved reductions of 2.25%, 2.1%, and 3.56%, respectively. This work advances MG energy management by addressing overlooked factors and demonstrating the benefits of integrating demand response programs into energy optimization strategies.

Introduction

Microgrids (MGs) play a fundamental role in the future of power systems by providing a solution to the sustainability of energy systems¹. Simply put, an MG refers to a subset of a low-voltage grid comprising different elements that enable its active operation under both grid-connected and islanded modes². Typical elements employed in MGs consist of normal network components, such as loads and control devices, as well as renewable or non-renewable distributed generation (DG) components integrated or not integrated with energy storage equipment. MGs are growingly integrated into power networks to the extent that larger grids are now prevailed by the interconnection of several MGs forming multi-microgrids (MMGs). MMGs are usually composed of geographically nearby individual MGs connected to a unit distribution network (DN). The interconnection of MGs constituting an integrated distribution system improves the resilience of the grid in the face of unpredicted incidents, e.g., faults and meteorological events, and enhances its reliability and efficiency by helping maintain its stable operation under grid-connected or islanded conditions^3–5. Thus, much interest has been raised toward interconnecting vicinal MGs via the point of common coupling (PCC) to form a resilient MMG. On this account, various issues may occur, which should be studied thoroughly. Amongst all, the outage management and coordinated operation of MMGs, factors that need to be investigated, have gained less attention in the ample literature available for energy management in a single MG. However, some methods have been proposed for these issues in the literature, which are explored in the following. For the coordinated operation of MMGs, a holistic energy management strategy (HEMS) is required with regard to specific operational objectives⁶. Note that the power flow is managed in MGs by regulating the import/export of power from/to the adjustable units, such as the exterior space, dispatchable distributed energy resources (DERs), distributed energy storage units, and controllable loads, enabling the individual MGs to trade power with the DN in various normal or emergency operating conditions. Thus, power flows between the MGs and the DN and within the DN and the upstream network (UN) should be taken into account. Given the model complexities considered, the literature has addressed the energy management issue in MMGs in three main groups: centralized, decentralized (distributed), and hybrid approaches.

The centralized structure has eased the management of MGs and DGs using a central control unit, coordinately controlling the processes. More specifically, this approach employs a unified controller to undertake the system’s operation and maintenance tasks within certain time durations. Such an exercise ensures achieving a globally optimal solution. However, the profit-oriented attitude of microgrid operators (MGOs) is violated by neglecting local benefits seen from the individual point of view⁷. Additionally, the entire set of MGs is prone to disruption of operation in case of a failure in the centralized energy management unit, thus having lower reliability. Furthermore, such an approach is associated with higher delays in communication due to the longer distances between the system’s components⁸. Despite these setbacks, the capability of such a structure in outage management is still subject to debate in research discussions. On this ground, the centralized structure has been evaluated in terms of reliability for an MMG system’s coordinated outage management strategy in⁸, in which various outage contingencies and durations have been successfully tackled. The technologies essential to the manufacturing and operation of hydrogen fuel cell vehicles—which are becoming more and more acknowledged as a viable substitute for traditional internal combustion engine vehicles—are thoroughly examined in⁹. The research explores several fuel cell types, hydrogen storage techniques, refueling logistics, and battery integration in fuel cell cars. It also takes into account how the development of fuel cell technology might be impacted by recent breakthroughs in artificial intelligence and quantum computing. In order to support sustainable transportation networks, the research highlights the major obstacles to the broad adoption of fuel-cell vehicles and emphasizes the necessity of ongoing investment and concerted efforts among industry stakeholders. Nevertheless, the researchers ignore the technical features of the system and the demand response (DR) program in their assessment. Considering the issues outlined above, the centralized architecture is not very popular for MMG control because it is vulnerable to disturbances¹⁰. A decentralized control approach, which is more applicable, is achieved by leaving the responsibility of management and control to each MG operator separately. This task is, therefore, conducted based on the rules, constraints, and objectives defined for maximizing local profits¹¹. In this architecture, although the MGOs primarily solve the local operation problems within their individual MG, the globally optimal solution of the entire system is only attained as the MGs come into direct contact with the distribution network operator (DNO)¹². Such an aim is reached when enough generation and storage are available for each single MG to maintain an adequate level of supply for operation. The distributed energy management structure has been addressed based on different schemes proposed in the literature^13,14. One of the most popular approaches is through the consensus-based algorithm (C-bA), benefiting from a simple implementation structure^15–17. In this technique, each MG employs the information from the adjacent MGs to set its parameters. This approach has been used in¹⁵, where MG programming within a distribution system has been carried out by a decentralized scheme based on a two-stage stochastic process, where the exchange of power between the DNO and MGs occurs via C-bA for the sake of energy management in the MMG. In another example¹⁶, an average C-bA has been used in a decentralized architecture for sharing power among the MGs to enhance the system’s performance in case of contingencies. The C-bA has been implemented via a multi-agent scheme in¹⁸, enabling MMG management through a coordinated strategy for distributed power-sharing. Another popular approach toward the decentralized management of power flow is through the decomposition-based algorithm (D-bA)^19–21 in which a global optimization problem for the entire network is decomposed into n local sub-problems, each solved in coordination with the other sub-problems, altogether providing a solution for the entire grid. A simple method has been proposed in¹⁹, where the entire system is decoupled into several entities to achieve the optimal power flow solution accordingly. In^22,23 too, the decomposition scheme has been utilized in an algorithm for energy trade within a single period to enhance the MMG system’s reliability and response speed. Likewise, with the help of D-bA, a robust MMG power flow optimization method has been presented in²⁴, where its adaptivity to various operating conditions has been ensured by considering uncertainties associated with the energy supplies within and in between the MGs. In this context, researchers in²⁵ have proposed to optimize MMG scheduling by considering the effect of real-time uncertainties of the energy market in the decomposition approach. Overall, the literature review suggests that although the D-bA provides a more robust solution, it is also associated with complexity.

The advantages of both centralized and decentralized approaches can be grasped for coordinated energy management in MMGs by applying hybrid centralized-decentralized techniques. This approach has been put forth in²⁶ for enhancing computational burden, where a hybrid energy management strategy (EMS) is presented for solving the optimization problem of MGs coordinately within the MMG system. In this method, the control variables are selected by the power exchange among MGs, the power output of DGs, and the power transfer through the tie line. On the other hand, the disadvantages associated with centralized and decentralized structures, such as the uncertainty corresponding to the global and local optimal solutions, can be tackled by hybrid methods. For instance, authors in²⁷ used the game theory in a cooperative approach to achieve the coordinated operation of the MMG system and minimize the operation costs within. Note that although the majority of the published literature has rightfully focused on the limiting constraints, i.e., voltage levels and the capacity of power transmission lines, as well as the uncertainties arising from non-dispatchable units and consumption of loads, the uncertainty due to element failure has been neglected. Likewise, the reliability of system components has also been understudied, along with neglecting element failure and repair rates. Furthermore, the characteristics of power transmitting lines, including their type and length, have remained unexamined. In addition to the disruption of the balance between generation and consumption within an MMG, the element failures can also leave severe impacts, such as degraded efficiency of energy, unoptimized cost of operation, and interaction with the grid on a repeated basis due to the disturbance of energy scheduling. Since various elements of a system correspond to different failure probabilities, a deterministic analysis cannot provide a realistic picture of the system’s behavior. On this account, the random nature of system disturbances has been reflected in studies through Monte Carlo analysis^26–28. Employing such a technique, authors in²⁸ have demonstrated that the coordinated strategy for outage management within an MMG is adequately capable of dealing with various contingencies and uncertainties associated with outage duration. Nevertheless, this study has failed to consider the failures that may prevail in MGs upon assuming MMGs as whole entities. On the other hand, voltage magnitudes and reactive power have also been disregarded in this analysis. The outage management topic has also been addressed in²⁹, which has presented a hierarchical strategy for the network’s resilience improvement, where the optimization problem has been put forward via mixed-integer linear programming. The probabilities of contingencies have also been considered in the strategy proposed by³⁰ for MMG energy management, where the optimal solution is instructed by the DNO one day ahead. Alternatively, it has been proposed in³¹ that the element outage rates should be quantified based on their relationship with the system state variables for examining the impact of operating conditions on the MMG reliability. In this context, the uncertainties associated with loads and DGs have been considered in³² to improve service restoration with the aim of customer outage minimization. The optimal integration of battery energy storage systems (BESS) in distribution networks with high renewable energy penetration has been a primary focus of research. Sheikh et al.³³ examined the placement and sizing of BESS in radial distribution networks to mitigate the variability of renewable energy sources. Their study demonstrated that incorporating BESS enhances voltage profiles, reduces energy losses, and improves overall system reliability, which aligns closely with the present study’s aim of integrating energy storage to manage renewable energy uncertainties effectively. Another critical aspect of renewable energy systems is their control under varying conditions. Kaloi et al.³⁴ proposed a state feedback linearization control technique to achieve low voltage ride-through (LVRT) capability in grid-connected doubly-fed induction generator (DFIG)-based wind energy conversion systems (WECS). Their approach ensured stable operation during grid faults, highlighting the importance of advanced control strategies to maintain the resilience of renewable energy systems. These insights are particularly relevant for hybrid energy systems requiring stability in the face of contingencies, as discussed in the current study. The optimal placement of renewable energy sources, especially solar photovoltaic (PV) systems, is another area of interest. Kumar et al.³⁵ employed a multi-objective particle swarm optimization (PSO) algorithm to determine the optimal location of PV distributed generation units in radial distribution systems. Their findings underscored the benefits of optimal PV placement in reducing power losses and improving voltage stability, offering a foundation for the proposed research’s focus on optimizing hybrid renewable energy integration within microgrids. Communication systems also play a crucial role in enabling efficient coordination within complex energy systems. Jamali et al.³⁶ explored the potential of LiFi-based communication systems in vehicular collision avoidance, demonstrating the importance of robust communication frameworks. While their study focused on vehicular applications, the underlying principles can be extended to multi-microgrid environments, where effective communication is essential for coordinating demand response and energy management. Additionally, off-grid renewable energy systems have proven vital for rural electrification and addressing energy access challenges. Kumar et al.³⁷ designed an off-grid PV system for electrifying rural areas in Pakistan, demonstrating the feasibility and benefits of decentralized renewable energy systems. This work complements the focus of the current study on hybrid renewable energy systems, particularly in off-grid and islanded operations, by highlighting their potential to address energy access disparities. Authors in³⁸ have proposed a Shunt Active Power Filter (SHAPF) with an integrated Energy Storage System (ESS) and a Solar Energy System (SES). This architecture features VSCs in a parallel configuration, feeding DC elements. Then, the MSF of the Shunt Control System FLC is tuned using the GBOA. Authors in^39–41 have presented a new single-phase Unified Power Quality Conditioner that integrates a solar photovoltaic system with battery energy systems to improve power quality. An artificial neural network controller, which is trained with the Levenberg–Marquardt backpropagation, is used in the present work to generate the reference signals for the voltage source converters of the UPQC, thereby avoiding the traditional dq0, abc complex transformations. Moreover, the optimal setting of parameters for the adaptive neuro-fuzzy inference system is obtained by hybridizing the enhanced harmony search algorithm with the predator-prey-based firefly algorithm to come up with a hybrid metaheuristic methodology in the form of PPF-EHSA. Additionally, references^42–44 have presented a Firefly Algorithm-Trained ANN Controller (FF-ANNC) for the shunt active filter and a Proportional Integral Controller (PI-C) for the series active filter of the UPQC, integrated with the SES and battery energy storage through boost converters and buck-boost converters. The main objective of the FF-ANNC is to minimize the mean squared error and maintain a stable DLCV during variations in load and solar irradiation. Some other objectives may include reducing the imperfections in the current waveform, improving power factor, and mitigating voltage sag, swell, disturbance, or unbalance in grid voltage. However, all these studies have failed to consider the DR program or the system’s economic aspects in their evaluations. One of the most notable shortcomings of these studies is the application of either single or fixed-weighted multi-objective functions for optimization, which needs to consider changes in line with variable conditions (e.g., upon outages) in conventional functions due to the changing circumstances of the network. Accordingly, to achieve a coordinated operation capable of swiftly dealing with uncertainties via contingencies, a practical EMS is required to resolve the gaps mentioned. To this aim, a variable-weighted multi-objective function has been developed and further employed to propose a robust and efficient method for the optimum operation of MMGs. The proposed approach enables multiple operators (MOs) to update the objective function weights in accordance with the prevailing contingencies. Thus, the MOs are responsible for energy supply for the demands corresponding to various modes of the MMG system, considering fault types and locations.

Table 1 Presents a comprehensive list of the features of the method proposed in this work, compared to other recent state-of-the-art approaches, to help get a clear Understanding of the similarities and differences of the features.

Table 1.

A comparative assessment of the proposed method and recent State-of-the-Art approaches.

	6	7	10	15–17	22,23	25,26	27	31	39–41	This Paper
Operation Cost	✓	✓	✓	✓	✓	✓	✓	✗	✗	✓
Extensive power microgrid systems	✓	✓	✓	✗	✗	✓	✗	✗	✓	✓
Losses	✓	✗	✗	✓	✓	✗	✗	✓	✓	✓
Uncertainty	✓	✗	✗	✗	✗	✗	✗	✗	✗	✓
variable weighted multi-objective	✗	✗	✗	✗	✓	✗	✗	✗	✓	✓
Microgrids Energy Trading	✗	✗	✓	✗	✓	✓	✗	✓	✗	✓

In light of the research gaps specified in the above discussion, this paper aims to develop a model suitable for optimal energy dispatch in both grid-connected and off-grid MGs comprising hybrid power sources and storage units. To examine the effect of flexible loads on system operation, different strategies are accurately evaluated for DR. The research body is established on the formulation of a mixed-integer linear programming problem for a multi-objective solution of MG energy management. The developed multi-objective function must be inclusive of criteria for minimizing total operating costs, emission costs, and power loss costs. Nevertheless, the MGEM problem grows drastically in terms of execution time for the multi-objective optimization algorithms due to the presence of numerous decision variables and the dynamic nature of the problem itself. In this regard, an approach is proposed based on developing a global criterion from which the new single-objective problems are attained. This paper provides the main contributions as follows:

• The microgrid energy management (MGEM) problem in the presence of hybrid sources of energy and storage units is approached by proposing a multi-objective optimization approach.

• Different types of hybrid sources, e.g., photovoltaic (PV), wind turbine (WT), diesel generator (DG), microturbine (MT), fuel cell (FC), and energy storage systems (ESSs), are considered to be included in the microgrid.

• The proposed multi-objective problem aims to determine the most optimal operating capacity for power generation and storage systems.

• This investigation is conducted based on both conditions of grid-connected and standalone for the microgrids.

• Further enhancement of the microgrids’ techno-economic benefits is obtained via the DR program.

• The proposed scheme, which is scalable, can also be integrated into real-world network-interconnected microgrid systems.

• As for the uncertainty entailed with the energy management decisions, the capability of being “robust” is an essential feature in contrast to the deterministic environment.

• The presented framework considers the impacts of contingencies in the upstream network.

Finaly, The remainder of this paper is structured as follows: Section Microgrid hybrid energy source modelling approach presents the modeling framework for the microgrid energy management (MGEM) problem, including the integration of hybrid power sources, energy storage systems (ESS), and demand response (DR) strategies. Section MGEM problem formulation formulates the multi-objective optimization problem and defines the constraints associated with system components. Section Results and discussion details the simulation setup and provides a comprehensive discussion of the results, highlighting the impact of DR programs and real-time pricing on operational performance. Finally, Section Conclusion concludes the study by summarizing key findings and outlining potential directions for future research.

Microgrid hybrid energy source modelling approach

The conceptual model proposed for solving the MGEM problem integrates a DR strategy in the model to alter consumption patterns based on demand forecasts, pricing, and control protocols. This modified demand, along with all vital data on MGs, provides the input of an optimization algorithm, which decides optimal energy dispatch, power transfer rates, and ESS scheduling statically if a schedule exists or dynamically if no schedule exists. The approach ensures efficient and responsive energy management on an hour-to-hour basis for the next day. Figure 1 is a block diagram of the different stages of the proposed approach procedure.

Fig. 1.

Stages of the procedure and conceptual model for the proposed approach.

The first step in formulating the optimization problem for energy dispatch within an MG system is to model its constituting components, i.e., PV, WT, DG, MT, FC, and ESS units. These elements are modeled below.

PV system model

The PV array power generation () can be obtained by⁴⁵:

1

2

where , , ,, andare PV rated capacity and PV derating factor, PV solar radiation, PV solar radiation considering standard test condition, and power temperature factor, respectively. Further, , , , and are ambient temperature, PV cell temperature, PV efficiency at the maximum power point, and nominal operating cell temperature, respectively.

Wind power generation unit modeling

The output power of a WT () is described by the following equations²:

3

4

where , , , , , , and represent wind power generation, WT efficiency, rated wind power, available wind power, cut-in speed, rated speed, and cut-out speed, respectively.

Battery energy storage unit modeling

With the growing penetration of renewable sources and electric vehicles in modern hybrid systems, the preservation of frequency within permissible ranges has become a challenge. Supplementary energy units help maintain the supply-demand balance, thereby preventing frequency deviations in real-time. An ESS can be used as an auxiliary power reserve, compensating for frequency deviations upon sudden generation variations within renewable sources. The operating constraints for an ESS are defined by several factors, including battery unit arrangement, backup duration, temperature, battery unit life expectancy, discharge depth, power reserve requirements, and renewable generations within the grid. The charge/discharge program of an ESS unit can be characterized as :

5

6

where , ,,,, andare the powers of ESS, DG, FC, MT, grid, and load demand, respectively. Also, and are charging and discharging powers of ESS, respectively. Principally, only one operating condition at a time, i.e., either charge or discharge, can be imagined for an ESS unit. The power of the ESS corresponding to each condition is calculated as follows⁴⁶:

Charging state:

7

8

Discharging state:

9

10

where , , ,, , and denote the battery charge state, charging energy, discharging energy, self-discharge rate, charging/discharging efficiency, and converter efficiency, respectively.

There are two main factors involved in the life expectancy of a battery unit: throughput of the lifetime (Q_lifetime) and storage float life (R_{batt, f}). The MGO is responsible for determining the battery lifetime limiting factor by time, throughput, or both. The lifetime expectancy of an ESS unit can be achieved by:

11

where and are the number of batteries and the annual throughput of storage, respectively.

The storage float life is defined as the time interval an ESS unit can operate before needing to be replaced. Note that the float life is only applicable in case the battery life expectancy is selected to be characterized by time, so it cannot be used for the condition where only the throughput is selected. The wear cost of an ESS () unit can be described as⁴⁶:

12

where and are storage replacement cost and the roundtrip efficiency of storage, respectively.

Power converter model

Power converter units are necessary for hybrid grids comprising both AC and DC equipment. The inverters can be characterized by Eq. (13)⁴⁷:

13

where , , and are inverter capacity and inductive and non-inductive loads, respectively.

Power generator units

The operating constraints for units constituted by power generators are defined based on upper and lower limitations given by:

14

15

16

Demand response (DR)

The network operators usually motivate customers to participate in demand-supply through incentive offers. The incentive costs (IC) for the DR can be calculated as:

17

where b is an arbitrary bus and nb denotes the number of buses. Further, and are incentive rate and the shifted load installed in the b-th bus at time t, respectively.

Modelling the uncertainty in loads and renewable energy sources (RES)

In this analysis, the load and RES uncertainties are included based on forecasting with reference to the historical records. The forecast quantities are calculated by the point prediction method⁴⁸, using long-term observations at a specific time course in a particular area. However, in response to such uncertainties as wind speed, solar radiation, and load demand, the forecasts by the point value method are erroneous⁴⁹, so it is fundamental to consider the forecast errors in practice. In this study, these factors are taken into consideration with the help of the interval prediction technique⁵⁰, which estimates the lower/upper bounds of the uncertain quantities based on the confidence level at each forecast point.

Considering a point forecast value equal to L, corresponding to the forecast error PDF of f(φ), the set for general forecast quantities U_D can be characterized as⁵⁰:

18

with and denoting the parameters indicated by the confidence level of .

Based on the interval prediction theory, and according to Eq. (18), the lower/upper bounds of the renewable power generation can be calculated with respect to the base point forecast for renewable power generation and the forecast error PDF selected as follows⁵⁰:

19

20

Nevertheless, in practice, the renewable power generation units are also limited by their own power output considerations, and hence, the boundaries calculated in (19) and (20) must be corrected as⁵⁰:

21

22

In this context, the forecast set for renewable power generation with uncertainty considerations is obtained as:

23

For the load, the forecast error PDF, , can be considered a normal distribution, and thus, according to (18), the uncertain forecast set for the load can be obtained based on the point forecast for load demand as:

24

MGEM problem formulation

This section presents the MGEM model formulation based on the multi-objective optimization problem stated in Eq. (25), bound to the constraints explained further.

Objective function

The optimization model proposed for this study is a multi-objective problem comprised of several conflicting objectives, which, contrary to conventional optimization problems, do not correspond to a unique solution. Every solution not violating the defined constraints can be chosen as the optimum, where the selection of an individual solution among the obtained points (the Pareto Front) is a task for the decision-maker. To meet the specified objectives in the MGEM problem in satisfying the constraints defined, data should be determined on various parameters, including the unit commitment and the generated power of every controllable DG unit, power trade with the upstream network, and the ESS charge/discharge schedule, for every hour one day in advance³⁹. Although the environmental impacts of MGs are generally lighter than those of conventional power systems due to the integration with renewable energy resources, they should still be included in the objective function. Furthermore, considering the low voltage level and high resistivity of the distribution lines in an MG, the power loss should not be neglected. The final goal of this investigation is to state, implement, and confirm an energy management scheme for MGs integrating with hybrid power resources. To this aim, a mixed-integer linear programming formulation is used for the optimized energy dispatch problem. The MGEM problem is defined by a multi-objective function, according to Eq. (25).

25

26

27

28

29

30

31

32

33

34

where , , , , , , and represent the main grid cost, fuel and start-up costs for controllable generators, cost of RESs, greenhouse gas emission cost, incentive cost of DR, the power loss cost, and the voltage regulation of the MG, respectively.is the power price of the main grid, denotes the emission factor of the main grid,represents the emission factor of the i-th unit, shows the fuel cost of the i-th unit, is the voltage magnitude, indicates the start-up cost of the i-th unit, and ,, and are the coefficient of the power cost function for the i-th unit of RESs.

The term specifies the operating mode, where the MG is in islanded mode if . The power is bought from the upstream network if and is sold to the upstream network if . Note that the i-th unit is turned on at the time instance t if and is turned off in case .

Constraints

There can be various constraints conceivable for the operation of system components within an MG. Accordingly, several constraints are also defined for the MEMG problem as follows.

Supply-demand balance constraint The balance between the consumed and the generated power is an essential operational issue in all power systems. The total power consumption via loadings and losses must be equal to the total generated power, thus holding the unserved energy zero in all instances. This can be characterized by Eq. (35).

35

Generation capacity constraint An upper and a lower limit, as in Eqs. (14) -(16), are defined for the controllable power generation units, which must be met during the operation.

Consumer loads According to the instructions and considerations within a network, supplying the loads can be prioritized based on their classification as sheddable (), transmissible (), and other demands ().

36

37

38

ESS charge/discharge constraints The power for charge () or discharge () of an ESS unit is to be held below its ratings.

39

40

where is the rated capacity of ESS.

Accordingly, every ESS should also follow the charging and discharging constraints as:

41

where and denote the minimum and the maximum permissible power transfer of the i-th ESS, respectively. implies that the energy storage unit is in the discharging mode, while means that it is in the charging mode.

The dynamic performance of energy storage units

42

43

where the charge state, charge/discharge efficiency, and storage capacity of the i-th unit are characterized by , , and respectively. The ESS unit life expectancy is determined by Eq. (11).

Energy management in multiple MGs

For multiple MGs connected to a DN, each MG should maximize its own benefit, considering the equipment’s failure probability and simultaneously the possibility of bidirectional energy trading between MG and DN. Considering different operation modes for MGs, the multi-objective function for energy management of multiple MG is mathematically expressed as follows:

44

where is the weight coefficient of the OFs that are given in (26) –(32). Also, p and k are the counters of OFs and MG, respectively.

The weight adjustment for the objective function must be performed by taking every event individually into consideration. According to different system situations regarding the repairment time, replacement time, and the system element probability of failure, various fault events (based on their persistence and location) are imaginable in the MMG system, each leading to a separate system operating condition. Such conditions can be categorized into several groups, as follows:

Hybrid (islanded/grid-connected)

In the case of fault occurrence within an MG, the faulted region is isolated, and hence, the power demand of other sections connected to the DN can be supplied. It is also possible for the connected sections to transmit their extra power back to the DN. Thus, given that the change of operating strategy is an option for the MGO, the service continuation can be preserved for the customers within these regions. Note that the consumers not connected to the DN might face interruption. Accordingly, determining the efficient dispatch of locally available resources in an islanded condition is left to the MGOs. Thus, the proposed approach suggests that the priorities of the objectives would be determined by the MGOs. On the contrary, in case of a fault occurrence within the DN, the power supply can be maintained for any portions that are connected to the UN. Hence, the continuity of operation is preserved for customers in these regions. The optimal scheduling is defined by the DNO for the DN/islanded portion after determining the lack/excess of power among all MGs within the islanded portion.

Fully islanded

Due to short circuit fault conditions, an entire MG disconnects from the DN, or the DN disconnects from the UN. Upon such contingencies where the set of MMG systems may be isolated, the MGs can operate in the islanded mode if they can supply the power demand during specific time intervals. Further, the extra power of the MGs, along with the local generations within the DN, may be adequate to prevent, or at least shorten, the service interruption of the customers. In such a condition, network issues are of higher importance than economic considerations, and the principal objective is to minimize interrupted loads. Thus, the operators should be enabled to determine the weights of the functions based on the objective they desire to prioritize.

As justified by the arguments presented above, the weights for objective functions are set based on the importance attached to the objectives desired during various conditions. Note that the weight coefficients are selected considering the level of importance corresponding to each OF. Nevertheless, the summation of the weight coefficients in each operating mode must equal 1. Table 2 reports the weight coefficients for different operating modes of the MG.

Table 2.

Specifications of coefficients given in Eq. (44) considering different operating modes of the MG.

Island Operation	0.15	0.15	0.15	0.15	0.1	0.1	0.2
Islanding Due to Unscheduled Contingency	0.15	0.15	0.15	0.15	0	0.1	0.3
Grid Connected	0.2	0.2	0.2	0.2	0	0.1	0.1

Demand response (DR) implementation

Network operators tend to involve the customer side in energy management programs to reduce the demand burden of the network more economically and reliably²⁸, which can be attained through incentive plans to persuade customers to arrange their consumption based on the operator’s instructions, mainly in the form of electricity price. Adjustable customer loads can be categorized into shiftable and curtailable. This is known as the DR. In addition to the economic advantages of the DR strategy for customers, their service continuity is also enhanced. The MG operators also benefit from DR by reducing operational expenses, achieving a more optimal operation, having less requirement for expensive generation units, reducing dependency on the upstream network, and, above all, flattening the energy demand curve. The DR strategies are principally grouped into time-based rate (TBR) and incentive-based (IB) protocols. Through the TRB protocol, the consumption pattern is managed by enforcing different service prices over time. On the other hand, the IB scheme utilizes incentive-based/disciplinary plans to instruct consumer demands.

Consumption management through a time-based rate DR scheme

As mentioned above, the objective of this scheme is to adjust consumer demands according to the service pricing enforced. The modified consumption pattern upon TBR DR strategy during i-th and j-th hour is calculated by:

45

Consumption management through incentive-based DR scheme

This strategy tries to modify the customer consumption pattern by defining a reward and penalty system. The adjusted power demand upon the incentive-based DR scheme is calculated by:

46

General MGEM problem-solving framework

Figure 2 depicts the flowchart of the procedure for solving the proposed multi-objective formulation for the MGEM problem. The design process begins by integrating the DR strategy, which requires determining several key factors, including the previously forecasted electricity demand, service pricing, self and cross-elasticity parameters, and the incentive and disciplinary protocols for controllable loads. These factors are crucial for calculating the modified consumption patterns of the customers, allowing for more precise and responsive energy management. Once these parameters are established, the optimization algorithm is provided with the outputs from the load control system, along with detailed characteristics of the MG components and controllable generators. This comprehensive input set enables the algorithm to identify the optimal solutions for energy dispatch within the MG and to determine the power transfer rates with the upstream network on an hourly basis one day in advance. In cases where an energy scheduling program has not been pre-defined for the ESS units, the MGEM problem must be approached dynamically. This involves simultaneously determining the optimal operating points for controllable generators, the power trade rates with the upstream network, and the charge/discharge schedule for the ESS. These calculations are also performed on an hourly basis, one day ahead, ensuring that the system is prepared for the next day’s energy demands. The proposed method thus ensures a highly responsive and efficient EMS, adapting to both forecasted and real-time conditions within the MG while optimizing the balance between energy generation, storage, and consumption.

Fig. 2.

The Flowchart of Energy Management in MG.

Results and discussion

Simulations were carried out using the MG test system demonstrated in Fig. 3⁴⁰. The MG test system is replaced as a portion of the load at buses 7, 25, and 32 in an IEEE 33 bus distribution network⁴¹. Note that for case studies given in subsections 7.1 to 7.3, only MG1 is utilized. Table 3 provides the required information regarding the emissions and costs of the controllable DGs, together with the average emission and the flat rate price of the main network. Also, the other parameters of the system are mentioned in Table 4. According to Table 4, the emission penalties for CO₂, SO2, and NOx were selected to be equal to 0.035, 2.3, and 8.95 $/kg, respectively. For the DG, an operating capacity bounded to a maximum of 65 kW and a minimum of 15 kW was considered, while the MT and FC were bounded to a maximum capacity of 40 kW and a minimum capacity of 5 kW. Further, the power exchange limitation of the main network was set to 120 kW. The energy storage units were assumed to have a maximum charge/discharge power of 40 kW and a capacity of 100 kWh in total. The SOC maximum and minimum values were assumed to be equal to 15% and 95%, respectively. It should be noted that the proposed framework was programmed and implemented using MATLAB software (2021a) on a specified computer with a Core™ i7 CPU @ 2.90 GHz and 36GB of installed RAM.

Fig. 3.

The test system for performance evaluation of the proposed energy management algorithm.

Table 3.

The specifications of the power cost and the rate of emission.

Resource	Cost of Investment ($)	Cost of Operation			Rate of Emission (g/kwh)
		a	B	c	CO2	SO2	NOx
Grid	-	-	-	-	902	1.75	1.62
FC	1.4	0.0002	0.027	0.4	440	0.002	0.014
MT	2.1	0.0005	0.04	0.389	650	0.004	0.19
DG	2.8	0.0011	0.031	1.31	702	0.22	0.53

Table 4.

The system parameters for the microgrid test system.

Parameter	Value/Description
Microgrid test system	Part of the load at buses 7, 25, and 32 in the IEEE 33 bus distribution network
Emission penalties	CO2: $0.035/kg SO2: $2.3/kg NOx: $8.95/kg
Controllable DG operating capacity	Maximum: 65 kW Minimum: 15 kW
Microturbine (MT) & fuel cell (FC) capacity	Maximum: 40 kW Minimum: 5 kW
Main network power exchange limitation	120 kW
Energy storage units	Maximum Charge/Discharge Power: 40 kW Total Capacity: 100 kWh
SOC (state of charge) limits	Minimum SOC: 15% Maximum SOC: 95%
Software used	MATLAB (2021a)
Device specifications used for simulations	Computer with Core™ i7 CPU @ 2.90 GHz, 36GB RAM

It should be noted, In this study, Real-Time Pricing (RTP) is integrated into the microgrid energy management framework to dynamically adjust demand and optimize power dispatch within the current operational day. The analysis is conducted over a 24-hour duration to capture intra-day variations in pricing and demand, ensuring that the impact of RTP on microgrid operations is realistically reflected. While shorter time resolutions (e.g., 30-minute, 15-minute, or 5-minute intervals) could provide finer granularity, the hourly resolution is chosen as a practical balance between computational efficiency and real-world applicability. Many existing demand response programs and microgrid implementations operate on hourly RTP adjustments due to forecasting accuracy limitations and available market structures.Furthermore, sub-hourly intervals significantly increase computational complexity, requiring higher-frequency market data, advanced forecasting models, and more intensive optimization techniques. While this study focuses on demonstrating the effectiveness of RTP within an hourly framework, future research will explore the feasibility of shorter time intervals to improve real-time adaptability to rapid price fluctuations and renewable energy uncertainties.

MGEM with demand response (DR) program disregarded

Figures 4 and 5 depict the results obtained from the simulations by applying the global criterion. As shown, using the objective function (25), the optimal value was calculated at 0.437. For the day ahead, the total operating costs, emission penalties, and power losses were equal to 269.8 USD, 79.14 USD, and 66.03 kWh, respectively. Although an MT has a lower overall emission than a DG, its feeder’s impedance is more significant and is thus prioritized for shutdown in case of light loadings. Table 5 compares different evolutionary optimization algorithms applied to energy management problems in terms of solving performance and capability. Note that the population and maximum iteration quantities were considered 300 and 1500 for all analyzed algorithms, respectively. The existence of numerous decision variables resulted in failed convergence to the optimum solution in algorithms such as bibliography (BBO) and differential evolution (DE) despite even changing the crossover and mutation parameters. Overall, the teaching learning-based optimization (TLBO) and particle swarm optimization (PSO) algorithms showed the first and second-best performances among the analyzed evolutionary algorithms, respectively.

Fig. 4.

The output of the proposed algorithm disregarding demand response program for (a) SoC, (b) operation cost, (c) power loss, and (d) emission cost of MG1.

Fig. 5.

The results of energy management disregarding demand response program for (a) scheduling and (b) power generation of MG1.

Table 5.

The performance comparison between the optimization algorithms for the proposed energy management algorithm.

Optimization Algorithm	OF value	Total Operation Cost ($)	Total Emission Penalty ($)	Total Power Loss (kwh)	Iteration	Computational Time (minute)
BBO	2.912	-	-	-	1500	22
DE	1.872	-	-	-	1500	15
PSO	0.519	272.4	80.6	65.78	860	13
TLBO	0.437	269.8	79.14	66.03	1100	9

It is important to note that the values presented in Figs. 4D, 7D, and 9D represent carbon emission costs rather than direct emission quantities. The emission cost is calculated based on predefined emission penalties, reflecting the financial impact of emissions rather than their physical quantities in kilograms or metric tons. This distinction ensures a proper understanding of the economic implications of emissions within the microgrid energy management framework.

Fig. 7.

The output of the proposed algorithm considering real-time pricing demand response program for (a) SoC, (b) operation cost, (c) power loss, and (d) emission cost of MG1.

Fig. 9.

The output of the proposed algorithm considering direct load control demand response program (a) SoC, (b) operation cost, (c) power loss, and (d) emission cost of MG1.

MGEM with demand response (DR) program included

This study used TBR programs to apply RTP and incentive-based programs to apply direct load control (DLC). As displayed in Fig. 6, the load demand alteration subsequent to the application of the DR program is clearly visible. In this case, 20% of the total load was considered to participate in the DR programs. Also, the values dedicated to the self and cross elasticity and the flat rate prices were to 0.22, 0.015, and 11.5 USD/kWh, respectively. The peak was considered to occur from 11:00 to 16:00, and the incentive rate for load reduction during peaking hours was considered equal to 2.2 USD/kWh. The optimum solutions achieved for the objective function while considering DR programs in the energy management problem (Eq. 25) are demonstrated in Figs. 7, 8, 9 and 10. By implementing the RTP program, the values of operating costs, emission penalties, and power losses would be 260.4 USD, 75.83 USD, and 63.58 USD, respectively, showing a reduction of 3.49% in operating costs, 4.18% in emission penalties, and 3.7% in loss of power compared to the case with DR disregarded. Contrarily, by implementing the DLC program, the values of operating costs, emission penalties, and power losses would be 261.9 $, 76.13 USD, and 64.4 kWh, respectively, showing a reduction of 2.9% in operating costs, 3.8% in emission penalties, and 2.5% in power loss compared to the case with DR disregarded. Clearly, as the participation percentage and the incentive rates grew, the role of the DR program became bolder.

Fig. 6.

The load profile.

Fig. 8.

The results of energy management considering real-time pricing demand response program for (a) scheduling and (b) power generation of MG1.

Fig. 10.

The results of energy management considering direct load control demand response program (a) scheduling and (b) power generation of MG1.

Optimum energy dispatch in standalone MGs comprising hybrid power sources

The load demand at the peak was 195 kW with a per day average energy consumption of 4050 kWh/day and a yearly average of 1,553,934 kWh/year. The power generated yearly by the hybrid power network to meet the demand requirement amounted to 749,396 kWh/year for PV, 89,915 kWh/year for WT, 149,392 kWh/year for DG, 492,712 kWh/year for MT, and 60,304 kWh/year for FC. The optimal operation of the hybrid system would provide a power of 35 kW for FC, 65 kW for MT, 25 kW for PV, 60 kW for DG set, 210 kW for the WT, 135 kW for battery strings, and 180 kW for converters. The values of 0.245$/kWh and 4,519,743$ were considered for the levelized energy cost and net present cost in the hybrid system, respectively. Figure 11 illustrates the solution for the scheduling program of power sources for one typical day.

Fig. 11.

The results of energy management disregarding demand response program for (a) scheduling and (b) power generation of MG1.

Optimum energy dispatch in grid-connected MGs considering upstream contingency

This section deals with multiple energy management designed for multiple MGs. It was assumed that three MGs with almost similar loading conditions were connected to buses 7, 25, and 32 in the IEEE 33-bus distribution network. Due to a fault in the upstream network in the line between buses 1 and 2, the line was disconnected, and three MGs became islanded simultaneously. Note that the energy management of the system was optimized before the unscheduled islanding. Table 6 presents the performance of the proposed energy management algorithm of different MGs after contingency.

Table 6.

The performance comparison of the microgrids before/after the contingency.

Optimization algorithm	Voltage regulation (%)	Total operation cost (USD), before contingency	Total operation cost (USD), after contingency	Total Power loss (kWh), before contingency	Total Power loss (kWh), after contingency
MG1	3.48	269.8	275.94	66.03	70.16
MG2	5.21	270.4	278.14	65.58	72.75
MG3	4.89	273.5	281.64	68.24	79.43

Figure 12; Table 6 present the results of energy management disregarding the DR program. The results reveal that due to voltage regulation caused by the contingency, the total operation cost and power losses significantly increased. As seen, the proposed method can consider the impacts of unscheduled islanding into account. In the following, To provide a clearer representation of the trade-offs among the different objective functions in the optimization process, a Pareto-based evaluation has been conducted for the final scenario (Scenario 4.4). Since the study involves seven objective functions, it is not feasible to visualize the Pareto front graphically, as conventional Pareto plots are limited to three-dimensional representations. Instead, a Pareto-optimal result table is presented to illustrate the relationship between key cost components, power loss, and voltage regulation at ten different operating points. Table 7 highlights the main grid cost, fuel and start-up costs of controllable generators, cost of RESs, greenhouse gas emission cost, incentive cost of DR, power loss, and voltage regulation. These results demonstrate how the optimization framework balances multiple objectives, ensuring an efficient and cost-effective energy management strategy within the microgrid.

Fig. 12.

The results of energy management disregarding demand response program, (a) MG1, (b) MG2, and (c) MG3.

Table 7.

Pareto-optimal solutions for multi-objective microgrid energy management in scenario 4.4.

Objective Function	Point 1	Point 2	Point 3	Point 4	Point 5	Point 6	Point 7	Point 8	Point 9	Point 10
Main Grid Cost ($)	220	215	210	205	200	195	190	185	180	175
Fuel & Start-up Cost ($)	150	145	140	135	130	125	120	115	110	105
RES Cost ($)	100	105	110	115	120	125	130	135	140	145
GHG Emission Cost ($)	80	78	76	74	72	70	68	66	64	62
Incentive Cost of DR ($)	60	58	56	54	52	50	48	46	44	42
Power Loss (KWh)	300	290	280	270	260	250	240	235	232	230
Voltage Regulation (%)	5.0	4.9	4.8	4.7	4.5	4.3	4.1	4.0	3.95	3.9

The results presented in the table illustrate the trade-offs among different objective functions in the optimization process. As seen across the ten operating points, the main grid cost, fuel and start-up costs, and renewable energy system costs vary depending on the selected optimization solution, highlighting the impact of different cost components on the overall energy management strategy. The greenhouse gas emission cost and incentive cost of demand response also change accordingly, demonstrating the role of emission penalties and demand-side management in shaping the microgrid’s operational efficiency. The variations in power loss and voltage regulation further emphasize the technical constraints that must be considered alongside economic factors. A lower power loss and improved voltage regulation typically lead to better grid stability and efficiency, yet they require a balance with operational costs. The Pareto-optimal solutions demonstrate that optimizing for a single objective, such as minimizing the main grid cost, may lead to higher emissions or increased power losses, whereas a balanced trade-off among multiple objectives ensures a more sustainable and cost-effective microgrid operation. These results highlight the flexibility of the proposed optimization framework in providing diverse solutions that accommodate different priorities, allowing microgrid operators to make informed decisions based on their specific operational constraints and market conditions. The selection of an appropriate operating point depends on the desired balance between economic efficiency, environmental impact, and system reliability.

Conclusion

This study introduced a novel multi-objective approach for optimizing microgrid energy management (MGEM) with a focus on power dispatch and techno-economic considerations in both standalone and grid-connected microgrids (MGs). The framework integrates hybrid power generation and energy storage systems (ESSs) to enhance operational efficiency. Key factors, such as capital and operational costs, fuel and energy prices, emission penalties, and overall system costs, were comprehensively analyzed. The results highlighted the significant impact of distributed generation (DG) and microturbine (MT) fuel costs on energy prices, as well as the added complexity introduced by energy storage systems. Despite these challenges, the proposed approach outperformed other evolutionary algorithms in simulations. The integration of demand response (DR) programs further improved microgrid operations, leading to reductions in system costs, emissions, and power losses. Notably, the implementation of real-time pricing (RTP) and direct load control (DLC)-based programs resulted in significant operational benefits. In standalone MGs, CO₂ emissions were reduced by 51.60% annually compared to conventional networks, demonstrating the environmental advantages of the proposed strategy. This study provides valuable insights for microgrid operators (MGOs) in investment planning and the development of competitive power dispatch strategies, while also offering practical guidance for engineers in microgrid design and cost management. For future research, addressing the computational complexity of the proposed method, particularly for large-scale MGs with multiple storage units, remains a key priority. Further work could explore advanced optimization techniques to enhance efficiency, refined DR strategies tailored to varying configurations, and real-time implementation with shorter time intervals to improve system responsiveness and resilience. Additionally, ensuring the scalability of the approach to larger microgrids and its adaptability to diverse geographic and climatic conditions will be essential for broader real-world applications. By refining the methodology and extending its application scope, future research can further enhance the robustness and practicality of microgrid energy management in dynamic and uncertain environments.

Author contributions

Mohsen Moosavi , Javad Olamaei , Hossein Mohmmadnezhad Shourkaei wrote the main manuscript text and prepared figures. All authors reviewed the manuscript.

Data availability

All data generated or analysed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.