A Mixed-Integer Programming Approach for Unit Commitment in Micro-Grid with Incentive-Based Demand Response and Battery Energy Storage System

Abstract

In the context of the increasing penetration of intermittent renewable energy resources (RES), one of the significant challenges facing traditional bulk power systems and microgrids is the scheduling generation units problem. Many studies have focused on solving the energy management problem for microgrids integrating RES. To address the intermittency caused by RES, flexible components such as battery energy storage systems (BESS) or demand response (DR) are considered. To clarify the problem of integrating these flexible components, a mixed-integer programming (MIP) approach for the unit commitment (UC) problem for microgrids with BESS and DR is proposed in this paper. An incentive-based demand response model as a negative power source and a detailed model for the vanadium redox battery (VRB) are introduced to improve the efficiency and reliability of microgrids. The objective optimization function, including the costs of generation, emissions, and maintenance, is minimized considering the uncertainty of the load and renewable energy sources. The obtained simulation results are compared with the genetic algorithm (GA) method as the basis for verification in different case studies. The obtained results have clarified the effect of using the BESS model and DR program on system operation.

1. Introduction

In recent years, with the strong development of renewable energy sources (RES) as well as information and communication technology (ICT), the traditional power system has begun to shift from a centralized power system to a decentralized power system. The increasing number of renewable energy sources that are connected to the utility grid as well as an increasing demand for electricity create a significant challenge for the utility grid system. Therefore, a new concept called “microgrid” has been proposed as a solution to these challenges. With microgrids operating similarly to the utility grid, the microgrid is located near energy-consuming areas. The microgrid helps to reduce the burden on the utility grid. Instead of connecting all the power generation sources directly to the utility grid, microgrid operators will operate within a grid of generators and renewable energy sources. This helps to reduce the instability of the RES to the utility grid. In addition, the microgrid is available in two grid-connected or isolated modes, which gives microgrid operators more flexibility. However, the fact that microgrids operate independently without utility grid support is a matter of concern for power balance. Accordingly, battery energy storage systems (BESS) and demand response (DR) programs could become critical to ensuring a reliable power supply to the microgrid beyond the traditional power generation equipment [1].

Previously, for the traditional power system, the load was considered a passive component, unable to interact with the system. However, with the integration of advanced metering infrastructure (AMI) and ICT into the power system, the load can now completely interact with the system through DR programs. The concept of the DR program was defined as the actions by end-use customers that change their regular demand for electric power in response to electricity price, incentives, or controls from grid operators [2]. Over the years, the effectiveness of the DR program has been proven through theoretical studies as well as practical applications in many countries. On this basis, the classification of DR schemes based on incentive and price signals is the most popular [3,4,5]. In price-based programs, customers’ demand changes in accordance with the electricity prices. The price of electricity differs at preset times or varies dynamically according to the time (day, week, or year). Examples of this scheme are time of use (ToU), critical-peak price (CPP), and real-time price (RTP) [3]. In incentive-based programs, consumers are offered monetary incentives and agree to change their power consumption. There are a variety of incentive-based DR programs, such as emergency DR (EDR), interruptible load program (ILP), curtailable load program (CLP), and direct load control (DLC) [5]. The DR programs based on these two categories have various benefits and drawbacks, but obtaining monetary incentives or other kinds of discounts will encourage active involvement in the DR program and coordination with the power system operator from the customer’s perspective [6].

In addition to DR, energy storage systems, especially BESS, are gradually becoming an indispensable component in modern power grids. With the ability to flexibly regulate as well as the cost per unit of installed capacity decreasing, microgrid models with the appearance of BESS increasingly attract a large number of studies. Studies on BESS integration often ignore the operating cost of BESS or simply approximate its fixed cost [7]. However, the capital cost for BESS is still very high. Therefore, the integration of BESS should consider the operating costs of BESS as a way to optimize the operating mechanism of BESS in the microgrid.

Accordingly, it is necessary to consider and analyze the problems of microgrid operation with the integration of new components into microgrids such as RES, DR, and BESS. The microgrids through energy management systems (EMS) also perform scheduling problems for the microgrid’s generating units. This problem is similar to the problems of unit commitment or economic dispatch for the day-ahead market and hour-ahead market in the electricity market operation of power systems.

In [8], the authors proposed a unit commitment model that integrates incentive-based DR considering different types of DR sources. This study also considers the uncertainty of DR. The results demonstrate the economic efficiency and reliability of the power supply for the system. A two-stage stochastic unit commitment model was proposed in [9], which considered incentive-based DR. The results showed that in addition to reducing peak load and decreasing the standard deviation of the load profile, the model also helped to improve the benefits of the consumer, reducing electricity bills. The authors in [10] proposed a two-stage formulation for the day-ahead energy scheduling problem with DR, in which the first stage solved a network-constrained unit commitment problem with DR, and the second stage solved an incentive or penalty minimization problem. In [11], the authors proposed a memetic algorithm to solve the bi-objective problem of maximizing operator profits and minimizing customer costs. To this end, an incentive payment-based DR program was introduced. This target was applied to residential customers with reduced electricity consumption. In [12], the main objective of the paper was to maximize the profit of the system operator and the end customer. The problem was to apply an incentive payment-based DR program. However, MT and WT sources were not considered in the proposed model. With the goal of minimizing operating and emission costs, the proposed problem used whale optimization algorithm to solve the problem [13]. With the application of the incentive payment-based DR program, the results were given in two cases: with DR and without DR. However, the results were not convincing. In [14], the authors proposed a model of pool-based DR in the stochastic day-ahead scheduling considering the uncertainty of RES. For the problem of BESS operation in the unit scheduling problem, there have been studies that consider the operating cost of BESS. A BESS operation cost model was suggested in [15], which considered a battery as an equivalent fuel-run generator in order to include it in a dynamic programming-based unit commitment problem. Research in [16] presented two types of cost models for BESS. The first battery cost model depended on three factors: efficiency, life cycle, and state of health (SOH), whereas the second model depended on the depth of discharge (DoD). A DR model for a cluster of manufacturing plants with BESS and taking into account operating costs of BESS was presented in [7]. This study proposed a hybrid optimization method integrating an evolutionary algorithm and branch-and-bound algorithm to solve the operation cost minimization problem.

In the early 1960s, a series of studies on the scheduling of power generation units were published, starting with Garver in 1963 [17]. Since then, many authors have studied and published various approaches to the unit commitment problem, such as dynamic programming (DP), priority lists (PL), linear programming (LP), mixed-integer linear programming (MILP), mixed-integer quadratic programming (MIQP), Lagrange relaxation (LR), and meta-heuristic algorithms. The development of computers and optimization solvers such as CPLEX or Gurobi [18] has led to a revolutionary wave from using traditional methods such as DP, PL, and LR to using MIP approaches [19,20]. The MIP problem can be solved by using an advanced solver, which helps to find a unique solution. At the same time, the methods using meta-heuristic algorithms, such as ant colony optimization, evolutionary computation, particle swarm optimization, and genetic algorithm, often have problems finding the global optimal value in problems where the objective function is non-convex [21]. In recent years, several studies have been carried out on operational scheduling for MG that consider the use of BESS and DR programs. In [22], the authors presented an approach to using an improved water wave optimization algorithm to solve the problem of scheduling resource operations. The given objective function is to minimize the operating costs of MG with multi-carrier energy infrastructure. Of these, incentive-based DR programs, renewable resources, fossil fuels, batteries, power and natural gas grid infrastructure, energy hubs, combined heat and power units (CHP units), boilers, and thermal energy storage devices are considered in the grid-connected microgrid system. However, this paper evaluated the effect of the DR program on the system, not the effect of BESS on the MG system and the impact of the DR program on the use of BESS. In [23], a proposed hybrid algorithm (GA combined with an artificial bee colony algorithm) approach was proposed to address the goal of minimizing operating costs and demand-side management costs. The results are given to evaluate the influence of the PV system and DE units on the grid-connected MG system. However, DR programs were not considered, and the impact of BESS was not assessed. In [24], the objective function was given to maximize the profit obtained by the microgrid aggregator approaching MILP to solve the problem. Risk-neutral or risk-averse decisions are taken into account at the discretion of the microgrid aggregators’ market analysis. The approach of the K-means clustering technique and fast backward scenario reduction method was proposed to reduce the number of scenarios to improve processing speed. In addition, the effect of BESS was not evaluated. Furthermore, the DE source was not mentioned. In [25], with the intent to calculate the total operating cost of the sources participating in the grid-connected MG system, the researchers implemented a schedule of customer demand reduction based on the positivity/pessimism of the customer incentive-based DR program. The authors modeled green hydrogen storage systems to store excess energy from RES sources. The MILP approach was proposed to solve the problem. However, the cost functions of DE were incomplete and the impact of using green hydrogen storage systems was unclear. With the enhancement of the management system of interconnected isolated microgrids, three levels of management are proposed with the use of the two-round fuzzy-based speed algorithm in [26]. The first level of control was forecasting the operating mode of the MG. The second level was the management of the exchange between MGs if required by the operator, and finally, the operation of the MG will be predetermined in the future based on the Markov chain model. However, this paper model only considered using WT, PV, and BESS. DR programs and traditional power generation units were not considered. The authors in [27] proposed the use of particle swarm optimization (PSO) and artificial neural network (ANN) algorithms to improve the power management model of PV generators in the grid-connected microgrid model. The authors used BESS to manage the instability of the PV source using the PSO algorithm. They then applied ANN to optimize the implementation of the PSO algorithm. However, sources such as MT, WT, and DR programs are not mentioned in the article. In [28], the authors presented a genetic algorithm (GA) approach to the unit commitment problem for microgrids. However, the microgrid model in that study did not mention DR nor consider the operating cost of BESS.

In this paper, we propose an improved microgrid model, shown in Figure 1, taking into account incentive-based DR and an operational cost model for BESS. In addition, we use the mixed-integer programming (MIP) approach for our problem, then use the GA method presented in the previous study as the basis for comparing the two approaches. To summarize, the novel features of this study include the following:

• Improving the microgrid model, including an incentive-based DR program. DR sources are simply seen as the negative power source, which operates simultaneously with other types of power generation;

• Considering a detailed model of a vanadium redox battery (VRB) for the BESS system and the operating costs of the BESS system based on depth-of-discharge;

• Considering the impact of the DR program and the vanadium redox battery for the BESS system designed to optimally schedule the isolated-microgrid system without support from the utility grid;

• Evaluating the impact of the DR program on the operation of the BESS model;

• Solving the optimization problem with the MIP approach then comparing the results obtained with the use of GA through specific case studies.

The paper is presented in the following order. Section 2 presents the formulas of the mathematical model, including the constraints of the unit commitment problem, the DR model, the operating cost for BESS, and the objective function. Section 3 presents the simulation results of the problem using both the GA and MIP approach and a detailed analysis of the results achieved with the integration of DR and BESS. Finally, in Section 4, the content of the work of the paper is presented briefly.

2. Problem Formulations

In previous studies, the integration of DR programs into large power systems was researched considering the benefits for system operators and end-users. In this paper’s model, we propose the integration of DR programs into the microgrid system without support from the utility grid to evaluate the impact of the DR model on the isolated-microgrid system. In addition, the charging/discharge characteristics of BESS are considered in the model of integrating energy storage systems and DR programs. Furthermore, constraints related to the operation of the isolated-microgrid system, the uncertainty of RESs, the constraints of BESS, and the DR program are explained in detail.

In this section, all of the constraints of the problem based on the MIP approach are shown. Section 2.1 gives a detailed explanation and shows the demand forecasting equations. Section 2.2 presents the power calculation equations for PV panels. Section 2.3 presents the equations for calculating the output power of WT based on wind speed. Section 2.4 shows the constraints of the MIP. In Section 2.5, the constraints of BESS modeling are presented. In Section 2.6, the constraints of DR modeling are presented. In Section 2.7, the objective function is constructed. In addition, formulas for calculating the cost of each power generation source are also given.

2.1. Demand Forecasting

The accuracy of the data is one essential factor that significantly affects how the problem will be solved. The microgrid’s energy consumption implies that energy resources must be used wisely to maintain high supply reliability. However, the demand in a microgrid is typically predicted based on user behavior and data records. When little information about the grid is known, or new entities connect to the network, this demand forecasting may become inaccurate. This study considers an estimated demand curve impacted by a final inaccuracy. Every time instant $t,N\left(t\right)$, this error is assumed to follow a normal distribution, with an average of zero and a standard deviation that varies depending on the level of accuracy needed to solve the problem. Accordingly, if we take a significant value of t into account, the uncertainty in demand forecasting will increase, necessitating the contribution of a more robust solution to ensure the electrical supply during regular operation. Equation (1) shows that the total capacity demand at time t is always guaranteed by the sum of the estimated power demand and the forecast demand estimate error. Equation (2) presents the estimated allowable demand power range.

(1)${\tilde{P}}_{DM}\left(t\right)+e_{DM}\left(t\right)=P_{DM}\left(t\right),\forall t$

(2)${\tilde{P}}_{DM}\left(t\right)\in [{\tilde{P}}_{DM}\left(t\right)-3{\sigma }_t,{\tilde{P}}_{DM}\left(t\right)+3{\sigma }_t]$

where $e_t$ represents the estimation error and ${\sigma }_t$ determines standard deviation of the estimated error. The value of ${\sigma }_t$ is given based on the electricity demand data of the previous day, which means that the electricity demand of the next day cannot be significantly different from the previous day. This difference will be compensated for using the spinning reserve of DE and MT to ensure the safe operation of the system. This estimated spread is preset to 3${\sigma }_t$ [28]. The range of error estimates is given based on the normal distribution obtained from the historical data, shown in Figure 2.

2.2. Photovoltaic Generator

One or more solar inverters are powered by a group of photovoltaic panels (PV) connected in series to form a PV generator. These inverters convert the received DC power into AC power, which is then used by the grid. The power generated by a PV plant is influenced by a variety of variables, including solar radiation, ambient temperature, solar cell temperature, and module degradation. Because the power from PV panels cannot be stored, a PV generator is a must-run power source, which has to operate at maximum power. The equation for calculating the power of PV panels is given in [28].

(3)$P_{pv}\left(t\right)=P_{STC}\frac{n.E_m\left(t\right)}{E_{STC}}[1+k(T_m\left(t\right)-T_{STC})],\forall t$

where $P_{pv}\left(t\right)$ is the output power of PV panels at time t, $E_m\left(t\right)$ is the solar irradiance at time t, and $P_{STC}$, $E_{STC}$, and $T_{STC}$ are the maximum power, solar irradiance, and temperature measured under standard test conditions (STC), respectively. The STC is the one applied with a standard temperature of 25 °C, solar radiation of 1000 W/m${}^2$, and an air mass of 1.5. The expression n is the number of PV panels, and k is the power temperature coefficient (°C); $T_m\left(t\right)$ is the temperature of the PV panels at time t and can be calculated through Equation (4).

(4)$T_m\left(t\right)=T_{amb}+{\epsilon }_{PV}\frac{E_t}{E_{STC}}$

where $T_{amb}$ is the ambient temperature and ${\epsilon }_{PV}$ is the constant of the PV panels given by the manufacturer.

2.3. Wind-Turbine Generator

Wind turbines placed in different locations or with different designs will produce different levels of power. All these wind turbines must ensure that the operating wind speed of the wind turbines must be within the limits of the wind speed that can generate electricity. When the operating wind speed of these wind turbines is below or exceeding the wind speed limit, the electrical power output is zero. When the operating wind speed is within the range of the minimum input wind speed at which wind-turbine (WT) can generate power up to the rated wind speed of WT, the output power of WT will be calculated relative to the wind speed. When the operating wind speed is between the rated wind speed and the maximum wind speed allowed by the WT, the wind power was fixed to the rated power of the WT. The equation for calculating the electrical output power of the wind turbines [28] is

(5)$P_{wt}\left(t\right)=\left\{\begin{array}{cc}0\hfill & \mathrm{for}(v<v_{ci}),\forall t\hfill \\ P_r\frac{v^3-v_{ci}^3}{v_r^3-v_{ci}^3}\hfill & \mathrm{for}(v_{ci}<v<v_r),\forall t\hfill \\ P_r\hfill & \mathrm{for}(v_r<v<v_{co}),\forall t\hfill \\ 0\hfill & \mathrm{for}(v>v_{co}),\forall t\hfill \end{array}\right.$

where $P_{wt}\left(t\right)$ is the output power of the wind turbine at time t; $P_r$ is the rated power of the wind turbine; $v_{ci}$ is the minimum input wind speed that can generate electricity; $v_{co}$ is the maximum input wind speed that the wind turbine still allows for generating power; $v_r$ is the rated wind speed of the wind turbine; and v is the operating wind speed of the wind turbine.

2.4. Constraints to the MIP Approach Problem

During operation, at time slot t, the power demand is always guaranteed to be fully supplied. The power balance constraint at each time is given by Equation (6):

(6)$P_{DM}\left(t\right)=P_{pv}\left(t\right)+P_{wt}\left(t\right)+P_g\left(t\right)+P_m\left(t\right)+P_b\left(t\right)+P_{DR}\left(t\right),\forall t$

where $P_{DM}\left(t\right)$ represents the electricity demand at time t; $P_{pv}\left(t\right)$ and $P_{wt}\left(t\right)$ are the output power obtained by PV and WT units at time t, respectively; $P_g\left(t\right)$ and $P_m\left(t\right)$ are powers of DE and MT units at time t, respectively; $P_b\left(t\right)$ represents the capacity of the BESS at time t; $P_{DR}\left(t\right)$ represents the power of DR at time t; $P_b$ is considered positive/negative when discharging/charging; and $P_{DR}$ is considered positive/negative when consumers reduce/increase demand.

The constraints on the allowable operating limits of DE and MT at time t are presented in Equations (7) and (8). The generating capacity at time t of the generating units is limited within the allowable power generation limit.

(7)$P_g^{min}{u}_j\left(t\right)\le P_g\left(t\right)u_j\left(t\right)\le P_g^{max}{u}_j\left(t\right),\forall t$

(8)$P_m^{min}{z}_j\left(t\right)\le P_m\left(t\right)z_j\left(t\right)\le P_m^{max}{z}_j\left(t\right),\forall t$

where $P_g^{max}$/$P_g^{min}$ is the maximum/minimum generated power of the DE units; $P_m^{max}$/$P_m^{min}$ represents the maximum/minimum generated power of the MT units; and $u_j$ and $z_j$ are active indicator variables for DE and MT units, respectively, with $v_j$ and $z_j$ being 1 or 0, representing the on/off state.

In the MIP approach, the constraints related to ramp-up/ramp-down of DE and MT are considered. The allowable ramp-up/ramp-down limits of DE and MT are presented in Equations (9)–(12).

(9)$0\le r_g^U\le M_g^U{u}_j\left(t\right)$

(10)$0\le r_m^U\le M_m^U{z}_j\left(t\right)$

(11)$0\le r_g^D\le M_g^D{u}_j\left(t\right)$

(12)$0\le r_m^D\le M_m^D{z}_j\left(t\right)$

where $r_g^U$ and $r_g^D$ represent ramp-up/ramp-down of DE units; and $r_m^U$ and $r_m^D$ represent ramp-up/ramp-down of MT units. Similarly, $M_g^U$ and $M_g^D$ represent the maximum ramp-up/ramp-down of DE units; and $M_m^U$ and $M_m^D$ represent the maximum ramp-up/ramp-down of MT units.

Equations (13)–(16) represent the limit ramp-up/ramp-down of DE and MT units. The ramp-up/ramp-down of DE and MT units is limited from time t to $(t+1)$. The change in power generation should not exceed the limit ramp-up/ramp-down of the given DE and MT units.

(13)$P_g(t+1)-P_g\left(t\right)\le r_g^U$

(14)$P_g\left(t\right)-P_g(t+1)\le r_g^D$

(15)$P_m(t+1)-P_m\left(t\right)\le r_m^U$

(16)$P_m\left(t\right)-P_m(t+1)\le r_m^D$

where $P\left(t\right)$ is the generation power of each unit DE, MT at time t, and $P(t+1)$ is the generation power of each unit DE, MT at time $(t+1)$.

Equations (17) and (18) present formulas for calculating DE and MT power at time t, relative to the operating state at the previous time ($t-1$) and ramp-up/ramp-down.

(17)$P_g\left(t\right)=P_g(t-1)u_j(t-1)+r_g^U\left(t\right)-r_g^D\left(t\right)$

(18)$P_m\left(t\right)=P_m(t-1)z_j(t-1)+r_m^U\left(t\right)-r_m^D\left(t\right)$

The spinning reserve constraints of DE and MT are given in Equations (19)–(21).

(19)$R_g\left(t\right)=P_g^{max}{u}_j\left(t\right)-P_g\left(t\right)u_j\left(t\right),\forall t$

(20)$R_m\left(t\right)=P_m^{max}{z}_j\left(t\right)-P_m\left(t\right)z_j\left(t\right),\forall t$

where $R_g\left(t\right)$ and $R_m\left(t\right)$ represent the spinning reverse of DE and MT at time t, respectively.

It is crucial to note that to ensure the validity of the solution, the estimation error must be taken into account in the problem while considering the uncertainties in demand forecasting. The spinning reserve’s well-sizing satisfies this reliability. To solve the issue, the following constraint must be added:

(21)$R_g\left(t\right)u_j\left(t\right)+R_m\left(t\right)z_j\left(t\right)\ge n_r{\sigma }_t$

where $n_r$ is the scalar parameter, and ${\sigma }_t$ is the standard deviation of the estimation error, which is noted in Section 2.1.

2.5. BESS Modeling

2.5.1. Overview

Until now, batteries have always been an essential component in life as well as production. From alkaline batteries for small electronic devices to lithium-ion batteries for cars and laptops, everyone needs batteries for their devices. In recent years, energy storage technology has been increasingly developed; today’s batteries can store up to a hundred megawatts of electricity, equivalent to the capacity of about 50 wind turbines combined. This leads to the development of renewable energy being extremely promising and possible because the energy storage battery system is a solution with high performance and reliability. The lithium-ion battery system is cost-effective, easy to maintain, and has long battery life. Despite such advantages, lithium battery systems still have disadvantages, such as higher protection requirements, restricted capacity, and battery performance that degrades over time. Today, a new battery system called vanadium redox battery (VRB) is being researched and applied in many electrical systems. This type of battery system has outstanding advantages over lithium-ion battery systems. Producing a VRB system creates less waste than a Li-ion battery system. VRB electrolytes may be reused, unlike lithium, which has expensive disposal costs. Another considerable advantage of VRB over the Li-ion battery is its better safety and longer lifespan. A VRB is water-based, thus non-flammable and non-explosive, and the cycle life of a VRB mainly depends on the life expectancy of its proton exchange membrane and its pumps, which are easy to replace. In the future, VRB might soon become a growing trend as it continues to develop. Numerous VRB systems have been installed and put into operation in many countries. Particularly, a VRB system in Dalian, China has been commissioned in the first phase of 100 MW/400 MWh, and the second phase will bring it up to 200 MW/800 MWh. It will help to reduce peak load on the Dalian City grid and may even play a role at the provincial level, improving power supply and the ability to connect new power sources such as solar and wind to the grid. In this paper, a simplified BESS model is proposed with the use of a vanadium redox battery system shown in [15].

A VRB (illustrated in Figure 3) is a flow-type battery that stores chemical energy and generates power through reduction–oxidation processes in the electrolytes between distinct ionic forms of vanadium. Two closed electrolyte circuits make up the batteries. The electrolyte is stored in a separate tank (catholyte and anolyte) in each circuit and cycled through the cell stacks via pumps where the electrochemical reactions take place. The Catholyte contains $V{O}_2^{+}$ and $V{O}_{}^{+2}$ ions, and the anolyte contains $V_{}^{+3}$ and $V_{}^{+2}$ ions suffused in an H₂SO₄ solution; $V_{}^{+2}$ is oxidized to $V_{}^{+3}$ in the negative half-cell during discharge, creating electrons and protons. Therefore, a DC current is generated and transmitted through the inverter to be consumed. Protons diffuse through the membrane, and electrons flow to the positive half-cell via the external electrical circuit, where $V{O}_{}^{+2}$ is reduced to $V{O}_2^{+}$. During the charge cycle, the redox process is reversed. For the VRB storage system to function effectively, environmental controls are essential. High temperatures can damage the VRB membrane and cause overheating of the electrical equipment, whereas freezing temperatures can obstruct electrolyte flow. Therefore, a heat control system is installed to control the temperature of the entire battery system.

The specifications of the above VRB model are detailed, especially the BESS charge/ discharge capacity constraints. The BESS model has two main functions in the integration into the power system. It is the charge/discharge function used when the power supply is excessive/insufficient. In this section, the power consumption of the BESS in the two functions is formulated in detail.

2.5.2. Modeling

To enhance the performance of the BESS, there must be accurate modeling of the charging profiles. There are numerous battery modeling approaches for various battery types, including electrochemical models, mathematical models, circuit-oriented models, and integrated models. In this paper, electrochemical modeling of the VRB is presented to indicate the operating parameters of BESS, such as state of charge (SOC) and the charging/discharging power [30]. Similar to other battery models, VRB systems also have limitations on charge/discharge rate and output power:

(22)$SO{C}_{max}\ge SOC\left(t\right)\ge SO{C}_{min}$

where $SOC\left(t\right)$ determines the state of charge of the battery, $SO{C}_{max}$ determines the maximum charge rate, and $SO{C}_{min}$ illustrates the minimum charge rate of the battery. The charging and discharging state of the battery is determined as follows:

(23)$SOC\left(t\right)=SOC(t-1)+\left\{\begin{array}{cc}{H}_b\left(t\right)\hfill & \mathrm{for}P\left(t\right)<0\hfill \\ L_b\left(t\right)\hfill & \mathrm{for}P\left(t\right)>0\hfill \end{array}\right.$

where $H_b$ represents the consumption of the battery during discharge, $L_b$ represents the consumption of a battery during charge, and $P\left(t\right)$ demonstrates the output power of the VRB system.

The consumption of a BESS during discharge is defined as the energy usage for supplying a load during a unit time:

(24)$H_b\left(t\right)=P_{d,b}\left(t\right)+P_{ld,b}\left(t\right)$

The consumption of a BESS during charge is defined as the energy loss for charging the battery during a unit time:

(25)$L_b\left(t\right)=P_{lc,b}\left(t\right)$

where $H_b$ represents the consumption of the battery during discharge; $P_{d,b}$/$P_{c,b}$ represents the discharge/charge power of BESS; $P_{ld,b}$ represents the power loss during discharge; $L_b$ represents the consumption of a battery during charge; and $P_{lc,b}$ represents the power loss during charge.

To solve the problem, formulas for battery consumption during discharge/charge are given in Equations (26) and (27).

During discharge:

(26)$\begin{array}{ccc}{P}_{ld,b}\left(t\right)\hfill & =& {10}^{-3}{I}_{stack,b}^d\left(t\right)V_{oc}\left(t\right)\hfill \\ & =& {10}^{-3}(a_v^{o}SOC\left(t\right)+b_v^o)[a_i^d{P}_{d,b}\left(t\right)+(b_i^{d}SOC\left(t\right)+c_i^d)]\hfill \end{array}$

During charge:

(27)$\begin{array}{ccc}{P}_{lc,b}\left(t\right)\hfill & =& P_{c,b}\left(t\right)-{10}^{-3}{I}_{stack,b}^c\left(t\right)V_{oc}\left(t\right)\hfill \\ & =& [1-{10}^{-3}(a_v^{0}SOC\left(t\right)+b_v^0)(a_i^{c}SOC\left(t\right)+b_i^c)]P_{c,b}\left(t\right)\hfill \\ & & -{10}^{-3}(a_v^{0}SOC\left(t\right)+b_v^0)(c_i^{c}SOC\left(t\right)+d_i^c)\hfill \end{array}$

where $I_{stack,b}^d$ / $I_{stack,b}^c$ represents the stack voltage during discharge/charge, respectively; $V_{oc}$ is the open circuit voltage; $SOC$ represents the charged state of the battery; and $a_i$, $b_i$, $c_i$, and $d_i$ represent the coefficients of the proposed VRB system. The coefficients of the VRB system, given by the manufacturer, are shown in Table 1 [15].

2.6. DR Modeling

In the era of information and communication technology in the power system, the load becomes a flexible component in the power grid because it can be controlled in a timely manner and with high reliability. As a result, demand response, a program that allows consumers to play a crucial role in the operation of the grid by reducing or shifting their electricity use during peak times in response to time-based rates or other forms of financial incentives, becomes an indispensable component in the smart grid. This is quite understandable when DR is a flexible source that can be operated at a much lower cost than investing in other frequency control power plants. Transferring or reducing a portion of the load can be done based on two types of DR programs: Type 1, incentive-based programs, and Type 2, price-based programs.

Type 1 DR programs offer incentives for customers to participate in peak hours load cuts. When customers join the program and properly meet the reduction requirements, they will receive an incentive bonus or electricity bill coupon. This category includes direct load control, interruptible service, capacity market program, demand bidding/buy back, emergency demand response program, and ancillary service markets. These programs provide customers additional incentives payment for their load reduction, independent of their retail electricity price.

Type 2 DR programs operate by increasing the electricity price during peak hours, so the customers tend to shift their consumption to the off-peak hours. Price-base programs include several programs, such as real-time pricing, critical peak pricing, and time-of-use tariffs, and provide clients with time-varying prices that are representative of the value and cost of electricity throughout various time periods. If the difference between prices in each hour or period is significant, customers may adjust their power consumption from high-price periods to low-price periods to take advantage of the programs. Therefore, a significant peak load shaving can be achieved.

It can be seen that transferring or reducing part of the load at peak hours helps to reduce the burden on the power system and at the same time makes the operation more reliable and more stable. Following the above trend, the DR program is integrated and considered in the microgrid model within the framework of this paper, especially in the case of an islanding mode microgrid. The integration of DR into the microgrid system is to assess the impact of DR on the operation of the system and at the same time consider the influence of the DR program on the operation of the proposed BESS model. The proposed DR program is based on incentive rewards to stimulate consumers to participate in the program. In this section, reward determination formulas are considered along with the consumer benefit/impact of participating in the DR program.

2.6.1. Participating

The DR program is responsible for reducing the peak load of the consumer or sending a control signal. As agreed, participants will be paid in advance for agreeing to reduce power usage upon request [31]. In the above cases, DR pays incentives to customers. In this article, DR is economically modeled based on grid prices and incentives for utilities in the event of an emergency.

2.6.2. Determining Reward

Elasticity is defined as demand sensitivity with respect to the price [32]. It means the utility should provide more incentives for a higher amount of curtailment.

(28)$E_i\left(t\right)=\frac{\partial D\left(t\right)}{\partial \rho \left(t\right)}=\frac{{\rho }_0\left(t\right)}{D_0\left(t\right)}\frac{dD\left(t\right)}{d\rho \left(t\right)}$

where $E_i\left(t\right)$ represents the self elasticity for load i at time t; ${\rho }_0\left(t\right)$ represents the nominal electricity price at time t; and $D_0\left(t\right)$ represents the initial demand value at time t.

How much electricity the customer should consume to maximize the benefits and convenience of participating in DR [33] is given as follows:

(29)$A_i\left(t\right)=\frac{\Delta d_i\left(t\right){\rho }_0\left(t\right)}{E_i\left(t\right)}$

(30)$d_i\left(t\right)=d_0\left(t\right)+E_i\left(t\right)\frac{A_i\left(t\right)}{{\rho }_0\left(t\right)}$

(31)$P_{i,DR}\left(t\right)\le 0.2Demand$

where $A_i\left(t\right)$ represents the incentive for load i at time t; $d_i\left(t\right)$ represents the required demand for utility at time t; and $d_0\left(t\right)$ represents the initial demand of load i at time t.

Survey results have demonstrated that participants are only willing to curtail or shift unnecessary loads, such as air conditioners or wet appliances. It is assumed that operators are allowed to curtail a load of customers up to 20% of current usage during contingencies.

2.7. Objective Function

In this section, the objective function is constructed and shown by Formula (32), in which the economic cost is equal to the total maintenance cost, start-up cost, operating cost of DE and MT units, plus BESS maintenance cost and DR participation cost.

(32)$C{R}_{ec}=C_{O{M}_g}+C_{O{M}_m}+C_{S{U}_g}+C_{S{U}_m}+\sum _{\forall t}^{}(C_g\left(t\right)+C_m\left(t\right))+C_{O{M}_b}+C_{DR}$

where $C{R}_{ec}$ represents the economic cost, in which the smaller the economic cost, the better for the power supply side; $C_{O{M}_g}$ and $C_{O{M}_m}$ represent the maintenance costs of DE and MT, respectively; $C_{S{U}_g}$ and $C_{S{U}_m}$ represent the startup costs of DE and MT, respectively; $C_g\left(t\right)$ and $C_m\left(t\right)$ represent the operating costs of DE and MT, respectively; $C_{O{M}_b}$ represents the maintenance cost of BESS, and $C_{DR}$ represents the cost of DR. These costs are calculated and expressed in Equations (33)–(38).

2.7.1. Operation Cost of the Controllable Generation System

• Operating Costs:

  (33)$C_g\left(t\right)=a_g+b_g{P}_g\left(t\right)+c_g{P}_g{\left(t\right)}^2,\forall t$

  (34)$C_m\left(t\right)=a_m+b_m{P}_m\left(t\right)+c_m{P}_m{\left(t\right)}^2,\forall t$

• Maintenance Costs:

  (35)$C_{O{M}_g}=k_{O{M}_g}\sum _{\forall t}^{}{P}_g\left(t\right){\Delta }_t,\forall t$

  (36)$C_{O{M}_m}=k_{O{M}_m}\sum _{\forall t}^{}{P}_m\left(t\right){\Delta }_t,\forall t$

• Start-up Costs:

  (37)$C_{S{U}_g}=d_g+e_g(1-e^{\frac{-T_g}{f_g}}),\forall t$

  (38)$C_{S{U}_m}=d_m+e_m(1-e^{\frac{-T_m}{f_m}}),\forall t$

where $a_g$, $b_g$, $c_g$ are the given parameters related to the cost during operation of DE; $a_m$, $b_m$, $c_m$ are given parameters related to operating costs of MT; $k_{O{M}_g}$ and $k_{O{M}_m}$ are the maintenance cost coefficients per 1 kWh of DE and MT, respectively; $d_g$, $e_g$, $T_g$, $f_g$ are the given parameters related to the startup cost of the DE; and, similarly, $d_m$, $e_m$, $T_m$, $f_m$ are given parameters related to the startup cost of MT.

2.7.2. Operation Cost of BESS

In this section, formulas related to the cost of batteries are given and can be determined:

(39)$C_b\left(t\right)=C_{a,b}\left(t\right)$

(40)$C_{a,b}\left(t\right)=\frac{C_{R,b}\left(t\right)}{T_{R,b}\left(t\right)}$

where $C_b$ represents the total operating cost of the battery; $C_{a,b}$ is defined as the cost to have 1 kWh of storage and is defined as 0.4 €/1 kWh; $C_{R,b}$ represents the replacement cost of the battery; $T_{R,b}$ represents the total lifetime of the battery; and $T_{R,b}$ is determined by Formula (41):

(41)$T_{R,b}\left(t\right)=C_{ra,b}\left(t\right)DO{D}_b\left(t\right)L_{ra,b}\left(t\right)$

where $C_{ra,b}$ represents the rated capacity of the battery; $DO{D}_b$ represents the depth of discharge of the battery; and $L_{ra,b}$ represents the battery-rated lifetime.

In the proposed BESS model, instead of supplying power to the BESS by conventional generators, the use of RESs to power the BESS is considered. The purpose of this is to utilize energy resources to power the BESS. During the night hours, WT is providing excess electricity due to no power consumption. Charging for BESS at this time is most profitable due to WT’s excess capacity, while WT’s generation costs are considered free and available. At the same time, it helps to make the operation of the BESS more stable.

2.7.3. Cost of DR Program

DR costs are understood as the total incentive payments that the operator pays to the consumer when the consumer meets capacity reduction requirements. With consumers getting more load reduction during peak load times, the higher is the incentive reward, presented by Formula (42):

(42)$C_{DR}=\sum _{\forall t}^{}{A}_i\left(t\right)$

In Table 2, the electricity price at peak/normal hours is 0.43/0.12 €/kWh, and the DR reward is 0.31 €/kWh.

3. Numerical Results

After determining the constraints and building the objective function, the problem was solved on the CPLEX solver, and the results for each case study were obtained. In addition, to clarify the superiority of the MIP approach, the results of each case study based on the GA approach performed previously are included for discussion and comparison. The results of the problem based on the GA approach are given and explained in detail in [28].

With the GA approach, the simulated binary crossover (SBX) method is used regarding the crossover operation, in which a hyper-parameter $eta$ is given representing the similarity of the offspring to the parents. With high $eta$, the degree of similarity is greater, and conversely, low $eta$ gives more solutions. Other crucial parameters of the GA are the $P_{cx}$ and the $P_{mut}$, which represent the crossover and mutation probabilities, respectively. Both $P_{cx}$ and $P_{mut}$ are hyper-parameters of the GA that should be selected carefully to guarantee feasible converge of the GA. In the first case study, the optimization variable or an individual in GA is the output power of dispatchable generators during the 24 h, using intervals of 1 h. Therefore, the size of each individual is 48 genes (illustrated in Figure 4). In the second case study, part of the optimal variable to be added is the output of the new DR source over 24 h. As a result, the size of each individual in the second case study is 72 genes (illustrated in Figure 5).

In order to perform the calculation and to process the aforementioned computational model, the parameters of the DE, MT power generation units, and the parameters of the VRB battery model are given in detail.

These parameters of DE and MT are given in Table 3. The DE minimum/maximum output power rating is 5/80 kW and the maintenance cost factor $K_{O{M}_g}$ = 0.01258 €/kWh. The MT minimum/maximum output power rating is 20/140 kW and the maintenance cost factor $K_{O{M}_m}$ = 0.00587 €/kWh [28].

Figure 6 shows the price cost for power supply of DE and MT, with the operating cost of power supply gradually decreasing as the amount of capacity supplied increases [28].

In Table 4, the specifications related to BESS operation are given, in which the battery-rated lifetime is defined as 4000 cycles. The depth of discharge of the battery is defined as 23.3%. The rated capacity of the battery is equal to 300 kWh. The min/max SOC is equal to 0.2333/0.9333. The initial SOC is equal to 0.4667 [28].

Two case studies are validated. Case study 1: The system only integrates using BESS. Case study 2: Integrated system uses BESS and DR. The results are given and discussed in detail in the following sections.

3.1. Result for Case Study 1

The UC problem is considered simulated in 24 h time with each interval of 1 h. In this case study, the isolated-mode microgrid model contains generators such as DE and MT to fill up the gap between the electricity consumption and the must-run renewable energy sources. Along with that, an energy storage battery system is also considered in order to balance the load demand and the PV and the WT output power. Simulation results for this case study are compared between the two approaches.

In Figure 7 and Figure 8, the load demand curve under the two approaches is the same. From 12 a.m. to 12 p.m., the energy consumption increased gradually from 60 kW to 250 kW each hour. The load demand then remains unchanged in the next hour before plummeting to 160 kW in the 17th hour. After an increase in the energy consumption in the 18th hour, it drops significantly to just 20 kW in the 23rd hour. One of the renewable energy sources, WT, slightly fluctuated between 44 and 71 kW throughout the period. The other inexhaustible energy source is PV, which only started to appear in the 9th hour. It reaches its peak at 40 kW in the 13th hour before gradually dropping and disappearing at the 20th hour.

First, in Figure 7, the graph shows that the WT accounted for the most power generated among the dispatchable units. From 5 to 18, the dispatched power of WT remained stable around 100 kW to 140 kW, reaching the highest value at 140 kW at 10 a.m. The DE output power figure only appeared between 1 and 4 h, 7 and 11 h, and 18 and 19 h. It can be seen that the generated power from the DE is only in the range of 20 to 55 kW.

Second, in Figure 8, it can be seen that the MT still generated the majority of the dispatchable units. It turned on first at 4 a.m. The MT then got turned off in the next hour before being turned on again. The amount of generated power by MT rose gradually for the next 8 h, reaching its peak at 140 kW at the 14th hour. It then fell significantly to 70 kW at the 16th hour before a comeback to 140 kW in the 18th hour. Finally, it dropped significantly and vanished at the 21st hour. Similar to the DE in the GA figure, the DE in the MIP figure also only appeared in a few hours and only generated a minor amount of electricity.

Third, in Figure 9, dissimilar to the two dispatchable units, the battery system output fluctuated significantly between approximately 50 kW and −50 kW. It reached its highest point of discharging 49 kW and lowest point of charging −52 kW at the 20th hour and 23th hour.

In contrast to the previous units, the battery in the MIP-based solution operated completely differently from the one in the GA. The battery only discharged a considerable amount of electricity in a certain few hours while hibernating for other hours before 9 p.m. The discharged power is also not as large as it is in the GA figure, which is only discharged less than 15 kW through the periods. It also can be seen that the battery is only charging from the 21st hour to the 23rd hour. This represents the utilization of the excess capacity of the WT when load demand is not high enough to consume it, which saves the cost of charging and discharging the battery instead of charging at times of high load consumption. This also helps avoid wasting the amount of WT power transmitted at that time.

Table 5 and Table 6 show the operational status of DE, WT, and BESS. With DE and WT: 0 is the off indicator, and 1 is on. With BESS, there are three indicators: 1 is discharged, −1 is the charge, and 0 is off.

Table 7 shows the results of the objective function with each mutation probability, and cross variation as given in the GA. The results show that the optimal cost function is 620.8 € with $P_{cx}$ = 0.6, $P_{mut}$ = 0.4, and $eta$ = 0.01, where $P_{cx}$ and $P_{mut}$ represent the probability of crossover and mutation of the generated generations, respectively; $best\left(C{F}_{ec}\right)$ represents the best value of the cost function for each crossover and mutation probability; and $mean\left(C{F}_{ec}\right)$ represents the average value of the cost function for each of the crossover and mutation probabilities. It can be seen that the optimal cost function with the MIP approach is much cheaper than for GA, as shown in Figure 8, which is 605.032 €, 15.768 € less than GA. This big difference occurs because, in the GA approach, the system is less stable, and the BESS output power changes up and down continuously, causing the cost to rise. On the other hand, the MIP approach makes the system more stable, while the BESS output only slightly fluctuates, which makes the objective cost function significantly less.

Overall, it can be seen that the obvious difference between BESS in the GA approach is different from BESS in the MIP approach. The variation in battery charging and discharging in Figure 9 comes from the fact that the GA generates random variables, which increases the instability of the RES. Along with that is the probability of mutation; crossover of the GA makes the solution less accurate. This will lead to a significant reduction in the lifetime of the BESS while it has to operate more and at greater intensity. While applying the MIP approach, the BESS output power changes less than for GA, as shown in Figure 10, which will save a significant amount of power loss in the charging and discharging process of BESS and extend its life-cycle. This is because the MIP is a linear-program solver, which will have less computing burden and calculate a more precise solution than a meta-heuristic algorithm such as GA.

3.2. Result for Case Study 2

In this case study, the BESS and DR models are integrated and used in the microgrid at the same time. DR is considered a negative power source, helping to reduce peak load. The BESS model was introduced to accommodate the instability of the RES. Simulation results are given for two approaches: GA and MIP.

In Figure 11 and Figure 12, it can be seen that the actual load graphs of the two approaches are different. With the GA approach, the integration of BESS and DR has helped reduce the peak load graph significantly, and the load curve has become less steep, as shown in Figure 7. The BESS model, in this case, has been greatly improved, with less fluctuation of charging or discharging power compared to case study 1. In contrast, the diesel and micro turbine generator still show the same figure. MT still generated the majority of the dispatchable units.

With the MIP approach, the integration of DR helps to keep the difference between two consecutive peak periods not too large. As shown in Figure 12, the graph is little changed, helping to reduce the on–off cost of the units. It can also be seen that, with the use case of the MIP approach, the DE source power is always used at a minimum. This results in a better MIP optimal cost function than for GA.

In Figure 13 and Figure 14, it can be seen that the BESS model has been significantly improved in both approaches compared to the previous case. In Figure 13, the BESS model has changed with less difference in the charge/discharge capacity between the time periods compared to case study 1. This helps to prolong the life of BESS compared to case study 1 with the same GA approach, which will reduce the cost of the operation of BESS. Figure 14 shows that, in this case, the BESS model is the best in both case studies as well as in both approaches. The BESS model in this approach to the MIP is inactive between 5 a.m. and 8 p.m., while the power demand is still supplied.

The BESS model in both cases is the same because both utilize the excess power generated by the WT from 9 p.m. to 12 p.m. to charge and emit at other times of the day, which helps to make the most of the charging/discharge cost of BESS.

In Table 8 and Table 9, the operational status of DE, MT, BESS, and DR program participation are presented. For generators DE and MT: 0 is the off indicator, and 1 is on. For the operating state of BESS, three indications are given: 1 is discharged, −1 is the charge, and 0 is off. With participation in the DR program: 0 is the indicator of no participation, and 1 is the indicator of participation.

Table 10 shows the results of the optimal cost function using the GA in case study 2. The optimal cost function obtained is 608.42 € at $P_{cx}$ = 0.6, $P_{mut}$ = 0.4, and $eta$ = 0.01. The result of the optimal cost function of MIP is lower than that of the GA, only 601.495 €, which is 6.925 € lower. This shows that the combined use of DR significantly improves the operating cost of the system. In addition, it can be seen that the MIP approach in each case always gives better results than the GA.

Another considerable thing to notice is the residual load, which is the capacity left for conventional generators to operate as shown in Figure 15. Residual load is calculated by eliminating the share of must-run power sources out of the demand for electrical power in a power grid. The solution of the model in case study 2 shows a less fluctuating figure than in case study 1. Furthermore, from 7 a.m. to 12 p.m., the residual load in the DR integrated model remains stable at 140 kW, which is the maximum output of the MT, whereas in case study 1, sometimes the residual load exceeds 140 kW. This leads to the micro turbine operating at maximum capacity in that period, which is the point that the average cost of operation of the MT is at a minimum. In addition, at the same time, other sources will be turned off because the MT has already fulfilled the demand, whereas in the case study 1 model, the DE, and BESS will have to be turned on to meet the demand because the power produced by MT is not sufficient.

It can be seen that the integrated use of BESS and DR into the microgrid system is much better than using only BESS. The resulting maximum cost function of using BESS and DR in the GA is 608.42 €, 12.38 € less than just using BESS in the GA. For the MIP algorithm, the optimal cost function using both BESS and DR is 601.495 €, which is 3.537 € lower than in the case without the integration of the DR program. This confirms that the integration of both BESS and DR into the microgrid system is extremely good for system operation. Operating costs are lower, BESS life is longer, and system stability is better than just using BESS.

For the UC problem-solving approach, there are two approaches: GA and MIP algorithms. Simulation results in the case studies show that the MIP approach is much superior to the GA. First, the MIP approach gives a much faster solving speed than GA (only a few minutes). Second, the MIP approach solves the problem with higher accuracy than the GA, which solves the problem by probability. This makes the UC problem more stable using the MIP approach instead of the GA. Third, the MIP approach is superior to the GA if the UC problem has a large number of input variables because the initialization of random variables, mutations, and crossovers of the GA is not suitable. The number of variables is too large.

4. Conclusions

This paper proposes microgrid models considering the integration of BESS and DR programs to address the uncertainty of RES. An operation cost model of BESS is constructed based on electrochemical modeling of a VRB system, and the price-based DR program is presented. A mixed integer programming approach is applied to find the optimal day-ahead scheduling for this microgrid model with the minimized operation cost as the objective function. The result shows that the proposed model can maintain the system’s optimal operation with a lower operating cost if both the BESS and DR are integrated. Future work in this area will include the integration of a hybrid battery model that might be the combination of VRB with other battery technology, such as Li-ion battery and absorbed glass mat battery.

The results showed the advantages of the MIP approach over GA. In case 1, with consideration of operating an isolated microgrid with BESS, without DR, the optimal cost function is 620.8 €, with $P_{cx}$ = 0.6, $P_{mut}$ = 0.4, and $eta$ = 0.01 for the GA approach, 15,768 € higher than the MIP approach with only 605,032 €. The performance of BESS in the MIP approach is better than that of the GA approach where the charge-discharge of the BESS is less variable. In case 2, with consideration of operating an isolated microgrid with BESS, with DR, the optimal cost function obtained is 608.42 € at $P_{cx}$ = 0.6, $P_{mut}$ = 0.4, and $eta$ = 0.01 for the GA approach, 6,925 € higher than the MIP approach with only 601,495 €. The operating results of BESS with case 2 show that the participation of DR programs in operation helps BESS operate more stably than in case 1. The optimal cost function is significantly reduced with both GA and MIP approaches. It can be seen that DR programs, when participating in isolated microgrid operations, help operate the system more stably, with lower operating costs as well as an increase in the lifetime of BESS through the more stable operation of BESS. The results were obtained from model processing by python software for both MIP and GA approaches.

Author Contributions

Conceptualization, H.T.-X.; Data curation, L.H.-T. and L.D.-V.; Formal analysis, H.T.-X. and L.D.-V.; Funding acquisition, H.T.; Investigation, T.N.-D., H.T.-X., L.D.-V. and H.T.; Methodology, T.N.-D., L.H.-T., H.T.-X. and H.T.; Project administration, T.N.-D. and H.T.; Resources, L.H.-T.; Software, L.H.-T., H.T.-X. and L.D.-V.; Supervision, T.N.-D. and H.T.; Validation, L.D.-V.; Writing—original draft, L.H.-T. and L.D.-V.; Writing—review & editing, T.N.-D. and H.T. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data sharing not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Abbreviations

The following abbreviations are used in this manuscript:

Abbreviation
ANN	Artificial neural networks
AMI	Advanced metering infrastructure
BESS	Battery energy storage systems
CHP	Combined heat and power
CLP	Curtailable load program
CPLEX	ILOG CPLEX
CPP	Critical-peak price
DE	Diesel engine
DLC	Direct load control
DoD	Depth of discharge
DP	Dynamic programming
DR	Demand response
EDR	Emergency DR
EMS	Energy management systems
GA	Genetic algorithm
ICT	Information and communication technology
ILP	Interruptible load program
LP	Linear programming
LR	Lagrange relaxation
MG	Microgrid
MILP	Mixed-integer linear programming
MIP	Mixed-integer programming
MIQP	Mixed-integer quadratic programming
MT	Micro-turbine
PL	Priority lists
PSO	Particle swarm optimization
PV	Photovoltaic
RES	Renewable energy soures
RTP	Real-time price
SOC	State of charge
SOH	State of health
STC	Standard testing conditions
ToU	Time of use
UC	Unit commitment
VRB	Vanadium redox battery
WT	Wind turbine
Nomenclature
$A_i\left(t\right)$	The self-elasticity required reward to motivate load to decrease the consumption of load i from $d_0\left(t\right)$ to $d_i\left(t\right)$ at time t
$C_{a,b}$	The availability cost of battery capacity
$C_b$	Battery cost
$C_{DR}$	Cost price of DR
$C_g\left(t\right)$	The operating cost of DE at time t
$C_m\left(t\right)$	The operating cost of MT at time t
$C_{O{M}_b}$	The maintenance cost of BESS
$C_{O{M}_g}$	The maintenance cost of DE
$C_{O{M}_m}$	The maintenance cost of MT
$C_{R,b}$	The replacement cost
$C_{ra,b}$	The battery rated capacity
$C_{S{U}_g}$	The startup cost of DE
$C_{S{U}_m}$	The startup cost of MT
$d_i\left(t\right)$	The required demand for utility at time t
$D_0\left(t\right)$	The initial demand value at time t
$d_0\left(t\right)$	The initial demand of load i at time t
$DO{D}_b$	The depth of discharge
E	The elasticity of the demand
$E_m$	The solar irradiance at time t
$E_{STC}$	The solar irradiance measured under STC
$E_i\left(t\right)$	The self-elasticity required reward to motivate load to decrease the consumption of load i from $d_0\left(t\right)$ to $d_i\left(t\right)$ at time t
$e_{DM,t}$	The estimation error of the demand forecasting
$H_b$	The consumption of a battery during discharge
$I_{stack,b}^c$	The stack voltage during charge
$I_{stack,b}^d$	The stack voltage during discharge
k	The power temperature coefficient (°C) of PV
$L_b$	The consumption of a battery during charge
$L_{ra,b}$	The rated lifetime
$M_g^D$/$M_g^U$	Maximum ramp-down/maximum ramp-up of DE units
$M_m^D$/$M_m^U$	Maximum ramp-down/maximum ramp-up of MT units
n	The number of PV panels
$n_r$	The scalar parameter
$P_{c,b}$	The battery charge power
$P_{d,b}$	The battery discharge power
$P_{DM}\left(t\right)$	The real power demanded at time t
${\overline{P}}_{DM}\left(t\right)$	The estimation power demand at time t
$P_{DR}$	The electricity is cut
$P_{lc,b}$	The power loss during charge
$P_{ld,b}$	The power loss during discharge
$P_{pv}\left(t\right)$	The output power of PV panels at time t
$P_{wt}\left(t\right)$	The output power of the wind turbine at time t
$P_g^{max}$/$P_g^{min}$	Maximum/minimum output power of DE at time t
$P_m^{max}$/$P_m^{min}$	Maximum/minimum output power of MT at time t
$P_r$	The rated power of the wind turbine.
$P_{STC}$	The maximum power of PV panels measured under STC
$P_{r,b}$	The reserve power in the battery
$r_g^D$/$r_g^U$	Ramp-down/ramp-up of DE units
$r_m^D$/$r_m^U$	Ramp-down/ramp-up of MT units
$R_g\left(t\right)$	Spinning reserve of DE at time t
$R_m\left(t\right)$	Spinning reserve of MT at time t
$SO{C}_b$	The state of charge
$T_{amb}$	The ambient temperature of PV
$T_m\left(t\right)$	The temperature of the PV panels at time t
$T_{STC}$	The temperature measured under STC of PV
$T_{R,b}$	The total lifetime cycling battery
u	DE units on–off indicator
v	The operating wind speed of WT
$v_{co}$	The maximum input wind speed WT
$v_{ci}$	The minimum input wind speed WT
$v_r$	The rated wind speed WT
$V_{oc}$	The open circuit voltage
z	MT units on–off indicator
${\epsilon }_{PV}$	The constant of the PV panels
${\sigma }_t$	The standard deviation of the estimation error of demand

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Figures and Tables

Figure 1. Structure of the considered microgrid.

Figure 2. Normal distribution plot obtained from historical data.

Figure 3. Vanadium redox battery model [29].

Figure 4. Solution representation of GA in case study 1.

Figure 5. Solution representation of GA in case study 2.

Figure 6. Cost of operation of the DE and MT in terms of the power supply.

Figure 7. UC uses BESS based on the GA approach.

Figure 8. UC uses the BESS-based MIP algorithm approach.

Figure 9. Management of BESS is based on GA approach to case 1.

Figure 10. BESS management is based on MIP algorithm approach to case 1.

Figure 11. UC uses BESS and DR-based GA approach.

Figure 12. UC uses BESS and DR-based MIP approach.

Figure 13. Management of BESS based on GA approach to case 2.

Figure 14. Management of BESS based on MIP approach to case 2.

Figure 15. Residual load.

Table 1

VRB loss model coefficients.

$(\mathit{i},\mathit{k})$	${\mathit{a}}_{\mathit{i}}^{\mathit{k}}$	${\mathit{b}}_{\mathit{i}}^{\mathit{k}}$	${\mathit{c}}_{\mathit{i}}^{\mathit{k}}$	${\mathit{d}}_{\mathit{i}}^{\mathit{k}}$
$(o,v)$	$0.2414V_r$	$0.9925V_r$	-	-
$(d,i)$	$\frac{1.0719}{V_r\times {10}^{-3}}$	$0.0183I_r$	$0.0210I_r$	-
$(c,i)$	$\frac{-0.3093}{V_r\times {10}^{-3}}$	$\frac{1.0397}{V_r\times {10}^{-3}}$	$0.0604I_r$	$-0.112I_r$

Table 2

Electricity price.

Peak Hour Price	Normal Hour Price	DR Reward
$0.43$ (€/kWh)	$0.12$ (€/kWh)	$0.31$ (€/kWh)

Table 3

The coefficients of the generator cost functions.

i	${\mathit{P}}_{\mathit{i}}^{\mathit{m}\mathit{i}\mathit{n}}$(kW)	${\mathit{P}}_{\mathit{i}}^{\mathit{m}\mathit{a}\mathit{x}}$(kW)	${\mathit{a}}_{\mathit{i}}$(€/h)	${\mathit{b}}_{\mathit{i}}$(€/kWh)	${\mathit{c}}_{\mathit{i}}$(€/kW${}^2$h)
$\mathrm{DE}$	5	80	$1.9250$	$0.2455$	$0.0012$
$\mathrm{MT}$	20	140	$7.4344$	$0.2015$	$0.0012$
$\mathit{i}$	${\mathit{d}}_{\mathit{i}}$ (€)	${\mathit{e}}_{\mathit{i}}$ (€)	${\mathit{f}}_{\mathit{i}}$ (€)	${\mathit{K}}_{\mathit{O}\mathit{M}\mathit{i}}$ (€/kWh)
$\mathrm{DE}$	$0.3$	$0.4$	$5.2$	$0.01258$
$\mathrm{MT}$	$0.4$	$0.28$	$7.1$	$0.00587$

Table 4

Parameter table of VBR model.

	${\mathit{L}}_{\mathit{r}\mathit{a}}$	${\mathit{D}\mathit{O}\mathit{D}}_{\mathit{i}}$	${\mathit{C}}_{\mathit{r}\mathit{a}}$	${\mathit{V}}_{\mathit{r}}$
$\mathrm{VRB}$	4000 cycles	23.3%	300 kWh	380 V
	${\mathit{L}}_{\mathit{r}\mathit{a}}$	${\mathit{D}\mathit{O}\mathit{D}}_{\mathit{i}}$	${\mathit{C}}_{\mathit{r}\mathit{a}}$	${\mathit{V}}_{\mathit{r}}$
$\mathrm{VRB}$	$0.2333$	$0.9333$	$0.4667$	$0.16$ (€/kWh)

Table 5

The on–off status of the units each time period of the day using the GA.

Period	0	1	2	3	4	5	6	7	8	9	10	11
DE	0	1	1	1	1	0	0	0	1	1	1	1
MT	0	0	0	0	0	1	1	1	1	1	1	1
BESS	1	−1	1	1	1	−1	−1	1	1	−1	−1	−1
Period	12	13	14	15	16	17	18	19	20	21	22	23
DE	0	0	0	0	0	0	0	1	1	0	0	0
MT	1	1	1	1	1	1	1	0	0	0	0	0
BESS	1	1	−1	1	1	−1	1	1	1	−1	−1	−1

Table 6

The on–off status of the units each time period of the day using the MIP algorithm.

Period	0	1	2	3	4	5	6	7	8	9	10	11
DE	0	0	1	0	1	0	0	0	0	0	1	1
MT	0	0	0	1	0	1	1	1	1	1	1	1
BESS	1	1	0	0	1	0	0	0	1	1	0	0
Period	12	13	14	15	16	17	18	19	20	21	22	23
DE	0	0	0	0	0	0	0	0	0	0	0	0
MT	1	1	1	1	1	1	1	1	0	0	0	0
BESS	0	0	0	0	0	0	0	0	0	−1	−1	−1

Table 7

Objective function results of the GA approach system with the use of BESS.

${\mathit{P}}_{\mathit{c}\mathit{x}}$	${\mathit{P}}_{\mathit{m}\mathit{u}\mathit{t}}$	$\mathit{e}\mathit{t}\mathit{a}$	$\mathit{b}\mathit{e}\mathit{s}\mathit{t}\left({\mathit{C}\mathit{F}}_{\mathit{e}\mathit{c}}\right)$	$\mathit{m}\mathit{e}\mathit{a}\mathit{n}\left({\mathit{C}\mathit{F}}_{\mathit{e}\mathit{c}}\right)$	$\mathit{\delta }\left({\mathit{C}\mathit{F}}_{\mathit{e}\mathit{c}}\right)$
0.6	0.4	0.01	620.8	624.72	4.02
0.7	0.3	-	625.22	628.9	4.2
0.8	0.2	-	627.94	626.02	5.13
0.6	0.4	0.1	622.77	627.5	5.9
0.7	0.3	-	621.22	626.11	5.6
0.8	0.2	-	632.62	636.97	5.56
0.6	0.4	1	623.12	633.85	4.4
0.7	0.3	-	623.54	628.13	5.23
0.8	0.2	-	625.45	632.65	5.51
0.6	0.4	10	625.66	631.52	5.13
0.7	0.3	-	624.78	628.42	5.71
0.8	0.2	-	627.84	629.12	1.31

Table 8

The on–off status of the units each time period of the day using the GA.

Period	0	1	2	3	4	5	6	7	8	9	10	11
DE	0	1	1	0	0	0	0	0	1	0	0	0
MT	0	0	0	1	1	1	1	1	1	1	1	1
BESS	1	1	1	−1	1	−1	−1	1	1	1	−1	−1
DR	0	0	0	0	0	0	0	0	1	1	1	1
Period	12	13	14	15	16	17	18	19	20	21	22	23
DE	0	0	0	0	0	0	0	1	1	0	0	0
MT	1	1	1	1	1	1	1	0	0	0	0	0
BESS	−1	0	−1	0	−1	−1	−1	1	1	−1	−1	−1
DR	1	1	0	0	0	0	1	0	0	0	0	0

Table 9

The on–off status of the units each time period of the day using the MIP.

Period	0	1	2	3	4	5	6	7	8	9	10	11
DE	0	0	0	0	0	0	0	0	0	0	0	0
MT	0	0	0	0	0	1	1	1	1	1	1	1
BESS	0	0	1	1	0	0	0	0	0	0	0	0
DR	1	1	1	1	1	0	0	0	1	1	1	1
Period	12	13	14	15	16	17	18	19	20	21	22	23
DE	0	0	0	0	0	0	0	0	1	0	0	0
MT	1	1	1	1	1	1	1	1	0	0	0	0
BESS	0	0	0	0	0	0	0	0	1	−1	−1	−1
DR	0	0	0	0	0	0	1	0	1	0	0	0

Table 10

Objective function results of the GA approach system with the use of BESS and DR.

${\mathit{P}}_{\mathit{c}\mathit{x}}$	${\mathit{P}}_{\mathit{m}\mathit{u}\mathit{t}}$	$\mathit{e}\mathit{t}\mathit{a}$	$\mathit{b}\mathit{e}\mathit{s}\mathit{t}\left({\mathit{C}\mathit{F}}_{\mathit{e}\mathit{c}}\right)$	$\mathit{m}\mathit{e}\mathit{a}\mathit{n}\left({\mathit{C}\mathit{F}}_{\mathit{e}\mathit{c}}\right)$	$\mathit{\delta }\left({\mathit{C}\mathit{F}}_{\mathit{e}\mathit{c}}\right)$
0.6	0.4	0.01	608.42	611.41	3.97
0.7	0.3	-	619.23	623.74	8.78
0.8	0.2	-	615.21	622.43	6.13
0.6	0.4	0.1	609.13	620.39	4.97
0.7	0.3	-	615.20	623.74	4.79
0.8	0.2	-	618.22	623.87	4.02
0.6	0.4	1	613.40	621.38	4.21
0.7	0.3	-	619.28	626.74	5.23
0.8	0.2	-	622.12	628.24	8.33
0.6	0.4	10	609.39	616.39	4.12
0.7	0.3	-	612.85	615.22	4.11
0.8	0.2	-	623.72	626.91	5.20

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