Multi-Objective Optimization for Peak Shaving with Demand Response under Renewable Generation Uncertainty

Abstract

With high penetration of renewable energy sources (RESs), advanced microgrid distribution networks are considered to be promising for covering uncertainties from the generation side with demand response (DR). This paper analyzes the effectiveness of multi-objective optimization in the optimal resource scheduling with consumer fairness under renewable generation uncertainty. The concept of consumer fairness is considered to provide optimal conditions for power gaps and time gaps. At the same time, it is used to mitigate system peak conditions and prevent creating new peaks with the optimal solution. Multi-objective gray wolf optimization (MOGWO) is applied to solve the complexity of three objective functions. Moreover, the best compromise solution (BCS) approach is used to determine the best solution from the Pareto-optimal front. The simulation results show the effectiveness of renewable power uncertainty on the aggregate load profile and operation cost minimization. The results also provide the performance of the proposed optimal scheduling with a DR program in reducing the uncertainty effect of renewable generation and preventing new peaks due to over-demand response. The proposed DR is meant to adjust the peak-to-average ratio (PAR) and generation costs without compromising the end-user’s comfort.

1. Introduction

Recently, the awareness of sustainable renewable energy development, increments in power demand and the use of advanced communication technology have altered microgrid infrastructures [1,2]. The aim of microgrids in both grid-tied and stand-alone modes is to manage renewable and nonrenewable power generation and load aggregation [3]. Microgrids boost the adoption of renewable energy resources (RESs) to transform sustainable electricity networks [2]. The inherent nature of the RESs brings intermittence and fluctuation problems to power generation, to a high penetration level in the power systems [4,5]. The intermittency of RESs can be mitigated by several technical approaches, such as grid integration, spinning reserves, energy storage (ES) and distributed generation (DGs), modern forecasting techniques and demand-side management (DSM) or demand response (DR). The aim of these technical approaches is to dynamically maintain balance of power supply and demand at all times [3].

The topics of grid operation, energy resources and optimal demand management have become crucial. In the conventional power networks, the system operator adjusts the supply and demand with standby generation units and brings the power from third parties [5]. Moreover, it is difficult to schedule and manage generation units to compensate for the intermittence problems. In modern power distribution networks and microgrids, the uncertainty problems of high RES penetration can be mitigated by the active DSM scheme [3]. The microgrid can provide an energy management model locally, which can optimally control the performance of available resources at the generation level and load aggregation at the demand level with the DSM [3]. Thus, the DSM is a helpful method to improve the efficiency of the distribution systems and microgrids [6].

The DSM is an active management option in a smart distribution network. Basically, the DSM controls and monitors consumer consumption patterns. Consumers can modify their consumption patterns to mitigate negative impacts on system stability during peak demand periods [7]. Rather than attempting to generate more power, the DSM takes demand variation action with the available power level. In this regard, the DSM can significantly reduce the network’s new installation cost and the impacts of peak load problems. A powerful DSM program was achieved by aggregate load profile improvement [8]. According to the previous analysis, a smooth load profile provided a high-efficiency generation profile and network stability [9].

Additionally, DR is a helpful demand-side management technology. The DR encourages consumers to reduce and change energy usage during peak demand periods [6]. Two types of the DR are generally offered to consumers: (i) incentive-based and (ii) time-based DR programs. The incentive-based DR gives rewards to the consumers who adjust their load profiles or allow some level of control over their apparatus. Direct load control, uninterruptible service, demand bidding, capacity market programs, and ancillary service markets are classified as incentive-based DR. On the country, in the time-based DS, the price of electricity is changed over time according to the generation and demand conditions. Critical-peak pricing, time-of-use (TOU) pricing, real-time pricing and peak-load-reduction credits are some approaches to the time-based DR [5].

Furthermore, the DR has become an option for smart microgrids in critical situations, such as inadequate spinning reserves and expensive power exchange from tie-line capacity to compensate for lost or insufficient local generation and sudden load changes. In this regard, optimal generation resource scheduling with the DR becomes the topic of the microgrid planning stage during network contingency to guarantee particular operation conditions [10]. Different possible issues are involved in the planning stage while solving optimization in the power systems [11,12]. Thus, the microgrid resource scheduling model can be considered as a multi-objective and multi-constrained optimization problem [13].

Recently, many research articles have focused on a multi-objective and multi-constrained optimization problem. Moreover, the DS can be widely used for the residential, commercial and industry sectors from the economic ancillary service and technical perspectives. The work in [14] presented a multi-objective stochastic optimization method with a price-based DS program for the operation cost and emission minimization. The multi-objective model was handled by the augmented epsilon constraint method. The article in [15] analyzed the effects of optimal spinning reserve (SR) approaches to recover wind power and net demand uncertainties. The optimal work provided economic benefit and can reduce unexpected interruption. The day-ahead actual power scheduling in stand-alone microgrid mode was carried out with weighting factors in multi-objective non-linear programming. The objectives of this work were to minimize fuel and emission costs [16].

The modified teaching–learning algorithm (MTLA) used to solve the economic load dispatch problem was presented in [17]. This optimization problem focuses on the uncertainties of fuel and emission cost minimization under wind and load demand. The optimal distributed generation management with demand response was analyzed in [6]. The non-dominated sorting firefly algorithm (NSFA) was applied for the test system, in which the objectives were technical index enhancement, considering power losses and voltage stability [6]. The problem of DG planning with demand response for virtual power players (VPPs) considering profit maximization analysis with meta-heuristic multi-dimensional signaling was examined by the authors of [18]. The work in [19] highlighted the light daily scheduling of a microgrid with two types of DR programs considering intermittent RESs and demands. This optimization problem was executed by the PSO algorithm to minimize network operation costs. The authors of [20] proposed a demand-response-based home energy management system to reduce electricity costs and the peak-to-average ratio (PAR). The proposed system applied an enhanced differential evolution (DE) harmony search technique. A multi-objective building energy management system (BEMS) with DR was analyzed in [21]. This work provided the effective performance of the DR for the smart house regarding security, economy, and efficiency.

Although DSM can provide system stability, along with technical and economic benefits, the effective implementation of the DSM programs still affects consumer comfort [22]. The DSM or DR can disturb the convenience to consumers [3,5]. Operation-cost minimization and consumption bill reduction are no longer advanced infrastructure solutions. The electricity service’s qualities and the power communities’ satisfaction level have become challenges in power networks. The consideration factors can promote the role and achievement of the DSM in practical situations [5]. The variability in wind and solar resources created issues in scheduling to meet the hourly demand in one setting [23]. The work in [24] highlighted the effective deployment of demand response with heterogeneous energy storage. The risk-averse stochastic method was applied to maximize profit, minimize risk, and handle the RES and environmental uncertainty.

Although the peak demand at peak time can be avoided, the peak demand will increase at valley times due to a nonuniform demand shift toward the troughs. Therefore, this condition could create a loss of network diversity. Thus, in this work, we propose a multi-optimization-based method to control this over-demand response using peak-to-average ratio minimization at each time interval without adverse effects on consumer satisfaction. This target of the proposed work focuses on the generation scheduling with various generation units considering operation cost minimization, peak load controlling, and end-user comfort.

The main contributions of this paper are summarized as follows:

1.

The meta-heuristic-based multi-objective gray wolf optimizer (MOGWO) is proposed to simultaneously solve three multi-objective problems to achieve the Pareto-optimal solution.

2.

A demand response (DR) program is designed to reshape the flexibility of load profiles under the uncertainty of RESs.

3.

The optimal generation scheduling problem is executed by considering multi-objective optimization.

4.

The optimal uniform demand shifting program is applied to adjust the peak to average ratio (PAR) and generation cost without compromising the end-user comfort to prevent new peaks at valley time.

The rest of the paper is organized as follows. Section 2 presents the proposed methodology of the paper. In this section, the multi-objective optimization technique and problem formulation are comprehensively discussed. Section 3 presents verification results and discussions. Finally, Section 4 concludes the paper.

2. Proposed Methodology

In this section, an overview of multi-objective optimization is briefly described, followed by an introduction to the multi-objective gray wolf optimization (MOGWO) technique. Then, the best compromise solution and mathematical model of the optimization problem are proposed.

2.1. A Brief Introduction to Multi-Objective Optimization

The multi-objective optimization problem is used to find the optimal solution to handle different criteria with different sets of inequality and equality constraints. Single-objective optimization was developed to solve a single problem, and multi-objective optimization to handle more than one optimization problem simultaneously [6]. The problems involve different criteria that conflict with each other and must be considered simultaneously. Therefore, multi-criteria optimization searches for optimal solutions to different problems rather than the best solution for a particular problem, i.e., Pareto-optimal front [3]. The general formulation of the multi-objective optimization problem can be written as

$$\begin{array}{cc}\hfill \mathrm{Min}F\left(\mathbf{x}\right)& ={\left[f_1\left(\mathbf{x}\right),f_2\left(\mathbf{x}\right),...,f_N\left(\mathbf{x}\right)\right]}^T,\hfill \\ \hfill \mathrm{Subject}\mathrm{to},\end{array}$$

(1)

$$\begin{array}{cc}\hfill g_i\left(\mathbf{x}\right)& \le 0,i=1,2,\dots ,N_{neq},\hfill \end{array}$$

(2)

$$\begin{array}{cc}\hfill g_i\left(\mathbf{y}\right)& \le 0,i=1,2,\dots ,N_{eq},\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill \mathbf{x}& =(x_1,x_2,\dots ,x_k),\hfill \end{array}$$

(4)

$$\begin{array}{cc}\hfill \mathbf{y}& =(y_1,y_2,\dots ,y_k),\hfill \end{array}$$

(5)

$$\begin{array}{cc}\hfill {\forall }_i& \in \{1,2,\dots ,k\},f\left(x_i\right)\ge f\left(y_i\right)\wedge \exists i\in 1,2,\dots ,k:f\left(x_i\right)],\hfill \end{array}$$

(6)

$$\begin{array}{cc}\hfill P_f& :=\left\{F\left(x\right)\right|x\in P_s\},\hfill \end{array}$$

(7)

where $\mathbf{x}$ and $\mathbf{y}$ are the vectors representing Equations (4) and (5), respectively. $\mathbf{x}$ is the dominated vector and is shown in Equation (6). Here, no vector can dominate the other vector solution, so it is the non-dominated solution. A set of all non-dominated solutions is called the Pareto-optimal set. A set with Pareto-optimal solutions in the Pareto-optimal set is the Pareto-optimal front. The Pareto-optimal front allows for a better solution for the conflicting objectives [12]. Unlike the single-objective problems, large and highly complex searching are the limitations to accurately solving the majority of multi-criteria problems. The multi-objective optimization provided a non-dominated solutions set as an approximation method [10].

Different methods have been used to solve the multi-objective problem. Classical and meta-heuristic methods are the two possible optimization approaches for the multi-objective functions [17]. Usually, the classical approaches transform the multi-objective optimization problem into a single-objective optimization problem [13]. Currently, the meta-heuristic techniques are more capable of searching for optimal solutions than the classical methods for the advanced microgrid problem because of their fast convergence and high accuracy. The meta-heuristic optimization also provides a more accurate Pareto-optimal solution than the classical methods [17]. In the next subsection, the proposed multi-objective gray wolf optimizer is introduced.

2.1.1. Multi-Objective Gray Wolf Optimization

The multi-objective gray wolf optimizer (MOGWO) was developed by the authors of [12]. It was inspired by gray wolves’ hunting behavior. The top three tiers of wolves lead this algorithm to search for the best solution. The leader wolf is donated as alpha ($\alpha$), which is the wolf nearest to the prey. The beta ($\beta$) is an alpha follower responsible for maintaining harmony in the hunting group. In the hierarchy, delta ($\delta$) wolves are in the third position and act as scapegoats. The remaining wolves in the hunting group are donated as delta ($\delta$). The position updating of the MOGWO algorithm is mathematically represented by

$$\begin{array}{cc}\hfill {\mathbf{Y}}_1& ={\mathbf{Y}}_{\alpha }-{\mathbf{R}}_1{\mathbf{P}}_{\alpha },\hfill \end{array}$$

(8)

$$\begin{array}{cc}\hfill {\mathbf{Y}}_2& ={\mathbf{Y}}_{\beta }-{\mathbf{R}}_1{\mathbf{P}}_{\beta },\hfill \end{array}$$

(9)

$$\begin{array}{cc}\hfill {\mathbf{Y}}_3& ={\mathbf{Y}}_{\delta }-{\mathbf{R}}_1{\mathbf{P}}_{\delta },\hfill \end{array}$$

(10)

$$\begin{array}{cc}\hfill {\mathbf{Y}}_{(\mathrm{iter}+1)}& =\frac{{\mathbf{Y}}_1+{\mathbf{Y}}_2+{\mathbf{Y}}_3}{3},\hfill \end{array}$$

(11)

$$\begin{array}{cc}\hfill {\mathbf{R}}_1& =2\mathbf{a}{\mathbf{r}}_1-\mathbf{a},\hfill \end{array}$$

(12)

$$\begin{array}{cc}\hfill \mathbf{Q}& =2{\mathbf{r}}_2,\hfill \end{array}$$

(13)

$$\begin{array}{cc}\hfill \mathbf{a}& =2·\left(1-\frac{\mathrm{iter}}{\mathrm{Max}\mathrm{iter}}\right),\hfill \end{array}$$

(14)

where ${\mathbf{Y}}_1$, ${\mathbf{Y}}_3$, and ${\mathbf{Y}}_3$ are the positions of the wolves; ${\mathbf{R}}_1$, $\mathbf{Q}$, and $\mathbf{a}$ are the coefficient vectors; and ${\mathbf{r}}_1$ and ${\mathbf{r}}_2$ are the random vectors in [0, 1].

The MOGWO algorithm consists of two new items: (i) archive and (ii) leader selection. The first component is applied to store the non-dominated Pareto-optimal solutions throughout the process. The second is used to choose leaders’ (alpha, beta, and delta) solutions for the hunting process from the existing solution in the archive. The archive serves as a storage unit in which non-dominated Pareto-optimal solutions can be saved and retrieved with the help of the archive controller. During the iteration process, the archive controller controls and compares the new solution with existing solutions that try to enter into the archive. Four different non-dominated sorting cases are given as follows:

• The archived solution will not be updated if the new solution dominates the archive’s residences.
• The archived solution will be replaced with the new solution if the former is dominated by the new solution.
• The new non-dominated solution will be allowed to enter the archive if the archive has enough space.
• The grid mechanism will rearrange the segmentation and search for the most crowded solution to omit it if the new non-dominated solution has to enter and the archive is full.

The MOGWO algorithm is superior in coverage speed because of the new archiving and leader-selection processes. The obtained solutions are continually removed from the most crowded segments of the archive, and the leaders are selected from the most-populated solution of the archive. The MOGWO algorithm is suitable for solving problems with three objectives [12]. The pseudo-code of the MOGWO adopted from [25] is given as Algorithm 1.

Algorithm 1 Pseudo-code of MOGWO.

1: Initialize wolf solutions as $S_i(i=1,2,\dots ,N_{woft})$, in which $N_{wolf}$ is the number of the gray wolf population 2: Generate vectors of the movement coefficients 3: Evaluate the fitness of each wolf as ${\mathbf{P}}_{\alpha }$, ${\mathbf{P}}_{\beta }$ and ${\mathbf{P}}_{\delta }$ 4: $\mathrm{iter}=1$ 5: Repeat 6: for$i=1$ to $N_{woft}$ do 7:     Repositioning the wolves based on Equations (8)–(11) 8: end for 9: Estimate the fitness value of the wolves 10: Update ${\mathbf{P}}_{\alpha }$, ${\mathbf{P}}_{\beta }$ and ${\mathbf{P}}_{\delta }$ 11: Update the vectors of movement coefficients considering Equations (12)–(14) 12: Specify the non-dominate solution P: Update Archive 13: $\mathrm{iter}=\mathrm{iter}+1$ 14: Until $\mathrm{iter}\ge \mathrm{Max}\mathrm{iter}$ 15: Output P: Archive

2.1.2. Best Compromise Solution

Our method applies the best compromise solution (BCS) to find the best solution from the Pareto-optimal set. The BCS method is based on the Euclidean distance technique. The reference point ($f_{i,min}$, $f_{j,min}$ and $f_{k,min}$) from the corresponding objective function is selected as the minimum value of the available solution for all objectives. The best solution is obtained as the point which is the minimum distance (d) from the reference point in the Pareto-optimal set [26]. The following expression is minimum distance formulation.

$$\begin{array}{cc}\hfill D& =\sqrt{\left[\left(f_{ai}\right)-f_{i,min}{)}^2+\left(f_{bj}\right)-f_{j,min}{{)}^2+\left(f_{ck}\right)-f_{k,min})}^2\right]},\hfill \end{array}$$

(15)

$$\begin{array}{cc}\hfill d& =\min \left(D\right),\hfill \end{array}$$

(16)

where $f_{ai},f_{bj}$, and $f_{ck}$ are the points of corresponding objective functions in the feasible region.

2.1.3. Mathematical System Modeling

In the power network, the proposed algorithm will optimize power generation and responsive loads locally to meet peak power demand for 24 h. The peak power demand is planned for the day ahead (24 h) using the combination of dispatchable and non-dispatchable power generation resources. This paper considers the combination of PV and wind, grid power, and fuel base generation units. The system’s optimization problems are the minimization of generation costs, peak-to-average ratio (PAR), and consumer dissatisfaction with equality and inequality constraints. The operation cost includes operation cost, spinning reserves, and energy exchange costs. The optimal resource scheduling, formulated as deterministic, is implemented based on PV and wind forecast values. Based on the forecast wind speed and solar irradiance values, the multi-objective problem is solved by employing the multi-objective gray wolf optimizer (MOGWO). The following are the three defined objectives of the paper.

The first objective is the system’s operation cost minimization, which involves wind, PV, fuel base generations, and grid power exchange costs as

$$\mathrm{Min}{C}_{operation}^t=\sum _{t=1}^T{P}_{PV}^t{\lambda }_{PV}+P_{wind}^t{\lambda }_{wind}+[a{\left(P_g^t\right)}^2+b{P}_g^t+c]+P_{grid}^t{\lambda }_{grid}(u_{grid}^t-u_{sell}^t),$$

(17)

where $C_{operation}^t$ is the total cost of generation at time t ($/kWh); $P_{PV}^t$ and $P_{wind}^t$ are the output powers of PV and wind at time t, respectively; $P_g^t$ and $P_{grid}^t$ are total power generation and power exchange with grid at time t, respectively; $a,b,c$ are the generation coefficients; $u_{grid}^t$ and $u_{sell}^t$ are the power exchange coefficients at time t; and ${\lambda }_{PV}$, ${\lambda }_{wind}$ and ${\lambda }_{grid}$ are the prices of generation costs.

The second objective is peak-demand minimization for a particular hour. The term PAR of a particular time is the ratio of preferred peak to demand at a particular time. The second objective is given as

$$\mathrm{Min}{\Pi }_{PAR}^t=\frac{P_L^{max}}{{\sum }_{t\in T}{P}_L^{avg}},$$

(18)

where $P_L^{max}$ is the target peak demand at time t and $P_L^{avg}$ the average demand at time t.

The third objective is to minimize consumer dissatisfaction concerning the time and power gaps. In consumer comfort, operation delay and power gap are the metrics for measuring consumer satisfaction in the scheduling problem. The power gap is defined as the preferred and scheduled power ratio, and the time gap is the waiting time ratio to total operation time. The third objective is expressed by

$$\mathrm{Min}{\mathsf{\Gamma }}_{dissatisfaction}=\frac{T_{shift}^t}{T_{operation}^{total}}+\frac{P_{shift}^t}{P_{operation}^{total}}·{\mu }_{elasticity}^t,$$

(19)

where ${\mathsf{\Gamma }}_{dissatisfaction}$ is the end-user dissatisfaction index; $T_{shift}^t$ and $P_{shift}^t$ are the shiftable time and power at time t, respectively; $T_{shift}^{total}$ and $P_{shift}^{total}$ are the total shiftable time and power at time t, respectively; and ${\mu }_{elasticity}^t$ is the the demand elasticity coefficient at time t.

The following are equality and equality constraints that are used in the optimization problem.

Power balance constraint:

$$\sum _{t=1}^T{P}_{PV}^t+P_{wind}^t+P_{DG}^t+P_{grid}^t-P_{sell}^t=P_d^t.$$

(20)

Power exchange constraints:

$$u_{grid}^t+u_{sell}^t\le 1.$$

(21)

The spinning reserve is to protect the system from unexpected conditions, power outages, and sudden load changes:

$$\sum _{g=1}^G[P_{max}^g-P_g^t]\le P_{Rev}^t.$$

(22)

Generation capacities:

$$\begin{array}{cc}\hfill P_{PV}^{min}& \le P_{PV}^t\le P_{PV}^{max},\hfill \end{array}$$

(23)

$$\begin{array}{cc}\hfill P_{wind}^{min}& \le P_{wind}^t\le P_{wind}^{max},\hfill \end{array}$$

(24)

$$\begin{array}{cc}\hfill P_{DG}^{min}& \le P_{DG}\le P_{DG}^{max},\hfill \end{array}$$

(25)

$$\begin{array}{cc}\hfill P_{grid}^{min}& \le P_{grid}^t\le P_{grid}^{max}.\hfill \end{array}$$

(26)

Constraints to prevent new peaks:

$$P_{min}^t\le P_L^t\le P_{max}^t.$$

(27)

Dissatisfaction level, considering time gap and power gap constraints for the dissatisfaction index:

$$\begin{array}{cc}\hfill & T_{shift}^t=T_{start}^{shift}-T_{stop}^{shift}\le 6,\hfill \end{array}$$

(28)

$$\begin{array}{cc}\hfill & 0.2P_{d,total}^t\le P_{shift}^t\le 0.3P_{d,total}^t.\hfill \end{array}$$

(29)

3. Results and Discussion

In this section, the test system and generation characteristics that are used for the optimization problem are provided. There are two case studies given to verify the effectiveness of the proposed method.

3.1. Test System

The test system that was used for verification of the proposed technique is illustrated in Figure 1. As can be seen in the figure, two DGs were connected to buses 22 and 28, respectively. Additionally, there were PV and wind sources connected to buses 12 and 15, respectively. The test system was connected to the main grid at bus 1. All information of the test system can be found in [27]. The forecast’s PV and wind power generation are shown in Figure 2a,b, respectively. The figures clearly show that there were uncertainties between measurement and forecast data of the PV and wind sources. The characteristics of the two DGs were taken from [14] and are given in

Table 1. Generation characteristics of the two DGs.

DGs	a	b	c	${\mathit{P}}_{\mathit{min}}$, (kW)	${\mathit{P}}_{\mathit{max}}$, (kW)
1	40	180	20	5	100
2	60	100	10	5	100

. The electricity prices were assumed as the time of use (TOU). All points in the feasible region represent the non-dominated solution store in the archive, as seen in Figure 3. The concept of a non-dominated solution is according to Equations (4)–(7). In this study, the non-dominated solution was chosen with the BCS method.

3.2. Simulation Results

In this section, two case studies are given. In Case Study 1, the optimal scheduling process is implemented for uncertainties of the RES data considering the minimization of operational costs. Case Study 2 analyzes the multi-objective optimal demand response program. The simulation results were obtained using MATLAB 2021 software.

3.2.1. Case Study 1: Multi-Objective Operation Costs Optimization under RES Uncertainties

In this case study, the simulation results of the optimal generation scheduling are given for forecast and actual data. The optimal resource scheduling considering optimal operation cost curves of all the system’s generating units are shown in Figure 4 and Figure 5. According to the minimum cost problem, DG1 and DG2 are the most expensive generation units which are scheduled with minimum capacities in the system. The PV and wind units are more likely to schedule their maximum generation capacities according to cost minimization. The PV and wind generated more power in the daytime. Therefore, total generation capacities are higher during the off-peak period (daytime). The participation of load-response programs according to the uncertainty effect are illustrated in Figure 6 and Figure 7. As shown in Figure 8 and Figure 9, the proposed DR program shifted the load from peak periods of 1–5 h and 20–24 h to the valley time of 6–20 h. Therefore, the system scheduling altered the shape of the load profile after DR participation.

Table 2. Comparison of operational cost with RES uncertainty.

Time (h)	Operation Cost (Actual, $/kWh)	Operation Cost (Forecast, $/kWh)
7	3509	3339
8	3439	3232
9	4419	3467
10	4258	4144
11	5967	3595
12	5297	4220
13	3121	3151
14	5528	4419

shows the operational cost under the RES uncertainty based on actual and forecast data of PV and wind units. The PV generation was scheduled with higher output. The demand response requirements increase, and the operational cost is high. The wind output was scheduled with lower output, so the demand response decreases, and the operation level is low. In Case Study 1, it is essential to engage uncertainties of the RES units and the DR effect, which provide energy in new peak leads to the off-peak time. Figure 8 and Figure 9 show the statement of new peak creation. Peak-to-average ratio describes the stability of the system. In Case Study 1, the PAR is at 41% with actual RESs and at 44% with the forecast RESs.

3.2.2. Case Study 2: Multi-Objective Peak Reduction Problem

This work analyzes the flexible demand response to reshape the aggregated demand profile with multi-criteria decisions. The target of this work is to prevent the creation of a new peak in the off-peak time. In this part, the simulation results of simultaneous operation are shown in Figure 10, Figure 11, Figure 12 and Figure 13. The participation of responsive loads in the DR programs for Case Study 2 is shown in Figure 10 and Figure 12. Since the PV and wind powers are scheduled with uncertainty, the capacity of the DR created a new peak according to Case Study 1. In Case Study 2, and as shown in Figure 11, the amount of demand that is more than the optimal generation capacity is moved to an off-peak time based on the optimal hourly peak (less than 600 kW). The numerical information of the load shifting can be found in

Table 3. Load shifting considering peak load reduction.

Time (h)	Power (kW)	Waiting Time (h)
7	360.4108	5
8	578.5112	7
9	509.8774	6
10	545.7373	8
11	309.7874	8
12	521.0925	9
13	299.1939	7
14	360.8410	4
15	294.2400	6
16	352.9319	-
17	311.5162	5
18	588.9328	5

. According to Table 3, however, the total waiting time of the optimal peak reduction case is more than that of Case Study 1 (6 h), due to optimal demand distribution. The term peak-to-average ratio refers to the the quantitative measurement for load profile and the stability of the system. The system stability metric of the PAR is lower than that of Case Study 1 when considering the optimal peak load minimization (44% to 43%).

Uniform optimal load shifting considering consumer comfort is shown in Figure 12 and Figure 13. The dissatisfactory optimization index is the difference between actual and reference consumption at a particular period. The increase in the different levels described increases the discomfort. Therefore, the dissatisfaction should be a convex function, as shown in Figure 3. In this case, extra loads were changed to off-peak time according to optimal power-gap and time-gap information. The allowable DR is between 20% and 30% of hourly demand. The detailed information of the optimal load response for 24 h is presented in

Table 4. Optimal percentage of DR considering user comfort.

Time (h)	Demand Elasticity Factor (${\mathit{\mu }}_{\mathit{elasticity}}^{\mathit{t}}$)
1	0.3000
2	0.2000
3	0.2000
4	0.3000
5	0.2000
6	0.2200
7	0.2000
8	0.3000
9	0.2300
10	0.2000
11	0.3000
12	0.3000
13	0.3000
14	0.3000
15	0.2000
16	0.3000
17	0.3000
18	0.3000
19	0.3000
20	0.2300
21	0.2000
22	0.3000
23	0.3000
24	0.2300

. The index of the PAR was reduced to 37%, and the total waiting time was 6 h. As observed from simulation results, the peak shaving and load-profile reshaping had advantages for the proposed renewable energy of the microgrid system. It also prevented a new peak due to RES uncertainty and load response. Figure 11 and Figure 13 present the results related to the statements above. When the total generation capacity exceeded the optimal demand response, it can sell power back to the grid. The capacities of power exchanged from and sold to the grid were 200–300 kW and 100 kW, respectively. After the power moves from peak time to off-peak time, the extra power form off-time can be sold back to the main grid. The results in Figure 14 indicate that the power surplus at 12–17 h is sold back to the main grid. The total amounts of power shifted by the DR and the user comfort DR that can go back to the main grid are 1028 kW and 1287 kW, respectively. The profits resulting from exchanging power covering the production cost and the consumer comfort case are illustrated in Figure 11 and Figure 13. As the shiftable DR was adjusted between 20% and 30% for the user comfort, the extra power of user comfort DR was more than the shift by DR at off-peak time. The demand elasticity factor (${\mu }_{elasticity}$) represents the simulation results of optimal DR based on power gap and time-gap constraints in each hour. Numerical results for 0.2200 of the demand elasticity factor at 6 h were related to the case of 22% of DR. Results in Figure 13 illustrate that when the optimal DR programs were implemented at peak time, the level of the end-user dissatisfaction index had improved between 0.45 and 0.7. The level of the end-user dissatisfaction index decreased from 0.45 to 0.19 at an off-peak time. It is indicated that end-user dissatisfaction had better performance based on the lower waiting time (time gap) and allowable DR (20–30% power gap).

Figure 15 shows the end-user dissatisfaction index with DR over 24 h. A summary of the results of the three objective functions is provided in

Table 5. A summary of results of three objective functions.

Time (h)	Operation Cost ($/kWh)	PAR	Dissatisfaction Index
1	2746	1.5570	0.6083
2	4389	1.7572	0.4497
3	4984	1.8890	0.4568
4	2608	0.9394	0.4901
5	2788	1.2057	0.4579
6	3651	1.7335	0.2444
7	3339	3.0459	0.3923
8	3232	3.3208	0.2399
9	3467	2.4505	0.3673
10	4144	2.6960	0.2918
11	3595	2.4123	0.1721
12	4220	2.5852	0.3416
13	3151	2.0689	0.2084
14	4419	2.0399	0.2943
15	5313	1.9727	0.3929
16	2930	3.1326	0.3051
17	5833	3.1586	0.3513
18	3163	2.0325	0.3806
19	2884	2.3909	0.2820
20	4762	1.1677	0.5713
21	3230	1.0939	0.5221
22	2422	1.1061	0.5207
23	3555	0.9568	0.5236
24	4621	1.7299	0.6792

.

For comparison, the work in [29] was implemented using adaptive stochastic programming to cope with 10% of wind power uncertainty. From the optimal planning with DR, it has 30% of overall PAR. Moreover, the work in [30] presented optimal allocation resources with DR and day-ahead real-time pricing (DARTP). The total RES uncertainty of this work was reduced from 9.93% to 7.20% with the DARTP demand response model. The overall PAR for this method was 42.6156%. From

Table 6. Comparison with existing strategies.

Refs.	PAR (%)	RES Uncertainty (%)
[29]	30	10
[30]	42.6156	9.93
Proposed strategy	37	27.0136

, our proposed optimal DR system guaranteed the RES uncertainty increment up to 27.0136%. Additionally, it is noted that the configurations of power networks may affect the performance of our proposed method due to different locations of RESs and line losses from a different network topology.

4. Conclusions

In recent years, there has been increased attention in DR programs to address the problem of the peak load in the power distribution systems and microgrids. Moreover, owing to a significant amount of RES penetration and integration in power networks, advanced microgrid planning cannot consider the signal objective function. This paper proposed the optimal power resource management based on three objective functions with network constraints. The objective functions of the proposed method include the minimization problems of the operation cost, peak-to-average ratio (PAR), and consumer dissatisfaction over a 24 h period. Meta-heuristic MOGWO was applied to handle the multi-decision problem. Moreover, the BCS method was applied as a decision maker to search for the optimal solution from the conflicting objective functions. The performance of the proposed method was provided for two scenarios. First, the results illustrated the possible peak load at off-peak time due to the effects of RES uncertainty and over-demand response. Second, the simulation results showed that the performance of the proposed system was advantageous for generation scheduling due to the uncertainty effect. The power gap and time gap minimization were also considered through the index of end-user comfort. Peak-to-average ratio reduction was provided to show the effectiveness of the proposed method on the test system. For consumer’s comfort, the DR set the range between 20% and 30%. Multi-objective optimization can be solved via multi-decision variable simultaneously. The obtained results showed that the proposed strategy can handle RES uncertainty increment with less overall PAR.

Future work will focus on expanding our strategy of multi-objective planning to microgrid clusters.