The Innovative Research on Sustainable Microgrid Artwork Design Based on Regression Analysis and Multi-Objective Optimization

Abstract

One of the most vital issues in electrical systems involves optimally operating microgrids (MGs) using demand-side management (DSM). A DSM program lowers utility operational costs in one sense but also needs policies that encourage financial incentives in the other. The present study formulates the optimum functioning of MGs using DSM in the form of a problem of optimization. DSM considers load shifting to be a viable option. There are operational limitations and executive limitations that affect the problem, and its objective function aims at minimizing the overall operational prices of the grid and the load-shifting prices. The major problem has been solved using an improved butterfly optimization scheme. Furthermore, the suggested technique was tested in various case studies that consider types of generation unit, load types, unit uncertainties, grid sharing, and energy costs. A comparison was made between the suggested scheme and various algorithms on the IEEE 33-bus network to demonstrate the proficiency of the suggested scheme, showing that it lowered prices by 57%.

1. Introduction

There are many challenges facing the current electric grid, such as conserving power, improving flexibility, reducing emissions from traditional energy production, reducing fossil fuel consumption, optimizing environmental and economic effects, etc. Different distributed energy resources (DERs) can be integrated with a smart microgrid (MG) to address such problems. MGs consist of various loads and energy storage systems, as well as renewable and small-scale dispatchable energy systems like microturbines (MTs), photovoltaic (PV), wind turbines (WTs), diesel engine generators (DEs), fuel cell (FCs), and so on [1,2]. An important part of the smart grid system is the MG’s energy production manner. Most MGs operate in either islanded or grid-connected modes. MGs use renewable energy resources (RERs) as their main energy production resources, and these resources tend to be intermittent. An MG’s uncertainty is typically caused by supply and demand, due to the unpredictable behavior of RERs and the MG’s total load demand. This uncertainty makes balancing the energy between the overall production and load demand at the MG an important challenge. It is feasible to solve the problem of their unpredictable nature by implementing DSM strategies using different RERs. DSM schemes will be essential for today’s smart grids in order to manage the excess power requirements of users while also minimizing imbalances between energy production and load consumption. In order to implement DSM successfully, modern metering systems and communication and information technologies must be utilized [3]. Various price policies have been discussed by researchers regarding DSM load shifting, including real-time costing, acute peak costing, slope block rate, and time of use (ToU). Energy management will be essential for improving reliability, quality of power, sustainability, and ensuring reliable, economic, and environmentally friendly functioning in the MG [4,5].

The optimum MG efficiency and energy management issues have been extensively studied by researchers. Refs. [6,7] examined an online multi-objective optimization method using a revised game theory framework in order to improve both the environmental and economic goals of MG operations. Ref. [4] integrated the stimulus-driven demand response program with the MG energy-management problem in order to optimize dispatch methods. Ref. [1] applied four types of optimization methods in order to optimize MG: direct quest, particle swarm optimization, lambda logic, and iteration. Ref. [8] examined a combination of economic dispatch and a DSM scheme for an MG system with the aim of minimizing the entire price for household users. The MG optimum operational problem must account for uncertainty in supply and demand in order to obtain optimal planning. Ref. [9] applied Monte Carlo simulation for handling the uncertainty associated with unpredictable power resources and load. Ref. [10] used a linear two-step stochastic scheme in an uncertain environment in order to optimize MG operation. MG operating optimization problems have been discussed in several studies. The majority of investigations fail to adequately analyze the effects of domestic DSM strategies on MG operations and users’ satisfaction level objectives are not adequately addressed in their DSM methods.

Ref. [11] examined a probability-based day-ahead EMS approach for scheduling the MG network’s dispatchable and non-dispatchable power resources. That study used a pumped-storage unit and a stimulus-driven DRP for maintaining the production and load balance. Ref. [12] examined the effects of stimulus-based DR schemes on the intra-day and day-ahead markets. Instead of selecting values for static elastic coefficients used in that study, it may be possible to model users’ reactions to cost variations more realistically. Ref. [13] examined the effect of DRPs on network resilience using several MGs. Stochastic EMS in that study took into account not only the operational planning but also indicators of the reliability of local loads during an emergency. Ref. [14] combined optimum planning of tidal energy resources into a probabilistic EMS architecture using DRP, resulting in a reduction of 13.14 percent in overall operational prices.

The purpose of the present study is to formulate the problem of optimum operation of MGs and demand-side management (DSM) through the development of common strategies for electric grid operations and consideration of the required limitations. The objective function (OF) aims at minimizing operation prices and DSM prices, and optimization limitations consist of generator limitations and restrictions on energy balance. Additionally, the hours of load shifting are taken into account as variables, and an improved butterfly optimization algorithm (IBOA) is applied for solving the optimization problem. This paper is divided as follows: Section 1 introduces the DSM, Section 2 defines the OF and formulation scheme, Section 3 presents the problem-solving approach, Section 4 presents the simulation outcomes, and Section 5 presents the conclusion.

2. Problem Formulations

An optimization problem is proposed for optimum unit production scheduling. An MG’s optimum operating strategy takes into account both the minimum price and operational limitations as well as DSM limitations. The OFs in the problem consider the overall production prices and the prices of using DSM. As a result, Equation (1) is used to define the OF of the problem of optimum operation of MGs taking DSM into account [15]:

$$\min F={\omega }_1\times OC+{\omega }_2\times DC$$

(1)

in which $\mathit{F}$ shows the overall operation prices for the MG, OC represents the overall operational costs (OC) of the energy production units, and DC represents the overall price to implement the demand-side programs. ${\mathit{\omega }}_1$ and ${\mathit{\omega }}_2$ show the weight ratios of the operation prices of the system and the price to implement DSM programs, respectively.

Subscriber dissatisfaction is caused by the use-time variation scheme. Therefore, the present study models the price to implement the load-shifting program as the discomfort function as a ${\mathbf{3}}^{}$-degree function based on Equation (2):

$$\mathit{D}\mathit{C}=\sum _{\mathit{l}=1}^{\mathit{m}}\left[{\mathit{A}}_{\mathit{l}}{\mathit{s}\mathit{t}}_{\mathit{l}}^3+{\mathit{B}}_{\mathit{l}}{\mathit{s}\mathit{t}}_{\mathit{l}}^2+{\mathit{C}}_{\mathit{l}}{\mathit{s}\mathit{t}}_{\mathit{l}}\right]$$

(2)

in which $\mathit{l}$ represents the number of loads capable of shifting, $\mathit{A},\mathit{B}$ and $\mathit{C}$ represent the price of shifting for the load, ${\mathit{s}\mathit{t}}_{\mathit{l}}$ shows the times of loads $\mathit{l}$ transferring, and $\mathit{m}$ represents the overall number of shiftable loads. The operational cost of a production unit includes the cost of production, the cost of startup, and the cost of maintenance. Moreover, since power can be bought or sold to the utility in the MG, the price of purchasing or selling energy to the grid appears in the operational cost function. An OC operational cost function is shown in Equation (3) for the optimization problem [16]:

$$CF=\left(\sum _{t-1}^T\sum _{i=1}^{I}C\left(i,t\right)+MC\left(i,t\right)+SC(i,t)\right)+\sum _{t=1}^T[C\left(t\right)-R(t\left)\right]$$

(3)

in which $\mathit{C}(\mathit{i},\mathit{t})$ indicates the price to generate energy of agent $\mathit{i}$ for time t of operating, $\mathit{M}\mathit{C}(\mathit{i},\mathit{t})$ indicates the price of maintenance, and $\mathit{S}\mathit{C}(\mathit{i},\mathit{t})$ indicates the price of beginning agent $\mathit{i}$ for time $\mathit{t}$. In addition, $\mathit{C}\left(\mathit{t}\right)$ represents the price to purchase energy for time $\mathit{t}$ from the network, and during that time, $\mathit{R}\left(\mathit{t}\right)$ represents power sales revenue. $\mathit{I}$ shows the number of energy production agents and $\mathit{T}$ represents the study time $(\mathit{T}=24)$ in hours. $\mathit{I}$ includes many production units like PV, WT, MT, FC, and battery, with diverse cost functions. WT output power can be calculated based on wind speed using Equation (4) as follows:

$$P_{WT}=\left\{\begin{array}{ll}0& 0<V<V_{ci}\\ (a·V^2+b.V+c)\ast P_r& V_{ci}<V<V_r\\ P_r& V_r<V<V_{co}\\ 0& V_{co}<V<\infty \end{array}\right.$$

(4)

In this equation, the parameter ${\mathit{P}}_{\mathit{r}}$ represents the rated power of WT, ${\mathit{V}}_{\mathit{c}\mathit{i}}$ shows minimum permitted wind speed, ${\mathit{V}}_{\mathit{c}\mathit{o}}$ represents maximum permitted wind speed, ${\mathit{V}}_{\mathit{r}}$ shows the nominal velocity, and $\mathit{V}$ represents the real wind velocity. $\mathit{a},\mathit{b}$ and $\mathit{c}$ can be found from a current device’s catalog. Solar cells generate energy based on light intensity and ambient temperature and the relevant values can be determined based on Equation (5):

$$P_{PV}=P_{STC}\ast \frac{G_{INC}}{G_{STC}}\ast (1+k(T_C-T_r\left)\right)$$

(5)

in which ${\mathit{P}}_{\mathit{P}\mathit{V}}$ represents solar cell output power in terms of area irradiance severity, ${\mathit{P}}_{\mathit{S}\mathit{T}\mathit{C}}$ shows maximal cell production energy in standard trail statuses, ${\mathit{G}}_{\mathit{I}\mathit{N}\mathit{C}}$ shows area light severity, ${\mathit{G}}_{\mathit{S}\mathit{T}\mathit{C}}$ represents irradiance severity in standard trail statuses, $\mathit{k}$ shows output power temperature ratio, ${\mathit{T}}_{\mathit{r}}$ and ${\mathit{T}}_{\mathit{C}}$ show reference and cell temperatures. Wind and solar energy are used rather than fuel as the RERs of WTs and PVs. Due to this, there are no fuel expenses associated with such units. Aside from the substantial construction costs, maintenance costs must also be taken into account when assessing the economics of MGs. Therefore, Equation (6) is used to calculate the overall price of WTs and PV units:

$$C_{RES}=\sum _{t=1}^{24}{P}_{WT,t}\times (AC\times I_{WT}^{Inv}\times I_{WT}^M)+\sum _{t=1}^{24}{P}_{PV,t}\times (AC\times I_{PV}^{Inv}\times I_{PV}^M)$$

(6)

in which ${\mathit{C}}_{\mathit{R}\mathit{E}\mathit{S}}$ shows the price of renewable units, AC shows the yearly price factor, ${\mathit{I}}^{\mathit{I}\mathit{n}\mathit{v}}$ is coefficient of investiture price to produce the energy of the agent, ${\mathit{I}}^{\mathit{M}}$ shows agent repair price.

A governor controls the DE’s output power. As the second-class function of producing power, DE fuel usage $(\mathit{L}/\mathit{h})$ can be given by Equation (7):

$$C_{DE}=\alpha .{\left(P_{DE}\right)}^2+\beta .P_{DE}+\gamma$$

(7)

in which, ${\mathit{C}}_{\mathit{D}\mathit{E}}$ shows DE fuel usage price $\mathit{L}/\mathit{h}$, ${\mathit{P}}_{\mathit{D}\mathit{E}}$ shows the output power of DE, $\mathit{\alpha },\mathit{\beta }$, and $\mathit{\gamma }$ would be constant. Based on Equation (8), performance of FC equals the output power to the input fuel when they are computed in a similar unit:

$$C_{FC}=C_{gasFC}\ast \frac{P_{FC}}{{\mu }_{FC}}$$

(8)

in which ${\mathit{C}}_{\mathit{F}\mathit{C}}$ shows the price of fuel utilized via a FC (USD/h), ${\mathit{C}}_{\mathit{g}\mathit{a}\mathit{s}\mathit{F}\mathit{C}}$ represents the price of natural gas for feeding the FC $(\mathrm{U}\mathrm{S}\mathrm{D}/\mathrm{k}\mathrm{W}\mathrm{h})$, ${\mathit{P}}_{\mathit{F}\mathit{C}}$ shows the FC output power, ${\mathit{\mu }}_{\mathit{F}\mathit{C}}$ shows the FC performance. Based on Equation (9), an MT has the same economic scheme as an FC, but its performance improves as power rises:

$$C_{MT}=C_{gasMT}\ast \frac{P_{MT}}{{\mu }_{MT}}$$

(9)

Equations (10) and (11) are used to express the price of power bought $\mathit{C}\left(\mathit{t}\right)$ and sold $\mathit{R}\left(\mathit{t}\right)$ (Equation (3)):

$$C\left(t\right)=T_{pp}\times P_{pp}$$

(10)

$$R\left(t\right)=T_{sp}\times P_{sp}$$

(11)

${\mathit{T}}_{\mathit{p}\mathit{p}}$ represents the tariff to purchase power from the network, ${\mathit{P}}_{\mathit{p}\mathit{p}}$ shows the energy bought from the network, ${\mathit{T}}_{\mathit{s}\mathit{p}}$ shows the tariff to sell power to the network, and ${\mathit{P}}_{\mathit{s}\mathit{p}}$ shows the electricity sold to the network. The price to repair and maintain units depends directly on their energy production. Thus, the price of repairing and maintaining unit $\mathit{i}$ for time t can be determined by Equation (12):

$$MC(i, t)=P(i, t)\times K\left(i\right)$$

(12)

in which $\mathit{K}\left(\mathit{i}\right)$ shows the cost of repairing and maintaining agent $\mathit{i}$ per kW of electrical power and $\mathit{P}(\mathit{i},\mathit{t})$ represents the output power of agent $\mathit{i}$ per hour $\mathit{t}$. Only fossil fuel production units are included in the start-up price. Based on the fact that the start-up price of agent $\mathit{i}$ depends on the cycle during which the unit is operational, Equation (13) calculates the start-up price of agent $\mathit{i}$ for time $\mathit{t}$:

$$SC(i, t)=S_{cost}\left(i\right)\times \left(U\right(i, t)-U(i, t-1\left)\right)$$

(13)

in which ${\mathit{S}}_{\mathit{c}\mathit{o}\mathit{s}\mathit{t}}\left(\mathit{i}\right)$ shows the start-up price of agent $\mathit{i}$ and $\mathit{U}(\mathit{i},\mathit{t})$ shows a binary parameter indicating the mode of agent $\mathit{i}$ including off/on for time $\mathit{t}$. Coequality limitations in the problem would include the power equilibrium limitation, based on Equations (14) and (15):

$$P_k^G-P_k^L=\sum _{i=1}^N{V}_k{V}_i\left[G_{ki}\cos \left({\theta }_k-{\theta }_i\right)+B_{ki}\sin \left({\theta }_k-{\theta }_i\right)\right]$$

(14)

$$Q_k^G-Q_k^L=\sum _{i=1}^N{V}_k{V}_i\left[G_{ki}\sin \left({\theta }_k-{\theta }_i\right)+B_{ki}\cos \left({\theta }_k-{\theta }_i\right)\right]$$

(15)

Inequality limitations are agent output power limitations, control parameter limitations, line power limitations, and voltage limitations, and can be determined by Equations (16)–(19):

$$P^{min}\le P\le P^{max}$$

(16)

$$U^{min}\le U\le U^{max}$$

(17)

$$\left|P_{ij}\right|\le P_{ij}^{max}$$

(18)

$$V_j^{min}\le V_j\le V_j^{max}$$

(19)

Equation (20) considers the shifting time of all loads as a further limitation in the demand response program:

$${st}_l\le T_l l=1,\dots ,m$$

(20)

in which ${\mathit{T}}_{\mathit{l}}$ is the allowed time for shifting the load $\mathit{l}\mathit{t}\mathit{h}$. This optimization problem can be transformed into the optimum power flow (OPF) problem through knowing the load shift time. As a result of resolving the OPF issue, it will be possible to determine the power produced via all units, as well as the power sent and received by the global network. The present study applies the IBOA for solving the optimization issue.

3. Improved Butterfly Optimization Algorithm

Smell, taste, and hearing are several of the senses that butterflies use to find food or mating partners, lay eggs, and escape hunters. Research indicates that butterflies have a strong sense of smell, particularly when searching for food from afar [17].

Chemoreceptors are nerve cells that are responsible for butterflies’ ability to search for food. The butterfly’s chemoreceptors are utilized to smell and are distributed throughout its body. The butterfly also uses this sense to find the right mate for itself [18]. Butterflies are capable of sensing, locating, and even separating various fragrances [19]. Aroa and Singh developed the butterfly optimization algorithm (BOA) [20]. The BOA’s population consists of butterflies acting as search agents. The BOA’s OF price changes according to the position of the butterflies. Using the BOA, all butterflies share their experiences with their neighbors according to fragrances distributed across distances.

When the butterfly senses the scent of the other butterfly, it follows it by using the stage as a universal quest spot. Butterflies are subjected to another movement as part of their local search optimization. Generated randomness is used for this part. By balancing the smell senses and fragrance, the BOA is applied.

3.1. Fragrance

There are three sections to fragrance: power exponent, sensory modality, and stimulus intensity. I indicates the physical incentive size which has been associated via the fitness solution, i.e., when the butterfly emits lots of fragrance, the surrounding butterflies are able to sense and are attracted to it.

Two important factors contribute to butterflies’ substance: changes in fragrance formulation (f) and incentive intension (I). The below equation describes the fragrance scheme:

$$f=c{I}^{\beta }$$

(21)

in which $\mathit{f}$ shows the observed extent of the fragrance, $\mathit{I}$ shows the incentive intension, $\mathit{c}$ is the sensory modality, and $\mathit{\beta }$ shows the power exponent based on defining the changing level of attraction. $\mathit{\beta }$ and $\mathit{c}$ fall within $[\mathbf{0},\mathbf{1}]$.

3.2. Butterfly Movement

The BOA consists of three stages: the initialization, the questing, and the finalizing phases. The BOA evaluates OF values for all butterflies following the initialization of the primary butterfly swarm. The step also involves setting the parameters of the algorithm. The algorithm begins to optimize once the parameters have been assigned. A random position has been generated in the quest area for the butterflies. Artificial butterflies travel to the updated places in the quest area once the iteration begins, and their prices are calculated. The next equation is used to produce the fragrance by butterflies in their places:

$$x_i^{t+1}=x_i^t+(r^2\times g^{\ast }-x_i^t)\times f_i$$

(22)

in which ${\mathit{g}}^{\mathit{*}}$ shows the optimal solution for the iteration $\mathit{t},{\mathit{x}}_{\mathit{i}}^{\mathit{t}}$ shows the solution vector ${\mathit{x}}_{\mathit{i}}$ for ${\mathit{i}}^{\mathit{t}\mathit{h}}$ butterfly, the fragrance of the ${\mathit{i}}^{\mathit{t}\mathit{h}}$ butterfly is shown via ${\mathit{f}}_{\mathit{i}}$ and $\mathit{r}$ shows a randomly selected firm within zero and one. The local quest in the algorithm would be:

$$x_i^{t+1}=x_i^t+(r^2\times x_j^t-x_k^t)\times f_i$$

(23)

in which ${\mathit{x}}_{\mathit{j}}^{\mathit{t}}$ and ${\mathit{x}}_{\mathit{k}}^{\mathit{t}}$ show the ${\mathit{j}}^{\mathit{t}\mathit{h}}$ and ${\mathit{k}}^{\mathit{t}\mathit{h}}$ members of the butterfly swarm in the quest area. Food search and partner mating in butterflies are BOA variables that take place both on a global and local scale.

The BOA is effective when it comes to exploring optimum values, but it fails when it comes to converging. This paper proposes a novel technique for modifying the BOA’s key variables to increase convergence speed.

According to chaos theory, a vector of the BOA’s key variables $\mathit{V}=[\mathit{a},\mathit{c},\mathit{r}]$ is used as the solution.

In chaos theory, unexpected and random patterns are studied. A chaotic system is a very sensitive dynamic system influenced by even the smallest change. The technique improves the point distribution in the search space by generating points with fewer complexities and greater distributions. The BOA’s convergence speed is improved by the feature. Here is a general formulation of chaos theory:

$$V_{t+1}^j=f\left(V_i^j\right),j=\mathrm{1,2},\dots ,l$$

(24)

in which $\mathit{l}$ shows the map extent and $\mathit{f}\left({\mathit{V}}_{\mathit{i}}^{\mathit{j}}\right)$ indicates the chaotic scheme producer function. A sinusoidal chaotic map was used as the main parameter in the following way:

$$\begin{array}{l}a={\alpha }_1{p}_i^2\sin \left(\pi p_i\right)\\ c={\alpha }_2{p}_i^2\sin \left(\pi p_i\right)\\ r={\alpha }_3{p}_i^2\sin \left(\pi p_i\right)\\ p_0\in \left[\mathrm{0,1}\right], {\alpha }_1,{\alpha }_2,{\alpha }_3\in \left(0.4\right], i=\mathrm{1,2},3\end{array}$$

(25)

Figure 1 depicts the flowchart for the IBOA.

4. Simulation Outcomes

The following part presents the outcomes of evaluating the suggested approach in various scenarios. Figure 2 shows a sample of the MG presented in the study. From the PCC point, it has been linked to the main grid. There is a DE, a PV panel, and a number of loads on the grid.

The data concerning DEs are shown in

Table 1. DE Data [21].

Production agent	Diesel generator
Minimum power	100 kW
Maximum power	4000 kW
Cost function	$F\left(p\right)=0.02268p^2+15.06p+817.47$

. The PV power production curve over a day is shown in Figure 3. As can be seen in the figure, the PV generates power only at hours with adequate access to solar irradiance. Therefore, there is a shut-down time for the PV overnight which will later be compensated by the dispatchable units. The power purchasing and sale costs are shown in Figure 4, and critical loads and shiftable loads are shown in Figure 5. The daily costs of purchasing and selling electric power from the grid in USD/h are shown in Figure 4. Power sold to the network equals 40 $/h [9], and power bought from the network equals 60 $/h [9] when costs stay constant. The coefficients to implement the DSM program are shown in

Table 2. Factors of DSM cost function [21].

Load	1	2	3	4	5	6	7	8	9	10
A	0	0	0	0.032	0	0	0.02	0	0	0
B	0.23	0.53	0.61	0.96	0.52	0.11	0.33	0.25	0.16	0.48
C	1	2	1	5	3	4	5	3	2	3

.

4.1. Implementing the Suggested IBOA Scheme

The following part illustrates the implementation of the suggested algorithm on a network in Figure 2. Here, ${\mathit{\omega }}_1$ and ${\mathit{\omega }}_2$ are weighting coefficients equaling 1, and the purchasing and sale costs of energy are assumed to be variables (Figure 4). The population was equal to 500, and 200 iterations were performed.

Table 3. Load’s shifting amount and costs.

Time of Loads Shifting Regarding Hours				Costs		Coefficients
${ST}_1$	3	${ST}_6$	1	DC ($)	53,820	$W_1$	1
${ST}_2$	0	${ST}_7$	0
${ST}_3$	1	${ST}_8$	8	OC ($)	3,081,652.3	$W_2$	1
${ST}_4$	0	${ST}_9$	2
${ST}_5$	0	${ST}_{10}$	0	F	3,135,472.3

and Figure 6 give the outcomes of using the suggested algorithm. Every load’s shifting amount, the OC, and the DSM cost (DC) are shown in Table 3. In Figure 6, the output power of MG units is shown along with the energy supplied by the network.

We evaluated and analyzed the effects of weighting coefficients, PV panels, and energy prices on operation prices and the price of DSM programs.

4.2. Weighting Coefficients’ Impact

The operation price and the price to implement the DSM program are included in the OF of the optimization problem. These weighting coefficients were adjusted to estimate how every section impacts the overall price. This was accomplished by changing the weighting coefficients in accordance with

Table 4. Weighting Coefficients’ Impact on the OF.

Coefficients	$W_1$	1	1	1	Sans DSM
	$W_2$	0	1	2
Time of load shifting, hours	${ST}_1$	6	3	0	-
	${ST}_2$	0	0	1	-
	${ST}_3$	5	0	0	-
	${ST}_4$	6	0	0	-
	${ST}_5$	17	0	1	-
	${ST}_6$	4	1	0	-
	${ST}_7$	17	0	0	-
	${ST}_8$	9	8	1	-
	${ST}_9$	2	2	0	-
	${ST}_{10}$	23	0	0	-
Prices	F	3,016,445	3,135,472.3	3,193,278.2	3,144,023.3
	OC ($)	3,016,445	3,081,652.3	3,174,678.2	3,144,023.3
	DC ($)	0	53,820	18,600	-

; the outcomes are presented.

Table 4 assumes that the operation price has a weighting ratio of 1, whereas the price of DSMs has a weighting coefficient of 2. Load shifting becomes non-cost when ${\mathit{\omega }}_2$ equals 0. There is no doubt that in this state, the minimum operation price and most load shifting were achieved. When the weight coefficients equal 1, operation prices increase, and load shifting decreases in comparison with the prior case.

4.3. PV Panels’ Effects

The results in

Table 5. PV Panels’ Effects on the OF.

PV		Sans PV	Using PV
Time of load shifting, hours	${ST}_1$	1	3
	${ST}_2$	1	0
	${ST}_3$	1	0
	${ST}_4$	0	0
	${ST}_5$	0	0
	${ST}_6$	0	1
	${ST}_7$	1	0
	${ST}_8$	4	8
	${ST}_9$	0	2
	${ST}_{10}$	0	0
Prices	F	5,582,978.2	3,135,472.3
	OC ($)	5,556,267.2	3,081,652.3
	DC ($)	26,720	53,820

illustrate the effects of PV panels on the optimum function of the MG with and without PV panels. Based on the table, load transfer decreases as well as the price of DSM schemes without PV panels compared with the system with PV panels; however, operation costs increase considerably without PV panels. Due to the removal of PV panels, the DE supplies the entire power for the system.

4.4. Energy Costs’ Effects

The following part solves the optimization problem by considering fixed costs for the purchase and sale of power at various hours of the day and night, as illustrated in Figure 4.

Table 6. Energy Costs’ Effects on the OF.

Cost		Constant	Changeable
Time of load shifting, hours	${ST}_1$	3	3
	${ST}_2$	1	0
	${ST}_3$	1	0
	${ST}_4$	0	0
	${ST}_5$	0	0
	${ST}_6$	1	1
	${ST}_7$	0	0
	${ST}_8$	8	8
	${ST}_9$	3	2
	${ST}_{10}$	1	0
Prices	F	3,091,198.29	3,135,472.3354
	OC ($)	3,026,958.2900	3,081,652.3354
	DC ($)	64,240	53,820

shows the outcomes of implementing the two scenarios. Price stabilization enhances load shifting, and DSM program implementation costs increase but operating costs decrease.

4.5. Comparing IBOA Efficiency

The following part evaluates and validates the effectiveness of the suggested IBOA by implementing it on MGs using various kinds of production units and comparing the outcomes to a number of meta-heuristic algorithms. The second low-voltage MG investigated is shown in Figure 7. PV, WT, MT, and FC units were employed for energy production in this MG, while batteries were employed for power storage and energy production resources for other MGs.

Table 7. Range of power variations of production units.

Units	WT	FC	Grid	PV	MT	BAT
${\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}\left(\mathrm{k}\mathrm{W}\right)$	15	30	30	25	30	30
${\mathit{P}}_{\mathit{m}\mathit{i}\mathit{n}}\left(\mathrm{k}\mathrm{W}\right)$	0	3	−30	0.33	6	−30

shows all production units’ ranges of power. Ref. [22] provides network data, such as load demand, energy costs, and so on. Table 7 shows that negative power for batteries indicates the batteries will store power and that negative value for the grid indicates the MG will sell power to the main grid.

Figure 8 and Figure 9 show the output of the suggested scheme as the production power of MG agents, price decrease, and DSM outcomes. The MG and main grid production power are shown in Figure 8, and the network load profile variations due to DSM are shown in Figure 9.

4.6. Implementing the Suggested Scheme on the Standard 33-Bus IEEE System

The following part demonstrates the effectiveness of the proposed scheme by applying the standard IEEE 33-bus network for a variety of units. There are four DG units, two combined heat and power (CHP) agents, one WT agent, and one PV agent in the MG, and it has been linked to the utility by buses [1,20]. Figure 10 depicts a revised 33-bus IEEE MG, capable of buying or selling energy.

Table 8. Features of DG units.

Bus	25	8	7	2
${\mathrm{R}}_{\mathrm{d}\mathrm{n}}$ (kW/H)	700	250	250	100
${\mathrm{R}}_{\mathrm{u}\mathrm{p}}$ (kW/H)	700	250	250	200
$C_{DG }(\$/\mathrm{k}\mathrm{W}\mathrm{H})$	50	35	45	27
${SD}_{c } \left(\$\right)$	0	25	25	25
${SU}_{c } \left(\$\right)$	0	50	20	20
$P_{max }\left(\mathrm{k}\mathrm{W}\right)$	400	500	550	400
$P_{min } \left(\mathrm{k}\mathrm{W}\right)$	50	20	40	50

presents the details of theDG units linked to buses 2, 7, 8, and 25 MGs. ${\mathbf{S}\mathbf{D}}_{\mathbf{c}}$ shows the price of starting and ${\mathbf{S}\mathbf{U}}_{\mathbf{c}}$ represents the price of stopping, Rup shows the rising slope rate and ${\mathbf{R}}_{\mathbf{d}\mathbf{n}}$ represents the dropping slope rate of unit generation, ${\mathbf{P}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ shows the minimal generation capacity and ${\mathbf{P}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ shows the maximal generation capacity of the units. CHPs can be found in buses 8 and 16, and since CHPs have restricted capacity,

Table 9. Features of CHP units.

Bus	16	8
A	0.0345	0.0435
B	14.5	36
C	26.5	12.5
D	0.03	0.027
E	4.2	0.6
F	0.31	0.011
$H_{max }\left(\mathrm{k}\mathrm{W}\mathrm{t}\mathrm{h}\right)$	1356	1800
$P_{max }\left(\mathrm{k}\mathrm{W}\right)$	1258	2470
$P_{min }\left(\mathrm{k}\mathrm{W}\right)$	400	810

indicates the minimal and maximal amount of energy and heat produced by the two units, as well as the constant coefficients of a cost function. A day’s expected use of heat load is shown in Figure 11. It is shown that the peak electric load matches the peak heat load ${(\mathbf{H}}_{\mathbf{m}\mathbf{a}\mathbf{x}})$.

The following part compares the efficiency of the suggested scheme to other optimization techniques, using the third MG in four cases. The four cases are listed below:

• Case 1: With no consideration for DSM and in the absence of CHP agents in the MG.
• Case 2: With no consideration for DSM and using CHP units in the MG.
• Case 3: Through the consideration of DSM and in the absence of CHP agents in the MG.
• Case 4: Through the consideration of DSM and using CHP units in the MG.

Figure 12 shows the number of units involved and the energy received from the main grid in Case 1. Figure 12 shows that the MG usually purchases the most power from the utility via bus 1 during maximum demand. Moreover, having both WT and PV agents during 24 h would be a desirable condition for generation. As a result of the PV unit’s excellent performance daily from 8 AM to 5 PM, it produced enough electricity for 12 buses. In this case, the highest profit for MG would be USD 2185.7133.

The agent involvement rate for Case 2 is shown in Figure 13. Because buses 8 and 16 have highly efficient CHPs, MG usually sells active power to the utility with a revenue of $\mathit{\$}2682$ and the maximum benefit equals $5607.

The involvement ratio of agents in Case 3 is shown in Figure 14. As a result of implementing DSM, the MG revenue grew by USD 2194.4, resulting in a profit of $8.7 over Case 1.

The involvement ratio of agents in Case 4 is shown in Figure 15. As a result of CHP generation, the MG has a higher chance of selling energy to the grid. MG profit in this case would be USD 5617.7. Figure 16 shows that CHP bus 8 produces the most heat because of its lower generation price. As shown in Figure 17, the IBOA algorithm solved the OPF problem by determining the system voltage curve, as well as the transition power of all system lines for maximal load demand in Case 4.

The state of the suggested procedure in various cases is summarized in

Table 10. The outcomes of profit and price of MGs in various cases.

Case No.		1	2	3	4
Coefficients	${\mathit{W}}_2$	0	0	1	1
	${\mathit{W}}_1$	1	1	1	1
Profit ($)		2185.7133	5697.2560	2194.4243	5617.7067
Income ($)		7492	7956.636	7185.814	7898.686
Price ($)		5306.29	2349.38	4991.39	2280.98

. This table illustrates MG income, price, and profit in four cases. Energy sales are the source of income, DC and OC are the costs, and profit is the difference. Clearly, Case 4 achieves the highest profit by implementing DSM and having different units in the MG.

Table 11. Comparing the outcomes of the suggested IBOA.

Algorithms	IBOA	BOA	GA
Price decrease (%)	57.01	50.7	25
Price ($)	2281	2617	3978

compares the efficiency of the proposed approach with the other optimization schemes. According to the results, the suggested approach decreased prices by 57% and improved by 32% in comparison with the conventional BOA.

In order to reveal the convergence capability of the proposed model, Figure 18 shows the convergence curve of IBOA, BOA, and GA. According to this figure, the proposed algorithm first converges much sooner than the other algorithms.

5. Conclusions

The present study models the optimum performance of MGs and DSM program deployment in the form of an optimization problem. As part of the optimization problem, the OF minimizes the price of MG operation and the DSM program implementation in order to improve user satisfaction. The optimization problem was solved by using an IBOA. There were three test networks that implemented the IBOA, resulting in the following outcomes. First, the DSM scheme reduced the operational costs of the whole MG. The second outcome is that the weight factor of the DSM increased, resulting in a decrease in the number and hours of load transfers and therefore raising the operational costs. Furthermore, the instantaneous cost of power can significantly affect MG’s optimum performance. Lastly, this paper implemented the suggested approach on the IEEE 33-bus network in various case studies in order to demonstrate its effectiveness and compare the outcomes with classic BOA and GA algorithms. In conclusion, design characteristics include (1) providing shifting load rather than shedding and cutting load, and supplying critical load via MG; (2) improving the efficiency of IBOA compared with BOA; (3) assessing the price decrease effects of FC, MT, WT, PV, CHP, and BAT; (4) comparing IBOA to various algorithms; (5) reviewing the outcomes of the new approach under various conditions with the optimal efficiency decrease of 57%.