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Optimal demand response programs selection using CNN‐LSTM algorithm with big data analysis of load curves

Optimal demand response programs selection using CNN‐LSTM algorithm with big data analysis of... INTRODUCTIONDemand Response Programs (DRPs) are convenient for managing the load and energy and adapting consumption and generation patterns [1, 2]. Usually, few consumers are aware of the actual price of electricity, so there is no incentive for consumers to participate in the market and adapt their consumption towards the generation side, network conditions, and electricity prices [3, 4]. For consumers to be able to participate in all DRPs, smart meters must be provided to consumers. Advanced Metering Infrastructure (AMI) and Automatic Meter Reading (AMR) are some of these technologies. Meanwhile, AMI systems allow consumers to read the price of electricity [5, 6].Today, smart meters are abundant in distribution networks. Consumers’ load patterns can be found by collecting customer consumption data measured by these smart meters [7, 8]. Considering the number of devices in use, a significant amount of data is collected. Among these big data, identifying similar load patterns from network consumers requires data mining analysis by clustering and classification algorithms [9]. Generally, clustering algorithms can be divided into two types based on the need for an initial clustering centre and those that do not require one [10]. In order to classify or cluster load patterns, various algorithms have been developed, which can be categorized into five categories: partitioning methods, hierarchical clustering, fuzzy clustering, density‐based clustering, and model‐based clustering [11, 12]. DRPs will be more effective if consumers’ load patterns are accurately identified. By clustering or classifying these load patterns, electricity tariffs can be set separately for each cluster or group [13, 14].BackgroundMathematical models that show different behaviours of consumers can be used to implement DRPs. Linear model and non‐linear models (exponential, power, logarithmic and hyperbolic) are unrealistic models for implementing DRPs. Non‐linear and linear models are used for various time‐based and incentive‐based programs. These models can also model combined time‐based and incentive‐based programs [15, 16]. In modelling DRPs, the existing challenges are selecting and calculating the elasticity matrix's elements, the amount of reasonable tariffs, and the amount of consumers’ CoP in implementing the programs [15]. More details are explained in Section 3.2. Among DRPs models, the power model simulates consumers’ behaviour better than other models [16].In [15], various simulations have been performed to model consumer behaviour in the presence of non‐linear and linear DP sources. In these references, the authors compared linear and non‐linear models in DRPs and concluded that the power non‐linear model could show the natural consumer behaviour. In [16], a power non‐linear model is presented in terms of clustering different consumption patterns of customers. In this paper, consumers are clustered in different groups and all DRPS are implemented. Finally, the best program for each cluster is considered based on the best profit for the utility company. However, customers’ consumption has not been considered for all seasons of the year, and the consumers have been considered quite logically. Also, DRPs have been implemented only on a specific day. In [17], based on the concept of customer profitability and demand flexibility, a dynamic economic model of DRP has been proposed as a combination of Emergency Demand Response Program (EDRP) and Time of Use (TOU) programs and considering different indices of the developed model for enhancing customer satisfaction and load profile features. However, programs prioritization has been used, but not all DRPs and load pattern segmentation have been used.In [18], a study is evaluated on the extent of consumer willingness to participate in various incentive‐based programs and the need for policy development based on consumer feedback in the Kuwaiti electricity market. In [19], an incentive‐based DRP model for DG resources is proposed, and in [20], dynamic DRPs are designed by optimal transactive pricing in a smart grid. But, these are not enough for the implementation of DRPs optimally. In [21], the use and comparison of two ANN‐based load prediction techniques, the Feed‐Forward Neural Network (FFNN) and the Echo State Network (ESN), in a commercial building data set, concerning a possible DR test has been investigated. In [1], has been presented a DR classification and modelling in large‐scale models along with an overview of the advantages, challenges, and mathematical formulas for different types of DR. Still, in general, the linear model is used to implement DRPs. In [22], only linear programming of DRPs by using various scenarios and sensitivity analysis of generation optimization of Distributed Energy Resources (DERs) in Smart Grid is presented.In [23], a linear model for implementing DRPs to participate in the electricity market and applying policies in the electricity market is presented. However, they have not repeatedly implemented DRPs with clustering load curves. In [24], a mathematical model for optimizing DRPs for decreasing the generation costs of up‐grid networks and distributed generation resources, including wind turbines, photovoltaics, battery storages, and microturbines in 14‐bus and 11‐bus microgrids, is presented. In [25], an optimal model for the daily operation of a Multi‐Energy Virtual Power Plant (MEVPP), including electric, thermal, and natural gas sectors, is presented. Meanwhile, smart grid technologies such as Price‐Based Demand Response (PBDR) and Incentive‐based Demand Response (IBDR) are used for electric loads. The scheduling model presented in it is based on the simulation of this multi‐objective virtual power plant to maximize MEVPP profit and minimize carbon dioxide emissions. In [26], a multi‐objective optimization model is proposed for optimal planning of hot rolling load considering the actual conditions of production operation. This project develops an integrated scheduling model of hot rolling shop scheduling and electricity DR, and a multi‐objective production scheduling algorithm is designed. In [27], this paper uses an intelligent distribution system that includes electricity resources in addition to a DR scheme. Load reduction in smart homes is also considered based on load prioritization and customer participation in the DR plan to achieve the goals of the proposed plan.In [28], is proposed a method for detecting and predicting high energy demand events that are managed at the national level in DRPs. This method includes two stages of load forecasting with short‐term memory neural network and a dynamic filter of the highest potential peaks of electricity demand using an exponential moving average. The general application of this method to manage the DRP has been very well done by reducing energy consumption and indirect carbon emissions. In [29], k‐means CNN_LSTM (kCNN‐LSTM) is presented, a deep learning framework that operates on energy consumption data recorded at predefined intervals to provide accurate building energy consumption predictions. But not all DRPs have been used yet.Despite all the studies conducted, there is no model that illustrates the correct behaviour of consumers across different groups when implementing DRPs. In all studies, mathematical models have been used to illustrate the behaviour of consumers during the implementation of DRPs. Linear and non‐linear models of DRPs include only a few examples of consumers’ behaviour and do not show the rest of the other general behaviours and reactions in a year. This means that consumers must be assumed to be perfectly rational. Table 1 presents a comparison between the published works and this paper.1TABLEComparison of this paper with published studiesReference numberYearSelected DRPsDRPs modelThe method of optimal selection programsSegmentation of consumers’ load patternAlgorithms used for Implementing DRPsApplication of article[1]2022RTPLinear‐‐‐The impacts of smart home participation in power DR[15]2019All DRPsLinear and all non‐linearMCDM‐‐The behaviour of DRPs models in the transmission system[16]2019All DRPsPowerMCDM✓‐Selecting the most effective DRPs for utility/customer[17]2020EDRP, TOULinear‐‐‐Considering different indices of the developed model for enhancing customer satisfaction and load profile features[18]2020Incentive‐based DRPsLinear‐‐‐Expensing using a suitable energy management system[19]2021RTPLinear‐‐‐Establishing an integrated DR model for multiple energy carriers[20]2021RTPLinear‐‐‐Designing a dynamic DR pricing considering economic aspects and reserve[21]2021RTPmachine learning‐based‐✓Feed‐Forward Neural Network (FFNN)Predicting the electric load with high accuracy to participate in DR programs for commercial, industrial, and residential consumers[22]2022RTPLinear‐‐‐Scheduling of main grid, storages, boilers, distribution generations, and responsive loads[23]2010All DRPsLinearMCDM‐‐Selecting the most effective DRPs for utility/customer[24]2018All DRPsLinear‐‐‐The effects of DRPs on total operation costs, customer's benefit, load curve, and determining optimal use of energy resources in the micro grid operation[25]2022All DRPsLinear‐‐‐Simulation of this multi‐objective virtual power plant to maximize MEVPP profit and minimize carbon dioxide emissions[26]2022RTPLinear‐‐‐An integrated scheduling model of hot rolling shop scheduling and electricity DR, and a multi‐objective production scheduling algorithm is designed[27]2022RTPLinear‐‐‐Achieving the goals of the proposed plan and load reduction[28]2020TOUMachine learning‐based‐‐LSTMDetecting and predicting high energy demand events[29]2021RTPMachine learning‐based‐✓K‐meansCNN‐LSTMEnergy consumption data recorded at predefined intervalsThis paper‐All DRPsmachine learning‐basedMCDM✓WFA K‐means CNN‐LSTMSelecting the most effective DRPs for consumers with clustering of load curves with the prediction of loads consumptionContributionsIn this paper, the machine learning algorithm is used to run DRPs. Convolutional Neural Network (CNN) and Long Short‐Term Memory (LSTM) algorithms are used to execute DRPs. First, the consumers’ load profiles are clustered, and the same load patterns are grouped together. Second, DRPs are modelled as power. Time‐based and incentive‐based programs also combined models with a Coefficient of Participation (CoP) to increase the percentage of consumers in implementing DRPs in each cluster. With the help of newly collected data obtained by implementing the power model of DRPs, the power model of DRPs is implemented by the DL method. During the entire implementation of DRPs, the consumption of each cluster in different seasons is calculated using Time Series Prediction (TSP). Third, the power model of DRPs with CoPs is implemented to ensure the correctness of the answering algorithm. The Deep Learning (DL) model is trained using the data obtained from the power model, and fourth, DRPs are implemented in two ways using new data. Finally, the results of the power and the ANN models of DRPs are compared to show the correct responsibility of the DL model.Therefore, the main contributions of this article are summarized as follows:Clustering and classifying customers’ consumption load patterns by improved Weighted Fuzzy Average (WFA) K‐means clustering method.Implementing Demand Response Programs (DRPs) by CNN‐LSTM method in all different load patterns of customers’ consumption in the distribution network (All 12 DRPs are executed by the CNN‐LSTM algorithm in one year).Implementing all 12 Demand Response Programs (DRPs) without dynamic calculations of the elasticity matrix by the CNN‐LSTM method.Implementing Demand Response Programs (DRPs) during the year by Time Series Prediction (TSP) to predict customers’ consumption for all seasons.The existing challenges in the implementation of demand response programs include the following:Linear and non‐linear models of DRPs include these deficiencies:Linear and non‐linear models of DRPs can only be used if consumers are considered perfectly reasonable.The special elements of DRP models should be calculated for each day. This is very difficult and time‐consuming.To perform those will require rigorous calculations of the elasticity matrix.This paper uses the machine learning algorithm (CNN‐LSTM algorithm) to execute DRPs to obtain more precise solutions. The advantages of implementing machine learning‐based of DRPs over linear and non‐linear models can be noted in the following:Elasticity matrices will not be needed to execute programs, and only past consumer data will be used.DRPs will be much easier to implement for each consumer annually.The proposed CNN‐LSTM method achieves almost complete performance for predicting electricity consumption, which was previously difficult to predict. It also has the lowest root mean square error compared to methods of other deep learning algorithms [30].This paper uses load pattern clustering by the improved WFA K‐means algorithm due to better CDI index evaluation than other algorithms [16]. After clustering and implementing DRPs in order to maximize mutual economic benefits and enhance technical indicators, Multi‐Criteria Decision‐Making (MCDM) methods are employed in this paper [16]. This article aims to provide a general and practical solution for the optimal implementation of DRPs in the electricity industry for various load patterns of consumers.The structure of this article is as follows: In Section 2, the method of the problem will be mentioned, and all the steps of doing the work will be briefly explained in order. In Section 3 of the clustering algorithm used, the program model of non‐linear power DRPs and CNN‐LSTM method, and finally, the weighting and prioritization of programs are fully explained. In Section 4, the results and outputs obtained are presented and discussed, and in Section 5, a general conclusion of this article is given.PROBLEM APPROACHOrganizing this study can be divided into four general stages: clustering of consumers’ load patterns, applying the non‐linear power model of DRPs, applying the DL model of DRPs, and prioritizing the execution of programs in accordance with specified weights.The first stage involves collecting and clustering the load curves of consumers over a period of one year. Several clusters will be obtained at this stage, each containing similar curves. The sum of each cluster's curves is considered a load pattern that expresses that cluster's characteristics and consumer behaviour. Clustering consumers will be done using the improved WFA K‐means method [16]. The k‐means method requires the centre of the primary cluster; the calculation of the centre of the clusters is used in the repetition steps using the WFA technique. Finally, the Euclidean method uses the distance between each cluster's centre and load curve [16]. The algorithm of this method is indicated in Figure 1.1FIGUREFlowchart of clustering algorithm for consumers’ load patterns by WFA K‐means methodAfterward, time‐based DRPs include the Time Of Use (TOU), Real‐Time Pricing (RTP), Critical Peak Pricing (CPP), and incentive‐based programs, including Direct Load Control (DLC), Emergency Demand Response Programs (EDRP), Capacity Market Pricing (CAP), Interruptible/Curtailable (IC) and some combined programs such TOU+DLC, TOU+CAP, TOU+EDRP, and TOU + I/C are considered. It is important to determine tariffs and the amount of penalties and incentives for each program in order to identify the problems. The power model of all these programs is applied to each cluster, and the final load curves are obtained after implementing DRPs [15]. After the data is obtained from the power model of DRPs in each cluster, the DL model of DRPs can be obtained. It is only necessary to be able to carry out DRPs in the electricity network practically and accurately. DL model of DRPs is an excellent alternative to linear and non‐linear DRPs in the electricity industry and can easily be used to show consumers’ behaviour when implementing DRPs.The input and output data necessary to implement DRPs are entered into the DL algorithm for each group of consumers. Consumption data before implementing DRPs, incentives, penalties, initial prices, secondary prices, and annual hours of each cluster as input data, and consumption data after implementing DRPs of that cluster as target data (output) are entered into the DL. The choice of input and output data required for TSP varies depending on the predicted action type. TSP's input and output data include the transfer of consumed data before DRPs implementation, incentives, penalties, initial price, secondary price, and annual hour and the transfer of consumed data after DRPs implementation. In addition to all these things, a data memory should be set aside depending on the expected day of consumer load. In the next step, the time series is predicted by creating a delay and entering a noise with a particular standard deviation (if necessary), which is only to create the necessary environment for a better responsibility of the DL algorithm to enter new data. Training, validation, and test data are selected as a percentage and as desired, and then the number of hidden layers is selected by trial and error or optimally selected. Finally, by entering the input data into the trained DL algorithm, the output data of each DRPs is obtained.In this paper, the initial data are modelled by the power model of DRPs before performing the time series prediction. Because the results obtained from time series prediction by the CNN‐LSTM algorithm will be compared with the power model of DRPs. Among the desirable indicators that this article will obtain are peak reduction, energy consumption reduction (energy savings), peak to valley distance, load factor, and the final customer bill (after applying penalties and incentives). Therefore, This step uses the MCDM approach. The weighting of the indicators has been done by the entropy method, and the prioritization of programs has been done by Similarity to the Ideal Solution (TOPSIS) method. Figure 2 illustrates the steps that are required to perform the problem method described in this article.2FIGUREThe procedure of implementing the DRPs CNN‐LSTM model in the distribution network according to the clustering of consumers’ load patternsPRELIMINARIES AND PROBLEM FORMULATIONThis paper solves the problem by taking four general steps: clustering, implementation of DRPs, selection of indicators and their weight, and prioritization of programs.Clustering by improved WFA K‐meansAs shown in Figure 1, it is needed to determine the number of clusters in the first step. In this paper, consumer's curves are classified into four clusters (residential, commercial, agricultural, and industrial clusters). After placing the curves in the appropriate cluster, the cluster centres can be calculated with the following equations [16]:1μt,uc+1=∑t=1:twt,ucXt,uforu=1,…,N$$\begin{equation}\mu _{\left( {t,u} \right)}^{\left( {c + 1} \right)} = \mathop \sum \limits_{t = 1:t} w_{\left( {t,u} \right)}^{\left( c \right)}{X_{\left( {t,u} \right)}}{\rm{\;\;}}for{\rm{\;}}u\; = {\rm{\;}}1, \ldots ,N\end{equation}$$2wtc=exp−Xt−μc2σ2$$\begin{equation}w_t^{\left( c \right)} = {\rm{\;}}\exp\left[ {\frac{{ - \left( {{X_t} - {\mu ^{\left( c \right)}}} \right)}}{{2{\sigma ^2}}}} \right]\end{equation}$$In these equations, μ(t,u)(c+1)$\mu _{( {t,u} )}^{( {c + 1} )}$ is the tth component of the centre of the cluster with n consumers, in the c + 1th repetition. Also, w(t,u)(c)$w_{( {t,u} )}^{( c )}$ is the weight of the tth component of the nth consumer in the repetition of r. The pth component of the uthconsumer is marked with X(t,u)${X_{( {t,u} )}}$. In Equation (2), wt(c)$w_t^{( c )}$ is the weight of the tth component in the cth repetition, which according to its component or Xt${X_t}$, the component such as the centre of the cluster in the cth repetition and the variance of the component is obtained. In the modified method, σ2 or the variance of the vector of each cluster, is applied to consider more effects for data with higher variance [16].Extract DRPs models using CoPThere are different models of DRPs based on elasticity in mathematical functions. Using mathematical functions, linear and non‐linear models, including power, exponential, and logarithmic can be modelled during the day. Given that different models have different behaviours, non‐linear and linear models should be extracted, and their results should be compared with each other [23]. The elasticity of the load is determined by its sensitivity to price changes and is divided into self‐elasticity and cross‐elasticity [24]. Elasticity is defined in terms of self‐elasticities and cross‐elasticities concerning the following equation [23]:3E(i,j)=pjdj.∂di∂pi$$\begin{equation} E( {i,j}) = \frac{{p\left( j \right)}}{{d\left( j \right)}}\;.\frac{{\partial d\left( i \right)}}{{\partial p\left( i \right)}}\end{equation}$$4self−elasticityEi,j≤0ifi=jcross−elasticityEi,j≥0ifi≠j$$\begin{equation} \left\{ \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\;{\rm{self}} - {\rm{elasticity}}\;E\left( {i,j} \right) \le 0\;if\;i\; = \;j\;}\\[5pt] {{\rm{cross}} - {\rm{elasticity}}\;E\left( {i,j} \right) \ge 0\;if\;i \ne j} \end{array} \right.\end{equation}$$where p is the price and d is the demand. Equation (3) shows the degree of sensitivity of the load to price changes per period, and Equation (4) shows the definition of the elasticity matrix. To implement consumption management, consumers need to change their energy consumption from the initial value of d0(i)${d_0}( i )$ to d(i)$d( i )$. New energy consumption is denoted by Δd(i)${{\Delta}}d( i )$ and is defined as follows:5Δd(i)=di−d0ikWh$$\begin{equation} \def\eqcellsep{&}\begin{array}{*{20}{l}} {{{\Delta}}d(i) = \left| {d\left( i \right) - {d_0}\left( i \right)} \right|\;}&{kWh} \end{array} \end{equation}$$IC(i)$IC( i )$ is the amount of load reduction required in DRPs, and d′(i)$d^{\prime}( i )$ is the amount of load that the customer should be penalized. The total standard penalty (pen′$pen^{\prime}$) is obtained from Equation (7).6d′(i)=ICi−ΔdikWh$$\begin{equation} d^{\prime}(i) \def\eqcellsep{&}\begin{array}{*{20}{l}} = {IC\left( i \right) - {{\Delta}}d\left( i \right)}&{kWh} \end{array} \end{equation}$$7pen′(Δd(i))=peni.ICi−Δdi$$\begin{equation} pen^{\prime}({{{\Delta}}d(i)}) = pen\left( i \right).\left[ {IC\left( i \right) - {{\Delta}}d\left( i \right)} \right]\end{equation}$$A(i)$A( i )\;$is the amount of incentive received to reduce the burden on time, and pen(i)$pen( i )$ is the penalty to be paid for the non‐reduced burden that will follow the customer's closed contract. The amount of incentive paid in the ith (A′$A^{\prime}$) period is as follows [16]:8A′(Δd(i))=Ai.di−d0i$$\begin{equation} A^{\prime}({{{\Delta}}d(i)}) = A\left( i \right).\left| {d\left( i \right) - {d_0}\left( i \right)} \right|\end{equation}$$In modelling DRPs, maximizing customer profit is necessary due to encouraging customers to perform DRPs. The customer profit function is calculated as Equation (9) which in it B(d(i))$B( {d( i )} )\;$shows customer revenue if there is a profit, d(i)p(i)$d( i )p( i )$ shows the cost of electricity consumption, A′(Δd(i))$A^{\prime}( {\Delta d( i )} )$ shows incentive received, and pen′(Δd(i))$pen^{\prime}( {\Delta d( i )} )$ shows the amount of the penalty. Its maximum value will be obtained by Equation (10) deriving from the customer profit equation. Therefore [16]:9(di)−B(d(i))+d(i)p(i)=A′(Δd(i))−pen′(Δd(i))$$\begin{equation} ({d\left( i \right)}) - B({d(i)}) + d(i)p(i) = A^{\prime}({\Delta d(i)}) - pen^{\prime} ({{{\Delta}}d(i)})\end{equation}$$10∂Bdi∂di=pi+Ai+peni$$\begin{equation} \frac{{\partial B\left( {d\left( i \right)} \right)}}{{\partial d\left( i \right)}} = p\left( i \right) + A\left( i \right) + pen\left( i \right)\end{equation}$$The customer revenue function is defined by the Taylor series second‐order expansion of the power demand function as follows [16]:11Bi=B0(i)+p0idi1+E(i,i)−1did0iE(i,i)−1−1$$\begin{equation} B\left( i \right) = {B_0}(i) + \frac{{{p_0}\left( i \right)d\left( i \right)}}{{1 + E{{(i,i)}^{ - 1}}}}\left\{ {{{\left( {\frac{{d\left( i \right)}}{{{d_0}\left( i \right)}}} \right)}^{E{{(i,i)}^{ - 1}}}} - 1} \right\}\end{equation}$$where E(i,i)$E( {i,i} )$ is the matrix of elasticity at any time interval i, by simplifying the Equations (10) and (11), the one‐period model of the power demand function with its self‐elasticity will be as follows [16]:12di=d0ipi+Ai+penip0iEi,i$$\begin{equation} d\left( i \right) = {d_0}\left( i \right){\left( {\frac{{p\left( i \right) + A\left( i \right) + pen\left( i \right)}}{{{p_{{{\rm{\;}}_0}}}\left( i \right)}}} \right)^{E\left( {i,i} \right)}}\end{equation}$$Using the definition of reciprocal elasticity, the multi‐period model of the power function is obtained.13d(i)=d0(i).∏j=1j≠i24pj+Aj+penjp0jEi,j$$\begin{equation} d(i) = {d_0}(i).\mathop \prod \limits_{ \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {j = 1}\\ {j \ne i} \end{array} }^{24} {\left( {\frac{{p\left( j \right) + A\left( j \right) + pen\left( j \right)}}{{{p_0}\left( j \right)}}} \right)^{E\left( {i,j} \right)}}\end{equation}$$By combining two single‐period models with multi‐period comprehensive models, the power function is obtained as follows [16]:14di=α.d0i.EXP×∑j=124Ei,jlnpj+Aj+Penjp0j+1−α.d0i$$\begin{eqnarray} && d\left( i \right) = \;\alpha .{d_0}\left( i \right). \ {\rm EXP}\nonumber\\ &&\quad\times\, \left\{ \mathop \sum \limits_{j\; = \;1}^{24} E\left( {i,j} \right){\rm{ln}}\left( {\frac{{p\left( j \right) + A\left( j \right) + Pen\left( j \right)}}{{{p_0}\left( j \right)}}} \right)\right\} + \left( {1 - \alpha } \right).{d_0}\left( i \right)\nonumber\\ \end{eqnarray}$$In Equation (14), α represents the coefficient of consumer participation in DRPs. This coefficient will always be between 0 and 1. For example, to show 60% participation, α must be set to 0.6. Obviously, the model of DRPs only applies to the part of the load involved in DRPs.Weighing indicators and prioritizing DRPsIn studying the implementation of DRPs, selecting the best program according to several different criteria is mandatory. These issues are called MCDM issues. Depending on the perspective of the Independent System Operator (ISO), the retailer or distribution company, and the customer, these criteria and indicators will be of varying importance. In some cases, the profit of the utility company is the most important indicator, or the reduction of the customer bill is the most crucial indicator; by using these decisions, different DRPs are selected [16].Shannon entropy methodIn information theory, a mathematical function called Shannon entropy measures the “uncertainty” in a random process. The amount of uncertainty is expressed by a discrete probability distribution of each of the variables modelled with P. This uncertainty is denoted by E and is expressed as follows:15En=−Kn∑m=1fPm×LnPm,Kn=Lnf−1$$\begin{equation} {E_n} = - {K_n}\mathop \sum \limits_{m\; = \;1}^f \left[ {{P_m} \times Ln{P_m}} \right] \def\eqcellsep{&}\begin{array}{*{20}{l}} ,&{\;{K_n} = {{\left( {Ln{\rm{\;f}}} \right)}^{ - 1}}\;} \end{array} \end{equation}$$where k is a positive constant to supply 0 ≤ En${E_n}$ ≤ 1. Pm${P_m}$s are formed based on the normalization of decision matrix elements and to use the entropy method, the decision matrix should be formed:16D=x11…x1v⋮⋱⋮xz1⋯xzv$$\begin{equation}D\; = \left( { \def\eqcellsep{&}\begin{array}{@{}*{3}{l}@{}} {{x_{11}}}&\quad \ldots &\quad{{x_{1v}}}\\[9pt] \vdots &\quad \ddots &\quad \vdots \\[9pt] {{x_{z1}}}&\quad \cdots &{{x_{zv}}} \end{array} } \right)\end{equation}$$In Equation (16) xzv${x_{zv}}$ is the value of the vth index due to the application of the zth program. The p‐norm equation scales this matrix. The general definition for the p‐norm of a vector m that has n elements:17xp=∑m=1zxmnp1/p$$\begin{equation} {\left\| x \right\|_p} = {\left[ {\sum_{m = 1}^z {{x_{mn}}^p} } \right]^{1/p}}\end{equation}$$where p is any positive real value in the range from infinite positive to infinite negative. In entropy, p=1$p\; = \;1$ is used, and the decision matrix normalizer is defined as follows:18rmn=xmn∑m=1zxmn$$\begin{equation}{r_{mn}} = \frac{{{x_{mn}}}}{{\mathop \sum \nolimits_{m = 1}^z {x_{mn}}}}\end{equation}$$After calculating the value function for each column, the degree of deviation (dn${d_n}$) is determined for all columns:19dn=1−En$$\begin{equation} {d_n} = 1 - {E_n}\end{equation}$$Finally, the weight of the indicators (Wn${W_n}$) is determined by the following equation [16]:20Wn=dn∑n=1vdn$$\begin{equation}{W_n} = \frac{{{d_n}}}{{\mathop \sum \nolimits_{n = 1}^v {d_n}}}\end{equation}$$Suppose the decision‐maker wants to apply the importance of each of the indicators in entropy. In that case, it can use the corrected (λn${\lambda _n}$) to make the decision maker's judgment about the nth index. It should be noted that the sums λn${\lambda _n}$ are equal to one.21IWn=λn×Wn∑n=1vλn×Wn$$\begin{equation} I{W_n} = \frac{{{\lambda _n} \times {W_n}}}{{\mathop \sum \nolimits_{n = 1}^v {\lambda _n} \times {W_n}}}\end{equation}$$The weights obtainedIWn$\;I{W_n}\;$will be related to each of the mentioned characteristics.Prioritization by TOPSISThe input information of the TOPSIS method includes the weights of the indicators’ matrix (IWn$I{W_n}$) and its output will be obtained as a ranking of DRPs in each cluster. Generally, TOPSIS determines the best alternative based on its distance from the ideal solution and its distance from the worst alternative. For this reason, it shows the highest sensitivity to weight vectors and has the most accurate answer to linear normalization methods [16]. The above method can be applied as follows.First, the decision matrix must be scaled in TOPSIS, which uses the p‐norm normalizer defined in Equation (17) to normalize. The decision matrix is normalized to p=2$p = 2$:22rmn=Xmn∑m=1vXmn2$$\begin{equation}{r_{mn}} = \frac{{{X_{mn}}}}{{\sqrt {\mathop \sum \nolimits_{m = 1}^v X_{mn}^2} }}\end{equation}$$The calculation of the weighted dimensionless matrix (V) is obtained using the calculated weights of the indices:23Vmn=Wn×rmn$$\begin{equation}{V_{mn}} = {W_n}\; \times {r_{mn}}\end{equation}$$Calculate the ideal (Vn+${V_n}^ + $), and counter‐ideal (Vn−${V_n}^ - $) answers [16]:24Vn+=maxVmnn∈V+,minVmnn∈V−m=1,…,zVn−=minVmnn∈V+,maxVmnn∈V−m=1,…,z$$\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{2}{l}@{}} { \def\eqcellsep{&}\begin{array}{*{20}{l}} {{V_n}^ + = \left( {{\rm{max}}{V_{mn}}\left| {n \in {V^ + }} \right|,{\rm{min}}{V_{mn}}\left| {n \in {V^ - }} \right|} \right)\;}&{m\; = \;1, \ldots ,z} \end{array} }\\[9pt] { \def\eqcellsep{&}\begin{array}{*{20}{l}} {{V_n}^ - = \left( {{\rm{min}}{V_{mn}}\left| {n \in {V^ + }} \right|,{\rm{\;max}}{V_{mn}}\left| {n \in {V^ - }} \right|} \right)\;}&{m\; = \;1, \ldots ,z} \end{array} } \end{array} \end{equation}$$Here, the type of criteria should be specified. The criteria are either positive or negative. Positive criteria are criteria whose increase improves the system, and negative criteria are the opposite. To choose these criteria, the following should be considered:For criteria that have a positive load, the positive ideal is the largest value of that criterion.For criteria that have a positive charge, the negative ideal is the smallest value of that criterion.For criteria that have a negative load, the positive ideal is the smallest value of that criterion.For criteria that have a negative load, the negative ideal is the largest value of that criterion.Calculate distances from the ideal and counter‐ideal answers using the Euclidean distance. So, distance from the ideal answer [16]:25Sm+=∑n=1v(vmn−vn+)2$$\begin{equation}S_m^ + = \sqrt {\mathop \sum \limits_{n = 1}^v {{({v_{mn}} - v_n^ + )}^2}} \end{equation}$$distance from the counter‐ideal answer [16]:26Sm−=∑n=1v(vmn−vn−)2$$\begin{equation}S_m^ - = \sqrt {\mathop \sum \limits_{n = 1}^v {{({v_{mn}} - v_n^ - )}^2}} \end{equation}$$ranking options by calculating the value of Cm${C_m}$ [16]:27Cm=Sm−Sm++Sm−$$\begin{equation}{C_m} = \frac{{S_m^ - }}{{S_m^ + + S_m^ - }}\end{equation}$$Cm${C_m}$ values for each option, which must be between zero and one, is considered a score for each DRPs. The option with more C will have a higher rank, and therefore, it has more benefits.DL implementing method for DRPsANN methodTypically, neural networks are employed when there is no mathematical model or when there is a problematic relationship between input and output data. In addition, neural networks can be used in very complex systems. Each ANN layer can be described by (28) [31]:28Yo=ψ∑l=0nSwloXl+θo$$\begin{equation}{Y_o} = \;\psi \left( {\mathop \sum \limits_{l\; = \;0}^n S{w_{lo}}{X_l} + {\theta _o}} \right)\end{equation}$$where Swlo$S{w_{lo}}$ is the Synapse weight, θo${\theta _o}\;$is a constant, Xl${X_l}$ is the input vector, Yo${Y_o}$ is the output vector, and ψ is the active function. The term activation function refers to the ψ function, which binds the input value to the network output value. The most common activation functions are sigmoid, step, linear, sign, and hyperbolic tangent functions [32]. Each layer of artificial neural networks has a linear or non‐linear stimulus function model. The term bias θo${\theta _o}$ causes the displacement of the function curve in the input space and in other words, causes the neuron to be biased in a subspace of the input space, which justifies the selection of the bias for the term θo${\theta _o}$ [34]. More explanations are outlined in [33] and [34]. Figure 3 illustrates an ANN implementation with N inputs. As soon as the input value is given to the neuron, it calculates its state by applying a temporal activation function to the input value. The sum of the neuron record function's values is multiplied by Equation (28) [32].3FIGUREThe ANN prototypeDL methodTo better understand the difference between ANN and DL algorithms, it can be said that: Machine learning is a subfield of artificial intelligence. Deep learning is a subfield of machine learning, and ANNs form the backbone of deep learning algorithms. In fact, the distinguishing feature of a single ANN from the deep learning algorithm is the number of node layers or the depth of the neural networks, which must be more than three in the deep learning algorithm [35]. In this article, the CNN‐LSTM algorithm is used. The CNN‐LSTM Algorithm consists of the combination of two algorithms named CNN and LSTM. The CNN algorithm is a type of DL algorithm, and the LSTM algorithm is a Recurrent Neural Network (RNN) algorithm [36].In general, the CNN‐LSTM method uses CNN as an encoder to learn features from the subsequence of input data fed into an LSTM as time steps. The LSTM will function as a decoder, identifying and modelling both short‐term and long‐term temporal relationships inherent in the data stream. More details are addressed in refs. [30] and [37]. Figure 4 shows the basic architecture of this algorithm.4FIGUREThe basic architecture of the CNN‐LSTM networkThe training algorithm for defining the weights that make up the system must have an error close to zero, that is, the purpose of the DL algorithm is to determine a set of weights w that minimizes the sum of the Errors (E) as follows [32]:29E=∑lYl−fSwl,Xl2$$\begin{equation}E\; = \mathop \sum \limits_l {\left[ {{Y_l} - f\left( {S{w_l},{X_l}} \right)} \right]^2}\end{equation}$$where Yl${Y_l}$ is the final and actual value and f(Swl,Xl)$f( {S{w_l},{X_l}} )$ is the value of the final answer that the algorithm obtains or predicts after training [32].The design of CNN‐LSTM can be modified according to the type and parameter adjustment of the network's layers [38]. The CNN‐LSTM consists of visual features (in the CNN layer) and sequence learning (in the LSTM layer). Each layer can adjust the number of filters, the kernel size, and the number of strides. Changing the parameters of layers can affect learning speed and performance depending on the characteristics of the learning data [39].To evaluate the accuracy of the models developed with DLs, the criteria of Mean Squared Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Regression (R) are used. The following equations show how to calculate them [38, 39]:30RMSE=∑l=1NYl−Ŷl2N$$\begin{equation} RMSE = \sqrt {\frac{{\mathop \sum \nolimits_{l = 1}^N {{\left( {{Y_l} - {{\hat Y}_l}} \right)}^2}}}{N}} \end{equation}$$31MSE=∑l=1N(Yl−Ŷl)2N$$\begin{equation} MSE = \frac{{\mathop \sum \nolimits_{l = 1}^N {{( {{Y_l} - {{\hat Y}_l}})}^2}}}{N}\end{equation}$$32MAPE=∑l=1NYl−ŶlYlN$$\begin{equation} MAPE = \frac{{\mathop \sum \nolimits_{l = 1}^N \left| {\frac{{{Y_l} - {{\hat Y}_l}}}{{{Y_l}}}} \right|}}{N}\end{equation}$$33R=output=a′.target+b$$\begin{equation} R = output = a^{\prime}.target + b\end{equation}$$For this purpose, Equation (34) has been used to normalize the training and test patterns [40].34Xnorm=0.5Xl−X¯Xmax−Xmin+0.5$$\begin{equation}{X_{norm}} = \;0.5\left( {\frac{{{X_l} - \bar X}}{{{X_{max}} - {X_{min}}}}} \right) + 0.5\end{equation}$$where Xnorm${X_{norm}}\;$is the normalized value of the input Xl${X_l}$, X¯$\bar X\;$is the average value of data, Xmax${X_{max}}\;$and Xmin${X_{min}}$ is the maximum and minimum value of input data. For a better and easier understanding of data and more practical use, data are usually normalized for training artificial neural network algorithms. If the dispersion or standard deviation of the normalized data is bigger, the learning and generalization will be better [41].NUMERICAL STUDIESThe data used in this section is from 10,000 consumption load curves [42] and CNN‐LSTM is used as a machine learning algorithm. The power model of DRPs handles input and output data. The delay used in the TSP section is 200 h with an hourly range. An electricity tariff has been used for spring, summer, autumn, and winter tariffs. The affected consumers are divided into 4 clusters named residential, commercial, industrial, and agricultural clusters by the improved WFA K‐means algorithm. For the DRPs power model, Table 2 illustrates the 24‐h elasticity matrix for all clusters [16]. Figure 5 shows the initial consumption pattern of all consumers in this study. This naming of clusters is based on how each cluster is consumed with reality instead of numerical naming.2TABLESelf‐elasticities and cross‐elasticitiesPeakOff‐peakValleyPeak−0.10.0160.012Off‐peak0.016−0.10.01Valley0.0120.01−0.15FIGUREThe initial consumption load pattern of each clusterRunning DRPs on the networkAll 12 DRPs in each cluster have been operated with TSP operations due to the delay of 200 h with 7 different inputs in each program execution with matrix input dimensions of 1400×8560. Thus, each TSP implementation of the algorithm training will be conducted in a DRP with 11,984,000 input data and 200×8560 output data. According to the trained algorithm, different inputs are considered input data in spring, summer, autumn, and winter, and the output results are compared with the same inputs. In the CNN layer, windows with dimensions of 90 × 120 and (2 × 1) kernel function are used, and in the LSTM layer, 128 neurons with tanh function and with a batch size of 64 are used. All these points have been obtained by trial and error.The purpose of the results is to respond to each program as a power model and it is compared with the algorithm's output. Based on the weighting of the indicators, DRPs are prioritized based on the indicators for each chapter. Table 3 shows the performance of each DRP in each cluster. The regression of all programs is very close to 1, and most models’ error rate, especially in MAPE, are very low. In the TSP stage, it can be said that the algorithm has been well trained with all the programs in each cluster. The high MSE error rate is due to customers’ high consumption in all clusters.3TABLECalculation of errors and regression in TSP stepClusterProgramRRMSEMSEMAPEResidentialTOU0.9929.98899.000.61CPP0.9963.213995.491.09RTP0.9981.936713.491.31TOU+CPP0.9949.592460.130.93DLC0.9934.791210.710.59EDRP0.9954.732995.850.94CAP0.9927.86776.480.46I/C0.9945.462067.240.78TOU+DLC0.9942.141776.050.81TOU+EDRP0.9949.422443.170.92TOU+CAP0.9939.341548.380.76TOU+I/C0.9945.992115.390.86CommercialTOU0.9841.091688.4712.26CPP0.9937.221386.0111.75RTP0.9839.181535.2312.21TOU+CPP0.9838.711498.9012.59DLC0.9838.911514.6612.46EDRP0.9844.511981.2814.58CAP0.9840.011601.2911.93I/C0.9846.792189.8914.99TOU+DLC0.9841.911756.7413.51TOU+EDRP0.9841.831750.3113.51TOU+CAP0.9844.691997.4213.75TOU+I/C0.9846.092125.1914.36IndustrialTOU0.9941.461719.381.78CPP0.9940.791664.031.76RTP0.9940.001600.821.72TOU+CPP0.9942.901841.141.82DLC0.9942.321791.611.82EDRP0.9942.451802.331.84CAP0.9942.091771.621.80I/C0.9941.601730.801.80TOU+DLC0.9944.451976.421.88TOU+EDRP0.9941.581728.941.77TOU+CAP0.9941.421715.871.77TOU+I/C0.9942.161814.991.83AgricultureTOU0.9912.98168.485.46CPP0.9912.77163.184.76RTP0.9913.86192.265.57TOU+CPP0.9913.55183.775.94DLC0.9912.54157.384.78EDRP0.9914.28203.945.51CAP0.9913.21174.735.03I/C0.9913.57184.225.16TOU+DLC0.9913.71188.236.01TOU+EDRP0.9913.28176.595.67TOU+CAP0.9912.72162.005.39TOU+I/C0.9914.57212.417.53The behaviour of DRPs in winter load will be shown, and the rest of the loads will be have the same way in TSP if they are stored correctly. TSP has been simulated in the other parts of the year, but because of their large number, we have not displayed their graph. Figure 6 shows the behaviour of DRPs of the power model in the residential cluster. It can be seen that the residential cluster has two peaks between the hours of 10 to 14 and 17 to 22. The consumption of all DRPs in the power model has increased during the valley and off‐peak hours. The RTP program had the highest consumption during the valley hours, while the TOU + DLC and CPP programs had the highest consumption during the off‐peak hours. The TOU + I / C and TOU + CPP programs had the most considerable reductions in energy consumption during peak hours.6FIGUREThe behaviour of the power model of DRPs in the residential cluster during one dayIn Figure 7, DL model DRPs are shown in the residential cluster. There are many ups and downs in the DL model throughout the day. This is because residential consumers usually do not have the same consumption behaviour throughout the year. That's why the memory in this cluster is complicated to predict the time series, and with the most remarkable accuracy, it still has gaps in the accurate model. As a matter of fact, the priority of the DL model of DRPs has been the same as that of the power model in terms of the first and second priorities. It can be said that the DL model of DRPs is well anticipated.7FIGUREThe behaviour of the DL model of DRPs in the residential cluster during one dayThe behaviour of DRPs of the commercial cluster power model is shown in Figure 8. The number of peaks in the commercial cluster is the same as in the residential cluster. During the valley and peak hours, the behaviour of DRPs in commercial clusters is similar to that of residential clusters. But in the peak hours of the CPP program and with TOU + CPP program, they had the highest consumption. Figure 9 shows the behaviour of commercial cluster DRPs in the DL model. As can be seen, there is not much difference between the behaviour of power model DRPs and DL.8FIGUREThe behaviour of the power model of DRPs in the commercial cluster during one day9FIGUREThe behaviour of the DL model of DRPs in the commercial cluster during one dayFigure 10 shows the implementation of the power model, and Figure 11 shows the implementation of the DL model of DRPs in the industrial cluster. Both models exhibit very similar behaviour. Any result that is said for the power model load is the same as the results of the DL model. Combined programs and TOU had the highest peak consumption during peak hours, while combined programs and incentive‐based programs had the highest peak reduction during peak hours.10FIGUREThe behaviour of the power model of DRPs in the industrial cluster during one day11FIGUREThe behaviour of the DL model of DRPs in the industrial cluster during one dayFigures 12 and 13 show the implementation of the power and DL models of DRPs in the agricultural cluster on a 24‐h basis, respectively. The agricultural cluster has a peak and two valleys, which has a valley in summer and spring loads. The behaviour of the power and DL models of DRPs is always similar with a small amount of difference. The combined programs with TOU and RTP have increased energy consumption during valley hours, and have further reduced it during peak hours. Implementing DRPs in the agricultural cluster can increase energy consumption if they are incentive‐based or have low tariffs during valley hours.12FIGUREThe behaviour of the power model of DRPs in the agriculture cluster during one day13FIGUREThe behaviour of the DL model of DRPs in the agriculture cluster during one dayIndicators weighingTable 4 shows the specified weights of the indicators in the power model, and Table 5 shows the specified weights of the indicators in the CNN_LSTM model. These weights are obtained by entropy, and the weights specified in the power model and CNN_LSTM differ slightly. In the commercial, agricultural and residential clusters, energy reduction in power and CNN_LSTM models is the first indicator at all times. In summer, customer bill and peak reduction are the second indicators in other times. In the commercial cluster, peak reduction indices in spring and summer loads and energy reduction indices in autumn and winter loads are the first indicators in the power model. But in the CNN_LSTM model, the commercial cluster is the first indicator of energy reduction at all times. In general, the implementation of DRPs has had the most significant impact on reducing the total consumption of consumers.4TABLEWeight of attributes in power modelCluster typeType of loadCustomer billPeak reductionEnergy reductionLoad factorPeak to valleyResidentialSpring0.1100.2230.6430.00050.021Summer0.1430.0980.7430.00100.011Autumn0.1210.2230.6400.00050.013Winter0.1210.2230.6420.00030.012CommercialSpring0.2080.4490.3210.00500.014Summer0.1820.4020.3880.00380.021Autumn0.3030.1920.4720.00730.023Winter0.3230.1570.4910.00630.019IndustrialSpring0.1160.0140.8120.00100.054Summer0.1190.0530.7900.00080.035Autumn0.1160.0380.7690.00100.074Winter0.1140.0310.8070.00130.045AgricultureSpring0.0180.4810.4000.00300.066Summer0.1590.1240.6340.00220.061Autumn0.0450.1800.7610.00030.006Winter0.0420.0930.8330.00130.0155TABLEWeight of attributes in the CNN_LSTM modelCluster typeType of loadCustomer billPeak reductionEnergy reductionLoad factorPeak to valleyResidentialSpring0.1100.2150.6440.00100.028Summer0.1420.0920.7490.00140.011Autumn0.1190.3170.5320.00190.028Winter0.1210.3890.4510.00140.035CommercialSpring0.2650.2720.4370.00540.017Summer0.2140.3650.3910.00380.024Autumn0.2570.2380.4750.00660.020Winter0.3370.1690.4630.00650.021IndustrialSpring0.0920.0140.8420.00070.048Summer0.1440.0890.7120.00130.052Autumn0.0990.0540.7710.00100.074Winter0.1170.0410.7830.00160.056AgricultureSpring0.1100.2150.6440.00100.028Summer0.1420.0920.7490.00140.011Autumn0.1190.3170.5320.00190.028Winter0.1210.3890.4510.00140.035Programs prioritizingThe first priority and sometimes the second priority are the best choices, so if the first priority is equal in both models at all times, then the CNN‐LSTM algorithm has been trained correctly. It also shows that the DL model is able to simulate the power model of DRPs well. The prioritization of programs in any cluster is shown in Tables 6 and 7. The spring DL and load power models have different first priorities in the commercial cluster. There is a primary reason for the incorrect answer because there is insufficient information to place them as a memory that can correctly predict the TSP. This wrong answer is primarily due to the existence of the most MAPE errors in the TSP of the commercial cluster.6TABLEPriority of programs in all clusters in the power modelCluster importanceType of loadTOUCPPRTPRTP and CPPDLCEDRPCAPI/CTOU and DLCTOU and EDRPTOU and CAPTOU and I/CResidentialSpring111123821057496Summer111123821057496Autumn111123821057496Winter111123821057496CommercialSpring212111653987410Summer111122431076598Autumn111122451037896Winter111122561037894AgricultureSpring121116324597108Summer121112109874635Autumn816742531012911Winter716842531191210IndustrialSpring111126425397108Summer111126425397108Autumn121275364108119Winter1212753641081197TABLEPriority of programs in all clusters in the CNN‐LSTM modelCluster importanceType of loadTOUCPPRTPRTP and CPPDLCEDRPCAPI/CTOU and DLCTOU and EDRPTOU and CAPTOU and I/CResidentialSpring111123821067594Summer111124821057396Autumn111122841059673Winter121113951076284CommercialSpring111122531046798Summer111122431076598Autumn111123641029758Winter111122681034795AgricultureSpring121111032459786Summer121116109873524Autumn916843112751210Winter816742531112910IndustrialSpring121117425398106Summer121117425398106Autumn121275364108119Winter121275364108119The differences in the values determined in the indicators in power and DL models in the residential cluster are shown in Table 8. The CPP program has been selected for power and DL models at all times, and also the CPP program has increased the customer bill at all times. There are many differences in the peak reduction indicator in power and DL models, and these differences are evident in the load factor indicator. The DL model usually measures further peak reduction and load factor increase. Table 9 shows the values of the indicators when implementing commercial cluster DRPs. The RTP program power model and the CPP program DL model have been selected in the spring load. Because in the power model, the peak reduction has the highest weight among the indicators. But in the DL model, energy reduction has the highest weight among the indicators. There is not much difference in the other values of DL and power indicators.8TABLEThe results obtained from the necessary indicators of the first priority of DRPs in residential clusterType of loadType of modelLoadProgramCustomer bill (cent×104)Peak reduction (%)Energy reduction (%)Load factor (%)Peak to valley (MW)SpringInitial load0.4800076.683.51PowerSec .loadCPP0.76610.134.5581.442.57DLSec .loadCPP0.76511.034.5882.022.55SummerInitial load0.2790069.373.93PowerSec .loadCPP0.45412.777.8273.303.16DLSec .loadCPP0.45312.367.7472.923.18AutumnInitial load0.6560078.214.57PowerSec .loadCPP1.0839.023.3383.113.46DLSec .loadCPP1.07910.693.4284.313.12WinterInitial load0.8150081.034.89PowerSec .loadCPP1.3497.522.6885.283.78DLSec .loadCPP1.3477.962.7886.033.729TABLEThe results obtained from the necessary indicators of the first priority of DRPs in commercial clusterType of loadType of modelLoadProgramCustomer bill (cent×104)Peak reduction (%)Energy reduction (%)Load factor (%)Peak to valley (MW)SpringInitial load0.2110067.860.59PowerSec .loadRTP0.23310.101.3074.490.44DLSec .loadCPP0.2878.441.8373.420.48SummerInitial load0.2180067.990.62PowerSec .loadCPP0.4555.979.2165.650.52DLSec .loadCPP0.4516.069.2665.890.50AutumnInitial load0.2040067.970.58PowerSec .loadCPP0.4214.6110.8363.530.53DLSec .loadCPP0.4203.6310.5963.070.52WinterInitial load0.2150067.070.62PowerSec .loadCPP0.4484.8410.3063.220.57DLSec .loadCPP0.4474.7810.5463.010.58The values of industrial cluster indicators are given in Table 10. There is not much difference in the set values of the indicators in the DL models and the power model. The peak reduction amount is found more in the DL model in the summer load. Table 11 shows the values of the agricultural cluster's first priority indicators of TOPSIS DRPs. As can be seen, all times in DL models and CPP program power model has been selected, and in addition, there is not much difference in the values of the indicators.10TABLEThe results obtained from the necessary indicators of the first priority of DRPs in industrial clusterType of loadType of modelLoadProgramCustomer bill (cent×104)Peak reduction (%)Energy reduction (%)Load factor (%)Peak to valley (MW)SpringInitial load0.2600077.150.89PowerSec .loadCPP0.5298.565.8679.420.67DLSec .loadCPP0.5318.595.8280.010.68SummerInitial load0.3580075.321.27PowerSec .loadCPP0.7499.894.2680.020.94DLSec .loadCPP0.74710.314.3280.120.92AutumnInitial load0.2800076.230.98PowerSec .loadCPP0.58411.655.4381.600.67DLSec .loadCPP0.58511.515.4081.530.68WinterInitial load0.2530079.440.68PowerSec .loadTOU0.51212.626.0385.440.39DLSec .loadTOU0.51112.736.0985.470.4011TABLEThe results obtained from the necessary indicators of the first priority of DRPs in agriculture clusterType of loadType of modelLoadProgramCustomer bill (cent×104)Peak reduction (%)Energy reduction (%)Load factor (%)Peak to valley (MW)SpringInitial load0.0160073.880.19PowerSec .loadCPP0.0217.8716.8666.670.16DLSec .loadCPP0.0227.6517.0765.560.17SummerInitial load0.0200061.840.28PowerSec .loadRTP0.01328.2014.4973.650.20DLSec .loadRTP0.01227.8315.0172.970.21AutumnInitial load0.0120062.140.17PowerSec .loadCPP0.0217.571.6466.600.16DLSec .loadCPP0.0207.371.6865.970.15WinterInitial load0.0050061.440.07PowerSec .loadCPP0.01012.561.9768.030.06DLSec .loadCPP0.00912.531.8968.120.05CONCLUSIONDue to the rapid growth of data collected from smart meters in smart grids and the lack of knowledge about the type of loads of consumers, it will be necessary to develop a model to implement DRPs operationally. This paper discusses three phases of the implementation of DRPs: clustering, the application of machine learning‐based DRPs, and the prioritization of programs within each cluster. It should be noted prioritization of DRPs will outline the most effective programs for economic and technical criteria. This method will be flexible in terms of study type and desirable indicators. It is also possible to consider infrastructure and the implementation of DRPs costs. In prioritization, it should be noted that maximizing an index in a cluster may not result in maximizing the indicator in the entire network. The degree of profit and, consequently, the rank of each program (incentive‐based) strongly depend on the amount of incentives and penalties in each period. Therefore, this opportunity exists in incentive‐based programs that can be maximized by calculating optimal encouragement. In some grids, due to the increasing distributed generation and renewable energy resources, it is sometimes necessary to encourage consumption increment rather than trying to reduce it to adjust the valleys presented in the load curve.In this paper, the WFA K‐means clustering method was used for consumption management studies by creating the most differentiation and similarity in the curves of each category and the best CDI value. Furthermore, CNN‐LSTM algorithms are used as an implementation of DRPs in order to make them operational in reality. With the implementation of DRPs with the model of machine learning algorithms such as CNN‐LSTM, there is no need for heavy calculations of elasticity matrix. In the electricity industry, DRPs can be implemented accurately in more than one day for all load patterns. Implementing DRPs using the DL algorithm dynamically with a low error value compared to the power model of DRPs led to the same prioritization results in the meantime. The DL model for DRPs shows that the cluster of residential dwellings with the highest possible consumption has more errors compared to the cluster of industrial dwellings with the lowest possible consumption in the DL model.In order to achieve more accurate models for DRPs, various uncertainty modelling methods can be considered in future research. Different uncertainty associated with smart grids includes consumers’ behaviour and resources allocation regarding their generation output during a day. Also, the role of emerging components such as electric vehicles and power electronic devices in resources dispatch will need further study.NOMENCLATURE    Indicesi,j$i,j$Index of time and periodtIndex of componentuIndex of consumercIndex of iteration numberl,o$l,o$Index of the number of vectorsnIndex of the n‐th criterionmIndex of the m‐th alternativezIndex of the quantity of the alternativesvIndex of the quantity of the attributesParametersd0Initial load demand for consumerd0(i)${d_0}( i )$Initial load demand in the i‐th hour for consumerEThe elasticity of consumer load demandE(i,i)$E( {i,i} )$Self‐elasticityE(i,j)$E( {i,{\rm{j}}} )$Cross‐elasticityp0Initial electricity demand pricep0(i)${p_0}( i )$Initial electricity demand price in the i‐th hourpThe spot price of electricityp(i)$p( i )$The electricity price in the i‐th hourA(i)$A( i )$The incentive of DRPs in the i‐th hourpen(i)$pen( i )$penalty payout in the i‐th hourSw$Sw$The Synapse weightθThe constantXThe input vectorY,Ŷ$Y,\hat Y$The output vectorXnorm${X_{norm}}$The normalized value of the inputsXmax${X_{max}}$, Xmin${X_{min}}$The maximum and minimum value of input dataX¯$\bar X$The average value of dataσStandard deviationψThe active functionΛDecision maker's importance factorVariablesbError terms in regressionB(d(i))$B( {d( i )} )$Consumer's income considering load amount equal to d(t) in the i‐th hourdNew consumer loadd(i)$d( i )$New consumer load in the i‐th hourΔd(i)Equal to the change in initial and final consumptionIC(i)$IC( i )$Incentive‐based DRPs with penalties contract level in the i‐th hourA′(Δd(i))${\rm{A^{\prime}}}( {\Delta {\rm{d}}( {\rm{i}} )} )$Total incentive payment to the consumerp(i)$p( i )$The cost of electricity consumed by the consumerd′(i)$d^{\prime}( i )$the amount of load that the customer should be penalizedpen′(Δd(i))$pen^{\prime}( {{{\Delta}}d( i )} )$Total penalty paymentSn$Sn$The customer profitμ(t,u)(r+1)$\mu _{( {t,u} )}^{( {r + 1} )}$t‐th component of the centre of the cluster with u consumers, in the r + 1 th iterationX(t,u)${X_{( {t,u} )}}$t‐th component of the u‐th consumerw(t,u)(r)$w_{( {t,u} )}^{( r )}$Weight of the t‐th component of the u‐th consumer in the r‐th iterationσ2Variance of the vector of each clusterEn${E_n}$The entropy functionxzv${x_{zv}}$The decision matrix elementsdn${d_n}$The entropy deviation functionWThe weights of attributesIW$IW$The weights obtained of attributesVThe ideal‐solution/anti‐ideal solutionC, Cm${C_m}$The priority coefficient in the TOPSIS methodrThe elements of the normalized D matrixDThe decision matrixSDistance between each alternative and the ideal solution/anti‐ideal solutionKn${K_n}$The positive coefficient in the entropy methodEn$En$The sum of the errorsαCoefficient of consumer participationa′$a^{\prime}$The unknown regression parameterwThe weights of errorsNThe number of simulated dataRThe regression (dependent variable)AUTHOR CONTRIBUTIONSM.A.: Conceptualization; Data curation; Formal analysis; Funding acquisition; Investigation; Methodology; Project administration; Resources; Software; Supervision; Validation; Visualization; Writing‐original draft; Writing‐review & editing. M.P.M.: Conceptualization; Data curation; Formal analysis; Funding acquisition; Investigation; Methodology; Project administration; Resources; Software; Supervision; Validation; Visualization; Writing‐original draft; Writing‐review & editing. F.M.: Conceptualization; Data curation; Formal analysis; Funding acquisition; Investigation; Methodology; Project administration; Resources; Software; Supervision; Validation; Visualization; Writing‐original draft; Writing‐review & editingCONFLICT OF INTERESTThe authors declare no conflict of interest.FUNDING INFORMATIONThere is not funding to report for this submission.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available from the corresponding author upon reasonable request.REFERENCESYu, B., Sun, F., Chen, C., Fu, G., Hu, L.: Power demand response in the context of smart home application. 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Optimal demand response programs selection using CNN‐LSTM algorithm with big data analysis of load curves

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Abstract

INTRODUCTIONDemand Response Programs (DRPs) are convenient for managing the load and energy and adapting consumption and generation patterns [1, 2]. Usually, few consumers are aware of the actual price of electricity, so there is no incentive for consumers to participate in the market and adapt their consumption towards the generation side, network conditions, and electricity prices [3, 4]. For consumers to be able to participate in all DRPs, smart meters must be provided to consumers. Advanced Metering Infrastructure (AMI) and Automatic Meter Reading (AMR) are some of these technologies. Meanwhile, AMI systems allow consumers to read the price of electricity [5, 6].Today, smart meters are abundant in distribution networks. Consumers’ load patterns can be found by collecting customer consumption data measured by these smart meters [7, 8]. Considering the number of devices in use, a significant amount of data is collected. Among these big data, identifying similar load patterns from network consumers requires data mining analysis by clustering and classification algorithms [9]. Generally, clustering algorithms can be divided into two types based on the need for an initial clustering centre and those that do not require one [10]. In order to classify or cluster load patterns, various algorithms have been developed, which can be categorized into five categories: partitioning methods, hierarchical clustering, fuzzy clustering, density‐based clustering, and model‐based clustering [11, 12]. DRPs will be more effective if consumers’ load patterns are accurately identified. By clustering or classifying these load patterns, electricity tariffs can be set separately for each cluster or group [13, 14].BackgroundMathematical models that show different behaviours of consumers can be used to implement DRPs. Linear model and non‐linear models (exponential, power, logarithmic and hyperbolic) are unrealistic models for implementing DRPs. Non‐linear and linear models are used for various time‐based and incentive‐based programs. These models can also model combined time‐based and incentive‐based programs [15, 16]. In modelling DRPs, the existing challenges are selecting and calculating the elasticity matrix's elements, the amount of reasonable tariffs, and the amount of consumers’ CoP in implementing the programs [15]. More details are explained in Section 3.2. Among DRPs models, the power model simulates consumers’ behaviour better than other models [16].In [15], various simulations have been performed to model consumer behaviour in the presence of non‐linear and linear DP sources. In these references, the authors compared linear and non‐linear models in DRPs and concluded that the power non‐linear model could show the natural consumer behaviour. In [16], a power non‐linear model is presented in terms of clustering different consumption patterns of customers. In this paper, consumers are clustered in different groups and all DRPS are implemented. Finally, the best program for each cluster is considered based on the best profit for the utility company. However, customers’ consumption has not been considered for all seasons of the year, and the consumers have been considered quite logically. Also, DRPs have been implemented only on a specific day. In [17], based on the concept of customer profitability and demand flexibility, a dynamic economic model of DRP has been proposed as a combination of Emergency Demand Response Program (EDRP) and Time of Use (TOU) programs and considering different indices of the developed model for enhancing customer satisfaction and load profile features. However, programs prioritization has been used, but not all DRPs and load pattern segmentation have been used.In [18], a study is evaluated on the extent of consumer willingness to participate in various incentive‐based programs and the need for policy development based on consumer feedback in the Kuwaiti electricity market. In [19], an incentive‐based DRP model for DG resources is proposed, and in [20], dynamic DRPs are designed by optimal transactive pricing in a smart grid. But, these are not enough for the implementation of DRPs optimally. In [21], the use and comparison of two ANN‐based load prediction techniques, the Feed‐Forward Neural Network (FFNN) and the Echo State Network (ESN), in a commercial building data set, concerning a possible DR test has been investigated. In [1], has been presented a DR classification and modelling in large‐scale models along with an overview of the advantages, challenges, and mathematical formulas for different types of DR. Still, in general, the linear model is used to implement DRPs. In [22], only linear programming of DRPs by using various scenarios and sensitivity analysis of generation optimization of Distributed Energy Resources (DERs) in Smart Grid is presented.In [23], a linear model for implementing DRPs to participate in the electricity market and applying policies in the electricity market is presented. However, they have not repeatedly implemented DRPs with clustering load curves. In [24], a mathematical model for optimizing DRPs for decreasing the generation costs of up‐grid networks and distributed generation resources, including wind turbines, photovoltaics, battery storages, and microturbines in 14‐bus and 11‐bus microgrids, is presented. In [25], an optimal model for the daily operation of a Multi‐Energy Virtual Power Plant (MEVPP), including electric, thermal, and natural gas sectors, is presented. Meanwhile, smart grid technologies such as Price‐Based Demand Response (PBDR) and Incentive‐based Demand Response (IBDR) are used for electric loads. The scheduling model presented in it is based on the simulation of this multi‐objective virtual power plant to maximize MEVPP profit and minimize carbon dioxide emissions. In [26], a multi‐objective optimization model is proposed for optimal planning of hot rolling load considering the actual conditions of production operation. This project develops an integrated scheduling model of hot rolling shop scheduling and electricity DR, and a multi‐objective production scheduling algorithm is designed. In [27], this paper uses an intelligent distribution system that includes electricity resources in addition to a DR scheme. Load reduction in smart homes is also considered based on load prioritization and customer participation in the DR plan to achieve the goals of the proposed plan.In [28], is proposed a method for detecting and predicting high energy demand events that are managed at the national level in DRPs. This method includes two stages of load forecasting with short‐term memory neural network and a dynamic filter of the highest potential peaks of electricity demand using an exponential moving average. The general application of this method to manage the DRP has been very well done by reducing energy consumption and indirect carbon emissions. In [29], k‐means CNN_LSTM (kCNN‐LSTM) is presented, a deep learning framework that operates on energy consumption data recorded at predefined intervals to provide accurate building energy consumption predictions. But not all DRPs have been used yet.Despite all the studies conducted, there is no model that illustrates the correct behaviour of consumers across different groups when implementing DRPs. In all studies, mathematical models have been used to illustrate the behaviour of consumers during the implementation of DRPs. Linear and non‐linear models of DRPs include only a few examples of consumers’ behaviour and do not show the rest of the other general behaviours and reactions in a year. This means that consumers must be assumed to be perfectly rational. Table 1 presents a comparison between the published works and this paper.1TABLEComparison of this paper with published studiesReference numberYearSelected DRPsDRPs modelThe method of optimal selection programsSegmentation of consumers’ load patternAlgorithms used for Implementing DRPsApplication of article[1]2022RTPLinear‐‐‐The impacts of smart home participation in power DR[15]2019All DRPsLinear and all non‐linearMCDM‐‐The behaviour of DRPs models in the transmission system[16]2019All DRPsPowerMCDM✓‐Selecting the most effective DRPs for utility/customer[17]2020EDRP, TOULinear‐‐‐Considering different indices of the developed model for enhancing customer satisfaction and load profile features[18]2020Incentive‐based DRPsLinear‐‐‐Expensing using a suitable energy management system[19]2021RTPLinear‐‐‐Establishing an integrated DR model for multiple energy carriers[20]2021RTPLinear‐‐‐Designing a dynamic DR pricing considering economic aspects and reserve[21]2021RTPmachine learning‐based‐✓Feed‐Forward Neural Network (FFNN)Predicting the electric load with high accuracy to participate in DR programs for commercial, industrial, and residential consumers[22]2022RTPLinear‐‐‐Scheduling of main grid, storages, boilers, distribution generations, and responsive loads[23]2010All DRPsLinearMCDM‐‐Selecting the most effective DRPs for utility/customer[24]2018All DRPsLinear‐‐‐The effects of DRPs on total operation costs, customer's benefit, load curve, and determining optimal use of energy resources in the micro grid operation[25]2022All DRPsLinear‐‐‐Simulation of this multi‐objective virtual power plant to maximize MEVPP profit and minimize carbon dioxide emissions[26]2022RTPLinear‐‐‐An integrated scheduling model of hot rolling shop scheduling and electricity DR, and a multi‐objective production scheduling algorithm is designed[27]2022RTPLinear‐‐‐Achieving the goals of the proposed plan and load reduction[28]2020TOUMachine learning‐based‐‐LSTMDetecting and predicting high energy demand events[29]2021RTPMachine learning‐based‐✓K‐meansCNN‐LSTMEnergy consumption data recorded at predefined intervalsThis paper‐All DRPsmachine learning‐basedMCDM✓WFA K‐means CNN‐LSTMSelecting the most effective DRPs for consumers with clustering of load curves with the prediction of loads consumptionContributionsIn this paper, the machine learning algorithm is used to run DRPs. Convolutional Neural Network (CNN) and Long Short‐Term Memory (LSTM) algorithms are used to execute DRPs. First, the consumers’ load profiles are clustered, and the same load patterns are grouped together. Second, DRPs are modelled as power. Time‐based and incentive‐based programs also combined models with a Coefficient of Participation (CoP) to increase the percentage of consumers in implementing DRPs in each cluster. With the help of newly collected data obtained by implementing the power model of DRPs, the power model of DRPs is implemented by the DL method. During the entire implementation of DRPs, the consumption of each cluster in different seasons is calculated using Time Series Prediction (TSP). Third, the power model of DRPs with CoPs is implemented to ensure the correctness of the answering algorithm. The Deep Learning (DL) model is trained using the data obtained from the power model, and fourth, DRPs are implemented in two ways using new data. Finally, the results of the power and the ANN models of DRPs are compared to show the correct responsibility of the DL model.Therefore, the main contributions of this article are summarized as follows:Clustering and classifying customers’ consumption load patterns by improved Weighted Fuzzy Average (WFA) K‐means clustering method.Implementing Demand Response Programs (DRPs) by CNN‐LSTM method in all different load patterns of customers’ consumption in the distribution network (All 12 DRPs are executed by the CNN‐LSTM algorithm in one year).Implementing all 12 Demand Response Programs (DRPs) without dynamic calculations of the elasticity matrix by the CNN‐LSTM method.Implementing Demand Response Programs (DRPs) during the year by Time Series Prediction (TSP) to predict customers’ consumption for all seasons.The existing challenges in the implementation of demand response programs include the following:Linear and non‐linear models of DRPs include these deficiencies:Linear and non‐linear models of DRPs can only be used if consumers are considered perfectly reasonable.The special elements of DRP models should be calculated for each day. This is very difficult and time‐consuming.To perform those will require rigorous calculations of the elasticity matrix.This paper uses the machine learning algorithm (CNN‐LSTM algorithm) to execute DRPs to obtain more precise solutions. The advantages of implementing machine learning‐based of DRPs over linear and non‐linear models can be noted in the following:Elasticity matrices will not be needed to execute programs, and only past consumer data will be used.DRPs will be much easier to implement for each consumer annually.The proposed CNN‐LSTM method achieves almost complete performance for predicting electricity consumption, which was previously difficult to predict. It also has the lowest root mean square error compared to methods of other deep learning algorithms [30].This paper uses load pattern clustering by the improved WFA K‐means algorithm due to better CDI index evaluation than other algorithms [16]. After clustering and implementing DRPs in order to maximize mutual economic benefits and enhance technical indicators, Multi‐Criteria Decision‐Making (MCDM) methods are employed in this paper [16]. This article aims to provide a general and practical solution for the optimal implementation of DRPs in the electricity industry for various load patterns of consumers.The structure of this article is as follows: In Section 2, the method of the problem will be mentioned, and all the steps of doing the work will be briefly explained in order. In Section 3 of the clustering algorithm used, the program model of non‐linear power DRPs and CNN‐LSTM method, and finally, the weighting and prioritization of programs are fully explained. In Section 4, the results and outputs obtained are presented and discussed, and in Section 5, a general conclusion of this article is given.PROBLEM APPROACHOrganizing this study can be divided into four general stages: clustering of consumers’ load patterns, applying the non‐linear power model of DRPs, applying the DL model of DRPs, and prioritizing the execution of programs in accordance with specified weights.The first stage involves collecting and clustering the load curves of consumers over a period of one year. Several clusters will be obtained at this stage, each containing similar curves. The sum of each cluster's curves is considered a load pattern that expresses that cluster's characteristics and consumer behaviour. Clustering consumers will be done using the improved WFA K‐means method [16]. The k‐means method requires the centre of the primary cluster; the calculation of the centre of the clusters is used in the repetition steps using the WFA technique. Finally, the Euclidean method uses the distance between each cluster's centre and load curve [16]. The algorithm of this method is indicated in Figure 1.1FIGUREFlowchart of clustering algorithm for consumers’ load patterns by WFA K‐means methodAfterward, time‐based DRPs include the Time Of Use (TOU), Real‐Time Pricing (RTP), Critical Peak Pricing (CPP), and incentive‐based programs, including Direct Load Control (DLC), Emergency Demand Response Programs (EDRP), Capacity Market Pricing (CAP), Interruptible/Curtailable (IC) and some combined programs such TOU+DLC, TOU+CAP, TOU+EDRP, and TOU + I/C are considered. It is important to determine tariffs and the amount of penalties and incentives for each program in order to identify the problems. The power model of all these programs is applied to each cluster, and the final load curves are obtained after implementing DRPs [15]. After the data is obtained from the power model of DRPs in each cluster, the DL model of DRPs can be obtained. It is only necessary to be able to carry out DRPs in the electricity network practically and accurately. DL model of DRPs is an excellent alternative to linear and non‐linear DRPs in the electricity industry and can easily be used to show consumers’ behaviour when implementing DRPs.The input and output data necessary to implement DRPs are entered into the DL algorithm for each group of consumers. Consumption data before implementing DRPs, incentives, penalties, initial prices, secondary prices, and annual hours of each cluster as input data, and consumption data after implementing DRPs of that cluster as target data (output) are entered into the DL. The choice of input and output data required for TSP varies depending on the predicted action type. TSP's input and output data include the transfer of consumed data before DRPs implementation, incentives, penalties, initial price, secondary price, and annual hour and the transfer of consumed data after DRPs implementation. In addition to all these things, a data memory should be set aside depending on the expected day of consumer load. In the next step, the time series is predicted by creating a delay and entering a noise with a particular standard deviation (if necessary), which is only to create the necessary environment for a better responsibility of the DL algorithm to enter new data. Training, validation, and test data are selected as a percentage and as desired, and then the number of hidden layers is selected by trial and error or optimally selected. Finally, by entering the input data into the trained DL algorithm, the output data of each DRPs is obtained.In this paper, the initial data are modelled by the power model of DRPs before performing the time series prediction. Because the results obtained from time series prediction by the CNN‐LSTM algorithm will be compared with the power model of DRPs. Among the desirable indicators that this article will obtain are peak reduction, energy consumption reduction (energy savings), peak to valley distance, load factor, and the final customer bill (after applying penalties and incentives). Therefore, This step uses the MCDM approach. The weighting of the indicators has been done by the entropy method, and the prioritization of programs has been done by Similarity to the Ideal Solution (TOPSIS) method. Figure 2 illustrates the steps that are required to perform the problem method described in this article.2FIGUREThe procedure of implementing the DRPs CNN‐LSTM model in the distribution network according to the clustering of consumers’ load patternsPRELIMINARIES AND PROBLEM FORMULATIONThis paper solves the problem by taking four general steps: clustering, implementation of DRPs, selection of indicators and their weight, and prioritization of programs.Clustering by improved WFA K‐meansAs shown in Figure 1, it is needed to determine the number of clusters in the first step. In this paper, consumer's curves are classified into four clusters (residential, commercial, agricultural, and industrial clusters). After placing the curves in the appropriate cluster, the cluster centres can be calculated with the following equations [16]:1μt,uc+1=∑t=1:twt,ucXt,uforu=1,…,N$$\begin{equation}\mu _{\left( {t,u} \right)}^{\left( {c + 1} \right)} = \mathop \sum \limits_{t = 1:t} w_{\left( {t,u} \right)}^{\left( c \right)}{X_{\left( {t,u} \right)}}{\rm{\;\;}}for{\rm{\;}}u\; = {\rm{\;}}1, \ldots ,N\end{equation}$$2wtc=exp−Xt−μc2σ2$$\begin{equation}w_t^{\left( c \right)} = {\rm{\;}}\exp\left[ {\frac{{ - \left( {{X_t} - {\mu ^{\left( c \right)}}} \right)}}{{2{\sigma ^2}}}} \right]\end{equation}$$In these equations, μ(t,u)(c+1)$\mu _{( {t,u} )}^{( {c + 1} )}$ is the tth component of the centre of the cluster with n consumers, in the c + 1th repetition. Also, w(t,u)(c)$w_{( {t,u} )}^{( c )}$ is the weight of the tth component of the nth consumer in the repetition of r. The pth component of the uthconsumer is marked with X(t,u)${X_{( {t,u} )}}$. In Equation (2), wt(c)$w_t^{( c )}$ is the weight of the tth component in the cth repetition, which according to its component or Xt${X_t}$, the component such as the centre of the cluster in the cth repetition and the variance of the component is obtained. In the modified method, σ2 or the variance of the vector of each cluster, is applied to consider more effects for data with higher variance [16].Extract DRPs models using CoPThere are different models of DRPs based on elasticity in mathematical functions. Using mathematical functions, linear and non‐linear models, including power, exponential, and logarithmic can be modelled during the day. Given that different models have different behaviours, non‐linear and linear models should be extracted, and their results should be compared with each other [23]. The elasticity of the load is determined by its sensitivity to price changes and is divided into self‐elasticity and cross‐elasticity [24]. Elasticity is defined in terms of self‐elasticities and cross‐elasticities concerning the following equation [23]:3E(i,j)=pjdj.∂di∂pi$$\begin{equation} E( {i,j}) = \frac{{p\left( j \right)}}{{d\left( j \right)}}\;.\frac{{\partial d\left( i \right)}}{{\partial p\left( i \right)}}\end{equation}$$4self−elasticityEi,j≤0ifi=jcross−elasticityEi,j≥0ifi≠j$$\begin{equation} \left\{ \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\;{\rm{self}} - {\rm{elasticity}}\;E\left( {i,j} \right) \le 0\;if\;i\; = \;j\;}\\[5pt] {{\rm{cross}} - {\rm{elasticity}}\;E\left( {i,j} \right) \ge 0\;if\;i \ne j} \end{array} \right.\end{equation}$$where p is the price and d is the demand. Equation (3) shows the degree of sensitivity of the load to price changes per period, and Equation (4) shows the definition of the elasticity matrix. To implement consumption management, consumers need to change their energy consumption from the initial value of d0(i)${d_0}( i )$ to d(i)$d( i )$. New energy consumption is denoted by Δd(i)${{\Delta}}d( i )$ and is defined as follows:5Δd(i)=di−d0ikWh$$\begin{equation} \def\eqcellsep{&}\begin{array}{*{20}{l}} {{{\Delta}}d(i) = \left| {d\left( i \right) - {d_0}\left( i \right)} \right|\;}&{kWh} \end{array} \end{equation}$$IC(i)$IC( i )$ is the amount of load reduction required in DRPs, and d′(i)$d^{\prime}( i )$ is the amount of load that the customer should be penalized. The total standard penalty (pen′$pen^{\prime}$) is obtained from Equation (7).6d′(i)=ICi−ΔdikWh$$\begin{equation} d^{\prime}(i) \def\eqcellsep{&}\begin{array}{*{20}{l}} = {IC\left( i \right) - {{\Delta}}d\left( i \right)}&{kWh} \end{array} \end{equation}$$7pen′(Δd(i))=peni.ICi−Δdi$$\begin{equation} pen^{\prime}({{{\Delta}}d(i)}) = pen\left( i \right).\left[ {IC\left( i \right) - {{\Delta}}d\left( i \right)} \right]\end{equation}$$A(i)$A( i )\;$is the amount of incentive received to reduce the burden on time, and pen(i)$pen( i )$ is the penalty to be paid for the non‐reduced burden that will follow the customer's closed contract. The amount of incentive paid in the ith (A′$A^{\prime}$) period is as follows [16]:8A′(Δd(i))=Ai.di−d0i$$\begin{equation} A^{\prime}({{{\Delta}}d(i)}) = A\left( i \right).\left| {d\left( i \right) - {d_0}\left( i \right)} \right|\end{equation}$$In modelling DRPs, maximizing customer profit is necessary due to encouraging customers to perform DRPs. The customer profit function is calculated as Equation (9) which in it B(d(i))$B( {d( i )} )\;$shows customer revenue if there is a profit, d(i)p(i)$d( i )p( i )$ shows the cost of electricity consumption, A′(Δd(i))$A^{\prime}( {\Delta d( i )} )$ shows incentive received, and pen′(Δd(i))$pen^{\prime}( {\Delta d( i )} )$ shows the amount of the penalty. Its maximum value will be obtained by Equation (10) deriving from the customer profit equation. Therefore [16]:9(di)−B(d(i))+d(i)p(i)=A′(Δd(i))−pen′(Δd(i))$$\begin{equation} ({d\left( i \right)}) - B({d(i)}) + d(i)p(i) = A^{\prime}({\Delta d(i)}) - pen^{\prime} ({{{\Delta}}d(i)})\end{equation}$$10∂Bdi∂di=pi+Ai+peni$$\begin{equation} \frac{{\partial B\left( {d\left( i \right)} \right)}}{{\partial d\left( i \right)}} = p\left( i \right) + A\left( i \right) + pen\left( i \right)\end{equation}$$The customer revenue function is defined by the Taylor series second‐order expansion of the power demand function as follows [16]:11Bi=B0(i)+p0idi1+E(i,i)−1did0iE(i,i)−1−1$$\begin{equation} B\left( i \right) = {B_0}(i) + \frac{{{p_0}\left( i \right)d\left( i \right)}}{{1 + E{{(i,i)}^{ - 1}}}}\left\{ {{{\left( {\frac{{d\left( i \right)}}{{{d_0}\left( i \right)}}} \right)}^{E{{(i,i)}^{ - 1}}}} - 1} \right\}\end{equation}$$where E(i,i)$E( {i,i} )$ is the matrix of elasticity at any time interval i, by simplifying the Equations (10) and (11), the one‐period model of the power demand function with its self‐elasticity will be as follows [16]:12di=d0ipi+Ai+penip0iEi,i$$\begin{equation} d\left( i \right) = {d_0}\left( i \right){\left( {\frac{{p\left( i \right) + A\left( i \right) + pen\left( i \right)}}{{{p_{{{\rm{\;}}_0}}}\left( i \right)}}} \right)^{E\left( {i,i} \right)}}\end{equation}$$Using the definition of reciprocal elasticity, the multi‐period model of the power function is obtained.13d(i)=d0(i).∏j=1j≠i24pj+Aj+penjp0jEi,j$$\begin{equation} d(i) = {d_0}(i).\mathop \prod \limits_{ \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {j = 1}\\ {j \ne i} \end{array} }^{24} {\left( {\frac{{p\left( j \right) + A\left( j \right) + pen\left( j \right)}}{{{p_0}\left( j \right)}}} \right)^{E\left( {i,j} \right)}}\end{equation}$$By combining two single‐period models with multi‐period comprehensive models, the power function is obtained as follows [16]:14di=α.d0i.EXP×∑j=124Ei,jlnpj+Aj+Penjp0j+1−α.d0i$$\begin{eqnarray} && d\left( i \right) = \;\alpha .{d_0}\left( i \right). \ {\rm EXP}\nonumber\\ &&\quad\times\, \left\{ \mathop \sum \limits_{j\; = \;1}^{24} E\left( {i,j} \right){\rm{ln}}\left( {\frac{{p\left( j \right) + A\left( j \right) + Pen\left( j \right)}}{{{p_0}\left( j \right)}}} \right)\right\} + \left( {1 - \alpha } \right).{d_0}\left( i \right)\nonumber\\ \end{eqnarray}$$In Equation (14), α represents the coefficient of consumer participation in DRPs. This coefficient will always be between 0 and 1. For example, to show 60% participation, α must be set to 0.6. Obviously, the model of DRPs only applies to the part of the load involved in DRPs.Weighing indicators and prioritizing DRPsIn studying the implementation of DRPs, selecting the best program according to several different criteria is mandatory. These issues are called MCDM issues. Depending on the perspective of the Independent System Operator (ISO), the retailer or distribution company, and the customer, these criteria and indicators will be of varying importance. In some cases, the profit of the utility company is the most important indicator, or the reduction of the customer bill is the most crucial indicator; by using these decisions, different DRPs are selected [16].Shannon entropy methodIn information theory, a mathematical function called Shannon entropy measures the “uncertainty” in a random process. The amount of uncertainty is expressed by a discrete probability distribution of each of the variables modelled with P. This uncertainty is denoted by E and is expressed as follows:15En=−Kn∑m=1fPm×LnPm,Kn=Lnf−1$$\begin{equation} {E_n} = - {K_n}\mathop \sum \limits_{m\; = \;1}^f \left[ {{P_m} \times Ln{P_m}} \right] \def\eqcellsep{&}\begin{array}{*{20}{l}} ,&{\;{K_n} = {{\left( {Ln{\rm{\;f}}} \right)}^{ - 1}}\;} \end{array} \end{equation}$$where k is a positive constant to supply 0 ≤ En${E_n}$ ≤ 1. Pm${P_m}$s are formed based on the normalization of decision matrix elements and to use the entropy method, the decision matrix should be formed:16D=x11…x1v⋮⋱⋮xz1⋯xzv$$\begin{equation}D\; = \left( { \def\eqcellsep{&}\begin{array}{@{}*{3}{l}@{}} {{x_{11}}}&\quad \ldots &\quad{{x_{1v}}}\\[9pt] \vdots &\quad \ddots &\quad \vdots \\[9pt] {{x_{z1}}}&\quad \cdots &{{x_{zv}}} \end{array} } \right)\end{equation}$$In Equation (16) xzv${x_{zv}}$ is the value of the vth index due to the application of the zth program. The p‐norm equation scales this matrix. The general definition for the p‐norm of a vector m that has n elements:17xp=∑m=1zxmnp1/p$$\begin{equation} {\left\| x \right\|_p} = {\left[ {\sum_{m = 1}^z {{x_{mn}}^p} } \right]^{1/p}}\end{equation}$$where p is any positive real value in the range from infinite positive to infinite negative. In entropy, p=1$p\; = \;1$ is used, and the decision matrix normalizer is defined as follows:18rmn=xmn∑m=1zxmn$$\begin{equation}{r_{mn}} = \frac{{{x_{mn}}}}{{\mathop \sum \nolimits_{m = 1}^z {x_{mn}}}}\end{equation}$$After calculating the value function for each column, the degree of deviation (dn${d_n}$) is determined for all columns:19dn=1−En$$\begin{equation} {d_n} = 1 - {E_n}\end{equation}$$Finally, the weight of the indicators (Wn${W_n}$) is determined by the following equation [16]:20Wn=dn∑n=1vdn$$\begin{equation}{W_n} = \frac{{{d_n}}}{{\mathop \sum \nolimits_{n = 1}^v {d_n}}}\end{equation}$$Suppose the decision‐maker wants to apply the importance of each of the indicators in entropy. In that case, it can use the corrected (λn${\lambda _n}$) to make the decision maker's judgment about the nth index. It should be noted that the sums λn${\lambda _n}$ are equal to one.21IWn=λn×Wn∑n=1vλn×Wn$$\begin{equation} I{W_n} = \frac{{{\lambda _n} \times {W_n}}}{{\mathop \sum \nolimits_{n = 1}^v {\lambda _n} \times {W_n}}}\end{equation}$$The weights obtainedIWn$\;I{W_n}\;$will be related to each of the mentioned characteristics.Prioritization by TOPSISThe input information of the TOPSIS method includes the weights of the indicators’ matrix (IWn$I{W_n}$) and its output will be obtained as a ranking of DRPs in each cluster. Generally, TOPSIS determines the best alternative based on its distance from the ideal solution and its distance from the worst alternative. For this reason, it shows the highest sensitivity to weight vectors and has the most accurate answer to linear normalization methods [16]. The above method can be applied as follows.First, the decision matrix must be scaled in TOPSIS, which uses the p‐norm normalizer defined in Equation (17) to normalize. The decision matrix is normalized to p=2$p = 2$:22rmn=Xmn∑m=1vXmn2$$\begin{equation}{r_{mn}} = \frac{{{X_{mn}}}}{{\sqrt {\mathop \sum \nolimits_{m = 1}^v X_{mn}^2} }}\end{equation}$$The calculation of the weighted dimensionless matrix (V) is obtained using the calculated weights of the indices:23Vmn=Wn×rmn$$\begin{equation}{V_{mn}} = {W_n}\; \times {r_{mn}}\end{equation}$$Calculate the ideal (Vn+${V_n}^ + $), and counter‐ideal (Vn−${V_n}^ - $) answers [16]:24Vn+=maxVmnn∈V+,minVmnn∈V−m=1,…,zVn−=minVmnn∈V+,maxVmnn∈V−m=1,…,z$$\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{2}{l}@{}} { \def\eqcellsep{&}\begin{array}{*{20}{l}} {{V_n}^ + = \left( {{\rm{max}}{V_{mn}}\left| {n \in {V^ + }} \right|,{\rm{min}}{V_{mn}}\left| {n \in {V^ - }} \right|} \right)\;}&{m\; = \;1, \ldots ,z} \end{array} }\\[9pt] { \def\eqcellsep{&}\begin{array}{*{20}{l}} {{V_n}^ - = \left( {{\rm{min}}{V_{mn}}\left| {n \in {V^ + }} \right|,{\rm{\;max}}{V_{mn}}\left| {n \in {V^ - }} \right|} \right)\;}&{m\; = \;1, \ldots ,z} \end{array} } \end{array} \end{equation}$$Here, the type of criteria should be specified. The criteria are either positive or negative. Positive criteria are criteria whose increase improves the system, and negative criteria are the opposite. To choose these criteria, the following should be considered:For criteria that have a positive load, the positive ideal is the largest value of that criterion.For criteria that have a positive charge, the negative ideal is the smallest value of that criterion.For criteria that have a negative load, the positive ideal is the smallest value of that criterion.For criteria that have a negative load, the negative ideal is the largest value of that criterion.Calculate distances from the ideal and counter‐ideal answers using the Euclidean distance. So, distance from the ideal answer [16]:25Sm+=∑n=1v(vmn−vn+)2$$\begin{equation}S_m^ + = \sqrt {\mathop \sum \limits_{n = 1}^v {{({v_{mn}} - v_n^ + )}^2}} \end{equation}$$distance from the counter‐ideal answer [16]:26Sm−=∑n=1v(vmn−vn−)2$$\begin{equation}S_m^ - = \sqrt {\mathop \sum \limits_{n = 1}^v {{({v_{mn}} - v_n^ - )}^2}} \end{equation}$$ranking options by calculating the value of Cm${C_m}$ [16]:27Cm=Sm−Sm++Sm−$$\begin{equation}{C_m} = \frac{{S_m^ - }}{{S_m^ + + S_m^ - }}\end{equation}$$Cm${C_m}$ values for each option, which must be between zero and one, is considered a score for each DRPs. The option with more C will have a higher rank, and therefore, it has more benefits.DL implementing method for DRPsANN methodTypically, neural networks are employed when there is no mathematical model or when there is a problematic relationship between input and output data. In addition, neural networks can be used in very complex systems. Each ANN layer can be described by (28) [31]:28Yo=ψ∑l=0nSwloXl+θo$$\begin{equation}{Y_o} = \;\psi \left( {\mathop \sum \limits_{l\; = \;0}^n S{w_{lo}}{X_l} + {\theta _o}} \right)\end{equation}$$where Swlo$S{w_{lo}}$ is the Synapse weight, θo${\theta _o}\;$is a constant, Xl${X_l}$ is the input vector, Yo${Y_o}$ is the output vector, and ψ is the active function. The term activation function refers to the ψ function, which binds the input value to the network output value. The most common activation functions are sigmoid, step, linear, sign, and hyperbolic tangent functions [32]. Each layer of artificial neural networks has a linear or non‐linear stimulus function model. The term bias θo${\theta _o}$ causes the displacement of the function curve in the input space and in other words, causes the neuron to be biased in a subspace of the input space, which justifies the selection of the bias for the term θo${\theta _o}$ [34]. More explanations are outlined in [33] and [34]. Figure 3 illustrates an ANN implementation with N inputs. As soon as the input value is given to the neuron, it calculates its state by applying a temporal activation function to the input value. The sum of the neuron record function's values is multiplied by Equation (28) [32].3FIGUREThe ANN prototypeDL methodTo better understand the difference between ANN and DL algorithms, it can be said that: Machine learning is a subfield of artificial intelligence. Deep learning is a subfield of machine learning, and ANNs form the backbone of deep learning algorithms. In fact, the distinguishing feature of a single ANN from the deep learning algorithm is the number of node layers or the depth of the neural networks, which must be more than three in the deep learning algorithm [35]. In this article, the CNN‐LSTM algorithm is used. The CNN‐LSTM Algorithm consists of the combination of two algorithms named CNN and LSTM. The CNN algorithm is a type of DL algorithm, and the LSTM algorithm is a Recurrent Neural Network (RNN) algorithm [36].In general, the CNN‐LSTM method uses CNN as an encoder to learn features from the subsequence of input data fed into an LSTM as time steps. The LSTM will function as a decoder, identifying and modelling both short‐term and long‐term temporal relationships inherent in the data stream. More details are addressed in refs. [30] and [37]. Figure 4 shows the basic architecture of this algorithm.4FIGUREThe basic architecture of the CNN‐LSTM networkThe training algorithm for defining the weights that make up the system must have an error close to zero, that is, the purpose of the DL algorithm is to determine a set of weights w that minimizes the sum of the Errors (E) as follows [32]:29E=∑lYl−fSwl,Xl2$$\begin{equation}E\; = \mathop \sum \limits_l {\left[ {{Y_l} - f\left( {S{w_l},{X_l}} \right)} \right]^2}\end{equation}$$where Yl${Y_l}$ is the final and actual value and f(Swl,Xl)$f( {S{w_l},{X_l}} )$ is the value of the final answer that the algorithm obtains or predicts after training [32].The design of CNN‐LSTM can be modified according to the type and parameter adjustment of the network's layers [38]. The CNN‐LSTM consists of visual features (in the CNN layer) and sequence learning (in the LSTM layer). Each layer can adjust the number of filters, the kernel size, and the number of strides. Changing the parameters of layers can affect learning speed and performance depending on the characteristics of the learning data [39].To evaluate the accuracy of the models developed with DLs, the criteria of Mean Squared Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Regression (R) are used. The following equations show how to calculate them [38, 39]:30RMSE=∑l=1NYl−Ŷl2N$$\begin{equation} RMSE = \sqrt {\frac{{\mathop \sum \nolimits_{l = 1}^N {{\left( {{Y_l} - {{\hat Y}_l}} \right)}^2}}}{N}} \end{equation}$$31MSE=∑l=1N(Yl−Ŷl)2N$$\begin{equation} MSE = \frac{{\mathop \sum \nolimits_{l = 1}^N {{( {{Y_l} - {{\hat Y}_l}})}^2}}}{N}\end{equation}$$32MAPE=∑l=1NYl−ŶlYlN$$\begin{equation} MAPE = \frac{{\mathop \sum \nolimits_{l = 1}^N \left| {\frac{{{Y_l} - {{\hat Y}_l}}}{{{Y_l}}}} \right|}}{N}\end{equation}$$33R=output=a′.target+b$$\begin{equation} R = output = a^{\prime}.target + b\end{equation}$$For this purpose, Equation (34) has been used to normalize the training and test patterns [40].34Xnorm=0.5Xl−X¯Xmax−Xmin+0.5$$\begin{equation}{X_{norm}} = \;0.5\left( {\frac{{{X_l} - \bar X}}{{{X_{max}} - {X_{min}}}}} \right) + 0.5\end{equation}$$where Xnorm${X_{norm}}\;$is the normalized value of the input Xl${X_l}$, X¯$\bar X\;$is the average value of data, Xmax${X_{max}}\;$and Xmin${X_{min}}$ is the maximum and minimum value of input data. For a better and easier understanding of data and more practical use, data are usually normalized for training artificial neural network algorithms. If the dispersion or standard deviation of the normalized data is bigger, the learning and generalization will be better [41].NUMERICAL STUDIESThe data used in this section is from 10,000 consumption load curves [42] and CNN‐LSTM is used as a machine learning algorithm. The power model of DRPs handles input and output data. The delay used in the TSP section is 200 h with an hourly range. An electricity tariff has been used for spring, summer, autumn, and winter tariffs. The affected consumers are divided into 4 clusters named residential, commercial, industrial, and agricultural clusters by the improved WFA K‐means algorithm. For the DRPs power model, Table 2 illustrates the 24‐h elasticity matrix for all clusters [16]. Figure 5 shows the initial consumption pattern of all consumers in this study. This naming of clusters is based on how each cluster is consumed with reality instead of numerical naming.2TABLESelf‐elasticities and cross‐elasticitiesPeakOff‐peakValleyPeak−0.10.0160.012Off‐peak0.016−0.10.01Valley0.0120.01−0.15FIGUREThe initial consumption load pattern of each clusterRunning DRPs on the networkAll 12 DRPs in each cluster have been operated with TSP operations due to the delay of 200 h with 7 different inputs in each program execution with matrix input dimensions of 1400×8560. Thus, each TSP implementation of the algorithm training will be conducted in a DRP with 11,984,000 input data and 200×8560 output data. According to the trained algorithm, different inputs are considered input data in spring, summer, autumn, and winter, and the output results are compared with the same inputs. In the CNN layer, windows with dimensions of 90 × 120 and (2 × 1) kernel function are used, and in the LSTM layer, 128 neurons with tanh function and with a batch size of 64 are used. All these points have been obtained by trial and error.The purpose of the results is to respond to each program as a power model and it is compared with the algorithm's output. Based on the weighting of the indicators, DRPs are prioritized based on the indicators for each chapter. Table 3 shows the performance of each DRP in each cluster. The regression of all programs is very close to 1, and most models’ error rate, especially in MAPE, are very low. In the TSP stage, it can be said that the algorithm has been well trained with all the programs in each cluster. The high MSE error rate is due to customers’ high consumption in all clusters.3TABLECalculation of errors and regression in TSP stepClusterProgramRRMSEMSEMAPEResidentialTOU0.9929.98899.000.61CPP0.9963.213995.491.09RTP0.9981.936713.491.31TOU+CPP0.9949.592460.130.93DLC0.9934.791210.710.59EDRP0.9954.732995.850.94CAP0.9927.86776.480.46I/C0.9945.462067.240.78TOU+DLC0.9942.141776.050.81TOU+EDRP0.9949.422443.170.92TOU+CAP0.9939.341548.380.76TOU+I/C0.9945.992115.390.86CommercialTOU0.9841.091688.4712.26CPP0.9937.221386.0111.75RTP0.9839.181535.2312.21TOU+CPP0.9838.711498.9012.59DLC0.9838.911514.6612.46EDRP0.9844.511981.2814.58CAP0.9840.011601.2911.93I/C0.9846.792189.8914.99TOU+DLC0.9841.911756.7413.51TOU+EDRP0.9841.831750.3113.51TOU+CAP0.9844.691997.4213.75TOU+I/C0.9846.092125.1914.36IndustrialTOU0.9941.461719.381.78CPP0.9940.791664.031.76RTP0.9940.001600.821.72TOU+CPP0.9942.901841.141.82DLC0.9942.321791.611.82EDRP0.9942.451802.331.84CAP0.9942.091771.621.80I/C0.9941.601730.801.80TOU+DLC0.9944.451976.421.88TOU+EDRP0.9941.581728.941.77TOU+CAP0.9941.421715.871.77TOU+I/C0.9942.161814.991.83AgricultureTOU0.9912.98168.485.46CPP0.9912.77163.184.76RTP0.9913.86192.265.57TOU+CPP0.9913.55183.775.94DLC0.9912.54157.384.78EDRP0.9914.28203.945.51CAP0.9913.21174.735.03I/C0.9913.57184.225.16TOU+DLC0.9913.71188.236.01TOU+EDRP0.9913.28176.595.67TOU+CAP0.9912.72162.005.39TOU+I/C0.9914.57212.417.53The behaviour of DRPs in winter load will be shown, and the rest of the loads will be have the same way in TSP if they are stored correctly. TSP has been simulated in the other parts of the year, but because of their large number, we have not displayed their graph. Figure 6 shows the behaviour of DRPs of the power model in the residential cluster. It can be seen that the residential cluster has two peaks between the hours of 10 to 14 and 17 to 22. The consumption of all DRPs in the power model has increased during the valley and off‐peak hours. The RTP program had the highest consumption during the valley hours, while the TOU + DLC and CPP programs had the highest consumption during the off‐peak hours. The TOU + I / C and TOU + CPP programs had the most considerable reductions in energy consumption during peak hours.6FIGUREThe behaviour of the power model of DRPs in the residential cluster during one dayIn Figure 7, DL model DRPs are shown in the residential cluster. There are many ups and downs in the DL model throughout the day. This is because residential consumers usually do not have the same consumption behaviour throughout the year. That's why the memory in this cluster is complicated to predict the time series, and with the most remarkable accuracy, it still has gaps in the accurate model. As a matter of fact, the priority of the DL model of DRPs has been the same as that of the power model in terms of the first and second priorities. It can be said that the DL model of DRPs is well anticipated.7FIGUREThe behaviour of the DL model of DRPs in the residential cluster during one dayThe behaviour of DRPs of the commercial cluster power model is shown in Figure 8. The number of peaks in the commercial cluster is the same as in the residential cluster. During the valley and peak hours, the behaviour of DRPs in commercial clusters is similar to that of residential clusters. But in the peak hours of the CPP program and with TOU + CPP program, they had the highest consumption. Figure 9 shows the behaviour of commercial cluster DRPs in the DL model. As can be seen, there is not much difference between the behaviour of power model DRPs and DL.8FIGUREThe behaviour of the power model of DRPs in the commercial cluster during one day9FIGUREThe behaviour of the DL model of DRPs in the commercial cluster during one dayFigure 10 shows the implementation of the power model, and Figure 11 shows the implementation of the DL model of DRPs in the industrial cluster. Both models exhibit very similar behaviour. Any result that is said for the power model load is the same as the results of the DL model. Combined programs and TOU had the highest peak consumption during peak hours, while combined programs and incentive‐based programs had the highest peak reduction during peak hours.10FIGUREThe behaviour of the power model of DRPs in the industrial cluster during one day11FIGUREThe behaviour of the DL model of DRPs in the industrial cluster during one dayFigures 12 and 13 show the implementation of the power and DL models of DRPs in the agricultural cluster on a 24‐h basis, respectively. The agricultural cluster has a peak and two valleys, which has a valley in summer and spring loads. The behaviour of the power and DL models of DRPs is always similar with a small amount of difference. The combined programs with TOU and RTP have increased energy consumption during valley hours, and have further reduced it during peak hours. Implementing DRPs in the agricultural cluster can increase energy consumption if they are incentive‐based or have low tariffs during valley hours.12FIGUREThe behaviour of the power model of DRPs in the agriculture cluster during one day13FIGUREThe behaviour of the DL model of DRPs in the agriculture cluster during one dayIndicators weighingTable 4 shows the specified weights of the indicators in the power model, and Table 5 shows the specified weights of the indicators in the CNN_LSTM model. These weights are obtained by entropy, and the weights specified in the power model and CNN_LSTM differ slightly. In the commercial, agricultural and residential clusters, energy reduction in power and CNN_LSTM models is the first indicator at all times. In summer, customer bill and peak reduction are the second indicators in other times. In the commercial cluster, peak reduction indices in spring and summer loads and energy reduction indices in autumn and winter loads are the first indicators in the power model. But in the CNN_LSTM model, the commercial cluster is the first indicator of energy reduction at all times. In general, the implementation of DRPs has had the most significant impact on reducing the total consumption of consumers.4TABLEWeight of attributes in power modelCluster typeType of loadCustomer billPeak reductionEnergy reductionLoad factorPeak to valleyResidentialSpring0.1100.2230.6430.00050.021Summer0.1430.0980.7430.00100.011Autumn0.1210.2230.6400.00050.013Winter0.1210.2230.6420.00030.012CommercialSpring0.2080.4490.3210.00500.014Summer0.1820.4020.3880.00380.021Autumn0.3030.1920.4720.00730.023Winter0.3230.1570.4910.00630.019IndustrialSpring0.1160.0140.8120.00100.054Summer0.1190.0530.7900.00080.035Autumn0.1160.0380.7690.00100.074Winter0.1140.0310.8070.00130.045AgricultureSpring0.0180.4810.4000.00300.066Summer0.1590.1240.6340.00220.061Autumn0.0450.1800.7610.00030.006Winter0.0420.0930.8330.00130.0155TABLEWeight of attributes in the CNN_LSTM modelCluster typeType of loadCustomer billPeak reductionEnergy reductionLoad factorPeak to valleyResidentialSpring0.1100.2150.6440.00100.028Summer0.1420.0920.7490.00140.011Autumn0.1190.3170.5320.00190.028Winter0.1210.3890.4510.00140.035CommercialSpring0.2650.2720.4370.00540.017Summer0.2140.3650.3910.00380.024Autumn0.2570.2380.4750.00660.020Winter0.3370.1690.4630.00650.021IndustrialSpring0.0920.0140.8420.00070.048Summer0.1440.0890.7120.00130.052Autumn0.0990.0540.7710.00100.074Winter0.1170.0410.7830.00160.056AgricultureSpring0.1100.2150.6440.00100.028Summer0.1420.0920.7490.00140.011Autumn0.1190.3170.5320.00190.028Winter0.1210.3890.4510.00140.035Programs prioritizingThe first priority and sometimes the second priority are the best choices, so if the first priority is equal in both models at all times, then the CNN‐LSTM algorithm has been trained correctly. It also shows that the DL model is able to simulate the power model of DRPs well. The prioritization of programs in any cluster is shown in Tables 6 and 7. The spring DL and load power models have different first priorities in the commercial cluster. There is a primary reason for the incorrect answer because there is insufficient information to place them as a memory that can correctly predict the TSP. This wrong answer is primarily due to the existence of the most MAPE errors in the TSP of the commercial cluster.6TABLEPriority of programs in all clusters in the power modelCluster importanceType of loadTOUCPPRTPRTP and CPPDLCEDRPCAPI/CTOU and DLCTOU and EDRPTOU and CAPTOU and I/CResidentialSpring111123821057496Summer111123821057496Autumn111123821057496Winter111123821057496CommercialSpring212111653987410Summer111122431076598Autumn111122451037896Winter111122561037894AgricultureSpring121116324597108Summer121112109874635Autumn816742531012911Winter716842531191210IndustrialSpring111126425397108Summer111126425397108Autumn121275364108119Winter1212753641081197TABLEPriority of programs in all clusters in the CNN‐LSTM modelCluster importanceType of loadTOUCPPRTPRTP and CPPDLCEDRPCAPI/CTOU and DLCTOU and EDRPTOU and CAPTOU and I/CResidentialSpring111123821067594Summer111124821057396Autumn111122841059673Winter121113951076284CommercialSpring111122531046798Summer111122431076598Autumn111123641029758Winter111122681034795AgricultureSpring121111032459786Summer121116109873524Autumn916843112751210Winter816742531112910IndustrialSpring121117425398106Summer121117425398106Autumn121275364108119Winter121275364108119The differences in the values determined in the indicators in power and DL models in the residential cluster are shown in Table 8. The CPP program has been selected for power and DL models at all times, and also the CPP program has increased the customer bill at all times. There are many differences in the peak reduction indicator in power and DL models, and these differences are evident in the load factor indicator. The DL model usually measures further peak reduction and load factor increase. Table 9 shows the values of the indicators when implementing commercial cluster DRPs. The RTP program power model and the CPP program DL model have been selected in the spring load. Because in the power model, the peak reduction has the highest weight among the indicators. But in the DL model, energy reduction has the highest weight among the indicators. There is not much difference in the other values of DL and power indicators.8TABLEThe results obtained from the necessary indicators of the first priority of DRPs in residential clusterType of loadType of modelLoadProgramCustomer bill (cent×104)Peak reduction (%)Energy reduction (%)Load factor (%)Peak to valley (MW)SpringInitial load0.4800076.683.51PowerSec .loadCPP0.76610.134.5581.442.57DLSec .loadCPP0.76511.034.5882.022.55SummerInitial load0.2790069.373.93PowerSec .loadCPP0.45412.777.8273.303.16DLSec .loadCPP0.45312.367.7472.923.18AutumnInitial load0.6560078.214.57PowerSec .loadCPP1.0839.023.3383.113.46DLSec .loadCPP1.07910.693.4284.313.12WinterInitial load0.8150081.034.89PowerSec .loadCPP1.3497.522.6885.283.78DLSec .loadCPP1.3477.962.7886.033.729TABLEThe results obtained from the necessary indicators of the first priority of DRPs in commercial clusterType of loadType of modelLoadProgramCustomer bill (cent×104)Peak reduction (%)Energy reduction (%)Load factor (%)Peak to valley (MW)SpringInitial load0.2110067.860.59PowerSec .loadRTP0.23310.101.3074.490.44DLSec .loadCPP0.2878.441.8373.420.48SummerInitial load0.2180067.990.62PowerSec .loadCPP0.4555.979.2165.650.52DLSec .loadCPP0.4516.069.2665.890.50AutumnInitial load0.2040067.970.58PowerSec .loadCPP0.4214.6110.8363.530.53DLSec .loadCPP0.4203.6310.5963.070.52WinterInitial load0.2150067.070.62PowerSec .loadCPP0.4484.8410.3063.220.57DLSec .loadCPP0.4474.7810.5463.010.58The values of industrial cluster indicators are given in Table 10. There is not much difference in the set values of the indicators in the DL models and the power model. The peak reduction amount is found more in the DL model in the summer load. Table 11 shows the values of the agricultural cluster's first priority indicators of TOPSIS DRPs. As can be seen, all times in DL models and CPP program power model has been selected, and in addition, there is not much difference in the values of the indicators.10TABLEThe results obtained from the necessary indicators of the first priority of DRPs in industrial clusterType of loadType of modelLoadProgramCustomer bill (cent×104)Peak reduction (%)Energy reduction (%)Load factor (%)Peak to valley (MW)SpringInitial load0.2600077.150.89PowerSec .loadCPP0.5298.565.8679.420.67DLSec .loadCPP0.5318.595.8280.010.68SummerInitial load0.3580075.321.27PowerSec .loadCPP0.7499.894.2680.020.94DLSec .loadCPP0.74710.314.3280.120.92AutumnInitial load0.2800076.230.98PowerSec .loadCPP0.58411.655.4381.600.67DLSec .loadCPP0.58511.515.4081.530.68WinterInitial load0.2530079.440.68PowerSec .loadTOU0.51212.626.0385.440.39DLSec .loadTOU0.51112.736.0985.470.4011TABLEThe results obtained from the necessary indicators of the first priority of DRPs in agriculture clusterType of loadType of modelLoadProgramCustomer bill (cent×104)Peak reduction (%)Energy reduction (%)Load factor (%)Peak to valley (MW)SpringInitial load0.0160073.880.19PowerSec .loadCPP0.0217.8716.8666.670.16DLSec .loadCPP0.0227.6517.0765.560.17SummerInitial load0.0200061.840.28PowerSec .loadRTP0.01328.2014.4973.650.20DLSec .loadRTP0.01227.8315.0172.970.21AutumnInitial load0.0120062.140.17PowerSec .loadCPP0.0217.571.6466.600.16DLSec .loadCPP0.0207.371.6865.970.15WinterInitial load0.0050061.440.07PowerSec .loadCPP0.01012.561.9768.030.06DLSec .loadCPP0.00912.531.8968.120.05CONCLUSIONDue to the rapid growth of data collected from smart meters in smart grids and the lack of knowledge about the type of loads of consumers, it will be necessary to develop a model to implement DRPs operationally. This paper discusses three phases of the implementation of DRPs: clustering, the application of machine learning‐based DRPs, and the prioritization of programs within each cluster. It should be noted prioritization of DRPs will outline the most effective programs for economic and technical criteria. This method will be flexible in terms of study type and desirable indicators. It is also possible to consider infrastructure and the implementation of DRPs costs. In prioritization, it should be noted that maximizing an index in a cluster may not result in maximizing the indicator in the entire network. The degree of profit and, consequently, the rank of each program (incentive‐based) strongly depend on the amount of incentives and penalties in each period. Therefore, this opportunity exists in incentive‐based programs that can be maximized by calculating optimal encouragement. In some grids, due to the increasing distributed generation and renewable energy resources, it is sometimes necessary to encourage consumption increment rather than trying to reduce it to adjust the valleys presented in the load curve.In this paper, the WFA K‐means clustering method was used for consumption management studies by creating the most differentiation and similarity in the curves of each category and the best CDI value. Furthermore, CNN‐LSTM algorithms are used as an implementation of DRPs in order to make them operational in reality. With the implementation of DRPs with the model of machine learning algorithms such as CNN‐LSTM, there is no need for heavy calculations of elasticity matrix. In the electricity industry, DRPs can be implemented accurately in more than one day for all load patterns. Implementing DRPs using the DL algorithm dynamically with a low error value compared to the power model of DRPs led to the same prioritization results in the meantime. The DL model for DRPs shows that the cluster of residential dwellings with the highest possible consumption has more errors compared to the cluster of industrial dwellings with the lowest possible consumption in the DL model.In order to achieve more accurate models for DRPs, various uncertainty modelling methods can be considered in future research. Different uncertainty associated with smart grids includes consumers’ behaviour and resources allocation regarding their generation output during a day. Also, the role of emerging components such as electric vehicles and power electronic devices in resources dispatch will need further study.NOMENCLATURE    Indicesi,j$i,j$Index of time and periodtIndex of componentuIndex of consumercIndex of iteration numberl,o$l,o$Index of the number of vectorsnIndex of the n‐th criterionmIndex of the m‐th alternativezIndex of the quantity of the alternativesvIndex of the quantity of the attributesParametersd0Initial load demand for consumerd0(i)${d_0}( i )$Initial load demand in the i‐th hour for consumerEThe elasticity of consumer load demandE(i,i)$E( {i,i} )$Self‐elasticityE(i,j)$E( {i,{\rm{j}}} )$Cross‐elasticityp0Initial electricity demand pricep0(i)${p_0}( i )$Initial electricity demand price in the i‐th hourpThe spot price of electricityp(i)$p( i )$The electricity price in the i‐th hourA(i)$A( i )$The incentive of DRPs in the i‐th hourpen(i)$pen( i )$penalty payout in the i‐th hourSw$Sw$The Synapse weightθThe constantXThe input vectorY,Ŷ$Y,\hat Y$The output vectorXnorm${X_{norm}}$The normalized value of the inputsXmax${X_{max}}$, Xmin${X_{min}}$The maximum and minimum value of input dataX¯$\bar X$The average value of dataσStandard deviationψThe active functionΛDecision maker's importance factorVariablesbError terms in regressionB(d(i))$B( {d( i )} )$Consumer's income considering load amount equal to d(t) in the i‐th hourdNew consumer loadd(i)$d( i )$New consumer load in the i‐th hourΔd(i)Equal to the change in initial and final consumptionIC(i)$IC( i )$Incentive‐based DRPs with penalties contract level in the i‐th hourA′(Δd(i))${\rm{A^{\prime}}}( {\Delta {\rm{d}}( {\rm{i}} )} )$Total incentive payment to the consumerp(i)$p( i )$The cost of electricity consumed by the consumerd′(i)$d^{\prime}( i )$the amount of load that the customer should be penalizedpen′(Δd(i))$pen^{\prime}( {{{\Delta}}d( i )} )$Total penalty paymentSn$Sn$The customer profitμ(t,u)(r+1)$\mu _{( {t,u} )}^{( {r + 1} )}$t‐th component of the centre of the cluster with u consumers, in the r + 1 th iterationX(t,u)${X_{( {t,u} )}}$t‐th component of the u‐th consumerw(t,u)(r)$w_{( {t,u} )}^{( r )}$Weight of the t‐th component of the u‐th consumer in the r‐th iterationσ2Variance of the vector of each clusterEn${E_n}$The entropy functionxzv${x_{zv}}$The decision matrix elementsdn${d_n}$The entropy deviation functionWThe weights of attributesIW$IW$The weights obtained of attributesVThe ideal‐solution/anti‐ideal solutionC, Cm${C_m}$The priority coefficient in the TOPSIS methodrThe elements of the normalized D matrixDThe decision matrixSDistance between each alternative and the ideal solution/anti‐ideal solutionKn${K_n}$The positive coefficient in the entropy methodEn$En$The sum of the errorsαCoefficient of consumer participationa′$a^{\prime}$The unknown regression parameterwThe weights of errorsNThe number of simulated dataRThe regression (dependent variable)AUTHOR CONTRIBUTIONSM.A.: Conceptualization; Data curation; Formal analysis; Funding acquisition; Investigation; Methodology; Project administration; Resources; Software; Supervision; Validation; Visualization; Writing‐original draft; Writing‐review & editing. 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Journal

"IET Generation, Transmission & Distribution"Wiley

Published: Dec 1, 2022

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