# Incentive-based demand response model for maximizing benefits of electricity retailers

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## Abstract

The change of customer behaviors and the fluctuation of spot prices can affect the benefits of electricity retailers. To address this issue, an incentive-based demand response (DR) model involving the utility and elasticity of customers is proposed for maximizing the benefits of retailers. The benefits will increase by triggering an incentive price to influence customer behaviors to change their demand consumptions. The optimal reduction of customers is obtained by their own profit optimization model with a certain incentive price. Then, the sensitivity of incentive price on retailers’ benefits is analyzed and the optimal incentive price is obtained according to the DR model. The case study verifies the effectiveness of the proposed model.

## Keywords

Demand response Customer utility Price elasticity of demand Retailer profit Incentive price## 1 Introduction

With the progression of the smart grid, demand response (DR) is an effective measure to influence the behaviors of demand side by price policies or incentive compensation when there is a price spike or abnormal incidents, which can ensure the stability and economy of grid operation [1]. For example, DR programs were introduced to induce demand reduction or control prices and incentives in order to improve the efficiency of distributed energy generation [2, 3]. A novel model was proposed to integrate the uncertainties of wind power into the supply side and roof-top solar photovoltaic (PV) on the demand side [4]. In addition, various electrical devices in a smart home, such as electric vehicles and energy storages, can be the flexible loads devoted to DR programs [5, 6, 7]. Particularly, when considering the process optimization of industrial manufacturing, DR programs are economical to apply [8]. Whereas the non-critical load at the residential and commercial levels allows for demand reduction was relatively easy, reducing the demand of industrial processes requires more sophisticated solutions [9].

In current studies, DR can be divided into two types: price-based DR (PBDR) and incentive-based DR (IBDR) [10]. PBDR programs influence customer behaviors through different price policies, where time-of-use (TOU) price is widely applied. Customer response strategies modelled by price elasticity and TOU price can alleviate the risks of supply side and reduce the market energy costs [11]. IBDR programs are popular as they can regulate load by providing incentives to customers [12]. IBDR schemes based on game theory and coupon rewards were proposed to provide a state-dependent compensation [13, 14] in order to ensure the profits of both suppliers and customers. However, new peak load might be created during other periods due to the transferred load with only PBDR programs, which may cause additional cost for retailers to meet the requirement of customers. Besides, the profits of customers from power consumption are not considered. Therefore, only PBDR programs could not guarantee the benefits of suppliers and customers [14].

Meanwhile, the profits of retailers, who gain the benefits from selling electricity and providing related services, should also be considered. Retail choice means that electrical customers can directly choose their suppliers of electricity services, which facilitates the competition to lower energy costs and produce prices that are closer to the “price of free competition” [15]. In [16], an efficient pricing method based on Vickrey–Clarke–Groves (VCG) mechanism, aiming to maximize the social welfare, was proposed to ensure the benefits of customers and retailers. A reward-based DR strategy for a cyber-physical distribution system was designed to maximize retailer benefits [17]. The benefits of both suppliers and customers are equally important in DR programs. Moreover, a genetic algorithm-based distributed pricing optimization algorithm for DR management with the aim to maximize the retailer’s profits was designed in [18]. However, most current studies on DR considering the benefits of customers and retailers mainly focused on the benefit change caused by the fluctuation of price, or made the dispatch plan of retailers from the view of power market dispatch institute in order to minimize the total cost of power system, which is not from the view of retailers and cannot effectively influence customer behaviors or adequately guarantee the profits. And the retailers in the market didn’t take fully advantage of the positivity and flexibility. The incurred consequence is that either retailers or customers might lose benefits in the programs.

In order to influence the behaviors of customers in DR more effectively and maximize the benefits of retailers, this paper innovatively proposes an IBDR model involving customers’ utility and elasticity to maximize retailer benefits. During peak periods, customers determine the optimal demand reduction by solving their own profit optimization model to maximize their benefits based on the utility with a certain incentive price. During valley periods, the optimal demand change is decided by the demand elasticity. Based on the optimization results of customer reduction at various incentive prices, the optimal incentive prices can be obtained by analyzing the sensitivity of incentive prices to retailer benefits according to the DR model that maximizes retailer benefits. Compared with ordinary PBDR model and the IBDR model with constant incentive price, the new DR model considers the benefits of customers without creating new peaks caused by existing DR programs because of the proactive adjustability of incentives, and increases the benefits of retailers.

## 2 DR model

Considering the benefits of retailers, a common DR model based on incentive price involving the load variation of customers is proposed, including the profit optimization of customers and IBDR model.

### 2.1 Customer profit optimization model

*Q*at the retail price

*P*

_{R}. It is assumed that a calendar day has 24 settlement periods and

*k*represents the type of customers. Then, the profits of customers can be described as:

*F*

_{cus,k}represents the profit of customer

*k*;

*Q*

_{k,t},

*P*

_{R,k,t}and

*U*

_{k}(

*Q*

_{k,t}) are the demand, retail price and utility of customer

*k*at time

*t*.

*k*= 1,2,3 represents residential, commercial and industrial customers, respectively.

*α*,

*γ*,

*β*and

*µ*are constants;

*ω*represents the customer willingness to reduce their demand. All the parameters can be obtained based on the statistic assessment of local customer behaviors.

The elasticity and utility of customers are introduced to examine the impact of load variations in valley and peak periods in the letter respectively.

*Q*

_{k,t}is the load reduction of customer

*k*at time

*t*;

*P*

_{C,k}is the incentive price customer

*k*received.

By solving M1 and (7), the optimal customers’ reduction with a certain incentive price in peak periods can be calculated.

### 2.2 IBDR model

*Q*at the spot price

*P*

_{S,t}lower than the retail price

*P*

_{R,k,t}, and then sell it to customers. In this case, retailer benefits are equivalent to their financial loss. Then, the loss of retailers can be described as negative profits

*F*

_{ret}:

*a*

_{i},

*b*

_{i},

*c*

_{i}and

*d*

_{i}are the coefficients;

*i*represents the type of distribution of spot price.

*P*

_{S,i,t}is the spot price followed distribution

*i*at time

*t*. When

*i*= 1, the load is low.

*P*

_{S,i,t}follows the distribution:

*i*= 2, the load is high.

*P*

_{S,i,ft}follows the distribution:

The actual value of spot electricity *P*_{S,i,t} can be obtained by integrating the above two spot electricity price probability density as shown in (10) and (11).

*Q*

_{t}− Δ

*Q*

_{t}and gain a compensation. In the same way, customers can receive an incentive to increase consumption during valley periods, where Δ

*Q*

_{t}is negative. For maximizing retailer benefits, the IBDR model M2 is formulated as:

According to (5)–(7), the optimal customer reduction in the peak period and variation in valley periods can be obtained with different incentive prices. Then according to the optimization model M2 and the optimal demand variation of customers obtained by M1 and (7), the optimal incentive that retailers pay can be gained by analyzing the sensitivity of incentive price to retailers’ benefits prices.

### 2.3 Flowchart of proposed IBDR model

## 3 Case study

The typical residential, commercial, industrial customers in a selected area are used to validate the proposed model. The demand and retail price dataset of the customers in 24 hours is acquired. The main inputs including price and demand can be found in [22]. The optimization model is programmed with MATLAB Yalmip toolbox. By solving M1, the optimal customer reduction points can be obtained at a certain *P*_{C}. And then the optimal reduction at various incentive prices can be inputs of M2 to realize the maximization of retailer benefits.

### 3.1 Retailer benefits in peak periods based on DR model

As built in (2)–(4), the utility of commercial and industrial customers conforms to the logarithmic distribution, while the utility of residential customers is a piecewise function. With the parameter *ω* increasing, the value of customer utility becomes higher.

Besides, the retailer benefits applied the ordinary PBDR programs and IBDR with a constant incentive price are respectively $3698603 and $4127140, which is less than the benefits with the proposed model. Comparing with ordinary PBDR and IBDR model, the proposed DR model in this letter has better effect on controlling load peak and increasing retailer’s benefits.

### 3.2 Retailer benefits in peak and valley periods based on DR model

## 4 Conclusion

In this paper, an incentive-based demand response model is proposed to maximize the benefits of electricity retailers. The innovation is that the models involve the utility and elasticity of various customers, considering their different behaviors during both peak and valley periods. By solving the customer profit optimization model in peak periods, the optimal reduction of customers with a certain incentive price can be obtained. During valley periods, the variation of customers can be calculated according to the elasticity with a certain incentive price. Then through analyzing the sensitivity of incentive prices to retailer benefits, the optimal incentive price can be found based on the proposed DR model. Results show that retailers can maximize the benefits with the proposed model.

## Notes

### Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (No. 51807127), in part by the Fundamental Research Funds for the Central Universities of China (No. YJ201654), in part by the National Key Research and Development Program of China (No. 2018YFB0905200).

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