# Calculation Method for Electricity Price and Rebate Level in Demand Response Programs
## 1 Introduction  
Demand response programs (DRs) are defined as changes in electricity-consuming patterns in response to changes in electricity price or to incentive payment [1]. There are two major categories in DRs: one is the price-based DR, and the other is the incentive-based one. Time of use (TOU), real-time pricing (RTP), and critical-peak pricing (CPP) are well-known as the former. Unit prices of the electric power in these DRs become expensive during the periods of high electricity costs or critical power grid's conditions (peak periods) in comparison with those in off-peak periods. On the other hand, peak time rebate (PTR) and critical peak rebate (CPR) are categorized into the latter. In incentive-based DRs, power suppliers (or power producers, retailers, etc.) reward consumers, who respond to the request of DRs, with money rebates. Since DRs bring controllability in the power demand without huge investment costs in power plants or facilities, they have been attracting attention as one of the most economical and sustainable alternatives to traditional power supply-demand-balancing operations. Therefore, many DR-related studies have been carried out [2; 3; 4], as well as demonstrative field tests.  
There are various studies contributing to the design of DRs. In [5], states of DR-related activities are analyzed with highlighted deregulation in electricity markets. The authors in [5] defined evaluation indices and discussed effects of DRs in electricity prices. Reference [6] reviews the means by which power suppliers induce their preferable electricity consumption in DRs. Several mathematical problem frameworks and models are summarized, and their solution techniques are introduced. In [7], DRs are classified fromthe viewpoints of their control mechanisms, motivations offered to changes in electricity consuming patterns, and decision variables. Besides, several models for optimizing control strategies of the DRs are categorized in association with the application targets. The authors in [8] focused on price-based DRs and evaluated their advantages and disadvantages with experimental results. This reference also includes a review of case study results of the DRs in several countries. Reference [9], similarly, summarizes results of case studies, and its authors analyzed them to discuss preferable price settings in price-based DRs.  
Although these references indicate a great deal of useful information in the design of DRs, there are still difficulties on settings of electricity prices or rebate levels while ensuring resources of DRs. In fact, electricity prices or rebate levels in field tests have been decided, relying on knowledge, experience, and experimental results [10; 11; 12; 13; 14; 15; 16], and thus, it is difficult to discuss on the appropriateness of their settings. For these reasons, the design of efficient DRs becomes a crucial component for advancing technologies of the power grids' management.  
This paper presents a theoretical approach that calculates electricity prices and rebate levels in DRs. To set the basis of discussion, the framework of social welfare maximization (SWM), which has often been used to represent models of electricity markets [6; 7; 17; 18; 19; 20; 21], is applied. First, the authors set the utility functions of the power suppliers and the consumers and represent the power supply-demand-balancing operation under the SWM framework. In the process, contributions of the DRs become measurable as an increment/decrement in the utility functions. As a result, we can treat the DR-originated changes in the power demand as an influential factor in the power supply-demand management. Next, acceptable conditions of electricity prices and rebate levels are derived as a guide for the DR request, and then, their optimal values are defined in consideration of burden on both power suppliers and consumers. Finally, the validity of the authors' proposal is verified through numerical simulations with a model constructed by using the actual record of the electricity consumption.