Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes Deriving nonlinear models for incentive-based demand response programs Habib Allah Aalami a , Hamed Pashaei-Didani b , Sayyad Nojavan c, ⁎ a Department of Electrical and Computer, University of Eyvanekey, Tehran, Iran b Faculty of Electrical and Computer Engineering, University of Tabriz, P.O. Box: 51666-15813, Tabriz, Iran c Department of Electrical Engineering, University of Bonab, P.O. Box: 55517-61167, Bonab, Iran ARTICLE INFO Keywords: Customer benefit function Load economic model Price elasticity Incentive based demand response programs Nonlinear models ABSTRACT In the restructured electricity markets, the demand response programs (DRPs) are defined as participation of the retail consumers to observe and respond to changing prices over the time. Generally, DRPs are classified as incentive-based and time-based programs. By using the precise modeling of DRPs, the operator of the system can study the effect of price responsive loads in reliability and economic aspects of the system. In this paper, a nonlinear model of incentive-based DRP is developed based on the price elasticity of demand and benefit function of the customer. The behaviors of the derived models against elasticity change, incentive, penalty and potential of implementation are examined and degree of the reliance is determined. In order to investigate the performance of the proposed model, a numerical study is provided derived from a real world power system. The comparison results show that the power structure as non-linear model is the most conservative while the linear model is the most non-conservative. 1. Introduction A variety of operational and financial benefits is offered by DRP for load-serving entities, grid operators, and electricity customers. Variation of grid condition in different periods, highly capital-incentive system, and economics of electricity storage as well as long lead in- vestment time are the most important characteristics of the power system. These features besides the different uncertainty sources in the system are the main reasons to implement DRPs, which can provide flexibility at a considerably low cost [1,2]. The efficient operation of an electricity market relies on the proper interaction between demand and supply. The demand response pro- grams have some barriers, which are innate in the electricity markets. Different organizations and players in the electricity markets such as reliability organizations, distribution companies, transmission compa- nies, and electric end-users can use the benefits of the DPP [3,4]. The most notable advantages of the DRP can be summarized as follows: • decreased electricity energy prices • Reducing volatility of the power price • Increasing efficiency in the energy intensive industries • Risk management • Increasing choice and risk management opportunities of the cus- tomer • Environmental benefits • Market power mitigation [5]. Regarding the demand, properly modeling of the way that con- sumers react against the time-dependent electricity prices is essential. It is seen that when the consumer faced by the very large or sudden power price increases, they tend to curtail their electricity consumption. Although, during the long term, in order to cope with periodic fluc- tuations, the consumers try to shift their load demand to balance the potential cost saving against the extra or inconvenience expense which is obtained by changing the consuming time [6,7]. Developing a model, which properly presents the effects of DRP as part of a forward-looking network plan/operation is the main challenge of implementing and planning of the DRPs. Providing a framework to address both the economic and financial aspects of the system is the only way to solve the problem. Developing models, which are responsive to the power price, is essential to assay the effects of DRPs on different characteristics of market and network such as reserve margin, load profile, transmis- sion congestion, etc. It is obvious that many feasible structural forms are provided for the customer response. In [8–10], linear models of price responsive loads are developed for the DRPs. Developing eco- nomic nonlinear models for price responsive loads are required because of the nonlinear formulation of the customer profit problem, which gives more realistic modeling of the demand. Implementing various https://doi.org/10.1016/j.ijepes.2018.10.003 Received 22 July 2018; Received in revised form 3 September 2018; Accepted 5 October 2018 ⁎ Corresponding author. E-mail addresses: h.aalami41@eyc.ac.ir (H.A. Aalami), h.pashaei96@ms.tabrizu.ac.ir (H. Pashaei-Didani), sayyad.nojavan@bonabu.ac.ir (S. Nojavan). Electrical Power and Energy Systems 106 (2019) 223–231 0142-0615/ © 2018 Elsevier Ltd. All rights reserved. T