TY - GEN

T1 - Convex hull pricing for demand response in electricity markets

AU - Ito, Naoki

AU - Takeda, Akiko

AU - Namerikawa, Toru

PY - 2013/12/1

Y1 - 2013/12/1

N2 - Dynamic pricing (a.k.a. real-time pricing) is a method of invoking a response in demand pricing electricity at hourly (or more often) intervals. Several studies have proposed dynamic pricing models that maximize the sum of the welfares of consumers and suppliers under the condition that the supply and demand are equal. They assume that the cost functions of suppliers are convex. In practice, however, they are not convex because of the startup costs of generators. On the other hand, many studies have taken startup costs into consideration for unit commitment problems (UCPs) with a fixed demand. The Lagrange multiplier of the UCP, called convex hull pricing (CHP), minimizes the uplift payment that is disadvantageous to suppliers. However, CHP has not been used in the context of demand response. This paper presents a new dynamic pricing model based on CHP. We apply CHP approach invented for the UCP to a demand response market model, and theoretically show that the CHP is given by the Lagrange multiplier of a social welfare maximization problem whose objective function is represented as the sum of the customer's utility and supplier's profit. In addition, we solve the dual problem by using an iterative algorithm based on the subgradient method. Numerical simulations show that the prices determined by our algorithm give sufficiently small uplift payments in a realistic number of iterations.

AB - Dynamic pricing (a.k.a. real-time pricing) is a method of invoking a response in demand pricing electricity at hourly (or more often) intervals. Several studies have proposed dynamic pricing models that maximize the sum of the welfares of consumers and suppliers under the condition that the supply and demand are equal. They assume that the cost functions of suppliers are convex. In practice, however, they are not convex because of the startup costs of generators. On the other hand, many studies have taken startup costs into consideration for unit commitment problems (UCPs) with a fixed demand. The Lagrange multiplier of the UCP, called convex hull pricing (CHP), minimizes the uplift payment that is disadvantageous to suppliers. However, CHP has not been used in the context of demand response. This paper presents a new dynamic pricing model based on CHP. We apply CHP approach invented for the UCP to a demand response market model, and theoretically show that the CHP is given by the Lagrange multiplier of a social welfare maximization problem whose objective function is represented as the sum of the customer's utility and supplier's profit. In addition, we solve the dual problem by using an iterative algorithm based on the subgradient method. Numerical simulations show that the prices determined by our algorithm give sufficiently small uplift payments in a realistic number of iterations.

UR - http://www.scopus.com/inward/record.url?scp=84893592888&partnerID=8YFLogxK

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U2 - 10.1109/SmartGridComm.2013.6687949

DO - 10.1109/SmartGridComm.2013.6687949

M3 - Conference contribution

AN - SCOPUS:84893592888

SN - 9781479915262

T3 - 2013 IEEE International Conference on Smart Grid Communications, SmartGridComm 2013

SP - 151

EP - 156

BT - 2013 IEEE International Conference on Smart Grid Communications, SmartGridComm 2013

T2 - 2013 IEEE International Conference on Smart Grid Communications, SmartGridComm 2013

Y2 - 21 October 2013 through 24 October 2013

ER -