### Abstract

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.

Original language | English |
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Title of host publication | 2013 IEEE International Conference on Smart Grid Communications, SmartGridComm 2013 |

Pages | 151-156 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2013 |

Event | 2013 IEEE International Conference on Smart Grid Communications, SmartGridComm 2013 - Vancouver, BC, Canada Duration: 2013 Oct 21 → 2013 Oct 24 |

### Other

Other | 2013 IEEE International Conference on Smart Grid Communications, SmartGridComm 2013 |
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Country | Canada |

City | Vancouver, BC |

Period | 13/10/21 → 13/10/24 |

### Fingerprint

### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*2013 IEEE International Conference on Smart Grid Communications, SmartGridComm 2013*(pp. 151-156). [6687949] https://doi.org/10.1109/SmartGridComm.2013.6687949

**Convex hull pricing for demand response in electricity markets.** / Ito, Naoki; Takeda, Akiko; Namerikawa, Toru.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2013 IEEE International Conference on Smart Grid Communications, SmartGridComm 2013.*, 6687949, pp. 151-156, 2013 IEEE International Conference on Smart Grid Communications, SmartGridComm 2013, Vancouver, BC, Canada, 13/10/21. https://doi.org/10.1109/SmartGridComm.2013.6687949

}

TY - GEN

T1 - Convex hull pricing for demand response in electricity markets

AU - Ito, Naoki

AU - Takeda, Akiko

AU - Namerikawa, Toru

PY - 2013

Y1 - 2013

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

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

U2 - 10.1109/SmartGridComm.2013.6687949

DO - 10.1109/SmartGridComm.2013.6687949

M3 - Conference contribution

AN - SCOPUS:84893592888

SN - 9781479915262

SP - 151

EP - 156

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

ER -