Bilevel programming approach to demand response management with day-ahead tariff

András Kovács

doi:10.1007/s40565-019-0569-7

Abstract

This paper introduces a bilevel programming approach to electricity tariff optimization for the purpose of demand response management (DRM) in smart grids. In the multi-follower Stackelberg game model, the leader is the profit-maximizing electricity retailer, who must set a time-of-use variable energy tariff in the grid. Followers correspond to groups of prosumers (simultaneous producers and consumers of the electricity. They response to the observed tariff, schedule controllable loads and determine the charging/discharging policy of their batteries to minimize the cost of electricity and to maximize the utility at the same time. A bilevel programming formulation of the problem is defined, and its fundamental properties are proven. The primal-dual reformulation is proposed in this paper to convert the bilevel optimization problem into a single-level quadratically constrained quadratic program (QCQP), and a successive linear programming (SLP) algorithm is applied to solve it. It is demonstrated in computational experiments that the proposed approach outperforms typical earlier methods based on the Karush–Kuhn–Tucker (KKT) reformulation regarding both solution quality and computational efficiency on practically relevant problem sizes. Besides, it also offers more flexible modeling capabilities.

Highlights

A key to the stable operation of future electricity grid is realizing efficient demand response management (DRM)
The bilevel program is firstly transformed into an equivalent single-level optimization problem using a primal-dual reformulation, and solved using a successive linear programming (SLP) algorithm
The baseline model may trigger inappropriate end-of-horizon effects, namely, the followers sell all the energy stored in the batteries to maximize their revenue. This can be avoided by subtracting a term that valuates the energy stored in the batteries at the end of the planning horizon from the followers objective (5) as follows: As an alternative to the proposed solution, KKT reformulation and linearization can be applied to convert the proposed bilevel model (15)–(19) into a single-level mixed-integer linear program (MILP)

Summary

Introduction

A key to the stable operation of future electricity grid is realizing efficient demand response management (DRM). Electricity consumption is becoming more controllable due to new types of loads and storage (e.g., electric vehicles, home-level or small business energy management solutions) and various intelligent appliances at end consumers. The critical success factor for efficient DRM is an appropriate electricity tariff that motivates consumers to schedule their loads and manage their batteries in such a way that it contributes to grid stability. This paper studies the problem of optimizing the electricity tariff offered by an electricity retailer to its customers in a game theoretical setting. A bilevel programming approach is introduced, where the retailer is the leader and the groups of end consumers act as multiple independent followers. The bilevel program is firstly transformed into an equivalent single-level optimization problem using a primal-dual reformulation, and solved using a successive linear programming (SLP) algorithm

Methods

Findings

Discussion

Conclusion