Inverse optimization approach to the identification of electricity consumer models

Abstract

Stackelberg game models for demand response management in smart electricity grids have been studied extensively in the scientific literature. Still, a barrier to their practical applicability is the assumption that the retailer (leader in the game) has perfect knowledge about the consumers' (followers') decision model. This paper investigates the possibilities of reconstructing the consumers' decision model from historic tariff and consumption data. For this purpose, it introduces an inverse optimization approach to eliciting the parameters of electricity consumer models formulated as linear programs from the historic samples. The inverse problem is first transformed into a quadratically constrained quadratic program, and then solved using successive linear programming techniques. The approach is demonstrated on a common consumer model with multiple types of deferrable loads behind a single smart meter. Experimental results are presented, and directions for future research are proposed.

Demand response model identification and behavior forecast with OptNet

“…The decision-making process of a price-responsive DR participant can be modeled as an optimization problem with corresponding objective functions and constraints [14,15,[21][22][23][24]. The goal of a DR agent is to minimize its total operation cost, including a timevarying energy cost and a personal disutility cost due to deviations from their normal consumption.…”

“…Inverse optimization formulates DR agent model identification problem as a bi-level optimization problem [14,15,23,24,30], in which the upper-level problem minimizes the mean absolute error of the predicted and actual user demand response, and the lowerlevel problem models the user behavior for DR prediction. The authors in [14] and [15] reduced the bi-level optimization problem to a single-level problem by simplifying the user model and relaxing the complementary slackness conditions due to concerns of computation difficulties, and then solved the problem using heuristic procedure. Due to the heuristic nature of proposed solutions, the algorithm is sensitive to the initial search point and may get stuck in local optima.…”

“…Example 3: Aggregator with Multiple Responsive Loads. We follow the demand response model in [15] to represent an aggregator participating in the demand response program, with 𝐾 different types of price responsive loads and only aggregated load…”

“…With the identified model parameters, we predict agent behavior to future price signals, assuming agent behaviors are stationary. We compare our approach with blackbox neural network models and a benchmark inverse optimization model that are commonly used in the literature [14,15], and the results show that our proposed method achieves orders of magnitude improvements in both the parameter identification accuracy and demand response predictions. We envision future system operators adopting our proposed approach to design ex-ante prices in anticipation of demand response agent behaviors, with the objective to reduce total system operating cost and reduce system volatility.…”

Operations research in Hungary: VOCAL 2018

“…Electricity consumer models are identified by an inverse optimization approach in the paper of Kovács (2021). The method is demonstrated on a common consumer model with multiple types of deferrable loads behind a single smart meter.…”