Optimal Active-Reactive Power Dispatch Under Competition via Bilevel Programming

Abstract

This paper proposes an active-reactive power dispatch procedure that is expressed via a bilevel optimization problem whose upper and lower level criteria are, respectively, the minimum opportunity cost and minimum offered price of active power. It analyzes the impact of minimizing such criteria on system operation, and it investigates the behavior of marginal prices and opportunity costs and their use in mechanisms to compensate generators for power provision. The bilevel problem is solved using a version of interior point methods derived for mathematical programs with complementarity constraints. Results obtained with three test systems are analyzed.Index Terms-Active-reactive power dispatch under competition, bilevel optimization, opportunity costs.

Bi-Level Programming Approach for the Optimal Allocation of Energy Storage Systems in Distribution Networks

“…Bi-level programming has been widely applied in the field of economic management [29][30][31] and engineering technology [28]. In power system research, bi-level optimization has also been widely applied in research on the pricing and profit problem of power systems [32][33][34][35][36], reactive power optimization [28,37] and transmission capability evaluation. Figure 1 shows the structure of the distribution network studied in this paper.…”

Analysis of the effect of voltage level requirements on an electricity market equilibrium model

“…The companies' behavior is modeled using a strategic game where companies take an action knowing that the rest of companies play in the same way. Among the game theory models are Perfect Competitive models [1,2], Cournot models where companies compete in quantities [3][4][5][6][7][8], Bertrand models where companies compete in prices [3], Supply Function Equilibrium models where strategic behavior is modeled by means of supply functions that combine price and quantity competition [9][10][11][12][13][14][15][16], and Conjetural Variation Based Equilibrium models where the supply functions are parametrized with a parameter known as the company's conjecture [11,[17][18][19][20][21][22][23][24][25].…”

“…However, they only study the congestion caused by the thermal limits of the transmission lines. Therefore, they use a DC approximation of the power flow equations, and it is not possible to analyze other technical constraints such as voltage constraints or reactive power requirements.Few models [2,[7][8][9][10][11]17] study the effect of voltage constraints on the companies' strategic behavior. However, all of them are focused on nodal-price electricity markets, and none of them assess the effect on single-price electricity markets.…”

“…However, all of them are focused on nodal-price electricity markets, and none of them assess the effect on single-price electricity markets. Almeida and Senna [2] proposed a bilevel optimization problem that models the active and reactive power dispatch under competence. The first level corresponds to the active power market and the second level minimizes the opportunity cost of the reactive power which is defined in terms of the marginal price of the power active market.…”

Computation of Worst Operation Scenarios Under Uncertainty for Static Security Management

“…Reference [10] proposes an approximation of BP that avoids nonlinear constraints and reduces the problem to a combinatorial search. References [11] and [12] use an appealing approach that, following the reasoning of the linear case, transforms the BP into a single level nonlinear MPEC optimization problem. However, this approach is risky as nonlinear MPEC problems can present several difficulties: multiple solutions obtained from different initial points [11], [18] and reliability issues [18].…”