Reactive power planning under conditional‐value‐at‐risk assessment using chance‐constrained optimisation

Abstract

This study presents a risk-assessment approach to the reactive power planning problem. Chance-constrained programming is used to model the random equivalent availability of existing reactive power sources for a given confidence level. Load shedding because of random equivalent availability of those reactive power sources is implemented through conditional-value-at-risk. Tap settings of under-load tap-changing transformers are considered as integer variables. Active and reactive demands are considered as probability distribution functions. The proposed mathematical formulation is a two-stage stochastic, multi-period mixed-integer convex model. The tradeoff between risk mitigation and investment cost minimisation is analysed. The proposed methodology is applied to the CIGRE-32 electric power system, using the optimisation solver CPLEX in AMPL. NomenclatureThe following notations used throughout this paper are described below. The operators E, Pr, Var and Std are used as expectation, probability, variance and standard deviation measures, respectively.

A Data-Driven Stochastic Reactive Power Optimization Considering Uncertainties in Active Distribution Networks and Decomposition Method

“…This model is actually a large-scale mixed-integer nonlinear programming and several techniques including intelligent searches and standard branch-and-bound/cut methods were proposed to solve this complex model [4]- [6]. With a proposal of a two-stage multi-period mixed-integer convex model, [7] analyzed the tradeoff between risk mitigation and investment cost minimization. In [8], a voltage security constrained multi-period optimal reactive power flow model was proposed based on the generalized Benders decomposition method with an optimal condition decomposition approach to solve it.…”

“…where (2) aims to minimize total network loss over T time periods; (3)-(4) denote the power balance at each bus; (5)- (7) show the Ohm's law for each branch, including (6) for transformer branch; (8) shows a choice constraint by which only one trap ratio level is chosen; (9)-(10) are constraints for voltage magnitude and branch current; (11) is the constraint for the continuous reactive power compensators; (12)-(13) are the constraints for discrete reactive power compensators; (14)- (15) are restrictions that the total allowable operational times by discrete adjustment equipment should be limited. However, the model (2)-(17) is a mixed integer nonlinear nonconvex programming which is very difficult to solve.…”

Dependent-Chance Programming on Sugeno Measure Space

“…The first method of uncertain mathematical programming is the expected value model (EVM) [1][2][3][4] which optimizes the expected objective functions to satisfy some expected constraints. The second method is named chance-constrained programming (CCP) [5][6][7][8][9][10] which is a way to solve optimization problems by assigning a confidence level at which the constraint holds. Occasionally, a complex decision system undertakes multiple tasks called events, and the decision maker wishes to maximize the chance functions of satisfying some events [11].…”

Reactive power optimisation considering wind farms based on an optimal scenario method

“…At present, there are mainly three ways to deal with the volatility of wind power in RPO model, i.e. stochastic programming [5–9], wind power prediction [10, 11] and RP [12–15]. As for stochastic programming, CCP method [16] is mostly used ways to solving RPO.…”

“…However, stochastic programming methods generally demand a priori knowledge of wind speed distribution, and are time‐consuming due to usage of Monte Carlo procedure. These demerits make CCP method mainly used in the long‐term optimal reactive power planning [8, 9]. To avoid MCS, wind power prediction is used to remove the necessity of using wind speed distribution.…”