Chance-Constrained AC Optimal Power Flow: Reformulations and Efficient Algorithms

Abstract

Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we adopt a chance-constrained AC optimal power flow formulation, which guarantees that generation, power flows and voltages remain within their bounds with a pre-defined probability. We then discuss different chanceconstraint reformulations and solution approaches for the problem. We first describe an analytical reformulation based on partial linearization, which enables us to obtain a tractable representation of the optimization problem. We then provide an efficient algorithm based on an iterative solution scheme which alternates between solving a deterministic AC OPF problem and assessing the impact of uncertainty. The flexibility of the iterative scheme enables not only scalable implementations, but also alternative chance-constraint reformulations. In particular, we suggest two sample based reformulations that do not require any approximation or relaxation of the AC power flow equations.In a case study based on four different IEEE systems, we assess the performance of the method, and demonstrate scalability of the iterative scheme. We further show that the analytical reformulation accurately and efficiently enforces chance constraints in both in-and out-of-sample tests, and that the analytical reformulations outperforms the two alternative, sample-based chance constraint reformulations.

A Chance-Constrained Stochastic Electricity Market

“…Previous studies, e.g., [13], [17], [21], have shown that this approximation limits the joint violation probability effectively due to a few simultaneously active constraints. Further treatment of (2) depends on the assumption made on uncertainty ω.…”

Active Distribution Grids Offering Ancillary Services in Islanded and Grid-Connected Mode

“…In order to consider the impact of generation uncertainty, we follow our previous work [23], [33] and we re-formulate the problem using chance constraints [34], [35]. We assume that the PV power injection is the only source of uncertainty (load uncertainty can be also included in a similar way) and we use as input forecast error distributions with different forecasting horizons (1 to 24 hours ahead).…”

“…E.g., the voltage and current magnitude constraints are reformulated as P {V min ≤ |V j,t | ≤ V max } ≥ 1 − ε and P |I br i,t | ≤ I i max ≥ 1 − ε, respectively. To solve the resulting CC-OPF, we interpret the probabilistic constraints as tightened deterministic versions of the original constraints following the work of [34], [35]. The tightening represents a security margin against uncertainty, i.e., an uncertainty margin.…”

“…where superscript 0 indicates the current or voltage magnitude at the operating point with zero forecast error. Finally, an iterative algorithm is needed, because the uncertainty margins rely on the derived DER setpoints [34], [36]. Consequently, we alternate between solving a deterministic OPF with tightened constraints, and calculating the uncertainty margins…”

Cloud-AC-OPF: Model Reduction Technique for Multi-Scenario Optimal Power Flow via Chance-Constrained Optimization

“…Here in (3) explicit expression for G w , as a function ofx c ,x u , α, is skipped due to space limitations; the objective function is split in two parts, correspondent to mean and fluctuations, respectively. Following the approach of [8]- [10], we are able to evaluate the expectation and the probabilities in (3) analytically. Moreover, the analytic evaluation returns explicit dependencies onx c and α, therefore stating the Cloud-AC-OPF (3) as the following tractable deterministic optimization formulation:…”