Feasible Path Identification in Optimal Power Flow With Sequential Convex Restriction

Abstract

Nonconvexity induced by the nonlinear AC power flow equations challenges solution algorithms for AC optimal power flow (OPF) problems. While significant research efforts have focused on reliably computing high-quality OPF solutions, identifying a feasible path from an initial operating to a desired operating point is a topic that has received much less attention. However, since the feasible space of the OPF problem is nonconvex and potentially disconnected, it can be challenging to transition between operating points while avoiding constraint violations. To address this problem, we propose an algorithm which computes a provably feasible path from an initial operating point to a desired operating point. The algorithm solves a sequence of quadratic optimization problems over conservative convex inner approximations of the OPF feasible space, each representing a so-called convex restriction. In each iteration, we obtain a new, improved operating point and a feasible transition from the operating point in the previous iteration. In addition to computing a feasible path to a known desired operating point, this algorithm can also be used to locally improve the operating point. Extensive numerical studies on a variety of test cases demonstrate the algorithm and the ability to arrive at a high-quality solution in few iterations. I. INTRODUCTIONAC optimal power flow (OPF) is a fundamental optimization problem in power system analysis The classical form of an OPF problem [1] seeks an operating point that is feasible (i.e., satisfies both the AC power flow equations that model the network physics and the inequality constraints associated with operational limits on voltage magnitudes, line flows, generator outputs, etc.) and economically efficient, i.e., achieves minimum operational cost. Significant research efforts have focused on obtaining locally and globally optimal OPF solutions using algorithms based on local search, approximation, and relaxation techniques [2]- [5]. While previous research has improved the computational tractability of OPF algorithms and the quality of the resulting solutions, a number of challenging issues remain. One such issue is to determine a sequence of control actions that facilitate a safe transition from the current operating point to the desired operating point [6], [7].Previous literature has considered the problem of determining a limited number of active and reactive power redispatch [8]-[10] required to bring the system to a new safe or optimal operating point. References such as [9], [10] consider the sequence as a set of individual control actions, where the operating point after each action must be steady-state feasible. While this improves security relative to a setting where intermediate feasibility is not considered, the feasible space of the AC OPF problem is nonconvex and sometimes disconnected [11]. Hence, a feasible path connecting the two steady-state operating points (where each intermediate state is

Robust AC Optimal Power Flow with Robust Convex Restriction

“…This section introduces the OPF problem with consideration of uncertainty in power injections. We use a distributed slack generator formulation, generalizing the model in [21], [22]. The distributed slack plays an important role in determining the generators' response to the uncertain power injections.…”

“…where the matrices G c , G s , B c , B s ∈ R n b ×n l and G d , B d ∈ R n b ×n b are transformed admittance matrices for the respective conductance and susceptance terms. The exact definitions of the transformed matrices are available in [22]. The objective c : R ng → R is a monotonically increasing function of the active power generation.…”

“…In this paper, we address this open problem using convex restriction techniques [21] that provide convex sufficient conditions which ensure feasibility of both the AC power flow equations and the operational constraints in OPF problems. We previously used convex restrictions to solve OPF problems and compute feasible paths connecting different operating points [22] via sequential convex restriction, i.e., solving a sequence of convex quadratic problems formulated using convex restriction techniques. In this paper, we utilize the convex restriction to enforce robust feasibility.…”

Security Enhancement in Power System Using FACTS Devices and Atom Search Optimization Algorithm

“…Optimal power flow can be solved by various FACTS techniques and devices, which certainly allow safety restrictions in the power system. System security is guaranteed by the optimal placement of the FACTS device in the system, for example, SVC, TCSC [6], Thyristor-Controlled Phase-Shifting Transformer (TCPST), Static Synchronous Compensator (STATCOM) [5], UPFC [7] Thyristor-Controlled Voltage Regulator (TCVR), and IPFC [8]. The FACTS devices should provide the highest advantage to power networks for maintaining stability and security constraints.…”

Robust optimal operation of future power systems under uncertainties

“…A TR-SLP Approach for AC-OPF can be extended to find feasible paths from an initial set-point to a better optimal set-point, cf. [106]. Consequently, such methods have the potential to compute OPF solutions which are robust against plausible uncertain power injections by RESs.…”