Hsiao-Dong Chiang

The feasible region of Alternating Current Optimal Power Flow (ACOPF) models often comprises multiple disjoint feasible components. Each feasible component may contain one or more local optimal solutions (LOSs). Conventional ACOPF solution methodologies typically compute only a single OPF solution and may thereby overlook potential high-value alternative OPF solutions. This paper presents a deterministic numerical method, PGS-TT, to systematically compute all LOSs within each feasible component. PGS-TT integrates the Projected Gradient System with the Trust-Tech framework. This deterministic four-stage method consists of: (1) converging to an LOS; (2) escaping from the current LOS and moving toward another possible OPF solution; (3) detecting the existence of another LOS; and (4) computing the newly detected OPF solution. The proposed numerical PGS-TT method is enhanced by several novel numerical schemes designed to ensure computational efficiency and scalability for large-scale ACOPF models. The method's effectiveness is demonstrated on several modified IEEE test systems: 118-bus, 500-bus, 1,888-bus, and 30,000-bus. Notably, numerical studies reveal several OPF cases where the higher-cost OPF solution exceeds the lower-cost one by up to 51.45%, highlighting the critical need to compute multiple high-quality LOSs to improve the security and economic efficiency of power system operation and planning.

A theory-based Projected Gradient System (PGS)-based Transformation Under Stability-reTaining Equilibria Characterization (Trust-Tech, TT) method, termed PGS-TT, is proposed to systematically and deterministically compute multiple AC Optimal Power Flow (ACOPF) solutions within a feasible component. The theoretical basis for the PGS-TT method is rigorously established, including: (i) a one-to-one correspondence between stable equilibrium points (SEPs) of the PGS and local optimal solutions of ACOPF models; (ii) each feasible component is an invariant set of the PGS and consists of the closures of the stability regions of the SEPs located in that feasible component; (iii) each stability region contains exactly one OPF solution, which eliminates redundant searches for additional OPF solutions within the same stability region; and (iv) the existence conditions of multiple OPF solutions that are linked to the existence of PGS stability boundaries. Theorems and the proposed PGS-TT method are illustrated on 3-bus and 9-bus systems exhibiting multiple local OPF solutions. Additionally, the scalability of the implemented PGS-TT method is discussed based on large-scale systems, with network sizes ranging from 1,888 to 30,000 buses, underscoring its potential for complex power-grid optimization.

Electric power systems are undergoing a fundamental transition from synchronous generator (SG)‐dominated systems to inverter‐based resource (IBR)‐dominated systems. Lyapunov‐ and energy‐function‐based direct methods provide an effective way to estimate the stability region, also known as the region of attraction (ROA), and have become a fundamental tool for transient stability assessment (TSA). However, the fundamentally different large‐signal dynamics of IBRs make ROA estimation considerably more challenging, leading to a wide variety of Lyapunov‐function‐based methods. Motivated by these developments, this paper presents a methodology‐oriented review of Lyapunov‐function‐based ROA estimation for IBR‐dominated power systems. The review categorises existing methods into analytical and nonanalytical approaches, with the latter further classified into numerical Lyapunov, Lyapunov‐expansion and neural‐Lyapunov methods. For analytical approaches, the complete set of existing Lyapunov‐ and energy‐function constructions is reviewed and, where possible, extended to different IBR types. Nonanalytical methods are comparatively reviewed in terms of their underlying principles and scalability. The review clarifies the applicability of analytical and nonanalytical ROA estimation. Although systems containing grid‐following inverters generally do not admit a global energy function, heterogeneous systems composed of grid‐forming and voltage‐forming inverters remain amenable to analytical energy‐function‐based analysis. In contrast, nonanalytical methods provide broader applicability at the expense of substantially higher computational effort. Representative methods are reproduced and quantitatively compared in terms of conservativeness and computational complexity. The strengths and limitations of each method, practical engineering implementation and future research directions of the reviewed methods are finally summarised. This review provides a systematic reference for ROA estimation and its applications in TSA of IBR‐dominated power systems.

Grid-following (GFL) inverters have very different large-signal stability characteristics to synchronous generators. Existing studies mainly focus on the synchronization stability of an individual GFL inverter, while interactions between multiple inverters are less often addressed. This paper elucidates interaction mechanisms between heterogeneous inverters, covering GFL, grid-forming (GFM), and grid-supporting (GSP) types, to determine stability boundaries of systems with mixed inverter compositions. The generalized large-signal model for two-inverter systems is derived for various inverter combinations. This establishes that systems containing GFL inverters do not admit a global energy function, fundamentally limiting the applicability of traditional direct methods. To overcome this barrier, a manifold method is employed to determine the region of attraction (ROA). To address the computational complexity of the manifold method, reduced-order models of inverter are used. The large-signal stability margin is assessed by the shortest distance from a stable equilibrium point (SEP) to the boundary of the ROA, termed the stability radius (SR). Using the proposed framework, results of two-inverter system show that both GFM and GSP inverters significantly enhance large-signal stability where the other inverter is GFL, with GFM providing slightly superior performance. All findings are validated through both EMT simulations and power hardware-in-the-loop (PHIL) experiments.

This paper proposes a novel methodology for solving the state estimation (SE) problem with a global convergence property. The prevalent WLS-Gauss-Newton (WLS-GN) method may suffer from numerical divergence. To address this issue, we develop a Trajectory-Unified (TJU) method that employs a nonlinear dynamic system derived from the measurement constraints of the state estimation problem to ensure a SE solution if it exists. Consequently, the proposed WLS-TJU SE method serves as a valuable enhancement to the traditional WLS-GN, improving both the convergence property and robustness in power system state estimation. It is theoretically proven that the derived nonlinear dynamic system is completely stable, rendering the proposed WLS-TJU method a desired property–global convergence. From a theoretical viewpoint, numerical studies of the convergence regions of estimated SE solutions using both the WLS-GN and the proposed WLS-TJU SE method under various loading conditions and under different levels of measurement redundancy are conducted. The evaluation metric for the degree of convergence is the size of the convergence region. From a robustness viewpoint, the advantages of the proposed method in terms of convergence and robustness to network topology errors and loading conditions; particularly several cases are shown that the WLS-GN method diverges while the proposed WLS-TJU converges. Computationally speaking, the computational performance in large-scale systems including the 3120-bus system of the proposed SE method is also highlighted. The proposed WLS-TJU SE method shows a computational advantage of 3.22 times faster than the traditional WLS SE method in a 3120-bus system.

Alternating Current Optimal Power Flow (ACOPF) model is nonconvex and generally has multiple local optimal solutions (LOSs) distributed across multiple feasible components of its feasible region. In this paper, a novel, theory-based dynamic method, named QGS-TT, is proposed to compute multiple feasible solutions located in different disconnected feasible components. The proposed method incorporates a dynamic transformation that converts the feasible region of ACOPF problem into the union of regular stable equilibrium manifolds (RSEMs) through the construction of a quotient gradient system (QGS). Furthermore, the Transformation Under Stability Retaining Equilibria Characterization (Trust-Tech, TT) methodology is extended to explore the solution space in a tier-by-tier manner systematically. Starting from an arbitrary initial point, assisted by a QGS-based numerical method to detect the existence of, and then computation of other feasible components, supported by the stability boundary theory (properties). Five numerical studies are conducted on the IEEE 2-, 9-, 39-, 118-, and 500-bus systems, each of which exhibits multiple OPF solutions with significantly different objective function values. Regarding computational performance, it will be shown that the method is significantly faster than an existing one.

Power system state estimation (SE) is routinely performed in modern energy control centers using the weighted least squares (WLS) method to provide reliable inputs for advanced applications in energy management systems. The accuracy of the SE solution is crucial but can be easily affected by various factors, including gross errors in measurements, among others. In real-time applications, the selection of appropriate weights for measurements is one important factor influencing the accuracy of the WLS method. However, current schemes for weight adjustment may be ad-hoc in nature, lacking substantial theoretical support, which necessitates an iterative process for fine-tuning weight factors. To provide theoretical support and guidance for tuning weight factors in the WLS method, this paper establishes a theoretical foundation for the weight adjustment procedure in SE. A weight adjustment model for the WLS method is proposed by incorporating inequality constraints on uncertain measurements and the performance-driven, residual-based requirements to seek feasible weight adjustment. Given a weight adjustment problem in SE, a necessary and sufficient condition for the existence of a feasible weight adjustment scheme will be established. As a by-product, a weight adjustment scheme is obtained by the proposed method once the existence of feasible adjusted weight vectors is established. Both numerical validation of the derived theoretical results and performance evaluations of an obtained feasible adjustment factor are conducted on the IEEE 14-bus and 118-bus systems to illustrate the derived theorems and the numerical performance of the weight adjustment scheme for the SE problem.

This paper reports the second part of a two-part investigation into a novel Augmented Quotient Gradient System (AQGS) method for solving the general AC Optimal Power Flow (OPF) problem. The first part established the theoretical groundwork for the AQGS algorithm, providing formal justification for its advantages. In this second part, we detail the implementation of the robust numerical AQGS algorithm and introduce an enhanced version, referred to as the TJU-enhanced AQGS method, which was designed to improve computational efficiency. Both approaches demonstrate strong convergence, rapid computation, and exceptional robustness, particularly when applied to large-scale OPF problems involving 1888-, 2736-, and 13,695-bus systems. Notably, these methods consistently converge to the optimal solution within a single iteration across multiple test cases.