Moment-Based Relaxation of the Optimal Power Flow Problem

The optimal power flow (OPF) problem minimizes power system operating cost subject to both engineering and network constraints. With the potential to find global solutions, significant research interest has focused on convex relaxations of the non-convex AC OPF problem. This paper investigates ``moment-based'' relaxations of the OPF problem developed from the theory of polynomial optimization problems. At the cost of increased computational requirements, moment-based relaxations are generally tighter than the semidefinite relaxation employed in previous research, thus resulting in global solutions for a broader class of OPF problems. Exploration of the feasible space for test systems illustrates the effectiveness of the moment-based relaxation.Comment: 7 pages, 4 figures. Abstract accepted, full paper in revie

Solution of Optimal Power Flow Problems using Moment Relaxations Augmented with Objective Function Penalization

The optimal power flow (OPF) problem minimizes the operating cost of an electric power system. Applications of convex relaxation techniques to the non-convex OPF problem have been of recent interest, including work using the Lasserre hierarchy of "moment" relaxations to globally solve many OPF problems. By preprocessing the network model to eliminate low-impedance lines, this paper demonstrates the capability of the moment relaxations to globally solve large OPF problems that minimize active power losses for portions of several European power systems. Large problems with more general objective functions have thus far been computationally intractable for current formulations of the moment relaxations. To overcome this limitation, this paper proposes the combination of an objective function penalization with the moment relaxations. This combination yields feasible points with objective function values that are close to the global optimum of several large OPF problems. Compared to an existing penalization method, the combination of penalization and the moment relaxations eliminates the need to specify one of the penalty parameters and solves a broader class of problems.Comment: 8 pages, 1 figure, to appear in IEEE 54th Annual Conference on Decision and Control (CDC), 15-18 December 201

Strategies for Voltage Control and Transient Stability Assessment

As wind generation grows, its influence on power system performance will becoming increasingly noticeable. Wind generation di#11;ffers from traditional forms of generation in numerous ways though, motivating the need to reconsider the usual approaches to power system assessment and performance enhancement. The project has investigated the impact of wind generation on transient stability and voltage control, identifying and addressing issues at three distinct levels of the power system: 1) at the device level, the physical characteristics of wind turbine generators (WTGs) are quite unlike those of synchronous machines, 2) at the wind-farm level, the provision of reactive support is achieved through coordination of numerous dissimilar devices, rather than straightforward generator control, and 3) from a systems perspective, the location of wind-farms on the sub-transmission network, coupled with the variability inherent in their power output, can cause complex voltage control issues. The project has sought to develop a thorough understanding of the dynamic behaviour of type-3 WTGs, and in particular the WECC generic model. The behaviour of such models is governed by interactions between the continuous dynamics of state variables and discrete events associated with limits. It was shown that these interactions can be quite complex, and may lead to switching deadlock that prevents continuation of the trajectory. Switching hysteresis was proposed for eliminating deadlock situations. Various type-3 WTG models include control blocks that duplicate integrators. It was shown that this leads to non-uniqueness in the conditions governing steady-state, and may result in pre- and post-disturbance equilibria not coinciding. It also gives rise to a zero eigenvalue in the linearized WTG model. In order to eliminate the anomalous behaviour revealed through this investigation, WECC has now released a new generic model for type-3 WTGs. Wind-farms typically incorporate a variety of voltage control equipment including tapchanging transformers, switched capacitors, SVCs, STATCOMs and the WTGs themselves. The project has considered the coordinated control of this equipment, and has addressed a range of issues that arise in wind-farm operation. The #12;first concerns the ability of WTGs to meet reactive power requirements when voltage saturation in the collector network restricts the reactive power availability of individual generators. Secondly, dynamic interactions between voltage regulating devices have been investigated. It was found that under certain realistic conditions, tap-changing transformers may exhibit instability. In order to meet cost, maintenance, fault tolerance and other requirements, it is desirable for voltage control equipment to be treated as an integrated system rather than as independent devices. The resulting high-level scheduling of wind-farm reactive support has been investigated. In addressing this control problem, several forms of future information were considered, including exact future knowledge and stochastic predictions. Deterministic and Stochastic Dynamic Programming techniques were used in the development of control algorithms. The results demonstrated that while exact future knowledge is very useful, simple prediction methods yield little bene#12;fit. The integration of inherently variable wind generation into weak grids, particularly subtransmission networks that are characterized by low X=R ratios, aff#11;ects bus voltages, regulating devices and line flows. The meshed structure of these networks adds to the complexity, especially when wind generation is distributed across multiple nodes. A range of techniques have been considered for analyzing the impact of wind variability on weak grids. Sensitivity analysis, based on the power-flow Jacobian, was used to highlight sections of a system that are most severely a#11;ffected by wind-power variations. A continuation power flow was used to determine parameter changes that reduce the impact of wind-power variability. It was also used to explore interactions between multiple wind-farms. Furthermore, these tools have been used to examine the impact of wind injection on transformer tap operation in subtransmission networks. The results of a tap operation simulation study show that voltage regulation at wind injection nodes increases tap change operations. The tradeo#11;ff between local voltage regulation and tap change frequency is fundamentally important in optimizing the size of reactive compensation used for voltage regulation at wind injection nodes. Line congestion arising as a consequence of variable patterns of wind-power production has also been investigated. Two optimization problems have been formulated, based respectively on the DC and AC power flow models, for identifying vulnerable line segments. The DC optimization is computationally more e#14;fficient, whereas the AC sensitivity-based optimization provides greater accuracy