Over the past half-century, Optimal Power Flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey (this article) provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF.

Optimal power flow: a bibliographic survey I

The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks.

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Exact Convex Relaxation of Optimal Power Flow in Radial Networks

Locating series FACTS devices for congestion management in deregulated electricity markets

Solution approaches to chance constrained programming (CCP) have been recently developed and applied in many areas for optimization under uncertainty. Due to the nonlinear model with multiple uncertain variables as well as multiple output constraints, CCP has not been directly applied to optimal power flow (OPF) under uncertainty. The objective of this paper is twofold. First, we introduce the CCP approach to OPF under uncertainty and analyze the computational complexity of the chance constrained OPF. Second, the effectiveness of implementing a back-mapping approach and a linear approximation of the nonlinear model equations to solve the formulated CCP problem is investigated. Load power uncertainties are considered as multivariate random variables with correlated normal distribution. Based on both the nonlinear and the linearized model, results of a five-bus system and the IEEE 30-bus test system are presented to demonstrate the scope of chance constrained OPF.

Chance Constrained Programming for Optimal Power Flow Under Uncertainty

From the viewpoint of operational planning, this paper focuses on the evaluation of the impact of FACTS control on available transfer capability (ATC) enhancement. Technical merits of FACTS technology on ATC boosting are analyzed. An optimal power-flow-based ATC enhancement model is formulated to achieve the maximum power transfer of the specified interface with FACTS control. For better studying the capability of FACTS control, a power injection model of FACTS devices, which enables simulating the control of any FACTS devices, is employed. Studies based on the IEEE 118-bus system with all categories of FACTS devices demonstrate the effectiveness of FACTS control on ATC enhancement.

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Available transfer capability enhancement using FACTS devices

This paper focuses on developing an approach to steady-state power flow control of flexible AC transmission systems (FACTS) device-equipped power systems. Based on a power-injection model of FACTS devices and an optimal power flow model, a novel versatile power flow control approach is formulated, which is capable of implementing power flow control incorporating any FACTS device flexibly. Different from existing FACTS device control approaches, the active and (or) reactive power injections are taken as independent control variables. Therefore, using this method, Jacobian matrix need not be changed, although various FACTS devices possess different physical models and different control parameters. Furthermore, it enables the integration of FACTS devices into the existing power system analysis and control programs efficiently. Physical limits of the FACTS devices are also considered in the model. Numerical results on a reduced practical system and a 1500-bus practical system with various FACTS devices are presented to illustrate the vigorousness of the proposed approach.

Power flow control approach to power systems with embedded FACTS devices

A novel methodology is proposed to evaluate the available transfer capability (ATC) of prescribed interfaces in connected power networks. With respect to the major uncertain factors affecting the ATC value, a realistic stochastic model is formulated in which availability of generators and circuits are considered as random variables following binomial distributions. With reasonable assumptions, fluctuations of loads are taken into consideration as normally distributed variables. To deal with the complex problem formulated with both discrete and continuous variables involved efficiently, a hybrid stochastic approach which takes advantage of both two-stage stochastic programming with recourse and chance constrained programming is proposed. The necessity of considering the impact of uncertainties on ATC assessment is demonstrated clearly by using the IEEE 118-node standard. Numerical results also illustrate the capability and efficiency of the proposed methodology.

A hybrid stochastic approach to available transfer capability evaluation

In this paper, based on a decomposed power injection model of FACTS devices and stochastic programming, from the point view of operational planning, a novel methodology is proposed to enhance the available transfer capability (ATC) of prescribed interfaces in interconnected power networks, using control of FACTS devices. Taking into consideration the effect of FACTS devices, ATC is modelled as the largest value of unused transfer power that causes no thermal and voltage limit violations. With respect to the uncertainties of power systems, an effective stochastic model of evaluating ATC is formulated, in which availability of generators and circuits as well as fluctuation of loads are considered as random variables following binomial distribution and normal distribution respectively. A hybrid methodology which takes advantage of both two-stage stochastic programming with recourse (SPR) and chance constrained programming (CCP) is proposed to deal with this complex problem with both discrete and continuous variables. This methodology can calculate the ATC efficiently and accurately. Case studies with a reduced practical system are presented. The technical merits of FACTS technologies for reinforcing the ATC are demonstrated. The performance clearly illustrates the effectiveness of the proposed methodology.

Application of stochastic programming for available transfer capability enhancement using FACTS devices

More effective control means for line flow control and voltage support are required for better operation of modern power systems. In this paper, a novel framework and versatile model for deriving FACTS control parameters, based on the optimal multiplier Newton-Raphson power flow method (OMNR), the decomposed power injection model (PIM) and linear programming (LP), is proposed. In order to take full advantage of the OMNR method for power flow with embedded FACTS devices and linear programming for power flow control, a rectangular-polar hybrid formulation is adopted. Numerical results on a modified IEEE 30-node network are presented to illustrate the proposed approach.

Ying Xiao

Papers

Available transfer capability enhancement using FACTS devices

Power flow control approach to power systems with embedded FACTS devices

A hybrid stochastic approach to available transfer capability evaluation

Application of stochastic programming for available transfer capability enhancement using FACTS devices

Power injection method and linear programming for FACTS control