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 key of reactive power planning (RPP), or Var planning, is the optimal allocation of reactive power sources considering location and size. Traditionally, the locations for placing new Var sources were either simply estimated or directly assumed. Recent research works have presented some rigorous optimization-based methods in RPP. This paper will first review various objectives of RPP. The objectives may consider many cost functions such as variable Var cost, fixed Var cost, real power losses, and fuel cost. Also considered may be the deviation of a given voltage schedule, voltage stability margin, or even a combination of different objectives as a multi-objective model. Secondly, different constraints in RPP are discussed. These different constraints are the key of various optimization models, identified as optimal power flow (OPF) model, security-constrained OPF (SCOPF) model, and SCOPF with voltage-stability consideration. Thirdly, the optimization-based models will be categorized as conventional algorithms, intelligent searches, and fuzzy set applications. The conventional algorithms include linear programming, nonlinear programming, mixed-integer nonlinear programming, etc. The intelligent searches include simulated annealing, evolutionary algorithms, and tabu search. The fuzzy set applications in RPP address the uncertainties in objectives and constraints. Finally, this paper will conclude the discussion with a summary matrix for different objectives, models, and algorithms.

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Review of Reactive Power Planning: Objectives, Constraints, and Algorithms

An Efficient Technique for Reactive Power Dispatch Using a Revised Linear Programming Approach

The reactive-power dispatch is formulated as the minimization of real-power losses in the system, utilizing a full set of control variables: generator voltages, switchable shunt susceptances, and transformer taps. The solution of the loss problem is obtained by successively solving quadratic programming problems. First- and second-order loss sensitivity coefficients are derived for the quadratic problem formulation. The derivations are based on the Jacobian method for sensitivity calculations. Sensitivity relations for the dependent constraints are based on the complete reactive-power model of the fast decoupled load flow method. The active-set projection method for quadratic programming is described and utilized as the solution algorithm for the quadratic reactive-power dispatch problems. Tests are conducted on the IEEE 30-bus and Mexican 253-bus systems. The computer results are discussed. >

Reactive-Power Dispatch by Successive Quadratic Programming

The authors discovered that the convergent characteristic of load flow calculation by the Newton-Raphson method in rectangular coordinates has a unique linearity. It tends to converge straight toward two multiple solutions when they are located close to each other. On the basis of this feature, the authors propose a method for solving two close solutions in bulk power systems. The results of applying this method to a heavily loaded practical 233-bus system and the Klos-Kerner 11-bus system verify its robustness and ability to find solutions successfully and quickly. The proposed method is so fast that it can be applied to an online voltage security system. >

A method for finding a pair of multiple load flow solutions in bulk power systems

A method for reactive power planning is presented that it finds an optimal solution for both allocation and operation planning in large systems using linear programming (LP). The method utilizes calculated linear sensitivities including active power and voltage phase angle in the formulation. Although the overall method includes these relations, the number of constraints and variables are not augmented in its first procedure, APPROACH-1. Its second procedure, APPROACH-2, overcomes numerical problems caused by a dense constraint matrix. This is achieved by retaining untouched sparse sensitivities in the constraint matrix and by eliminating any calculations related to the inverse matrix. The results of applying this method to a practical 224-bus system and the IEEE-30 bus system verify its robustness and fast convergence. >

K.-I. Suzuki

Papers

Practical reactive power allocation/operation planning using successive linear programming