Introduction to linear and nonlinear programming

CVXGEN is a software tool that takes a high level description of a convex optimization problem family, and automatically generates custom C code that compiles into a reliable, high speed solver for the problem family. The current implementation targets problem families that can be transformed, using disciplined convex programming techniques, to convex quadratic programs of modest size. CVXGEN generates simple, flat, library-free code suitable for embedding in real-time applications. The generated code is almost branch free, and so has highly predictable run-time behavior. The combination of regularization (both static and dynamic) and iterative refinement in the search direction computation yields reliable performance, even with poor quality data. In this paper we describe how CVXGEN is implemented, and give some results on the speed and reliability of the automatically generated solvers.

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CVXGEN: a code generator for embedded convex optimization

An attempt is made in This work to present critical literature review and an up-to-date and exhaustive bibliography on the AGC of power systems. Various control aspects concerning the AGC problem have been highlighted. AGC schemes based on parameters, such as linear and nonlinear power system models, classical and optimal control, and centralized, decentralized, and multilevel control, are discussed. AGC strategies based on digital, self-tuning control, adaptive, VSS systems, and intelligent/soft computing control have been included. Finally, the investigations on AGC systems incorporating BES/SMES, wind turbines, FACTS devices, and PV systems have also been discussed.

Recent philosophies of automatic generation control strategies in power systems

This paper presents an enhanced genetic algorithm (EGA) for the solution of the optimal power flow (OPF) with both continuous and discrete control variables. The continuous control variables modeled are unit active power outputs and generator-bus voltage magnitudes, while the discrete ones are transformer-tap settings and switchable shunt devices. A number of functional operating constraints, such as branch flow limits, load bus voltage magnitude limits, and generator reactive capabilities, are included as penalties in the GA fitness function (FF). Advanced and problem-specific operators are introduced in order to enhance the algorithm's efficiency and accuracy. Numerical results on two test systems are presented and compared with results of other approaches.

Optimal power flow by enhanced genetic algorithm

A survey is presented of publications in the fields of optimal power flow and dispatching. It suggests a classification of methods based on the choice of optimization techniques. The survey is summarized in a single flow-chart-type figure, which indicates the relationship between methods, their chronology, and their popularity. This figure is based on a compilation of over three hundred publications. >

A survey of the optimal power flow literature

Strategic switching can be achieved by a current injection scheme which simulates the change in topology. The injected currents are applied to the terminals of the elements of a socalled base network corresponding to those actually switched. This requires that the base network must contain all elements in the "in" state. The injected currents to be used as a compensation in the commonly employed system matrices (Y, Z) for the real change in topology can be taken as control variables in an optimization procedure for the switching problem. With the aid of a method similar to linear programming (LP) objective functions such as line current, short circuit current or even losses can be formulated. By means of a switching sequence consisting of elementary switching operations the desired objective function will be brought to its optimum value.

Network Topology Optimization with Security Constraints

Systematic and fast switching for the purposes of reducing losses in power transmission networks is treated as an optimization problem whereby switching is to be understood in a general and comprehensive way. Injected currents applied to a base network are used to model the switching operation. These currents are used as variables in a linear programming (LP) problem formulation. The objective function, i.e. the change in losses, can be expressed by the injected currents, taking into account that all nodes are constrained by constant active powers except for the slack node. The change of power of the slack node is the change in losses, which is obtained by a two-step approximation. Each single optimal switching operation is obtained by an LP-like operation followed by a load-flow update. The interaction between LP and AC load-flow leads to a sequence of optimal switching operations whereby losses are reduced to a minimum subject to the given constraints. >

Loss reduction by network switching

It is shown that faster and highly localized power flow solutions can be obtained by exploring the difference in convergence rate of individual nodes. Nodes whose mismatches are smaller than a certain tolerance are processed as if their mismatches were actually zero. Computational effort is saved by skipping small mismatch computations and using sparse vector techniques for the nonzero mismatches. Since the proposed approach does not rely on network reduction or equivalencing, the accuracy of the solution remains high in all cases. The ZM (zero mismatch) approach can improve the speed of any Newton-like power flow algorithm without degrading solution accuracy. The relative advantage of ZM for contingency cases increases directly with network size. Its main advantage over other localization methods is that it uses the unmodified global factors of the FDPF (fast decoupled power flow) algorithm and requires no equivalents. ZM exploits the physical characteristics of power flows, the numerical characteristics of iterative solutions, and the sparsity of the matrix factors. >

Faster local power flow solutions: the zero mismatch approach

The authors describe the concept, mathematical formulation, and solution of a real-time OPF (optimal power flow) in an energy management system. The real-time OPF replaces a classical real-time economic dispatch whenever a network flow violation occurs. To meet performance requirements (solution speed and frequency of execution) a two-stage approach is proposed. A full OPF is first executed in a nontime-critical mode and the critical branch flows are determined. Then, a constrained economic dispatch is executed based on the critical constraint set determined during the first stage. The execution frequency of the second stage is the same as the execution frequency of a standard real-time economic dispatch. >

R. Bacher

Papers

Network Topology Optimization with Security Constraints

Loss reduction by network switching

Faster local power flow solutions: the zero mismatch approach

Real-time optimal power flow in automatic generation control

Optimization in Planning and Operation of Electric Power Systems