G.P. Granelli

Optimal capacitor placement using deterministic and genetic algorithms

A procedure for solving the power capacitor placement problem is presented. The objective is to determine the minimum investment required to satisfy suitable reactive constraints. Due to the discrete nature of reactive compensation devices, optimal capacitor placement leads to a nonlinear programming problem with mixed (discrete and continuous) variables. It is solved with an iterative algorithm based on successive linearizations of the original nonlinear model. The mixed integer linear programming problem to be solved at each iteration of the procedure is tackled by applying both a deterministic method (branch and bound) and genetic algorithm techniques. A hybrid procedure, aiming to exploit the best features of both algorithms is also considered. The proposed procedures are tested and compared with reference to a small CIGRE system and two actual networks derived from the Italian transmission and distribution system.

Emission constrained dynamic dispatch

Abstract Since the early 1970s thermal generation dispatch has been proposed as an effective means of dealing with the problem of air pollution. More restrictive recent legislation has led to the adoption of pollution-limiting techniques and/or the use of less polluting fuels. An emission constrained dispatch, however, is still required either when contingent difficulties in the availability of low pollutant fuels occur or in the presence of meteorological conditions adverse to the diffusion of effluents. In this paper a dynamic dispatch procedure is proposed which is capable of taking into account the integral nature of the emission constraints. The mixing of fuels with different pollution rates and the management of multifuel plants are taken into account with the purpose of obtaining a cost-effective operation for all thermal plants in compliance with emission limitations. A suitably modified version of the Han-Powell algorithm is employed to find a solution for the resulting large-scale nonlinear programming problem. A method is considered to obtain a suboptimal solution of the mixed integer nonlinear programming problem which arises when emission control is achieved by switching from one fuel to another. Tests on a small CIGRE network and on a medium-sized EHV Italian system are presented to validate the proposed procedures.

System-area operating margin assessment and security enhancement against voltage collapse

The (very) short term reactive power scheduling function, to be adopted by ENEL Spa, takes into account the voltage stability requirements in a preventive application of the security function. In this environment the procedure determines the voltage collapse distance of the global system and of the areas controlled by the secondary voltage regulation (SVR) both in short (24 hours ahead) and in a very short term (few hours or fractions of hour ahead). The procedure also schedules the control actions to be taken in emergency states in a preventive way. Area or system-wise indicators, based on nodal sensitivities and/or eigen (singular) value analysis, provide effective measures of the margins of the system with respect to the risk of voltage collapse and the related corrective actions. Applications of the procedure to the EHV network and to a subtransmission area of the ENEL system are presented in the paper.

Security-constrained economic dispatch using dual quadratic programming

Abstract This paper presents a procedure for efficiently handling real power transmission constraints on branch flows and inter-area exchanges to supplement the classic economic dispatch (ED) formulation. A sequential quadratic programming (SQP) method is employed to solve the resulting non-linear programming problem. Each quadratic subproblem is approached by a dual programming technique — a dual feasible starting point is obtained by relaxing transmission limits; constraint violations are then enforced using the dual quadratic algorithm by Goldfarb and Idnani. The Hessian matrix of the Lagrangian function is approximated by a diagonal matrix thus keeping the objective function of each quadratic subproblem separable. Two versions of the proposed procedure exploit different assumptions in the evaluation of the sensitivities of the slack bus balance equation and of transmission constraints. For comparison purposes, the exact model of the security-constrained economic dispatch (SCED) is solved using a standard SQP algorithm taken from the NAG library. Tests on a CIGRE sample network and on actual medium and large-scale systems show that feasible and nearly optimal solutions of the SCED problem can be obtained. The proposed method presents limited computation times and a sufficiently good accuracy; it can be profitably employed whenever computation speed and algorithmic robustness are important issues as in real time operation to update the trajectories of thermal generations, as well as in system planning and hydro-thermal co-ordination studies.

A genetic algorithm-based procedure to optimize system topology against parallel flows

Parallel (or loop) flows consist in the undesired circulation of power flows through certain interconnection corridors. Remedial actions available to transmission system operators or system planners include installation and operation of phase-shifting transformers and of dc transmission systems. Moreover, the invaluable experience of transmission system operators has shown that the network can be operated so as to reduce parallel flows also by properly selecting the topology of the system. In the present paper, a genetic algorithm-based procedure is designed for the topological optimization of the network against parallel flows. The control variables considered are the status of substation breakers and the location (and angle) of phase-shifting transformers. The problem is formulated as a multiobjective optimization. The main objective is that of reducing the power transfer distribution factor of an assigned transaction with reference to a set of lines; N and N-1 security levels are accounted for by means of subsidiary objective functions. The procedure is tested on a small CIGRE sample system and on a 4500-bus network representative of the European electric system (UCTE).

Vector computer implementation of power flow outage studies

An application of vector and parallel processing to power flow outage studies on large-scale networks is presented. Standard sparsity programming is not well suited to the capabilities of vector and parallel computers because of the extremely short vectors processed in load flow studies. In order to improve computational efficiency, the operations required to perform both forward/backward solution and power residual calculation are gathered in the form of long FORTRAN DO loops. Two algorithms are proposed and compared with the results of a program written for scalar processing. Simulations for the outage studies on IEEE standard networks and some different configurations of the Italian and European (UCPTE) EHV systems are run on a CRAY Y-MP8/432 vector computer (and partially on a IBM 3090/200S VF). The multitasking facility of the CRAY computer is also exploited in order to shorten the wall clock time required by a complete outage simulation. >

A W-matrix based fast decoupled load flow for contingency studies on vector computers

The authors deal with an application of the inverse factors method (W-matrix method) to a fast decoupled load flow procedure for steady-state contingency analysis. The W-matrix method, originally developed for the solution of sparse sets of linear equations on multiple instruction/multiple data (MIMD) computers, can also be made effective for vector computers. The recurrence problem is overcome by reordering the addition operations required in a forward and backward solution. Matrix partitioning is employed to find the best tradeoff between the number of fill-ins added to the W matrix and the increased efficiency of vector operations achieved through a reduced number of partitions. The effect of different bus ordering algorithms on the partition number is also considered. Operation reordering is employed to make the bus power computation phase very fast in comparison to traditional bus-wise calculation. Tests were performed on the IEEE 118 bus system, some different configurations of the Italian EHV system and a European equivalent network with up to about 700 buses using a 4-CPU CRAY Y-MP8/432 and a 4-CPU Alliant FX/80 computer. >

Robust state-estimation procedure based on the maximum agreement between measurements

Static state estimation is a fundamental tool for control and monitoring of electrical power systems. Commonly used solution methods such as least squares may be faulty when gross errors are present among the measurements and therefore suitable techniques have been developed to detect and identify bad data. In this work, a robust state-estimation procedure is presented. Similarly to the least median of the squares method, the proposed procedure is based on the idea of evaluating the different state vectors obtained by solving samples of the measurements of dimension equal to the number of the states. The remaining measurements agree or disagree with the solution according to the values of their residuals. The optimal solution is the one with the maximum agreement between the remaining measurements and those in the sample. A genetic algorithm is used instead of a random selection of the samples, to speed up the appearance of the optimal solution. The proposed procedure was implemented and tested with reference to some IEEE test systems.

Security constrained dynamic dispatch of real power for thermal groups

A dynamic approach to the real power dispatch of thermal generating units, suitable for time periods characterized by high rates of load variation, is presented. A discrete formulation of the dispatch problem is adopted, with step variations of the loads. Dynamic constraints on the rate of change of the present loading output of thermal units are added to the ordinary constraints of the static approach. Costs associated with the act of quickly changing the thermal generation are included in the model. The solution of the problem uses a modified version of the Han-Powell algorithm in a compact-reduced model formulation. A sparsity technique used in the construction and in the updating of the Hessian matrix of the Lagrangian function, allows the solution of large-scale problems arising from a minute subdivision of the dispatch interval in large electrical systems. >

Multiple bad data processing by genetic algorithms

The identification of multiple bad data, especially when mutually interacting, may be difficult to handle, since the well known procedures based on the normalized or weighted residuals may become faulty. The identification problem is formulated here as that of picking bad data from a set of suspect measurements in order to fulfill the requirements of maintaining observability and eliminating the minimum number of measurements. Three non-deterministic solution procedures based on the use of genetic algorithms are proposed. Aiming at reducing the computation burden, the possible advantage deriving from working with small populations has been investigated by implementing a micro-genetic approach and an evolution strategy in which a single individual population is employed. Numerical efficiency is improved by reducing the number of state re-estimations; a database of already computed cases is used and a filtering mechanism has been designed to skip non promising solutions. Tests are carried out with reference to the IEEE standard test systems.