Page 9 - Mathematical Models and Algorithms for Power System Optimization

Preface

model of the node load curtailment in the event of faults, where node load curtailment (P C )isa
variable (node load P L is a limit), and the objective function is to minimize the sum of node
load curtailment P C . Then, this chapter presents the maximizing load supply capability model
of the node under the normal condition that the node load P C is a variable, where the objective
function is to maximize the sum of the node power supply and load P L . Both models are
applicable to the actual situation of urban power grids.
Chapter 6 studies the discrete optimal reactive power (VAR) planning (a mixed-integer
nonlinear programming problem) models for some actual power systems. This chapter
describes how to develop a discrete VAR planning optimization model based on successive
linear programming (SLP), where the number “C” of the capacitor bank, “R” of the reactor
bank, and “T” of the transformer tap ratio are treated as discrete variables, and the other
variables (P, Q, U, and θ) are treated as continuous variables. First, a single state
discrete optimal VAR planning model is given. Then, a multistate model with a shape of a block
diagonal matrix is proposed, in which the corresponding decomposition coordination algorithm
is also presented by decomposing, coordinating, and solving all states to minimize the total
investment in reactive power equipment. This chapter also combines expert rules, fuzzy
mathematical concepts, and GA algorithms with traditional optimization methods to
improve the possibility of obtaining discrete solutions. The results of practical test systems
show that the proposed algorithm can effectively solve the discrete optimization VAR problems
of power systems.
Chapter 7 addresses the model of load frequency control under small disturbances. Based on the
Z-transform load frequency feedforward control method, this chapter describes how to develop
a model and algorithm for controlling the power angular acceleration of the generator in the
given interval level of seconds to maintain the frequency of the generator. First, the power
system load disturbance model is established by the identification method. Then, the system
state estimators are constructed according to the hierarchical decomposition principle. Finally,
the load frequency control rules are derived according to the invariance principle. Furthermore,
this chapter also proposes three practical mathematical model transformation methods, such as
the eigenvalue method, the logarithmic matrix expansion method and the successive
approximation method, to make the transformation of difference equations into differential
equations, and the mutual transformation of differential transfer functions. The results of
simulation showed that the control method proposed can effectively control different types of
disturbances in power systems.

Chapter 8 studies the local stability control problem of power systems under large disturbances.
Based on the decoupling control method, this chapter introduces a new state space that can
stably monitor the operation of the system based on local measurements without losing
synchronization in the case of large disturbances, and provides rules to control the stability of
the entire system in two stages with only locally applied stability control measurements.

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