Page 8 - Mathematical Models and Algorithms for Power System Optimization

Preface

system frequency f. The last part, Chapter 9, integrates the principles of microeconomics into
the practical operation of the power system and establishes an optimal decision model for all the
market participants based on the Nash equilibrium and the Walrasian general equilibrium.

Chapter 2 studies the optimization model of daily economic dispatch of a pump storage plant
in a practical multiregional system in a province in China. This chapter describes how to
optimize the arrangement for the generator output P G within a daily cycle based on hourly
intervals, of which the power output of each generating unit is treated as a continuous
variable and pump storage output as a discrete variable. It proposes a mixed-integer
programming (MIP)-based optimization model with both linear objective function and the
constraints and two categories of variables (continuous and discrete). The MIP method is then
used to solve the problem. The proposed model effectively optimizes the operation of the
pump storage plant and meets all constraints, thus achieving the goal of shifting the peak
load and filling the valley of the load curve. Therefore, it has a high relevance for the
current smart operation of the power grid.

Chapter 3 focuses on the optimization model of the annual generator maintenance scheduling
(GMS). This chapter describes how to optimize the arrangement for the generator output
PG within an annual cycle based on hourly intervals. The GMS model based on fuzzy logic
dynamic programming is proposed. Because GMS constraints (such as maintenance window
interval, spare capacity, maintenance manpower, regional maintenance capability, and
generator maintenance time) cannot be overlapped, the concept of a fuzzy set, which handles
the boundary of the objective function and constraints of GMS, is used to obtain a more
feasible solution for GMS. The objective function and constraint function in the GMS
model are both linear functions whose variables are continuous variables. Knowledge based
on expert systems is also used in the solution process. The method has been effectively
applied to GMS problems in an actual provincial power system.

Chapter 4 deals with two types of new power flow models, ill-conditioned power flow and
discrete optimal power flows, by way of construction of objective function and constraints. This
chapter first describe how to develop a new power flow model based on the combination of the
simulated annealing (SA) method and the Newton-Raphson power flow method. Then, it
describes how to develop a discrete optimal power flow (discrete OPF) model by constructing a
linear objective function with P G , Q G , U, and θ as constraints. The discrete OPF model is solved
by the successive linear programming (SLP) based algorithm and the approximate mixed-
integer linear programming algorithms, in which a method to change the increment of variables
in the iterative calculation of the linear programming is applied. Both models have been
successfully applied to practical power systems.
Chapter 5 addresses the models for minimizing load curtailment and maximizing load supply
capability based on the DC power flow algorithm to optimize the load P L , where U and θ
are treated as constants. This chapter first describe how to develop the node load minimization

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