童小娇、杨洪明所著的《电力市场的经济运行及其数学方法(英文版)》以作者近十年来的研究成果为主线，介绍市场化运营环境下电力系统的经济运行相关问题及其最新的研究方法。该专著结合了电力、数学和管理三个交叉学科的前沿研究，其成果可解决电力工业市场化运营环境下出现的经济和技术问题，并可推广解决涉及经济和工程中涉及最优决策问题。

This monograph covers two cross-disciplinary fields relating to operational research and management as well as electrical engineering. It discusses the key scientificissues of secure and economic operation in the new environment of power system.The oretically, based on mathematical semi-smooth functions, non-linear complementary functions and conditional valueatrisk （CVaR）,a series of new complicated ma the maticalmodels are established on the availability of transmission capacity, optimal power flow,risk management, dynamic equilibrium, and so on. Moreover, the efficient semi-smooth and smoothing Newton-type algorithms with good convergence properties are presented,and the relevant issues of Nash equilibrium and chaos control in the electricity marketare also studied. The research results can be used to solve the economic and technicalproblems of electricity industry in the market-oriented operating environment.

Readers can get to know the mathematical descriptions and calculation methods as well as some new problem-driven mathematical models on the secure and economicoperation of power system through the book. Meanwhile they can consider applying these new theories and methods to solve optimal decision-making problems in other economic and engineering aspects. Integrating their respective academic backgrounds of mathematics and engineering disciplines, the two authors of the book not only share the joy and interest of scientific research, but also build their profound friendship duringmore than ten years of cooperation.

Foreword

Preface

List of Notation

Chapter 1 Electricity Markets and Preliminaries of Mathematics

 1.1 Electricity Market

1.1.1 Deregulation and reformation of power industry

1.1.2 Competitive structure of electricity market

1.1.3 Concerned issues in electricity market

 1.2 Conditional Value-at-Risk (CVaR)

1.2.1 CVaR concept

1.2.2 CVaR calculation

 1.3 Semismooth Function and Nonlinear Complementarity Problem

1.3.1 Clarke generalized Jacobian

1.3.2 Semismooth function

1.3.3 Nonlinear complementarity problem (NCP)

1.3.4 A reformulated system of equations for general nonlinear optimization

 1.4 Semismooth Newton Method for Nonsmooth Equations

1.4.1 Local semismooth Newton method

1.4.2 Global semismooth Newton method

 1.5 Smoothing Newton Method for Nonsmooth Equations

1.5.1 Smoothing technology

1.5.2 Smoothing Newton method

 1.6 Notes and Comments

Chapter 2 Available Transfer Capability on Market Environment

 2.1 Available rlyansfer Capability (ATC)

 2.2 Semismooth Newton Method for ATC Calculation

2.2.1 New ATC model

2.2.2 Smoothing Newton method

2.2.3 Smoothing decoupled Newton algorithm

 2.3 Contract-Based ATC Region (ATCR)

2.3.1 ATCR model with single-contract

2.3.2 ATCR model with multi-contracts

2.3.3 Quadratic approximation for ATCR boundary

2.3.4 Approach and visualization of ATCR

 2.4 Numerical Examples

2.4.1 Examples for ATC calculation

2.4.2 Examples for ATCR calculation

 2.5 Notes and Comments

Chapter 3 Optimal Power Flow Based on Newton-type Methods

 3.1 Optimal Power Flow (OPF)

 3.2 Decoupled Optimal Power Flow Approach

3.2.1 Reformations of KKT systems

3.2.2 Convergent analysis for decoupled OPF

 3.3 Semismooth Newton Method for Solving OPF

3.3.1 Reformulated system of equations

3.3.2 Semismooth Newton methods

3.3.3 Decoupled semismooth Newton method

 3.4 Solution Method for OPF with Transient Stability Constraints

3.4.1 OTS model

3.4.2 An SIP reformulation of OTS model

3.4.3 Smoothing quasi-Newton algorithm

3.4.4 Iterative algorithm with active-set strategy

 3.5 NumericalExamples

3.5.1 OPF examples

3.5.2 OTS examples

 3.6 Notes and Comments

Chapter 4 Economic Operation of Electricity Market Under CVaR Management

 4.1 Portfolio Optimization Based on CVaR

4.1.1 Typical portfolio optimization models

4.1.2 Smoothing SQP algorithm

4.1.3 Global convergence

 4.2 Worst-case CVaR (WCVaR) Based Scenario Planning in Electricity Markets

4.2.1 WCVaR concept and some distributions of partial message

4.2.2 Robust portfolio optimization models with WCVaR

4.2.3 Examples for robust models with WCVaR

4.2.4 Allocation of generation asset

 4.3 a-Superquantile Risk-Based Security-Constrained Economic Operation

4.3.1 Mathematical description of security under uncertain environment

4.3.2 a-superquantile-based security constraint of system operation

4.3.3 Economic operation with risk-limiting security

4.3.4 Example: Risk-limiting dispatch considering transmission load limit

 4.4 Numerical Examples

4.4.1 Smoothing algorithm for allocation of generation assets with CVaR

4.4.2 Scenario planning under WCVaR management

 4.5 Notes and Comments

Chapter 5 Dynamic Equilibrium Analysis of Electricity Market

 5.1 Dynamic Cournot Game Model of Electricity Market

5.1.1 Dynamic cournot game model of market participants

5.1.2 Optimization model of consumption benefit considering network constraints

 5.2 Dynamic Supply Function Model of Electricity Market

5.2.1 Dynamic bidding model of market participants

5.2.2 Market-clearing optimization model considering network constraints

 5.3 Reformulation of Dynamic Model Based on NCP Function

5.3.1 Reformulation of dynamic cournot game model

5.3.2 Reformulation of dynamic supply function model

 5.4 Nash Equilibrium of Electricity Market

5.4.1 Nash equilibrium of dynamic cournot game model

5.4.2 Nash equilibrium of dynamic supply function model

 5.5 Local Stability of Nash Equilibrium of Electricity Market

5.5.1 Local stability of dynamic cournot game model

5.5.2 Local stability of Nash equilibrium of dynamic supply function model

 5.6 Numerical Simulation of Market Dynamics

5.6.1 Market dynamics for two-node system based on cournot game model

5.6.2 Market dynamics for IEEE 30-node system based on cournot game model

5.6.3 Market dynamics for three-node system based on supply function model

5.6.4 Market dynamics for IEEE 14-node system based on supply function model

 5.7 Notes and Comments

Chapter 6 Chaos Control of Electricity Market

 6.1 State Time-delayed Feedback Chaos Control

6.1.1 Chaos control for dynamic cournot game model

6.1.2 Chaos control for dynamic supply function model

 6.2 Parameter Perturbation Chaos Control

6.2.1 Chaos control for dynamic cournot game model

6.2.2 Chaos control for dynamic supply function model

 6.3 Numbercal Simulation of Chaos Control for Cournot Game Model

6.3.1 Chaos control for two-node system

6.3.2 Chaos control for IEEE 30-node system

 6.4 Numerical Simulation of Chaos Control Based on Supply Function Model

6.4.1 Chaos control for three-node system

6.4.2 Chaos control for IEEE 14-node system

 6.5 Notes and Comments

Bibliography