Load Flow Optimization and Optimal Power Flow

J. C. Das

• Publisher: CRC Press
• Year: 2017
• Print ISBN: 9781032339443
• eBook ISBN: 9781351230773
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

This book discusses the major aspects of load flow, optimization, optimal load flow, and culminates in modern heuristic optimization techniques and evolutionary programming. In the deregulated environment, the economic provision of electrical power to consumers requires knowledge of maintaining a certain power quality and load flow. Many case studies and practical examples are included to emphasize real-world applications. The problems at the end of each chapter can be solved by hand calculations without having to use computer software. The appendices are devoted to calculations of line and cable constants, and solutions to the problems are included throughout the book.

1 Load Flow—Fundamental Concepts

Historically, the development of technology for predictive and control analysis of load flow problems was rather slow—the analogue computing techniques: network analyzers taking much time to model and were slow for a specific load flow problem. Another limitation is that large systems could not be modeled. With the advent of digital computers, much advancement has taken place. This is discussed in the chapters to follow.

The load flow problem arises from the fact that consumers must be provided with reliable source of electrical power for their varying needs, which involves much planning, like generation, renewables, transmission, and distribution and in the deregulated environment, this has become a very competitive field. The economic provisions of electrical power to the consumers require knowledge of so many interrelated functions; for example, adequately sizing the electrical equipment in the long chain of generation, transmission, and distribution: see Volume 1 for the nature of modern electrical power systems. Even in the isolated systems, same fundamental considerations arise, the renewables, microgrids, solar and wind generation, government subsidies for green power adding to the complexity. The load flow and optimization techniques are the tools to provide guidance through this maze.

1.1 Security Assessments

The 1965 blackout led to the various efforts for improving reliability. Several emergency guidelines and criteria were introduced by the Federal Power Commission and North American Power System Interconnection subcommittee. In this respect, “load flow” is not a stand-alone problem. The stability, protection, and transient behavior of a system plus the system management are important links. The power system security means the ability to withstand sudden disturbances such as short circuits and unexpected loss of system components. In terms of planning and operation, a power system should

• Ride through the transients and return to a steady-state operation without much impact on the consumers
• In the new steady state, no system component should be overloaded and should operate within their design parameters

These ideal conditions may not always be met in practice.

We can define three states as follows:

1. Normal
2. Emergency
3. Restorative

Under normal operation, all consumer demands are met and all equipment operates slightly below its rated capability. Mathematically, under normal state

x1(a1,a2,…,an;b1,b2,…,bn)=0x2(a1,a2,…,an;b1,b2,…,bn)=0…xn(a1,a2,…,an;b1,b2,…,bn)=0⁢(1.1)

where a₁, a₂,… are a set of dependent state variables and b₁, b₂,… are a set of independent variables, representing demand, inputs, and control. These correspond to load flow equations.

Relative to equipment the constraints are as follows:

y1(a1,a2,…,an;b1,b2,…,bn)≤0y2(a1,a2,…,an;b1,b2,…,bn)≤0…yn(a1,a2,…,an;b1,b2,…,bn)≤0⁢(1.2)

The equipment constraints can be described, for example, as upper and lower limits of a generator reactive power limits, system plus minus voltage limits, and the like.

In the emergency state, for example, brought out by a short circuit, some of the inequality constraints may be violated—the frequency may deviate, the lines and machines may be overloaded, etc. Mathematically, we write

x1(a1,a2,…,an;b1,b2,…,bn)=0x2(a1,a2,…,an;b1,b2,…,bn)=0…xn(a1,a2,…,an;b1,b2,…,bn)=0⁢(1.3)

and

y1(a1,a2,…,an;b1,b2,…,b...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Series Preface
• Preface to Volume 2: Load Flow Optimization and Optimal Power Flow
• Author
• 1. Load Flow—Fundamental Concepts
• 2. Automatic Generation and Frequency Control—AGC and AFC
• 3. Load Flow over AC Transmission Lines
• 4. HVDC Transmission Load Flow
• 5. Load Flow Methods: Part I
• 6. Load Flow Methods: Part II
• 7. AC Motor Starting Studies
• 8. Reactive Power Flow and Voltage Control
• 9. FACTS—Flexible AC Transmission Systems
• 10. Three-Phase and Distribution System Load Flow
• 11. Optimization Techniques
• 12. Optimal Power Flow
• 13. Heuristic Optimization Techniques
• Appendix A: Calculation of Line and Cable Constants
• Appendix B: Solution to the Problems
• Index