**INTRODUCTION**

A major challenge for all power utilities is to not only satisfy the consumer demand for power, but to do so at minimal cost. Any given power system can be comprised of multiple generating stations, each of which has its own characteristic operating parameters. The cost of operating these generators does not usually correlate proportionally with their outputs, therefore the challenge for power utilities is to try to balance the total load among generators that are running as efficiently as possible. Further, the Power station has incremental operating costs for fuel and maintenance; and fixed costs associated with the station itself that can be quite considerable. Things get even more complicated when utilities try to account for transmission line losses, and the demand fluctuation within shorter time. In all of these cases, however, the basic objective is to operate the system as inexpensively as possible.

The economic dispatch program optimally allocates load demand specifying real power and reactive power to be generated by a power plant among various power generators in a manner so that each of the power generators are operated within its optimal operating conditions as defined by a reactive capability curve. Allocating a power demand with consideration of the reactive capability curves of the power generators results in optimal generation of real power and reactive power as specified by the load demand. Alternatively, the economic dispatch program allocates load demand specifying real power and reactive power to be delivered by a power grid among various power plants wherein one or more of the various power plants have capacity limits exhibited by reactive capability curves. The classic problem is the economic dispatch of the generation systems to achieve minimum operating cost. This problem area has taken on a subtle twist as the public has become increasingly concerned with environmental matters, so that “economic dispatch” now includes the dispatch of systems to minimize pollutants and conserve various forms of fuel, as well as to achieve minimum costs. In addition, there is a need to expand the limited economic optimization problem to incorporate constraints on system operation to ensure the “security” of the system, thereby preventing the collapse of the system due to unforeseen conditions.

The purpose of this course is to introduce and explore a number of engineering and economic matters involved in planning, operating, and controlling power generation and transmission systems in electric utilities. This course is designed to provide a good overview of the economic dispatch problem in power generation. It covers Power generation characteristics, Economic dispatch problem, Thermal unit economic dispatch and methods of solution, Optimization with constraints, Using dynamic programming for solving economic dispatch and other optimization problems, Transmission system effects, The unit commitment problem and solution methods, Generation scheduling in systems with limited energy supplies, Production cost models, Automatic generation control, Interchange of power and energy, Power system security techniques, Least-squares techniques for power system estimation, and Optimal power flow techniques and illustrative applications.

**COURSE OBJECTIVES**

The objectives of this course in economic dispatch include the desire to:-

• Acquaint participants with power generation systems, their operation in an economic mode, and their control.

• Introduce participants to the important “terminal” characteristics for thermal power generation systems.

• Introduce mathematical optimization methods and apply them to practical operating problems.

• Introduce methods for solving complicated problems involving both economic analysis and network analysis and illustrate these techniques with relatively simple problems.

• Introduce methods that are used in modern control systems for power generation systems.

• Introduce power system operation areas that are undergoing significant, evolutionary changes. This includes the discussion of new techniques for attacking old problems and new problem areas that are arising from changes in the system development patterns, regulatory structures, and economics.

**Welcome & Introduction**

Characteristics of Power Generation Units

• Characteristics of Steam Units

• Variations in Steam Unit Characteristics

• Cogeneration Plants

• Typical Generation Data

Economic Dispatch of Thermal Units and Methods of Solution

• The Economic Dispatch Problem

• Thermal System Dispatching with Network Losses Considered

• The Lambda-Iteration Method

• Gradient Methods of Economic Dispatch

Economic Dispatch of Thermal Units and Methods of Solution (cont’d)

• Newton’s Method

• Economic Dispatch with Piecewise Linear Cost Functions

• Economic Dispatch Using Dynamic Programming

• Base Point and Participation Factors

Economic Dispatch of Thermal Units and Methods of Solution (cont’d)

• Economic Dispatch Versus Unit Commitment

• Optimization within Constraints

• Dynamic-Programming Applications

Transmission System Effects

• The Power Flow Problem and Its Solution

• Transmission Losses

• Power Flow Input Data for Six-Bus System

Unit Commitment

• Constraints in Unit Commitment

• Unit Commitment Solution Methods

• Dual Optimization on a Nonconvex Problem

Generation with Limited Energy Supply

• Take-or-Pay Fuel Supply Contract

• Composite Generation Production Cost Function

• Solution by Gradient Search Techniques

Generation with Limited Energy Supply (cont’d)

• Hard Limits and Slack Variables

• Fuel Scheduling by Linear Programming

Production Cost Models

• Uses and Types of Production Cost Programs

• Probabilistic Production Cost Programs

Production Cost Models (cont’d)

• Sample Computation and Exercise

• Probability Methods and Uses in Generation Planning Problems

Interchange of Power and Energy

• Economy Interchange between Interconnected Utilities

• Interutility Economy Energy Evaluation

• Interchange Evaluation with Unit Commitment

• Multiple-Utility Interchange Transactions

Interchange of Power and Energy (cont’d)

• Other Types of Interchange

• Power Pools

• Transmission Effects and Issues

• Transactions Involving Nonutility Parties

Power System Security

• Factors Affecting Power System Security

• Contingency Analysis: Detection of Network Problems

Power System Security (cont’d)

• Calculation of Network Sensitivity Factors

Control of Generation

• Generator Model

• Load Model

• Prime-Mover Model

Control of Generation (cont’d)

• Governor Model

• Tie-Line Model

• Generation Control

Estimation in Power Systems

• Power System Estimation

• Maximum Likelihood Weighted Least-Squares Estimation

• Estimation of an AC Network

Estimation in Power Systems (cont’d)

• Estimation by Orthogonal Decomposition

• Introduction to Advanced Topics in Estimation

• Application of Power Systems Estimation

Optimal Power Flow

• Solution of the Optimal Power Flow

• Linear Sensitivity Analysis

• Linear Programming Methods

Optimal Power Flow (cont’d)

• Security-Constrained Optimal Power Flow

• Interior Point Algorithm

• Bus Incremental Costs

Presentation of Certificates

This course will be valuable to power system analysts and engineers, including generation and transmission planners, protection engineers, ISO/RTO technical staff, and operations supervisors. Others who will benefit include power developers and marketers, power exchange personnel, regulatory staff, and economic and management consultants.

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