Economic load dispatch (ELD) is a very crucial aspect of power system operations and planning. 

With the growing demand for electricity across the world and large power system operations involving multiple generation units, achieving economic load dispatch effectively becomes extremely important from both technical and economical perspectives. 

The main objective of economic load dispatch is to schedule the committed generating units’ outputs to meet the load demand at minimum fuel cost while satisfying all unit and system operational constraints. 

In this article, we will delve deep into the concept of economic load dispatch, its mathematical formulation, objectives, key aspects like unit commitment, and penalty factors involved. We will also discuss its relevance and importance in the context of system operations

What Is Economic Load Dispatch

Economic load dispatch can be defined as the allocation of loads to individual generating units in a power system in such a way that the total operating cost is minimized while satisfying all operational constraints.

In simple words, it is a process of determining the most economical way to share the load among different generating units in a power system and control their outputs to meet the load demand at minimum fuel cost.

The concept of economic load dispatch stems from the fact that in large power systems, electricity demand has to be met by coordinating operations of multiple generating units connected. It aims to supply the load most economically in terms of fuel costs by optimally deciding the outputs of individual generating units. 

This involves operational adjustments of unit outputs in such a way that results in minimum overall system operating costs while meeting load requirements at all times.

Some key characteristics of economic load dispatch include:

• It involves the optimization of system operating costs while meeting the load demand.
• Individual generating units have operating limitations like minimum and maximum loading which are considered as constraints.
• Real and reactive power generation outputs are optimally coordinated subject to transmission network security constraints.
• Fuel costs of individual generating units are expressed as functions of their power outputs for cost optimization.

Importance of Economic Load Dispatch In Power System

Economic Load Dispatch (ELD) is a key issue in power systems and its goal is to achieve minimum economic costs by allocating the output of generator units when satisfying the load demands and the operating constraints.

Economic Operation of Power System

Economic operation of power system is the objective is to minimize the total operating cost while meeting the load demand subject to various constraints. The total operating cost generally includes fuel cost which forms a major part, start-up costs, shut-down costs, maintenance costs, etc.

Basic Mathematical Equation

Mathematically, the economic dispatch problem can be represented as:

Assume n generators in the same plant or close enough electrically so that the line losses may be neglected.

Let C1, C2, …, Cn be the operating costs of individual units for the corresponding power outputs P1, P2,…., Pn respectively. 

If total operating cost of the entire system is C, and the total power received by the plant bus and transferred to the load is PR, then

By Combinding equation (1) and equation (2) we will get….

The above given equation shows that if transmission losses are neglected, the total demand PR at any instant must be met by the total generation. The above equation is known as the equality constraint.

This a constrained minimising problem, By using Lagrangian multiplier technique this problem can be solved.

Equation (5) can be solved for minimum by determining the partial derivate of the function C* on variable Pi and equating it equal to zero.

Since Ci is a function of Pi only. The partial derivates become full derivates, that is,

Therefore, the condition for optimum operation is

The increment cost generation for a generator is represented by dci/dpi. It is evident from the mentioned equation that the most cost-effective method for distributing load within a plant involves ensuring each unit operates at an identical incremental fuel cost. 

This approach is identified as the equal λ criterion or the equal incremental cost-loading principle, which is essential for the economical functioning of the plant.

Difference between unit commitment and economic load dispatch

Unit commitment decides which generating units should be in operation to meet the load demand over the scheduling period, usually a day ahead. It is a long-term scheduling process.

Economic load dispatch, on the other hand, determines the optimal output levels of the committed units on a regular short-term basis, usually every 5-15 minutes, to meet the load demand at minimum operating cost. It optimally allocates the load among committed units based on their incremental costs.

The key differences are:

• Time horizon: Unit commitment looks at daily/weekly scheduling while ELD works on hourly/half-hourly basis.
• Objective: Unit commitment aims to select cost effective units to be committed, ELD focuses on minimizing operational costs of committed units.
• Constraints: UC considers start-up/shut-down costs and minimum up/down times as constraints. ELD only deals with output levels of already committed units.
• Sequence: UC precedes ELD which determines economic dispatch of units selected by the commitment process.

So in summary, unit commitment deals with scheduling of units over long-term while economic load dispatch optimizes power sharing over short-term for committed units.

Penalty factor in economic load dispatch

Conclusion

In this article, we discussed in detail the key concepts of economic load dispatch including its definition, objectives, basic mathematical formulation and important aspects like unit commitment, penalty factors involved. 

We saw how ELD helps achieve optimization of power system operation costs in real-time by optimally allocating load demands to committed generating units respecting all unit and network constraints. The relevance and importance of understanding economic load dispatch both from theoretical knowledge and problem-solving perspectives for competitive exams were also highlighted. 

A thorough grasp of ELD principles is indispensable for individuals aspiring careers related to power system operations and planning.
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