The optimal capacitor allocation problem is the determination of the location, number, type and sizes of capacitor to be placed in a radial distribution system in an optimal manner. The objective of optimal capacitor allocation is to reduce the energy loss and peak power losses of the system while striving to minimize the cost of the capacitors in the system.


However, optimal capacitor allocation is not an easy task. Many of the previous researches employed simplifying assumptions to simplify the problem formulation, although these assumptions may diverge the computed results to the actual real time solution.

Optimal capacitor allocation problem is a well research topic. Earlier approaches differ from each other by the way of their problem formulation and the problem solution methods employed. Ng et al.[11] provide a brief survey of the capacitor allocation studies and classify them into four major methods: mathematical method, numerical programming methods, heuristics methods and AI based methods. 

Optimal Capacitor Allocation Techniques

Capacitor allocation for loss reduction on electric distribution system is an extensively researched problem. Published literature describing capacitor placement algorithms are abundant. Such research employ different problem approach, problem solution and simplifying assumptions. 

Ng et al.[11] describe the evolution of research and classify the capacitor allocation algorithms by method of approach and effectiveness. The solution techniques for the capacitor allocation problem are classified into four categories: analytical, numerical programming, heuristics and artificial intelligence (AI)-based.

Analytical Methods

All the early works of optimal capacitor placement used analytical methods. It was from these early researches that the famous “two-thirds” rule became established. These algorithms were devised when powerful computing resources were unavailable or expensive. Analytical methods involve the use of calculus to determine the maximum savings from capacitor placement. 

Although simple closed-form solutions were achieved, these methods were based on unrealistic assumptions like constant conduction size, uniform loading, and capacitor placement locations and sizes are modeled as continuous variables.

Numerical Programming Methods

As computing power became more readily available and computer memory less expensive, numerical programming methods were devised to solve optimization problems. Numerical programming methods are iterative techniques used to maximize (or minimize) an objective function of decision variables. For optimal capacitor allocation, the savings function would be the objective function and location, sizes, number of capacitors, bus voltages and currents would be the decision variables which must satisfy operational constraints.

Some of the numerical programming methods have the advantage of considering feeder node locations and capacitor sizes as discrete variables which is an advantage over analytical methods. However, the data preparation and the interface development for numerical techniques may require more time than analytical methods. The convexity of the capacitor placement problem must also be determine to determine if the results yielded by a numerical programming technique is a local or global extremum.

Heuristics Methods

Heuristics are rules of thumb that are developed through intuition, experience and judgement. Heuristics rules produce fast and practical strategies which reduce the exhaustive search space and can lead to a solution that is near optimal.

Heuristics methods are intuitive, easy to understand and simple to implement as compared to analytical and numerical programming methods. However, the results produced by heuristics algorithms are not guaranteed to be optimal.

Artificial Intelligence (AI)-Based Methods

The recent popularity of Artificial Intelligence (AI) has been investigated for its use in optimal capacitor allocation and other engineering problems. Such AI based methods are genetic algorithms (GAs), simulated annealing (SA), tabu search (TS), expert systems (ES), artificial neural networks (ANN) , fuzzy set theory. 

Assumptions in Optimal Capacitor Allocation

Optimal capacitor placement problem is not an easy optimization problem. As the problem formulation approaches real time problem the degree of complexity increases. Previous researches on capacitor placement optimization problem employed various simplifying assumptions to reduce the complexity of the problem. Usually, these assumptions are far from actual system and the solved solution may be far from real optimal values.

Rojo [12] review the assumptions made by previous researchers on optimal capacitor allocation studies. Such assumptions are listed as follows;

1. Zero or linear capacitor cost
2. Continuous or non-discrete capacitor sizes 
3. Uniform or equal capacitor sizes
4. Finding optimal solution given a pre-specified number of capacitors
5. Finding optimal solution given a pre-specified locations for capacitors
6. Capacitor compensations are assumed to be of fixed type
7. Constant current injected by the compensation capacitor
8. Simplified equivalent feeder/no laterals
9. Uniform cross-section area of the feeder/uniform wire sizes
10. Load does not vary with time.
11. Uniformly distributed load
12. Reactive compensation affects only the reactive components of the current
13. Constant voltage profile along the feeder
14. Balanced three-phase network with balanced loads
15. Ignores the effect of mutual coupling effect between conductors.

* This is a part of the Literature Review for my undergraduate thesis on Optimal Capacitor Allocation. Bibliography can be found HERE