# Capacitor Applications in Distribution Systems

Most common low voltage problems in distribution systems can be addressed by installing capacitors. But, how to optimally place and size the capacitors? And how would the capacitors impact the system due to harmonics and switching transients? In this article, we propose to address these questions.

#### Methodology

There are several different methodologies for determining capacitor size and location:

A. General:

- Place capacitors at loads which consume significant reactive power. For example, place capacitor in an industrial plant which have less than 85% power factor and bus voltage less than 95% nominal.
- Combination between rule of thumb (so called 2/3 rule) and running series of power flow simulations to fine-tune the capacitor size and location.
- 2/3 Rule: Place capacitor 2/3 of the feeder length from the substation, and size the capacitor 2/3 of the feeder load.

B. Use of Optimal Power Flow (OPF) program to optimize capacitor size based on potential capacitor locations selected by the engineer (refer to point “A1” for industrial loads in distribution system and point “A2” for feeder loads)

C. Use of Optimal Capacitor Placement (OCP) program to optimize the capacitor sizes and locations.

#### Assumptions Generally used in the Power Flow Model

Most approaches to optimizing capacitor allocation use a power flow model which represents … The aspects of the power flow model which are important to capacitor allocation are:

- Transmission grid is generally modeled as a swing bus feeding the main distribution transformers.
- In a relatively large distribution system, single phase feeders are generally lumped and modeled as 3 phase loads and similarly for industrial plants.

#### Power Factor and Voltage Regulation

Since the system condition is dynamic: change with the season, time of the day, and other special condition, the capacitor should be sized according to power factor criteria and such that it would provide an acceptable voltage regulation during most, if not all, such conditions.

For this purpose, historic measurement (annual measurement is preferred) helps obtain an idea about typical light load and peak load conditions in the system. Further, the light load condition can be modeled in the power flow program and used to determine the size of “fixed” capacitor banks; and the peak load condition is used to determine the size of “switched”capacitor banks.

#### Review the Impact of Installing Capacitor in the System

- Harmonic Resonance, placing capacitor in a system could cause resonance (very high impedance) at certain frequencies.
- For example resonance could occur at 300 Hz or 5
^{th}harmonic in 60 Hz system. If this 5^{th}harmonic resonance are located near the location of 5^{th}harmonic current source such as VSD drive in industrial plant, then this could cause very high voltage and current harmonic distortion and could cause equipment damages due to high voltage, excessive thermal problem, and current circulation between the capacitor and the system.

- For example resonance could occur at 300 Hz or 5
- Transient Switching, placing capacitor in relatively weak system could cause high voltage problem during switching period.

## Reader Question:

Please provide a sample calculation on how can we determine the size of the capacitor in the distribution system.

Answer:

Assuming that all capacitor banks are of equal size,

The c-ratio of eq. (2) is the ratio of the capacitor current to the current at the beginning of the line. For eq. (3), n is the number of capacitor banks; for n=1, then c = 2/3, which means the optimal amount of capacitance is 2/3 of the total reactive load.

xi is the optimal per unit distance of location along distribution feeder; i is the number of locations along the distribution feeder

Application:

Specify two capacitor banks, size and location, allocated along the feeder in order to minimize real power losses in the feeder.

#### Reference:

Electric Power Distribution System Engineering, T. Gonen, McGraw-Hill, 1986.