Calculation of Reactive Power of a Capacitor


This post gives is a quick derivation of the formula for calculating the steady state reactive power absorbed by a capacitor when excited by a sinusoidal voltage source.

Given a capacitor with a capacitance value of C in Farads, excited by a voltage source V in volts, it will draw a current i amps into its positive terminal. If  V  is a steady state sinusoidal source with frequency of  ω=2πf , then we may use a Laplace Transform to solve the circuit in the frequency domain where  V  is the phasor rms voltage,  I  is the phasor rms current, and  Zc  is the capacitive reactance in ohms of the capacitor as follows:



Note that the negative sign means that the capacitor is absorbing negative reactive power VARs which is equivalent to stating that the capacitor is supplying reactive power to the external circuit or system. For a three-phase system, multiply Q by 3 to get the total reactive power supplied by the Capacitor.


Thank you!

Comments

Post a Comment

Popular posts from this blog

Concept of Subtransient, Transient & Steady State

Image
The concept of Subtransient, Transient and Steady State arises in case of fault in an Alternator. Let us assume a sudden short circuit in three phase of alternator. The fault current will flow in all the three phases of alternator and its waveform will be as shown in figure below. When the alternator is short-circuited, the currents in all the three-phases rise rapidly to a high value of about 10 to 18 times of full load current, during the first quarter cycle. The flux crossing the air gap is large during a first couple of cycles. The reactance during these first two or three cycle is least and the short circuit current is high. This reactance is called subtransient reactance and is denoted by X". The first few cycles come under sub-transient state. After a first few cycles, the decrement in the r.m.s. value of short circuit current is less rapid than the decrements during the first few cycles. This state is called the Transient  State and the reactance in th
Read more

Open Circuit and Short Circuit Characteristics of Synchronous Machine

Image
Open Circuit Test and Short Circuit Test are performed on a Synchronous Machine to find out the parameters of Synchronous Machine and hence to have an idea of their performance.  Open Circuit Test of Synchronous Machine is also called No Load, Saturation or Magnetizing Characteristics for the reason which will be clear after going through the post. For getting the Open Circuit Characteristics of Synchronous Machine, the alternator is first driven at its rated speed and the open terminal voltage i.e. voltage across the armature terminal is noted by varying the field current. Thus Open Circuit Characteristic or OCC is basically the plot between the armature terminal voltage E f versus field current I f while keeping the speed of rotor at rated value. It shall be noted that for OCC, the final value of E f shall be 125% of the rated voltage. Figure below shows the connection diagram for performing the Open Circuit Test of Alternator. As clear from the figure above
Read more

Restricted Earth Fault Protection of Transformer

Image
Restricted Earth Fault (REF) protection is basically a Differential Protection. The only difference in between the Differential Protection and REF Protection is that, latter protection is more sensitive as compared to the former protection scheme. In earlier posts we have already discussed Differential Protection of Transformer and various characteristics of Differential Protection. In this post we will focus on Restricted earth Fault protection. Also Read, Transformer Differential Protection Percentage Differential Protection - Slope in Differential Protection Harmonic Restraining in Differential Protection For the sake of understanding REF Protection, we take a Transformer of configuration DYn i.e. HV side of Transformer is Delta connected while the LV side is Start connected and neutral is grounded solidly. As shown in figure above, there are a total of four Current Transformers (CTs), three CTs connected in each phase i.e. R, Y and B and one CT connected in neutral. The secondary o
Read more