Power System Harmonics: 1.3.b Complex Error of Capacitor Voltage Transformer (CVT) with Inductive Compensation

Parts of series of articles about Source Decision of Power System #Harmonics:

0) Introduction

1) How should a Source be defined? (What is a Source?)

2) How can an AC Voltage be amplified?

3.a) Complex Error of Basic Capacitor Voltage Transformer (CVT)

(current)--> 3.b) Complex Error of #Capacitor_Voltage_Transformer (#CVT) with Inductive Compensation

4) Summing Up

CVT with Inductive Compensation

Question: Is output voltage of Capacitor Voltage Transformer is reliable to use finding location of source (flow direction of active power)?

An equation for complex error of CTV is going to be investigated to calculate phase difference between primary & secondary voltages to determine reliability.

Second a model with inductive compensation for CTV, which is defined at Alstom's Network Protection & Automation Guide 2011 "Figure 6.6.(b): Capacitive divider with inductive compensation", is being handled.

General equations regarding the figure:

(1)

(2)

(3)

Equation for Vb:

(4)

Equation for V (6):

(5)

(6)

So, the equation (11) and steps (7-10) to it for complex ratio/error of CVT:

(7)

(8)

(9)

(10)

(11)

In most cases the output of voltage transformer used by several measuring and/or protection units because of physical and cost limitations to install more voltage transformers. So, actual burden won't be a single load but an equivalent description of parallel loads.

Anyway, if it is assumed that that there aren't any burden from old-fashioned electro-mechanical measuring and/or protection device, so the inductance and resistance ratio (L/R) can be considered very small, in other words burden is dominated by resistive characteristic and the inductance can be neglected.

(12)

So, if the equation (12) is taken into account, the complex ratio/error of CVT becomes:

(12)

(13)

(14)

Capacitive divider with inductive compensation is mainly used for eliminating the complex part at fundamental frequency. So, the required inductance magnitude for elimination in terms of fundamental frequency and capacitor magnitudes:

(15)

If the inductance is replaced at the equation (14) with given equation at the equation (15), the final equation (19) for complex error at higher frequencies can be derived.

(16)

(17)

(18)

(19)

Opposite to basic CVT, the complex error of CVT with inductive compensation is increasing as harmonic frequency is increasing.