Transcript No Slide Title

Power Measurements in Electrical Power System
in the Presence of Harmonics Voltages
Supervisor : Bob Morrison
Associate Supervisor : Peter Wallace
Author : Harnaak Khalsa
PROBLEM
The accuracy of measurement of reactive power and
also the techniques of measurement are not accurate.
Factors affecting accuracy mainly being
•
Assumption of periodicity of waveforms
•
Poor definition of quantities for distorted and
unbalanced systems
PROPOSED SOLUTION - Kh Technique
Utilises time domain analysis.
Define UNIDIRECTIONAL power Pu,
BIDIRECTIONAL power Pb and TOTAL power Pt
Define Khv Factor as
LOAD
Case Study on load combinations.
Compare with RMS and computed
values.
PROBLEM ENCOUNTERED
•
The result of ‘Khv’ method is affected by when
load is not pure resistance, inductance or
capacitance - case 7, case 10 (mainly resistance
with some inductance), case 9, case 12
(capacitance + series resistance). Error in
measured bidirectional power increases
Case 1 to 6 - fundamental voltage
Case 7 to 9 - fundamental (100%) + 3rd (33%) + 9th (20%)
Case 10 to 12 - fundamental (100%) + 2nd (33%) + 10th (20%)
Case 13 to 15 - fundamental (100%) + 2nd (33%) + 3th (20%)
Reactive Power
130.00%
125.00%
120.00%
115.00%
110.00%
•
Pu(t) = Khv . v(t)2
Khv determined from last one period is used to
estimate the next sample value of Pu(t).
•
Pb(t) = Pt(t) - Pu(t)
•
R+C
Case 15
Case 11
Case 4
Case 3
INSTANTANEOUS POWERS
•
Pt(t) = v(t) . i(t)
Case 2
Case 1
90.00%
85.00%
Case 14
R+L
R
Case 10
R
R+C
Case 9
Case 13
R+L
Case 8
R+C
R
Case 7
Case 12
R+L+C
Case 6
R+L
C
Case 5
R+C
L
100.00%
95.00%
R+L
105.00%
R
Khv is a measure of conductance of the circuit. It is
assumed constant for the period
RMS%
Comp%
Khv%
There is the turning point difference observed in
with Fundamental for
+ 3rd(33%)
+ 9th (20%)
theRC load
waveforms
Pu(t)
andHarmonic
Pb(t).Voltage
EFFECTIVE POWERS
•
Unidirectional Effective Power
•
Bidirectional Effective Power
ω is fundamental frequency, T is fundamental period
•
•
Total Effective Power
Power Factor
Pt(t) (red), Pu(t) (blue), Pb(t) (green), Volts (volts, magenta), Currrrent (amps, black) vs
Time (sec)
EXPLANATION OF PROBLEM
Further analysis revealed that the instantaneous
conductance/susceptance of the of an impure load is not
linear. e.g. a resistance with a inductance below
R=127 ohm
L= 0.155 H
50% inductance
Admittance(mho, red),
Conductance G(t) (mho,
green), Susceptance S(t)
(mho, blue), Khv(mho,
magenta) vs Time (sec)
The sign (lag/lead) is determined from phase of
fundamental current w.r.t. fundamental volt
MEASUREMENT
Perform measurements to test definition.
WHAT NEXT
Develop the definition further to take into account this
behavior.
Electrical and Computer Systems Engineering
Postgraduate Student Research Forum 2001