Transcript No Slide Title
Power Measurements
in
Electrical Power System
in the
Presence of Harmonics Voltages
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 Khv is a measure of conductance of the circuit. It is assumed constant for the period Supervisor : Bob Morrison Associate Supervisor : Peter Wallace
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
Reactive Power
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%) 130.00% 125.00% 120.00% 115.00% 110.00% 105.00% 100.00% 95.00% 90.00% 85.00% RMS% Comp% Khv% • • •
INSTANTANEOUS POWERS
Pt(t) = v(t) . i(t) 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)
• There is the turning point difference observed in •
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.