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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