Numerical Simulations for Energy Calculation in Power Measurements

Transcription

1 Numerical Simulations for Energy Calculation in Power Measurements SORIN DAN GRIGORESCU COSTIN CEPISCA ION POTARNICHE S.C. ICPE-Actel SA, Bucharest OCTAVIAN MIHAI GHITA MIRCEA COVRIG ELENA GRIGORESCU S.C. DASON ELECTRO S.R.L. Sos. Iancului 4, Bucharest Abstract: Measurements limitations of the reactive power flow in the power systems have represented, since the early stage of the processes of high voltage networks design, construction and operation, an important issue for the specialists. This paper analyses the most used competitive definitions for the reactive power, implemented in digital energy meters, and compares the most usual measuring methods used in reactive energy measurement. Numerical simulations of the measurement techniques provide an error based evaluation of performances. Key -Words: Reactive power, Power harmonics, Energy measurements. 1 Introduction The definition of the reactive power as a component of the apparent power led, in time, to several debates reported by the dedicated literature [1]-[8]. Experimental data indicate that the actual functional behavior of the electric networks is always disturbed, and thus the use of different data processing algorithms ISSN: ISBN:

2 for the reactive power calculation led to different results. This paper investigates the basic methods to measure reactive power for energy meters and uses simulation to estimate associated errors for reference tests and extended tests for electric energy instrumentation. 2 Definitions for the Reactive Power The dedicated literature abounds in references to different definitions for the reactive power, but the definitions do not maintain the physical aspect of the non-sinusoidal regime. Among them, mostly used in instrumentation design are the definitions formulated by C.Budeanu and S.Fryze [1], [2], [3]. If active power may be calculated and accurately measured in any circumstances of harmonic pollution because it s inherent definition: t nt P = ui = p( t) dt = UI cosϕ nt Unfortunately this is not the case for reactive power. t1 2.1 Budeanu s definition This definition splits the apparent power in two orthogonal components: S = P ± jq (2) The sign in equation (2) corresponds to the inductive and capacitive reactive power, respectively. for sinusoidal waveforms, the reactive power is: Q = UI sin ϕ (3) for non-sinusoidal waveforms, the reactive power is: = B h=1 (1) Q U I sinϕ (4) where h represents the order of the harmonic. 2.2 Fryze s definition Originating in 1932 this definition preserves the reactive power form in any waveform regime: h h 2 2 S P Q F = (5) The difference between the values Q B and Q F depends on the harmonic spectrum of the current and voltage and the phase displacement between the harmonic components. 3 Reactive Power Measurement Methods The theoretical definition, given by Budeanu in equation (4), of the reactive power under non-sinusoidal regime is h difficult to implement within an electronic system at a reasonable cost and accuracy. Various techniques try to implement practical forms for this definition. This paper analyses these solutions. 3.1 The Hilbert transform method This method, obeying equation (4), needs a dedicated DSP, witch should process the Hilbert transformation in real time, providing a constant displacement of π/2 for each harmonic, without the attenuation of that amplitude [3]. That feature makes Hilbert s transformation an ideal solution for Budeanu s method implementation. Reactive power is calculated using one signal (voltage or current) phase shift on all harmonics, followed by the same multiplication and mean value algorithms as for active power. The Hilbert transformation ensures the optimal accuracy for the reactive power under non-sinusoidal regime, depending on the deep of the associated FFT algorithm. The block diagram of the system implementing Hilbert transform is illustrated in figure 1. Fig.1. Block diagram of the system supporting Hilbert algorithm. 3.2 The power triangle method The power triangle method is based on the hypothesis that the three powers (apparent, active and reactive) create a rectangular triangle. Estimating the active and the apparent power, the reactive power is: 2 2 Q = S P (6) This method gives excellent results under sinusoidal regime, but the presence of the harmonics can induced large errors. The power triangle method corresponds to the Fryze s definition. 3.3 The quarter period time delay method This method copes with reactive power formulas translating phase displacement in time domain delay with T/4 (where T is the fundamental period). If N is the number of samples corresponding to T/4 time delay, and f s is the frequency of the sampling signal, then: NT s = T / 4 (7) ISSN: ISBN:

3 and f = f N (8) sampling line 4 The time shifting versus phase method has two alternatives: a T/4 delay, where T is considered constant for the ideal frequency of the network; that can generate major errors when time changing line frequency is present, with a block diagram in figure 2. The reactive power Q is calculated multiplying the digitized current signal with the processed voltage signal, the result being additionally processed by a digital mean value extractor represented by a low path filter. π/2 is obtained, for all frequencies, by a low-pass filter (LPF), with a cut-off-frequency much lower than the line frequency, for instance 2 Hz, as in the figure 4. Fig.4. Block diagram of the system using one pole low pass filter method. The frequency characteristic of a low-pass filter with a single pole, responsible for the equivalent π/2 phase shift, is described by the transfer function: Fig.2. Block diagram of the system using T/4 delay algorithm. an adaptive T/4 delay, where T is now the measured period of the network. The voltage and current signals are digitized (ADC), then the voltage signal is delayed, using a digital shift register to the quarter of the measured network period, as depicted in figure 3. jϕh ( jω) ( jω) = H ( jω) e H (1) Both module and phase are depending of frequency: ω ω >> ω H ( jω) = 2 lg (11) db ω π ω >> ω ϕ H ( jω ) = (12) 2 where: ω - represents the cut-off frequency of the filter. One can observe the frequency dependence of both amplitude and the phase. Fig.3. Block diagram of the system using compensated T/4 delay algorithm. In bought methods the reactive power Q is calculated multiplying the digitized current signal with the T/4 delayed voltage signal a quarter of a period delay, in order to obtain a voltage signal with a π/2 phase displacement for fundamental frequency: T 1 Q = i( t). u( t T / 4) dt T (9) 3.4 One pole low-pass filter method This method is used by both static analogue and digital energy meters. In this case the desired phase shift with 4 Results of Simulation Table 1 presents the test conditions, voltage and current, used to test the measurement performances of the five reactive power measurement solutions. Table 2 presents the errors obtained for different tests using notations: H- for Hilbert transform, LPF- for low pass filter, PTpower triangle, CTD- compensated time delay, TD-time delay. The traditional measurement methods, like Power triangle and the Time delay, comply with international standards but show limitations in the presence of harmonics or line frequency variation [1], [11], [12]. One can observe that Hilbert method give the best results, followed by the low pass filter method and then power triangle method. So, different energy meters implemented with different formulas can give discrepancies measuring the same loads. Simulations have been conducted in MATLAB for phase and amplitude harmonics. Supplementary to the basic tests from table 1, additional test was conducted using a strong bought even and odd harmonic content. In this particular case errors in the case of the power ISSN: ISBN:

4 triangle methods become very large showing an inappropriate method for highly distorted current signals in the case of reactive energy measurements. Table 1. Type of Test Current and Voltage (Normalized to rms values) In figure 5 are illustrated the errors in table 2 for different test and methods. Table 2. Type of test H LPF PT CTD TD IEC1268 -Reference Voltage and current input: sin wave, f line ; PF = ~ ~ ~ ~ ~ IEC1268 -Reference Voltage and current input: sin wave, ; PF = f line IEC Frequency variation (±2%) sin wave; PF =.87 ~ ~ ~ ~ 5.6 ~ ~ ~ ~ -5.7 IEC Frequency variation (±2%) sin wave; PF =. 87 IEC1268 -Harmonic of the third harmonics on the current signal IEC1268 -Harmonic of the third harmonics on the current signal of the third harmonics on voltage input and 2% of the third harmonics on current input ( ϕ 1 = ϕ3 = 3 ) ~ ~ 2 ~ ~ ~ Additional Test ~ of the third harmonics on voltage input and 2% of the third harmonics on current input ( ϕ 1 = ϕ3 = 3 ) Additional Test The negligible error values for the Hilbert transform stand for the reference considered in the simulations related to this method. ISSN: ISBN:

5 Fig.5. Errors distribution due different simulated situations and methods. 4.1 Identification of the load Data for the additional test in table 1 were collected using a power harmonic analyzer on a real load. Waveform reconstruction was performed in MATLAB and the current waveform is illustrated in figure 6. diagram of the circuit used in simulation in presented in figure 8. Fig. 8. Schematic of the equivalent load. Fig.6. Actual voltage and current reconstruction. Using basic knowledge on different industrial loads, the power consumer was identified as a three phase rectifier with filter [9]. Simulation of the load using the SPICE program confirmed the similarity of the current waveforms in the measured and modeled situations. Figure 7 illustrated the SPICE simulated signals. 8V 1 2 4V V -4V 4A 2A A -2A >> -4A 2ms 25ms 3ms 35ms 4ms 45ms 5ms 55ms 6ms 1 V(D1:1) V(V3:+) V(C1:2,D5:1) V(V2:+) 2 I(V1) Time Fig. 7. SPICE simulated current waveform. Schematic of the load producing the current waveforms in figure 6, was found to be an full wave three phase rectifier with coil-capacitor filter in the out put. The 5. Conclusions Results of simulation proved once again the fact that among the alternative definitions proposed for reactive power measurement of distorted waveforms, Budeanu s theory is still the most commonly and internationally accepted definition, and Hilbert transform is the best implementation of it. Recently, the main effort is to reduce the difference between active and apparent power, since the effect of distortion on losses cannot be neglected. The emphasis is shifting from a direct optimisation of the power factor, at the point of common coupling, to a global minimisation of the power loss throughout the system. The important difference between reactive energy measured with different methods demand a special attention on different energy meters available on the market, because in the pay chain of energy different, various instruments may leave the energy budget unclosed. To prevent this, one should request the meter manufacturer to provide details about the reactive power processing algorithm. It is to notice that, given the presence of non-linear loads in urban and rural households, the trend, increasing worldwide, is to include in the electricity bill not only the active energy but also the reactive one. References: [1] Arrillaga, J, N. R. Watson, S. Chen, Power System Quality Assessment, John Wiley & Sons, 21. [2] Svensson, S., Power Measurement Techniques for Nonsinusoidal Situations, Chalmers Tekniska Högskola, Göteborg, [3] Arseneau, R.; Baghzouz, Y.; Belanger, J.; Bowes, K.; Braun, A.; Chiaravallo, A.; Cox, M.; Crampton, S.; Emanuel, A.; Filipski, P.; Gunther, E.; Girgis, A.; Hartmann, D.; Shu-Dong He; Hensley, G.; Iwanusiw, D.; Kortebein, W.; McComb, T.; McEachern, A.; Nelson, T.; Oldham, N.; Piehl, D.; Srinivasan, K.; Stevens, R.; Unruh, T.; Williams, ISSN: ISBN:

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