University of Calabria, Italy Active Resonance Dampers Dept. of of Electronics, Computer Science and Systems A comparison of two Active Resonance Dampers Alessandro Burgio, Daniele Menniti and Giovanni Brusco 1

INTRODUCTION TO THE PROBLEM Harmonic propagation indicates the amplification of voltage harmonics along a power distribution line; such an amplification is mainly due to the harmonic resonance between the line inductors and the shunt capacitors used for power factor correction. the resonance involves only such capacitors because the capacitive coupling of the power distribution line with the grounding is usually neglected. Harmonic propagation usually appears in antenna power lines and nigth-time when power flows are strongly reduced. In the electric power system (e.g. residential area) illustrated above no significant linear or distorting loads are considered but, due to harmonic propagation, voltage harmonics at Bus1 propagate along the radial feeder and amplify at buses 2~4 up to 3 times in presence of loads and up to 8 times conversely. Harmonic propagation might deeply compromise the power quality. Due to the resonance phenomenon, all utilities connected at Bus4 will suffer of a low quality voltage, although distorting loads are absent. 2

IhARD = kv * Vh = (1/RARD) * Vh PROPAGATION DAMPING Several active filters have been operated as resonance damper; among them …. The active resonance damper (ARD) is an active power filter which acts as well as a 50Ohm terminator in signal transmission line, so representing a resistor RARD where: -) infinite resistance at the fundamental frequency -) null resistance at harmonic frequencies. The ARD is a controlled current source which injects harmonic currents to damp the harmonic propagation along the entire line; the injected current is in phase with the harmonic voltage measured at the connection point: IhARD = kv * Vh = (1/RARD) * Vh The connection point is the end bus of the distribution line as Akagi demonstrated this is the optimal sitting. The ARD also reduces the overall harmonic pollution but such a reduction is a welcome by-product as the amplitude of some harmonic voltages could worsen. such transformers are electromechanical systems incapable to intervene at the proper time in the case of voltage sags (momentary decreases of supply voltage RMS value which lost half a cycle up to many cycles), un-avoiding lamps may be turned off especially when operating under reduced power mode. […] H. Akagi, Control Strategy and Site Selection of Shunt Active Filter for Damping Harmonics Propagation in Power distribution Systems 3

THE ARD PERFORMANCE The ARD performance depends on the value of Kv which is the inverse of the resistance RARD represented by ARD itself; Since the optimal value of RARD equals the characteristic impedance of the distribution line calculated at the filter terminals, the constant Kv is obtained by calculating L and C, i.e. the line inductance and capacitance per length. The calculation of Z0 is not an easy task and it might vary with the connection/disconnection of loads and capacitor banks for power factor correction; hence Z0 must be calculated adaptively. We considered an ARIMAX estimator for automatically adjusting the value of Kv to the optimal value requiring just 5 cycles of the fundamental. […] W. C. Santana, K. Al-Haddad and L. Borges da Silva, “Design and Control Strategy of an Active Resonance Damper”, IEEE Transactions on Power Delivery, Nov. 2009. 4

INTRODUCING TO THE HARMONIC VOLTAGE COMPENSATOR (HVC) Thevenin equivalent circuits at the kth harmonic such transformers are electromechanical systems incapable to intervene at the proper time in the case of voltage sags (momentary decreases of supply voltage RMS value which lost half a cycle up to many cycles), un-avoiding lamps may be turned off especially when operating under reduced power mode. The autros’ damper is named harmonic voltage compensator (HVC) as it is designed for both harmonic propagation damping and harmonic voltage compensation. Tha main advantage in using the HVC consists in avoiding the calculation of the line characteristic impedance. Instead of injecting harmonic currents as the ARD does, the HVC generates harmonic voltages to damp harmonic propagation and compensate voltage harmonics. The voltages generated by the HVC are determined by using an iterative algorithm which only requires the voltage measurement at the PCC. 5

THE ITERATIVE METHOD This iterative method is appealing and feasible for practical purposes as it is extremely simple and easy to be implemented; sometimes this algorithm is time-consuming hence the authors designed a further algorithm which is faster than the iterative one. such transformers are electromechanical systems incapable to intervene at the proper time in the case of voltage sags (momentary decreases of supply voltage RMS value which lost half a cycle up to many cycles), un-avoiding lamps may be turned off especially when operating under reduced power mode. Burgio, D. Menniti, N. Sorrentino, A. Pinnarelli “Implementation of the shunt harmonic voltages compensation approach”, Electric Power Systems Research, 81 (3) (2011) 798. 6

THE SENSITIVE METHOD 3 WHILE THD(Vpcc) > THDref DO 4 FOR all harmonics must be compensated DO 5 6 ENDFOR 8 9 10 11 12 i:=i+1 13 ENDWHILE being sensitive to the variation of the total harmonic distortion (THD) of VPCC between two consecutive iterations, the sensitive algorithm is more robust and faster than the iterative one. The authors demonstrated also that, considering electrical circuits with ideal voltage or current sources and linear passive components, the HVC requires only three cycles of the fundamental frequency to completely annul the THD of VPCC. For all those harmonics which relevantly contribute to the THD of VPCC, the sensitive algorithm compensates such harmonics until the value of THD is lower than a desired value (THD minimizing stop criterion); due to the presence of nonlinear loads, the THD of VPCC could increase rather than decrease as a consequence of the HVC so a further stop criterion must be adopted. At this purpose, each iteration of the sensitive algorithm terminates comparing the current THD value with the previous one. such transformers are electromechanical systems incapable to intervene at the proper time in the case of voltage sags (momentary decreases of supply voltage RMS value which lost half a cycle up to many cycles), un-avoiding lamps may be turned off especially when operating under reduced power mode. Burgio, D. Menniti, N. Sorrentino, A. Pinnarelli “Implementation of the shunt harmonic voltages compensation approach”, Electric Power Systems Research, 81 (3) (2011) 798. 7

COMPARISON OF FILTERS IN TERMS OF… In order to compare the two active filters, ARD and HVC, several numerical experiments were carried out using Simplorer simulation software. The test system used for the comparison is illustrated in the circuit of Fig. 3 and it represents the single-phase equivalent circuit of a low voltage distribution line operated at the fundamental frequency of 50Hz. Linear or distorting loads are not considered so to evaluate the worst configuration for the harmonic propagation [9] which mainly occurs due to the presence of the three power factor correction capacitors, Cphf. The circuit of Fig. 3 is supplied by two ideal voltage sources where the first, named VS, is operated at the fundamental frequency and the second, named Vh, is operated at 5th, 7th and 11th harmonics (the skin effect is negligible for the considered harmonics); sources and line parameters are reported in Table I. The circuit was initially studied not considering active filters; the amplitude of voltages at buses 1-4 and the magnifying factor with respect the value measured at Bus1 are reported in Table II. such transformers are electromechanical systems incapable to intervene at the proper time in the case of voltage sags (momentary decreases of supply voltage RMS value which lost half a cycle up to many cycles), un-avoiding lamps may be turned off especially when operating under reduced power mode. 8

… IN TERMS OF MAGNIFICANT FACTORS The iterative and the sensitive algorithms essentially differ in term of speed, there is no difference in terms of final harmonic resonance damping. such transformers are electromechanical systems incapable to intervene at the proper time in the case of voltage sags (momentary decreases of supply voltage RMS value which lost half a cycle up to many cycles), un-avoiding lamps may be turned off especially when operating under reduced power mode. mi is the magnifying factor at the bus before a damping action; Mi is the magnifying factor at the bus after a damping action. 9

… IN TERMS OF CYCLES such transformers are electromechanical systems incapable to intervene at the proper time in the case of voltage sags (momentary decreases of supply voltage RMS value which lost half a cycle up to many cycles), un-avoiding lamps may be turned off especially when operating under reduced power mode. The performance of the ARD, the HVCITER and the HVCSENS are now evaluated in terms of cycles of the fundamental frequency required to damp the harmonic resonance along the distribution line; such a comparison is illustrated in Fig. 4a. the ARD action lasts five cycles since the AIRIMAX estimator must calculate the characteristic impedance of the network; in the same interval, the HVC reachs an Ip …. the amplitude of 7th harmonic of the voltage at PCC after the harmonic resonance damping; it is evident the advantage in using the HVC as such an amplitude is quite zero while the ARD decreases this amplitude only to 2.96V. 10

… IN TERMS OF POWER LOSSES such transformers are electromechanical systems incapable to intervene at the proper time in the case of voltage sags (momentary decreases of supply voltage RMS value which lost half a cycle up to many cycles), un-avoiding lamps may be turned off especially when operating under reduced power mode. A last comparison is now presented evaluating the power losses along the feeder1-2, feeder2-3 and feeder3-4 of the test system of Fig. 3. For sake of simplicity, the calculation of power losses is subject to the following assumption: a) only the currents reported in Table IV and flowing along the longitudinal impedances are considered and b) the longitudinal impedances equals 1 as they are identical. The power losses are so determined by calculating the sum of the squared amplitudes of the longitudinal currents; these sums are reported in the last column of Table IV. It can be noted that ARD decreases power losses from 1.94 to 0.45 (i.e. Of 75.56%) while the HVC to 0.31 (i.e. of 83.61%). 11