Voltage Sag Correction by Dynamic Voltage Restorer with Minimum Power Injection M.H. Haque Author Affiliation: School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore Abstract: A dynamic voltage restorer is a power quality device used to correct the voltage disturbances by injecting voltage as well as power into the system. A method of determining the exact amount of voltage injection required to systematically correct a specific voltage drop with minimum active power injection is described in this letter. Analytical expressions for both the magnitude and angle of the injected voltage are also derived. It has been found that a voltage drop of less than (1 − pf ) pu can easily be corrected without injecting any active power. For higher voltage drop, injection of active power is essential but its value can be minimized by drawing power from the supply at unity power factor. Keywords: DVR, power quality, voltage sag. Introduction: Voltage magnitude, waveform, and frequency are the major factors that dictate the quality of a power supply. Use of extensive nonlinear power electronic loads is one of the major reasons of deteriorating the quality of power supply. Faults at either the transmission or distribution level may also cause transient voltage sag or swell in the entire system or a large part of it. Also, under heavy load conditions, a significant voltage drop may occur in the system. Such voltage variations are not desirable for sensitive loads.
A dynamic voltage restorer (DVR) is a power quality device capable of protecting sensitive loads against the voltage variations or disturbances [1]-[3]. A DVR is a forced commutated voltage source inverter that injects a dynamically controlled voltage in series with the supply voltage through a booster transformer to correct the load voltage. When the injected voltage is in phase with the supply voltage, the desired voltage correction can be achieved with a minimum voltage injection but it may require a considerable amount of active power injection into the system [1], [4]. When the injected voltage leads the supply voltage, however, the same correction can be made with a lower value of active power injection [4]. This is possible at an expense of higher voltage injection. When the power injection by the DVR is minimized, the same energy storage can be used for a longer period. Such an operation requires careful determination of injected voltage magnitude and angle, however. The objective of this letter is to determine the magnitude and angle of the DVR injected voltage so that a given voltage drop or sag can be corrected with minimum active power injection into the system. Analytical expressions for the injected voltage magnitude and angle, in terms of voltage drop and load power factor, are also derived. Voltage Correction by DVR: Figure 1 shows the schematic diagram of a typical DVR used for voltage correction. When the supply voltage VS changes, the DVR injects a voltage Vi in such a way that the desired load voltage magnitude can be maintained. The DVR is simply a voltage source inverter that produces an ac output voltage and injects in series with the supply voltage through a booster transformer. To correct a given voltage drop, not only voltage injection but also active and/or reactive power injection are needed. The DVR itself is capable of generating the reactive power, however, but the injected active power must come from the energy storage part of the DVR. Thus minimization of active power injection is essential to increase the life of the energy storage. Injected Power: The active power flow at the load and supply sides of Figure 1 can be written as PL = VL I L cosθ L
(1)
PS = VS I L cosθ S .
(2)
Here θ L and θ S are the angle between VL and IL and VS and IL , respectively. Note thatθ L is the load power factor angle and IL is the current in both load and source sides. The DVR injected active power ( Pi ) is the difference between (1) and (2) and is given by Pi = ( PL − PS ) = VL I L ( cosθ L − (VS / VL ) cosθ S ).
Figure 1. Schematic diagram of a typical DVR
(3)
Consider the load voltage magnitude (VL ) and load apparent power (VL I L ) as base quantities. Thus, the injected power in pu can be written as Pi = ( pfL − VS cosθ S ).
(4)
Here pfL = cosθ L = load power factor, and VS is the supply voltage magnitude in pu. For given values of load power factor and supply voltage magnitude, the injected power is minimum when cosθ S = 1.
(5)
In other words, when θ S = 0 or VS and IL are in phase. Thus, VL must lead VS by the power factor angle θ L (for lagging power factor) and it can be realized by careful injection of Vi . The main purpose of the DVR is to maintain the desired load voltage magnitude (say 1.0 pu) despite a supply voltage drop of Vd pu. In this case, the supply voltage magnitude in pu can be written as VS = (1 − Vd ).
(6)
Using (4), (5), and (6), the minimum active power injection( Pi min ) of the DVR can be written as Figure 2. Variation of DVR active power injection against the voltage drop 56
0272-1724/01/$10.00©2001 IEEE
Pi min = Vd − (1 − pfL ).
(7)
IEEE Power Engineering Review, May 2001
Equation (7) indicates that, whenVd < (1 − pfL ), Pi min becomes negative and thus the power flows in reverse direction (from the system to DVR). The DVR may not cater to reverse power flow, however. Such a situation can be avoided by adjusting the value of θ S (instead of zero) so that the power flow becomes zero. The value of θ S for zero power flow can be obtained from (4) and is given by pf θ S = cos−1 L . 1 − Vd
(8)
Injected Voltage: It is demonstrated in the previous section that, when Vd ≤ (1 − pfL ), the voltage correction can be made without injecting any active power but the phase shift between VS and IL must be governed by (8). On the other hand, when Vd > (1 − pfL ), injection of active power is required to correct the voltage but its value can be minimized if VS and IL are kept in phase. Thus the voltage correction requires careful determination of injected voltage so that the desired phase shift (between VS and IL ) as well as load voltage magnitude can be maintained. The procedure of finding the injected voltage is discussed next. When Vd ≤ (1 − pfL ): In this case, the DVR should inject a voltage in such a way that (8) is satisfied as well as the desired load voltage magnitude (1.0 pu) is maintained. From Figure 1, the injected voltage Vi can be written as Vi = VL − VS .
Vd is less than or equal to (1 − pfL ), no active power injection is required to correct the voltage. In this region of voltage drop, both the injected voltage magnitude (see Figure 3) and angle (see Figure 4) increase rapidly with the increase of Vd . When Vd reaches (1 − pfL ), the magnitude and angle of the injected voltage become 1 − pfL2 pu and 90 ° (except for unity power factor), respectively. Note that for unity power factor, the injected voltage magnitude (for Vd = (1 − pfL )) is zero and thus its angle is meaningless. When Vd exceeds (1 − pfL ), the injected power increases linearly with Vd (see Figure 2). In this region of voltage drop, the injected power depends on the load power factor, and for a given value of Vd , it increases with the increase of load power factor. In this region, the injected voltage magnitude increases while its angle decreases with the increase of Vd . Finally, when Vd approaches 1 p.u. the entire load power is supplied by the DVR and the injected voltage magnitude and angle become the same as the desired load voltage magnitude and power factor angle, respectively. Conclusions: A technique of correcting the voltage drop or sag by a DVR with minimum active power injection is described in this letter. The expressions for the injected voltage magnitude and angle that minimize the active power injection are also derived. It has been found that a voltage drop of less than or equal to (1 − pf ) pu can be corrected without drawing any power from the energy storage of the DVR. In this case, only reactive power injection is required to correct the voltage and which can be generated by the DVR. For higher voltage drop, how-
(9)
Consider VS as reference. Thus VL must have an angle of (θ L − θ S ) to avoid reverse power flow. Note that the angle between VL and IL is the power factor angle θ L . Thus in polar form, (9) can be written as Vi ∠β = 1∠(θ L − θ S ) − (1 − Vd )∠ 0 °.
(10)
Here Vi and β are the magnitude and angle, respectively, of the injected voltage. After some mathematical manipulations, Vi and β can be expressed as Vi = Vd2 + 2(1 − Vd )[1 − cos(θ L − θ S )]
(11)
sin(θ L − θ S ) β = tan −1 . 1 V cos θ − θ − − ( ) ( ) L S d
(12)
When Vd > (1 − pfL ): In this case, the DVR should inject a voltage in such away that VS and IL are kept in phase while maintaining the desired load voltage magnitude. Since VS is considered as reference, the angle of both VS and IL should be zero. To satisfy the power factor angle (between VL and IL ), however, VL must lead VS by θ L (for lagging power factor). Thus in polar form, (9) can again be written as Vi ∠β = 1∠θ L − (1 − Vd )∠ 0 0 .
Figure 3. Variation of the magnitude of DVR injected voltage against the voltage drop
(13)
After some mathematical manipulations, the magnitude and angle of the injected voltage can be expressed as Vi = Vd2 + 2(1 − Vd )(1 − cosθ L )
(14)
sin θ L β = tan −1 . cos θ − − 1 V ( ) L d
(15)
Simulation Results: Correcting the voltage drop or sag with minimum active power injection by the DVR is tested on the simple system of Figure 1. The variations of DVR injected power, injected voltage magnitude, and angle against the voltage drop are shown in Figures 2-4, respectively. Five different load power factors are considered in plotting the above figures. It can be observed in Figure 2 that, when the voltage drop IEEE Power Engineering Review, May 2001
Figure 4. Variation of the angle of DVR injected voltage against the voltage drop 57
ever, both active and reactive power injections are required to correct the voltage. In this case, taking as much power as possible from the supply can minimize the amount of active power drawn from the energy storage. This can be achieved by maintaining unity power factor at the supply side. The results shown in this letter are valid for a wide range of voltage drops (0 to 100%) but in practice should be limited to an acceptable range for finite ratings of the booster transformer, voltage source inverter, energy storage, etc. References: [1] N.H. Woodley, L. Morgan, and A. Sundaram, “Experience with an inverter based dynamic voltage restorer,” IEEE Trans. Power Delivery, vol. 14, pp. 1181-1186, 1999. [2] T. Wunderlin, D. Amhof, P. Dahler, and H. Gruning, “Power supply quality improvement with dynamic voltage restorer (DVR),” in Proc. EMPD’98, vol. 2, 1998, pp. 518-525. [3] M. Fang, A.I. Gardiner, A. MacDougall, and G.A. Mathieson, “A novel series dynamic voltage restorer for distribution systems,” in Proc. POWERCON’98, vol. 1, 1998, pp. 38-42. [4] S.S. Choi, B.H. Li, and D.M. Vilathgamuwa, “Dynamic voltage restoration with minimum energy injection,” IEEE Trans. Power Syst., vol. 15, pp. 51-57, 2000. Copyright Statement: ISSN 0282-1724/01/$10.00 2001 IEEE. Manuscript received 7 December 2000. This paper is published herein in its entirety.
2001 PowerTech 10-13 September 2001, Porto, Portugal The PowerTech 2001 conference will be held 10-13 September 2001 in Porto, Portugal. The event is organized by the Power Systems Unit of INESC Porto, the faculty of engineering of the University of Porto, the IEEE Power Engineering Society (PES), and the local PES Chapter of the IEEE. Conference sessions explore topics such as: global restructuring of the electricity business; planning and operation under market conditions; system services in deregulated markets; quality of service; application of artificial intelligence (AI) techniques in power systems; handling uncertainties in power systems; security assessment and risk analysis; integration of dispersed generation in distribution networks; FACTS; electromagnetic transients; insulation coordination; new techniques for protective relays; control of electric machines and drives; online monitoring of underground cables; renewable energy sources; and storage devices. For more information, contact the conference secretariat, e-mail
[email protected], Web http://power.inescn.pt/powertech.
Synthesis of Harmonic Distortion Levels in an LV Distribution Network A. Dysko, G.M. Burt, J.R. McDonald, J. Clark Author Affiliations: Centre for Electrical Power Engineering, University of Strathclyde, Glasgow, U.K.; Energy Systems Research Unit, University of Strathclyde, Glasgow, U.K. Abstract: This letter describes a method of “tuning” an ATP/EMTP-based distribution network model for the purposes of harmonic analysis. When the impact of the nonlinear devices (loads or generators) is studied in terms of network harmonic distortion, it is important to build a reliable model of the network as well as the model of the specific nonlinear device. The letter employs substation-monitoring data to adjust the network model to characterize an existing level of distortion. The letter suggests a method to adjust the harmonic current and voltage sources in order to obtain a specified current and voltage harmonic spectrum at particular locations. Introduction: Increased attention is being given to issues of quality of supply as a result of many pressures including regulatory interest, connection of power electronic devices, and voltage sensitive loads. This is due to the appearance of inverter-connected, small-scale domestic renewable generation. As a result, the characterization of existing LV networks, and the analysis of the potential impact of increased penetration of such equipment, is of increasing importance. This letter presents a means of calibrating an LV distribution network model against power quality data monitored at a secondary substation, with a view to providing an accurate model by which to assess the quality of supply afforded to customers under future distributed generation scenarios. There are various methods of harmonic analysis, some of which are performed in the frequency domain and others in the time domain [1]-[2]. An ATP/EMTP-based model of the power network is simulated in the time domain, which gives relative flexibility to perform various types of studies (load flow, short circuits analysis, transients, etc.) using the same model [3]-[4]. For harmonic analysis in an LV distribution network, the model consists of an infinite voltage source, power system short circuit impedance, substation transformer, impedances of the LV distribution circuits, and loads. A general circuit diagram of such a model is presented in Figure 1. Power system simulation over a few cycles is performed producing sampled current and voltages, which subsequently can be analyzed by Fourier transforms. As it is usually difficult to gather enough information about nonlinearity of individual loads in large distribution networks, it is often easier to measure the current and voltage distortion at the substation level, which can then be used to calibrate the simulation model. The equivalent circuit shown in Figure 2 can usually represent the system shown in Figure 1. The substation monitoring data can provide information about the level of individual harmonic distortion contribution (voltage VDh and current I Dh ), which can be reproduced by the current and voltage harmonic sources I Sh and VSh . The current source I Sh represents the distortion injected into the network by the nonlinear loads connected to the substation. Voltage source VSh is present in order to simulate the harmonics induced from the supply side. Description of the Method: The method of calculating amplitudes and phases of the harmonic sources (voltage - VSh and current - I Sh ) presented here assumes linearity of the power system components. In such
Figure 1. General circuit diagram of an LV distribution network 58
0272-1724/01/$10.00©2001 IEEE
IEEE Power Engineering Review, May 2001
