Investigation and Improvement of Transient Response of DVR at ...

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 43, NO. 5, SEPTEMBER/OCTOBER 2007

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Investigation and Improvement of Transient Response of DVR at Medium Voltage Level Yun Wei Li, Member, IEEE, Poh Chiang Loh, Member, IEEE, Frede Blaabjerg, Fellow, IEEE, and D. Mahinda Vilathgamuwa, Senior Member, IEEE

Abstract—An area of interest for dynamic voltage restorer (DVR) research is the damping of transient LC oscillations initiated at the start and at the recovery instant from a voltage sag. Nonlinear loads, with harmonic currents close to the DVR LC filter resonance frequency, can also excite the resonance oscillations. To compensate voltage sags and dampen high-frequency oscillations simultaneously, an investigation of the transient response of DVR is first carried out. Possible control schemes and their effects on the oscillation attenuation are also studied. Such studied control schemes include the commonly used single voltage loop control, voltage feedback plus reference feedforward control, and double-loop control with an outer voltage loop and an inner current loop. Subsequently, an effective and simple resonance damping method is proposed by employing a closed-loop control with an embedded two-step Posicast controller. The proposed control methods have been extensively tested on a 10-kV DVR system. It is shown that the proposed damping methods improve both the transient and steady-state performance of the DVR. Index Terms—Double-loop control, dynamic voltage restorer (DVR), Posicast control, resonance attenuation, resonant controller, transient oscillation.

I. I NTRODUCTION

A

DYNAMIC voltage restorer (DVR) is proposed for use in the medium-voltage or low-voltage distribution network to protect consumers from sudden sags in grid voltages. A typical DVR-connected distribution system is shown in Fig. 1, where the DVR consists of essentially a series-connected injection transformer, a voltage source inverter, an inverter output filter, and an energy storage device that is connected to the dc link. The power system upstream to the DVR is usually represented by an equivalent voltage source and a source impedance connected in series. The basic operational principle of the DVR is to inject an appropriate voltage in series with the supply through an injection transformer when a voltage sag is

Paper IPCSD-07-025, presented at the 2006 Industry Applications Society Annual Meeting, Tampa, FL, October 8–12, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial Power Converter Committee of the IEEE Industry Applications Society. Manuscript submitted for review June 8, 2006 and released for publication March 24, 2007. Y. W. Li is with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2V4, Canada (e-mail: yunwli@ ieee.org). P. C. Loh and D. M. Vilathgamuwa are with the Centre for Advanced Power Electronics, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail: [email protected]; [email protected]). F. Blaabjerg is with the Institute of Energy Technology, Aalborg University, 9220 Aalborg East, Denmark (e-mail: [email protected]). Digital Object Identifier 10.1109/TIA.2007.904430

Fig. 1. Typical DVR circuit topology (single-phase representation).

detected at the point of common coupling (PCC). Loads that are connected downstream are thus protected. To date, an area of interest for DVR research, which has not been investigated, is its transient behavior, which triggered at the start of a voltage sag and at the recovery moment from a voltage sag. The DVR filter circuit that is connected to eliminate the high-frequency inverter switching noises will cause the DVR model to be lightly damped and to initiate LC resonance with the occurrence of a sudden change in the DVR reference. Widely used nonlinear loads, with high-frequency harmonic currents around the LC filter cutoff frequency, would also continuously excite the LC resonance. To suppress the transient LC resonance, either passive or active damping methods can be used with the latter having an advantage in terms of a less costly system. However, in the past, the damping of transient resonance in a DVR system has not been actively investigated even though a number of classical control schemes have been reported to improve the accuracy of its sag compensation. These control schemes can be briefly categorized as open-loop control [1], [2], single voltage loop control [3], [4], and double-loop control with both inner current and outer voltage loops [5]–[7]. Although effective in sag compensation, most of these reported control schemes are not tested for their abilities in damping transient resonance imposed on the DVR injected voltages. For compensating of voltage sags and damping of highfrequency oscillations simultaneously, an investigation of the DVR transient response is carried out in this paper, with the inclusion of the source of LC resonance and factors affecting the resonance. Different control schemes and their effects on the oscillation attenuation are also studied. Subsequently, an efficient and simple resonance damping method is proposed by employing a closed-loop control and an embedded two-step Posicast controller. By inserting a Posicast controller

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Fig. 2. DVR system overshoot and resonant frequency in open-loop control with (a) varied load resistance, (b) varied load inductance (Rload = 4 p.u.), and (c) varied source resistance (Rload = 4 p.u., Lsource = 0.1 p.u.).

into the feedback control path, the lightly damped system can be successfully compensated with reduced controller sensitivity to parameter variations [14]–[16]. Finally, the proposed control methods have been extensively tested on a 10-kV DVR system with both linear and nonlinear loading conditions emulated.

II. I NVESTIGATION OF THE DVR T RANSIENT R ESONANCE The cause of DVR transient oscillations is mainly due to the LC filter circuit, which is connected at the DVR ac output for filtering out high-frequency inverter switching noises. The LC filter causes the DVR system to be lightly damped and introduces transient oscillations at the LC cutoff frequency. Nonlinear voltages or currents with harmonic components around the LC filter cutoff frequency would also continuously excite the LC resonance even under steady-state conditions. Intuitively, it is expected that the impact of this resonance on the system would depend on both the system (load and source) impedances and control schemes adopted. The following sections illustrate the significances of these influencing factors on the system response.

A. Load and Source Impedance Effects Both the load and source impedances would affect the system response at LC resonance. Fig. 2 depicts the load voltage response with varied load and source impedances (for a 10-kV DVR and a 400-kVA rated load). As shown in Fig. 2(a), the load resistance has an obvious effect on the resonance behavior. With

a larger load resistance (or a lighter load), the resonance is more serious with less damping. To emulate the effects of RL load or widely used induction motor load on the DVR system resonance, the load inductance variation is also examined. As shown in Fig. 2(b), the load inductance tends to reduce the damping effects by increasing the overshoot. This phenomenon can be explained from an energy point of view. A smaller load resistance will dissipate the resonance energy more quickly than a larger load resistance as the DVR guarantees a fixed load voltage. However, with the presence of a series reactance, the voltage drop across the load resistance is reduced, thus reducing the resonance energy absorption by the load. In addition, as shown in Fig. 2(a) and (b), the resonance frequency variation is very limited with the variation of load impedance. In contrast, the source resistance has almost no effect on the DVR system resonant overshoot as illustrated in Fig. 2(c), where the load used is a 4-p.u. resistive load. Note that, in Fig. 2(c), the increase of source resistance slightly reduces the resonance frequency. However, since the source impedance is mainly inductive, the influence of the source resistance on both the resonance peak and frequency is expected to be negligible. On the other hand, the source inductance has no effect on the resonance overshoot and frequency; therefore, the plot of the source inductance variation is not drawn here. B. Resonance Damping Effects of Different Control Schemes To control the DVR output voltages, numerous voltage control schemes have been proposed [3]–[7]. A brief discussion

LI et al.: INVESTIGATION AND IMPROVEMENT OF TRANSIENT RESPONSE OF DVR AT MEDIUM VOLTAGE LEVEL

Fig. 3.

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Control schemes for DVR in stationary frame using (a) single-loop feedback or feedforward+feedback, and (b) double-loop control.

on these control schemes with a focus on their effectiveness in damping the LC filter resonance is presented in this section. 1) Single Voltage Loop Control: Single voltage loop control of DVR [Fig. 3(a)] is commonly used to save extra sensor cost and to provide a simple implementation while still maintaining its ability to achieve good reference voltage tracking and satisfying a steady-state performance. However, its tradeoff between steady-state response, transient response, and stability is quite demanding since large control gains are generally required for good steady-state and transient performance, but they generally deteriorate the system stability. On the other hand, if smaller gains are used to ensure an adequate stability margin, a significant steady-state error may appear, and the system may react much slower. A possible solution to resolve the conflicting requirements is to use a P+resonant controller in the control loop for voltage regulation. In effect, the P+resonant controller is derived by transforming a synchronous frame PI controller to the stationary frame [8]–[12], and it can practically be implemented using the following equation: GPr (s) = kP +

2kI ωcut s s2 + 2ωcut s + ω02

(1)

where kP is the proportional gain, kI is the integral term for the fundamental frequency (ω0 = 2∗ π ∗ 50 rad/s), and ωcut is the cutoff bandwidth that determines the controller’s performance under frequency variations [8]. With a large gain only at the fundamental frequency (by selecting a large kI ), the P+resonant controller has the ability to regulate the fundamental signal with very good steady-state performance. In addition, the controller is less sensitive to parametric variations (and, hence, more stable) since it has nearly zero gains at all other frequencies (ensured by using a small kP ). The Bode plot for the single voltage loop control of DVR with a P+resonant voltage controller is illustrated in Fig. 4. It can be seen that the system exhibits good reference tracking at 50 Hz, but its transient response is still slow due to the limited

Fig. 4. Bode plot of single voltage loop control with and without reference feedforward (kP = 0.0125, kI = 30, ωcut = 5, feedforward gain kf = 1).

proportional gain kP that is needed to maintain system stability, but unfortunately gives rise to an extremely narrow bandwidth. Besides the 50-Hz peak, a resonance peak is also noted at ≈650 Hz and is solely introduced by the LC filter. To improve the transient response, a reference feedforward ∗ ∗ and VInverter [see Fig. 3(a)] path is often added between VDVR [3], [4]. As shown in Fig. 4, this addition obviously widens the control bandwidth that is needed for a faster dynamic response, but its drawback is the accompanied lifting upward of the resonance peak, representing an amplification of resonance. 2) Double-Loop Control: To have a system with both good transient and steady-state performances, multiloop control can be used with an inner proportional current loop added to ensure a fast response as well as good attenuation of the filter LC resonance peak. It is commented that a large kC would flatten the LC filter resonant peak as well as improve the load current disturbance rejection capability of the final system. However, kC is always limited due to practical considerations

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the elimination of oscillatory response that is caused by the DVR LC filter. A. Two-Step Posicast Controller

Fig. 5. Bode plot of double-loop control with different inner current feedback variables (voltage controller kP = 0.5, kI = 400, ωcut = 5, and current controller kC = 1.2).

such as amplifications of capacitor current noise, measurement noise, and dc offset. Finally, with considerations of all these factors, the criteria of tuning kC are to choose a kC as large as possible, provided that the stability of the system from the current feedback disturbance is adequately maintained. In this paper, kC = 1.2 is selected. Fig. 5 shows Bode magnitude plots of the double-loop control with an inner proportional current loop and an outer P+resonant voltage loop for the two cases of feeding back the filter inductor current If and filter capacitor current IC . As anticipated, much better transient as well as steady-state performance is obtained using the double-loop control, as compared to the single voltage loop method. Despite these improvements, the filter resonance peak is not completely flattened due to the limited current controller gain kC . A zoomed-in view of the resonance peak in Fig. 5 would also reveal that the choice of current feedback variable has a slight impact on the controller resonance attenuation ability. In particular, feeding back the filter inductor current is observed to provide more damping to the system than feeding back the filter capacitor current. This is because feeding back the filter inductor current gives a larger overall current loop gain when the same proportional gain kC is used. Although the difference between inductor and capacitor current feedbacks is not so obvious for the LC filter resonance damping shown in Fig. 5, inductor current feedback is shown in [13] to work better in a resonance system with capacitive loads.

III. P ROPOSED C ONTROL S TRATEGY FOR THE I MPROVEMENT OF DVR T RANSIENT R ESPONSE As discussed in Section II, both the single voltage loop control and double-loop control of DVR would experience transient LC oscillations. To improve the DVR transient response, a twostep Posicast controller is proposed for use within the closedloop control path, as shown in Fig. 6(a) and (b). Functionally, the Posicast controller performs wave shaping and is useful for

The two-step Posicast (also referred to as “half-cycle” Posicast) controller functions by splitting up a step input command into two monotonically increasing (or decreasing) intermediate steps. By carefully timing these intermediate stepping instants, the system response produced by the second step can cancel the oscillatory response that is excited by the first step. To minimize its sensitivity to parametric variations, the Posicast controller has also been recently proposed for use with a closed-loop controller with the same tracking performance attained, while introducing an additional degree of control freedom to damp any triggered transient oscillations [14]. Fig. 7 illustrates the principle of the two-step Posicast control. It can be seen that a unit step is separated into two steps with the first step leading the second by a time interval of Td . Timed properly, the two resulting step responses could cancel each other’s oscillations, resulting in a fast and oscillation-free step command response. The magnitude M1 of the first step and the transfer function of the two-step Posicast controller are, respectively, expressed in (2) and (3) to achieve smooth cancellation of oscillation 1 1+δ δ 1 + e−sT d = 1+δ 1+δ

M1 = Gtsp

(2) (3)

where δ is the step response overshoot of the lightly damped system, and Td is half of the resonance period. To illustrate this smooth transition, a step response example is shown in Fig. 8, where it can be seen that, at the first oscillatory peak of the first step response, the second step is initiated. By using (2) and (3), the second step response would have the same oscillatory wave shape as the first, but 180◦ out-of-phase, allowing it to cancel the oscillations excited by the first step command. The resulting step response, which is given by the summation of the two intermediate step responses, is then a smooth monotonically rising wave shape without overshoot and with a well-defined settling time of Td (see bottom trace of Fig. 8). The frequency domain analysis of the two-step Posicast controller Gstp is also performed with its Bode diagrams drawn in Fig. 9. In Fig. 9, the Posicast controller is shown to exhibit multiple-notch filter characteristics with an infinite number of zeros spaced at odd multiples of the system’s natural damped frequency. For resonance damping, the first pair of zeros is used to cancel the dominant pair of poles introduced by the LC filter. Although conceptually similar to the model inversion pole cancellation technique, Posicast pole cancellation is less affected by high-frequency noises since it has limited high-frequency gains, unlike model inversion whose high-frequency gains increase monotonically [14]. Despite its improved performance features, inaccurate knowledge of the plant dominant poles can still result in residual oscillations in Posicast compensation. To


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Fig. 6.

Two-step Posicast controller for DVR embedded in (a) single-loop feedback and reference feedforward control, and (b) double-loop control.

Fig. 7.

Two-step Posicast controller.

Fig. 9. Bode diagram of two-step Posicast controller.

To provide a simple design guide to tune these parameters, the DVR model is first derived and expressed as GDVR =

Lf Cf

s2

1 + Rf Cf s + 1

(4)

where Lf , Rf , and Cf are the filter inductance, filter resistance, and filter capacitance, respectively. The delay time and overshoot can subsequently be deduced and are expressed in the following equations: Td = Fig. 8. Two-step Posicast intermediate step responses, from top to bottom: first step response, second step response, and summation of the two step responses.

mitigate these effects, the Posicast controller can be inserted within a feedback control loop to obtain a more robust option. Sensitivity analysis of feedback Posicast control can be found in [14] and is therefore not documented in this paper. As mentioned earlier, the effectiveness of the Posicast control depends on the tuning of delay time (Td ) and overshoot (δ).

π = ωr

δ = e−ζπ/

√

π 1 Lf Cf

1−ζ 2

−

−Rf π

=e

(5)

Rf2 4L2f

√

Cf /

4Lf −Rf2 Cf

(6)

where ωr and ζ are the resonant frequency (natural damped frequency) and damping ratio of the second-order DVR model. By using (5) and (6), the Posicast parameters are, respectively, calculated as Td = 0.785 ms and δ = 98.1%, assuming that the values given in Table I are used to implement the DVR.

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TABLE I SYSTEM PARAMETERS

Fig. 10.

In this paper, the step response overshoot and the resonant frequency of the implemented DVR are not affected much by the connected loads and the source impedance, as discussed in Section II. The calculated parameters using (5) and (6) are therefore accurate enough for implementation. In situations where the source impedance and load information (such as real and reactive power flowing through the DVR) is known or measured occasionally [17], the Posicast controller parameters can also be occasionally and precisely calculated using a more accurate higher order DVR model with the source and load impedances considered. Although accurate, formulation of the more complex expressions of the natural damped frequency and damping ratio with source and load impedances included can be relatively tedious. In this paper, an alternative method is recommended where the values calculated using (5) and (6) are used as bases to which small increments/decrements are sequentially added until the LC resonance oscillations triggered by existing harmonic load current fall within a permitted limit. As a result, the source and load effects can be compensated. By using this method, the LC parameter variations due to aging or thermal effects can also be compensated, as the control parameter tuning is based on online operation performance. In this paper, the proposed tuning method gives the best performance when the parameters are tuned to Td = 0.784 ms and δ = 91.8%, which are only slightly different from the values calculated using (5) and (6). For digital implementation, the two-step Posicast transfer function in (3) must first be discretized as GZtsp =

δ 1 + z −int(T d/T s) 1+δ 1+δ

(7)

where Ts is the sampling period, and int( ) represents the integer number of the delayed samples. This discrete form of the Posicast controller implies that the accuracy of Posicast compensation is dependent on the ratio of sampling to system resonant frequency. If Td /Ts is not an integer, the fractional

Three-step method for transient damping.

portion could result in delay time error. A higher sampling frequency or a lower resonant frequency would, therefore, give rise to a high ratio of Td /Ts and, hence, finer delayed samples (implying higher accuracy) for timing the second intermediate step command. With a DSP sampling frequency of 5 kHz used in the experimental studies, the number of delayed samples filling a delay interval of Td = 0.784 ms is four, with a time error of ∆t = 0.016 ms introduced by the discretization process. The influences of this time deviation on the performances of different control schemes are more appropriately discussed in their respective sections. However, before proceeding to those discussions, it is commented that a conceptually similar threestep damping method has been reported in [18]. As shown in Fig. 10, the three-step damping method functions by splitting an original reference unit step into three intermediate steps, occurring at times t0 (rising), t1 (falling), and t2 (rising). With this stepping arrangement, the first intermediate step is expected to trigger an initial oscillatory response, which is subsequently cancelled by the other two intermediate step responses. Similarly, it also has two parameters t1 and t2 that need tuning and are, respectively, represented as 1/6 and 1/3 of the resonance period. Comparing both damping methods, it is noted that the settling time of the three-step method (1/3 of resonance period) is shorter than that of the two-step Posicast (1/2 of resonance period). However, with shorter time delays of (t1 − t0 ) and (t2 − t1 ), the resolution problems associated with digital implementation are expected to be more serious. Because of this lack in accuracy, the three-step method is not further considered in this paper. Note that, for accurate threestep compensation, a Td /Ts ratio of multiple integer number of six is necessary. B. Single Voltage Loop With Embedded Posicast Controller The frequency response of single voltage loop feedback plus reference feedforward control with embedded Posicast controller is illustrated in Fig. 11. As shown, the calculated value of Td perfectly compensates the resonance notch in the Bode plot. However, due to the 5-kHz sampling frequency used in the experiment, a delay time of Td1 = 0.8 ms (four delayed samples), instead of the best tuned Td = 0.784 ms, is physically implemented. Clearly, the digitization process introduces only very slight distortion to the resonance compensation, as reflected in the zoomed-in view of Fig. 11. Compared to the control scheme without Posicast in Fig. 4, the amount of attenuation is significant, with the 37-dB resonant peak in Fig. 4 reduces to nearly zero in Fig. 11. Note also that the highfrequency attenuation characteristics of the original control scheme are not affected by the additional Posicast control, as


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Fig. 11. Bode plot of single voltage loop feedback plus reference feedforward with Posicast controller (Td = 0.784 ms, Td1 = 0.8 ms). Fig. 13. Experimental 10-kV DVR system setup.

Posicast controller since it introduces no high-frequency amplification (see Fig. 9). IV. E XPERIMENTAL V ERIFICATION

Fig. 12. Bode plot of double-loop feedback with Posicast controller (Td = 0.784 ms, Td1 = 0.8 ms).

shown in Fig. 11. This is expected since the high-frequency gains of the Posicast control are uniformly maintained at 0 dB, except for occasional notches introduced by its multiple zeros.

C. Double Loop With Embedded Posicast Controller Fig. 12 shows the frequency response obtained using the double-loop control with an embedded two-step Posicast controller. Again, the Posicast controller with Td = 0.784 ms cancels the LC resonance completely. However, with an approximate digitized delay of Td1 = 0.8 ms used for the experimental studies, slightly imperfect resonant cancellation is again observed in Fig. 12. Note that this imperfection lies outside the control bandwidth and will therefore not seriously degrade the overall controller performance during practical testing. Similarly, compared to the double-loop control without Posicast in Fig. 5, the high-frequency roll-off characteristics of the double-loop control are not affected by the embedded

The transient performances of the different control schemes and the effectiveness of the proposed Posicast-embedded method have been tested extensively on a medium voltage level (10 kV) DVR system. The DVR prototype is illustrated in Fig. 13. A star–delta transformer steps up the ac supply voltage to 10 kV, while the load voltage is stepped down using a delta–star transformer. The DVR is connected at the 10-kV level using injection transformers, and its dc-bus voltage is charged to 600 V using two dc power supplies. The proposed control scheme is implemented on a dual DSP–microcontroller system, with an Analog Devices AD21026 floating-point Sharc DSP used to implement the control algorithm and a SAB 80C167 Microcontroller used to generate pulsewidth modulation signals. A dual-port RAM unit (DPRAM) is used as an interfacing link between the DSP and microcontroller, where the results calculated by the DSP are stored in the DPRAM for subsequent reading by the microcontroller. To calculate the appropriate control actions, analog signals are measured and converted to digital signals for reading by the DSP once per switching cycle using two eight-channel AD7891 A/D converters. Other system parameters used for the experimental work are listed in Table I. A. Linear Load The first experiment is conducted with a linear load (67 Ω). The PCC voltage drops to 70% of its nominal value from 40 to 140 ms. With the linear load connected, the startup and recovery transient of injection voltages with the single-loop control is shown in Figs. 14 and 15. The well-damped LC resonance with the Posicast control is clearly shown, which results in the

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Fig. 14. Startup transient of injected voltages with single-loop feedback and feedforward (linear load): (a) without Posicast control and (b) with Posicast control.

Fig. 16. Startup transient of load voltages with single-loop feedback and feedforward (linear load): (a) without Posicast control and (b) with Posicast control.

Fig. 15. Recovery transient of injected voltages with single-loop feedback and feedforward (linear load): (a) without Posicast control and (b) with Posicast control.

Fig. 17. Recovery transient of load voltages with single-loop feedback and feedforward (linear load): (a) without Posicast control and (b) with Posicast control.

improvement of load voltage transient, as illustrated in Figs. 16 and 17. Compared to the single-loop control, the double-loop method has better transient performance, as shown in Fig. 18. However, the transient improvement with the Posicast control is still noticeable. As discussed, the slight deviation of delay time Td during digital implementation causes no performance degradation in the experiment. Note that during DVR startup, the relatively high accuracy of voltage synthesis in Fig. 14 (than in Fig. 18) is related to the feedforward loop used in the singleloop control.

value from 40 to 140 ms. The single voltage loop with/without the Posicast controller is first investigated. With nonlinear load connected, the Posicast controller improves not only the system transient response but also its steady-state performance, as reflected by the DVR injected voltages in Figs. 19 and 20. In Fig. 19(a), without the Posicast control, high-frequency harmonic currents introduced by the nonlinear load continuously excite the LC resonance, causing slight oscillations to be superimposed on the DVR injected voltages even after it stabilizes into a new steady-state condition. On the other hand, with Posicast control added, Fig. 19(b) shows an improved steadystate LC damping, which obviously is another advantage of the Posicast control besides transient damping. This improvement in the steady-state performance is also reflected in Fig. 21, where the high-frequency harmonics (11th, 13th, and 17th) around the DVR LC resonant frequency are effectively reduced

B. Nonlinear Load The nonlinear load used is a diode rectifier bridge with a capacitor bank (200 µF) and resistive load (80 Ω) connected in parallel. Again, the PCC voltage drops to 70% of its nominal


Fig. 18. Startup transient of injected voltages with double-loop control (linear load): (a) without Posicast control and (b) with Posicast control.

Fig. 19. Startup transient of injected voltages with single-loop feedback and feedforward (nonlinear load): (a) without Posicast control and (b) with Posicast control.

by the introduced Posicast control, resulting in a decreased total harmonic distortion (THD) of 4.8%, as compared to 7.6% without Posicast control. The performance of the double-loop control is also investigated in the experiment. The DVR injected voltages are shown in Fig. 22. Again, the frequency spectral analysis in Fig. 23 shows a reduction of high-frequency harmonics as well as a decrease of THD due to the embedded two-step Posicast controller. A final note is that, with a higher LC filter cutoff frequency, the resonant frequency will increase, and the resonant harmonic distortion will be limited to higher order harmonics, which means that the harmonic magnitude and, therefore, the DVR voltage THD under nonlinear loads can be improved. However, the Posicast control cannot improve the DVR voltage harmonics caused by the low-frequency source voltage harmonics.

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Fig. 20. Recovery transient of injected voltages with single-loop feedback and feedforward (nonlinear load): (a) without Posicast control and (b) with Posicast control.

Fig. 21. Frequency spectra of DVR injected voltage with single-loop feedback and feedforward: (a) without Posicast control and (b) with Posicast control.

V. C ONCLUSION This paper has presented an investigation of the highfrequency oscillatory response of the DVR injected voltage caused by the LC filter during the start of a voltage sag, recovery from a voltage sag, or when connected to nonlinear loads. Factors affecting this LC resonance, such as source impedance and load, were studied. Possible control schemes and their abilities to attenuate this oscillatory response were also investigated. An effective and simple resonance damping method was subsequently proposed by employing an embedded two-step Posicast controller, which ensures better transient and improved steady-state THDs during the DVR compensation. As a result, the power losses during DVR operation can be reduced. In addition, as the principle of the Posicast control is to split a single step into two smaller steps, it can contribute to the

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Fig. 22. Startup transient of injected voltages with double-loop control (nonlinear load): (a) without Posicast control and (b) with Posicast control.

[3] J. G Nielsen, M. J. Newman, H. Nielsen, and F. Blaabjerg, “Control and testing of a dynamic voltage restorer (DVR) at medium voltage level,” IEEE Trans. Power Electron., vol. 19, no. 3, pp. 806–813, May 2004. [4] J. G. Nielsen, “Design and control of a dynamic voltage restorer,” Ph.D dissertation, Inst. Energy Technol., Aalborg Univ., Aalborg, Denmark, 2002. [5] D. M. Vilathgamuwa, A. A. D. R. Perera, and S. S. Choi, “Performance improvement of the dynamic voltage restorer with closed-loop load voltage and current-mode control,” IEEE Trans. Power Electron., vol. 17, no. 5, pp. 824–834, Sep. 2002. [6] H. Awad and F. Blaabjerg, “Transient performance improvement of static series compensator by double vector control,” in Proc. IEEE APEC, 2004, pp. 607–613. [7] H. Awad, J. Svensson, and M. Bollen, “Mitigation of unbalanced voltage dips using static series compensator,” IEEE Trans. Power Electron., vol. 19, no. 3, pp. 837–846, May 2004. [8] D. N. Zmood, D. G. Holmes, and G. H. Bode, “Frequency-domain analysis of three-phase linear current regulators,” IEEE Trans. Ind. Appl., vol. 37, no. 2, pp. 601–610, Mar./Apr. 2001. [9] P. Mattavelli, “Synchronous-frame harmonic control for highperformance AC power supplies,” IEEE Trans. Ind. Appl., vol. 37, no. 3, pp. 864–872, May/Jun. 2001. [10] D. N. Zmood, D. G. Holmes, and G. H. Bode, “Stationary frame current regulation of PWM inverters with zero steady-state error,” IEEE Trans. Power Electron., vol. 18, no. 3, pp. 814–822, May 2003. [11] Y. W. Li, D. M. Vilathgamuwa, and P. C. Loh, “Microgrid power quality enhancement using a three-phase four-wire grid-interfacing compensator,” IEEE Trans. Ind. Appl., vol. 41, no. 6, pp. 1707–1719, Nov./Dec. 2005. [12] M. J. Newman, D. G. Holmes, J. G. Nielsen, and F. Blaabjerg, “A dynamic voltage restorer (DVR) with selective harmonic compensation at medium voltage level,” IEEE Trans. Ind. Appl., vol. 41, no. 6, pp. 1744–1753, Nov./Dec. 2005. [13] Y. W. Li, D. M. Vilathgamuwa, and P. C. Loh, “Robust control scheme for a microgrid with shunt-connected PFC capacitors,” in Conf. Rec. IEEE IAS Annu. Meeting, 2005, pp. 2441–2448. [14] J. Y. Hung, “Feedback control with posicast,” IEEE Trans. Ind. Electron., vol. 50, no. 1, pp. 94–99, Feb. 2003. [15] Q. Feng, J. Y. Hung, and R. M. Nelms, “Digital control of a boost converter using posicast,” in Proc. IEEE APEC, 2003, pp. 990–995. [16] P. C. Loh, D. M. Vilathgamuwa, S. K. Tang, and H. L. Long, “Multilevel dynamic voltage restorer,” Trans. IEEE Power Electron. Lett., vol. 2, no. 4, pp. 125–130, Dec. 2004. [17] L. Asiminoaei, R. Teodorescu, F. Blaabjerg, and U. Borup, “Implementation and test of an online embedded grid impedance estimation technique for PV inverters,” IEEE Trans. Ind. Electron., vol. 52, no. 4, pp. 1136– 1144, Aug. 2005. [18] Y. Neba, “A simple method for suppression of resonance oscillation in PWM current source converter,” IEEE Trans. Power Electron., vol. 20, no. 1, pp. 132–139, Jan. 2005.

Fig. 23. Frequency spectra of DVR injected voltage with double-loop control: (a) without Posicast control and (b) with Posicast control.

limitation of transformer saturation by shaping the command voltage and by limiting the in-rush voltage during the startup transient of the DVR compensation. The presented control methods are tested extensively using a 10-kV DVR system with both linear and nonlinear loading conditions emulated.

R EFERENCES [1] C. Zhan, V. K. Ramachandaramurthy, A. Arulampalam, C. Fitzer, S. Kromlidis, M. Barnes, and N. Jenkins, “Dynamic voltage restorer based on voltage-space-vector PWM control,” IEEE Trans. Ind. Appl., vol. 37, no. 6, pp. 1855–1863, Nov./Dec. 2001. [2] A. Ghosh and G. Ledwich, “Compensation of distribution system voltage using DVR,” IEEE Trans. Power Del., vol. 17, no. 4, pp. 1030–1036, Oct. 2002.

Yun Wei Li (S’04–M’06) received the B.Eng. degree in electrical engineering from Tianjin University, Tianjin, China, in 2002, and the Ph.D. degree from the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, in 2006. In 2005, he was a Visiting Scholar with the Institute of Energy Technology, Aalborg University, Aalborg, Denmark. From 2006 to 2007, he was a Postdoctoral Research Fellow in the Department of Electrical and Computer Engineering, Ryerson University, Toronto, ON, Canada. Since 2007, he has been an Assistant Professor with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada. His research interests include distributed generation, microgrid, power quality, and electric motor drives.


Poh Chiang Loh (S’01–M’04) received the B.Eng. (with honors) and M.Eng. degrees in electrical engineering from the National University of Singapore, Singapore, in 1998 and 2000, respectively, and the Ph.D. degree in electrical engineering from Monash University, Clayton, Australia, in 2002. During the summer of 2001, he was a Visiting Scholar with the Wisconsin Electric Machines and Power Electronics Consortium, University of Wisconsin, Madison, where he worked on the synchronized implementation of cascaded multilevel inverters and reduced common-mode, carrier-based, and hysteresis control strategies for multilevel inverters. From 2002 to 2003, he was a Project Engineer with the Defence Science and Technology Agency, Singapore, managing major defense infrastructure projects and exploring new technologies for intelligent defense applications. Since 2003, he has been an Assistant Professor with Nanyang Technological University, Singapore.

Frede Blaabjerg (S’86–M’88–SM’97–F’03) received the M.Sc.E.E. and Ph.D. degrees from the Institute of Energy Technology, Aalborg University, Aalborg, Denmark, in 1987 and 1995, respectively. He was with ABB-Scandia, Randers, Denmark, from 1987 to 1988. During 1988–1992, he was a Ph.D. student at Aalborg University. He became an Assistant Professor, an Associate Professor, and a Full Professor in power electronics and drives at Aalborg University, in 1992, 1996, and 1998, respectively. In 2006, he became the Dean of the Faculty of Engineering and Science, Aalborg University. His research areas are power electronics, static power converters, ac drives, switched reluctance drives, modeling, characterization of power semiconductor devices and simulation, wind turbines, and green power inverters. He is the author or coauthor of more than 300 publications in his research fields, including the book Control in Power Electronics (Academic Press, 2002). During the last several years, he has held a number of chairman positions in research policy and research funding bodies in Denmark. Dr. Blaabjerg is an Associate Editor of the IEEE TRANSACTIONS ON I NDUSTRY A PPLICATIONS , IEEE T RANSACTIONS ON P OWER E LEC TRONICS , Journal of Power Electronics, and of the Danish journal Elteknik, and in 2006, he became Editor-in-Chief of the IEEE TRANSACTIONS ON POWER ELECTRONICS. In 1995, he received the Angelos Award for his contribution to modulation technique and control of electric drives and the Annual Teacher Prize from Aalborg University. In 1998, he received the Outstanding Young Power Electronics Engineer Award from the IEEE Power Electronics Society. He has received five IEEE Prize Paper Awards during the last six years. He received the C. Y. O’Connor Fellowship from Perth, Australia, in 2002, the Statoil Prize for his contributions to power electronics in 2003, and the Grundfos Prize for his contributions to power electronics and drives in 2004.

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D. Mahinda Vilathgamuwa (S’90–M’93–SM’99) received the B.Sc. degree in electrical engineering from the University of Moratuwa, Moratuwa, Sri Lanka, in 1985, and the Ph.D. degree in electrical engineering from Cambridge University, Cambridge, U.K., in 1993. In 1993, he became a Lecturer with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, where he is currently an Associate Professor. His research interests are power electronic converters, electrical drives, and power quality. He has published more than 80 research papers in refereed journals and conference proceedings. Dr. Vilathgamuwa was the Cochairman of the Power Electronics and Drives Systems Conference 2005.