Design and Comparison of Two Control Strategies for Voltage-sag Compensation using Dynamic Voltage Restorers

The Dynamic Voltage Restorer (DVR) is one of the most frequently used devices for voltage-sag compensation. This work explains the design procedure and comparison of two different control strategies for the compensation of balanced and imbalanced voltage sags by using a DVR. The two strategies considered are the widely-used proportional-integral (PI) controller and a new approach based on the generalized proportional-integral (GPI) controller. Both control schemes are implemented in a synchronous reference frame (SRF) and use a feedforward term to improve the time response. The simulations in PSCAD/EMTDC show the performance of both control strategies for several voltage sags and for grid-frequency deviations. The obtained results show that the SRF-GPI approach is superior. DOI: http://dx.doi.org/10.5755/j01.eee.19.6.4553


II. MODEL OF THE DVR
Although a VSC has a nonlinear nature due to its switching operation, it will be considered as a linear amplifier under the assumption of a high switching frequency [7].In this situation, the DVR can be modeled as an ideal voltage source connected to an LC filter.Since the controllers will be implemented in a SRF, the resulting statespace model of the DVR shown in Fig. 1 is with where f L and f R are the leakage inductance and the copper losses of the transformer, respectively, f C is the output capacitor and 1 ω is the angular speed of the SRF i are the current components through the leakage inductance, sd i and sq i stand for the current of the load, and d u and q u are the VSC output voltage components.
The components sd i and sq i can be compensated by using the feedforward term 1 1

ˆ( ) s P
− , which it is shown in the control schemes depicted in Fig. 2 and Fig. 3.In these schemes, the transfer-function blocks for the model of the plant are The whole system can be decoupled by using the following equations [8]: ( ) ( ) ( ) Then, the generic transfer function in a d-q frame can be expressed as with c ( ) U s being the controller output, 2 The control strategy based on a SRF-GPI regulator is shown in Fig. 2. The scheme consists of a feed forward compensation (with f 1 K = ), which speeds up the transient response and a feedback loop with a GPI controller, which reduces the tracking error of the reference.In order to design the control system, the following errors must be defined: ) The error ( ) y e t is obtained by using (8) From the previous expression, the error derivative can be obtained by means of an integral reconstructor [9] as shown in (12) A PID control law can be defined in the time domain as The error derivative term of (13) is generally measured, but it can also be estimated as it is done in the GPI control design methodology.The derivative term can be estimated replacing ( ) y t e ɺ by the integral reconstructor, ˆ( ) y t e ɺ . Moreover, introducing several consecutive integrals of ( ) y e t , the error due to the initial conditions and possible disturbances can be reduced.Additionally, the tracking error is improved.In the example developed in Section V, a reasonable tradeoff between tracking accuracy and implementation complexity of the controller is achieved by using three consecutive integrals.Then, the time-domain equation of the GPI controller is The closed-loop transfer function is obtained by combining (15) and ( 8), which gives the following characteristic polynomial The design coefficients can be chosen to obtain a Hurwitz polynomial with the desired roots [10].If the six roots are considered to be equal ( s p = ), the design coefficients can be calculated as Fig. 4 shows the root locus of the control scheme and the closed-loop pole location, which are placed at 4200 s = − .The Bode plot for the closed-loop transfer function including the designed GPI controller is illustrated in Fig. 5.

IV. DVR CONTROL SCHEME BASED ON THE SRF-PI CONTROLLER
The control scheme based on a SRF-PI regulator is shown in Fig. 3. Similarly to the scheme presented in Section III, this one includes a feedforward action (with f 1 K = ) [3] and a feedback loop in which a PI controller is used in a SRF.
The closed-loop transfer function can be obtained combining the transfer function of the plant shown in equation ( 8) with the following transfer function of a PI controller plus a phase-lag compensator.This compensation is necessary to reduce the amplitude of the frequency response at the resonant frequency caused by the LC filter where p K and i K are the proportional and integral gains, respectively, and cut ω is the pole modulus of the phase-lag compensator.
The resulting closed-loop transfer function is therefore ( ) Equation ( 19) yields (0) 1 F | |= and (0) 0º F ∠ = , for any positive value of the parameters p K and i K .After analysing the root locus, the controller parameters which give a good tradeoff between control speed, stability and accuracy are: p 0 0033 K = .
, i 100 K = and cut 300 ω = rad/s.Fig. 6 shows the root locus of the control implemented.It can be observed that the dominant poles are located at ( 150 j85.8 s= − ± ), and therefore, the dynamic response will be slower when compared to the GPI control scheme.It should be remarked that increasing the SRF-PI control bandwidth would lead to overshoots that could exceed the maximum allowed voltage in the protected load.

V. SIMULATION RESULTS
In order to test the performance of both control strategies designed in the previous sections, extensive simulation results have been performed using PSCAD/EMTDC.The test system implemented is shown in Fig. 8.It consists of two linear loads connected to the PCC: an induction motor and a sensitive load consisting in a three-phase starconnected RL load, which is protected by the DVR.The DVR is composed by three H-bridge-topology converters, a coupling transformer and an output capacitor.The dc voltage of the VSC was set to 600 V.The most relevant parameters used in simulations are summarized in Table I.  to 0 43 s t = .
), a) Table II summarizes the 5% settling time of both control schemes for the different cases simulated.It is noteworthy that the settling time in each case depends not only on the dynamic response of the designed controllers and the filter, but also on the transient of the voltage-sag to be compensated.It can be seen that the transient response of the SRF-GPI scheme is faster than the one obtained with the SRF-PI scheme.

VI. CONCLUSIONS
In this paper, two control schemes implemented in a SRF for the compensation of balanced and imbalanced voltage sags using a DVR system are presented.Both control strategies use a unity feedforward action and are implemented in a SRF.The SRF-GPI control uses a feedback loop with a GPI controller, while the SRF-PI control is based on a feedback loop with a conventional PI controller.An extensive comparison of the performance of both control methods for balanced and imbalanced voltage sags, including frequency deviations, is carried out in PSCAD/EMTDC.The results show that the performance achieved with the SRF-GPI controller is superior to the one obtained with the widely used SRF-PI controller in terms of dynamic response and steady-state accuracy, particularly when the voltage sag is imbalanced.Both methods provide a robust response to frequency deviations, being the performance of the SRF-GPI control scheme superior once again when compared to the results obtained with the SRF-PI control scheme.
v are the d and q components of the capacitor voltage, which are the variables to be controlled,

Fig. 1 .
Fig. 1.Scheme of a power system with a DVR.
should be noted that only integral terms are present in the new control law.Applying the Laplace transform, the control output

Fig. 4 .
Fig. 4. Root locus plot and closed-loop pole location for the GPI control scheme.

Fig. 5 .
Fig. 5. Bode plot of the closed-loop system for the GPI control scheme.

6 .
Root-locus plot for the designed SRF-PI control scheme (a) and Detail of the root-locus plot (b).

Fig. 7
Fig.7shows the Bode plot of the designed SRF-PI control scheme.

Fig. 7 .
Fig. 7. Bode plot of the closed-loop system for the SRF-PI control scheme.

Fig. 13 .
Fig. 13.Frequency deviation of -5 Hz with an imbalanced voltage sag at phase B: line-to-neutral voltages at the PCC and in the sensitive load from 0 39 s t = .to0 43 s t = .),a) PCC BN V − b) Load BN V − and c) Load BN V − .

TABLE II .
SETTLING TIME OF THE SRF-PI AND SRF-GPI CONTROL SCHEMES.