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IEEE TRANSACTIONS ON SMART GRID, VOL. 4, NO. 2, JUNE 2013 1151

Direct Single-Loop -Synthesis Voltage Control for Suppression of Multiple Resonances in Microgrids

with Power-Factor Correction CapacitorsAlireza Kahrobaeian and Yasser Abdel-Rady I. Mohamed , Senior Member, IEEE

Abstract— This paper presents a robust single-loop direct voltagecontrol strategy featuring effective suppression of uncertain reso-nant modes generated due power-factor correction (PFC) capaci-tors and residential capacitive loads in distributed generation (DG)microgrids. The proposed controller adopts an improved uncer-tainty modeling approach, which facilities the realization of a ro-bust controller based on structured singular values analysis.The resultant controller is used as a direct voltage controller whereno additional damping technique, either passive or active, is re-quired. This feature reduces the sensor requirements in the DGinterface controller and enhances the bandwidth characteristics

of the closed-loop voltage-controlled converter. Mathematical andcomparative analyses are provided to show the advantages of pro-posed -synthesis controller over the conventional controllerin maintaining robust stability as well as robust performance of the microgrid in presence of parameter uncertainties and uncer-tain resonant peaks caused by connection of PFC capacitors. Sys-tematic design approach for the proposed controller is presented.Time-domain simulation studiesand comparative experimental re-sults are presented to show the effectiveness and robustness of theproposed controller in microgrid applications.

IndexTerms— Distributed generation, interaction dynamics, mi-crogrids, resonance damping, voltage control.

I. I NTRODUCTION

E FFECTIVE utilization and integration of distributed gen-eration (DG) microgrids has become a major driving forcein realizing the vision of clean and sustainable energy supply inthe near future. The use of DG microgrids as building blocks of large active distribution systems has the potential to increasethe service reliability and reduce the need for future genera-tion expansion or grid reinforcement. Moreover, it extends upthe possibility of making the DG responsible for local power quality in a way that is not possible with conventional central-ized generators [1]–[4]. However, robust operation of DG unitsin microgrids can be a challenging objective when differenttypes of loads and power system devices are connected in thevicinity of a DG unit. Power factor correction (PFC) capacitorsare widely used in power distribution systems to improve their ef ficiency and power quality. PFC capacitors are mainly used incustomer’s side to avoid utility power factor penalties. Reactive power compensation results in reduced losses in transmission

Manuscript received January 08, 2012; revised June 26, 2012 and September 04, 2012; accepted October 31, 2012. Date of publication April 09, 2013; dateof current version May 18, 2013. Paper no. TSG-00008-2012.

The authors are with Department of Electrical and Computer Engi-neering, University of Alberta, Edmonton, AB T6G-2V4 Canada (e-mail:[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TSG.2012.2228014

lines as well as transformer heating. Moreover, in long distribution lines, they are often used in order to increase the supplyvoltage at the load side. However, switching of PFC capacitorswithin a microgrid can cause performance degradation and evensystem instability [5]–[8]. This is due to 1) PFC capacitors af-fect the effective value of the capacitor filter of DG units; and2) PFC capacitors induce multiple uncertain resonant dynamicsreflected to DG units. On the other hand, capacitive loads (e.g.,residential capacitive loads) might generate uncertain resonant

modes reflected to DG converter control dynamics [9]. Accord-ingly, PFC capacitors and capacitive loads in DG microgrids di-rectly affect the closed loop voltage control stability and mightyield high resonant voltage and current disturbances.

Several hierarchical control strategies have been reported for DG units in grid connected and autonomous microgrid modes[1]–[4]. However, these methods do not incorporate the effectsof filter parameter variations and the system uncertainties alongwith the effect connection of PFC capacitor banks in the vicinityof DG units.

One of the well-established robust control approaches that isreported in many converter-based applications is control[2], [10]–[12]. A conventional multi-loop control scheme com-

posed of a robust outer voltage controller is proposed in[8] to increase microgrid robustness against effective filter capacitance var iations in presence of PFC capacitors. However,only uncertainty in the effective filter capacitance is consid-ered. Further, the uncertainty over the effective filter capaci-tance caused by connection of PFC capacitor has been mod-eled as a lumped unstructured uncertainty. This is usually ob-tained by comparing the nominal open loop transfer functionand the transfer function with the worst case filter capacitor variations. The proposed controller succeeds in maintaining thesystem stability in presence of PFC capacitors; however, the robust perf ormance of the system is compromised due to the in-herent conservative nature of a robust controller synthe-

sized for unstructured uncertainties [13], [14]. Therefore, pos-sible instabilities can be yielded under parameter variation; andthe voltage quality is highly affected as the PFC capacitor isconnected. It should be noted that this limitation is inherentlyrelated to the fundamental concept behind the control approach, which is optimum loop shaping under unstructured un-certainty model. Unstructured uncertainty modeling can be usedin lar ge control systems, where there is a dif ficulty in modelinguncertainties in each subsystem. For converter-based DG units,the system order is generally low. Therefore, the conservativeunstructured uncertainty assumption is not really needed in suchapplications. On the other hand, conventional control is applied with inductor current feedback control and inner capacitor

current loop to damp the resonant peak of the ac-side filter [8];

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KAHROBAEIAN AND MOHAMED: DIRECT SINGLE-LOOP -SYNTHESIS VOLTAGE CONTROL 1153

Fig. 2. The effect of PFC capacitor on the open loop system dynamics.

The voltage reference provided by the droop controller isapplied to the voltage controller, regulates the inverter outputvoltage. However, the relative stability of the medium-fre-quency modes, associated with the voltage control dynamics[11], [12], is mainly affected by the interaction dynamics between filter parameters and other microgrid entities. Notethat interaction dynamics at these modes can be yielded due to possible mode excitation by microgrid low-order harmonics.

PFC capacitor banks can affect those medium-frequencymodes, yielding to microgrid instability and performancedegradation. The sample DG unit shown in Fig. 1 (DG1) isconnected to the main feeder through an LC filter and theline impedance (line1), supplying common loads connectedto the feeder. The connected loads can be linear RL type,nonlinear rectifier type or motors accompanied with PFC capacitor banks to increase the total load power factor. However,PFC capacitors would increase the effective voltage-sourceinverter (VSI) filter capacitance, changing the LC filter cut-off frequency and subsequently affecting the stability of the VSIcontroller. Moreover, the additional capacitor located after the line impedance, introduces new resonance frequencies

which can cause resonant excitations once a disturbance near those resonances occur. Fig. 2 demonstrates the effect of PFCcapacitor-connection on the open loop system as part of theinteraction dynamics between the DG unit and the rest of themicrogrid. Note that in the model of Fig. 2, , and

are all considered as external disturbances modeling theinteractions between a DG unit and the network. When the PFCcapacitor is not connected, the open-loop transfer function can be obtained as in (9). When the PFC capacitor is connected,the new open-loop transfer function from the inverter voltage

to the bus voltage can be obtained by (10). Notethat the inner capacitor current feedback loop, with gain ,is also considered in Fig. 2 in order to account for the active

damping feature. (See the equation at the bottom of the page.)Considering the system parameters presented in Appendix,Fig. 3(a) compares the frequency response of the open loop

Fig. 3. The effect of adding PFC capacitor on the system open-loop frequencyresponse (a) without active damping (b) with active damping

.

resonance transfer functions with and without the PFC capac-itor. As shown in Fig. 3(a), connecting PFC capacitor, not onlycauses the original resonance peak associated with the LC filter to drift, but also a new resonant frequency is formed which canaffect system stability and performance in case of harmonicexcitations. Multiple uncertain resonances can be easily createdunder different values of the PFC capacitor (e.g., switchedcapacitors).

Active damping is a well-established method in order to sta- bilize the open loop system before designing the controller. Asshown by the solid-curve in Fig. 3(b), when the PFC capacitor is not connected, applying current feedback from the filter ca-

pacitor current effectively damps the resonance peak of the LCfilter. However, since there is no access to the current goingthrough the PFC capacitor, , the resonance peaks caused

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(10)

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1154 IEEE TRANSACTIONS ON SMART GRID, VOL. 4, NO. 2, JUNE 2013

Fig. 4. LFT representation of closed-loop system.

by its connection cannot be fully mitigated; and therefore, af-fecting system stability and performance. As shown in Fig. 3(b),this effect gets even more obvious as the capacitor value in-creases, which increases the low-frequency resonance peak. Theuncertain low-frequency resonant mode matches the bandwidthof low-order harmonics; therefore harmonic excitation and har-monic instabilities can easily occur even if the converter-side

LC filter resonance is damped.Fig. 3 implies that the system stability and performance

can be affected by the uncertainties imposed on the open loop by connecting the PFC capacitor even when active dampingmethods are used. This motivates the necessity of designing arobust voltage control strategy that maintains system stabilityand provides acceptable performance in a reasonably widerange of parameter variations that might be imposed by theun-modeled dynamics of the rest of the microgrid.

III. R OBUST CONTROL

A. Robust Control of Systems With Unstructured Uncertainty

Any linear interconnection of inputs, outputs, system perturbations and the controller can be rearranged to match the closed-loop format represented in Fig. 4 using linear fractional trans-formation (LFT), where is the open-loop transfer function,

is the controller and is the unstructured uncertainty block. The term unstructured refers to the fact that is assumedto be bounded but otherwise unknown.

The controller can be considered of a system component itself and therefor the standard configuration may be obtainedusing the lower LFT of and as presented in (11).

(11)

The variables , , , and , in Fig. 4 are vector signals,where denotes the exogenous input including reference com-mand and any possible disturbances; denotes the error output;

and are the input and output signals of the uncertainty block.Based on the 2-input, 2-output structure of Fig. 4, (12) can beconcluded as the input output relationship. The stabilizing con-troller should be designed in a way that not only the opti-mized performance of the nominal plant is achieved with re-spect to minimizing the effect of the exogenous input, , over output , but also the closed loop system remains stable for all possible plant uncertainties of .

(12)

Fig. 5. Standard configuration with analysis.

Ignoring the effect of perturbation block, [13] suggests that thenominal performance is achieved when . Note that

and stands for the singular value.

The robust stability of the closed loop system can be studied based on Theorem 1.

Theorem 1: Let be stable, for all , the perturbed system of Fig. 5 is robustly stable if

Although adopting the optimization approach, basedon singular values minimization, provides stable operation of

the perturbed system based on Theorem 1, lack of informationon the structure of leads to conservative solutions in many practical problems where the uncertainty consist of multiplenorm-bounded perturbations. In this case, the performance of the closed-loop perturbed system maybe degraded [13].

B. Robust Control of Systems With Structured Uncertainty

According to [13], having more knowledge on the uncer-tainty structure provides less conservative solutions on “struc-tured singular values analysis. Using -analysis, not onlycan provide robust stability but also the system performanceunder uncertainties will improve. Once again consider the

configuration shown in Fig. 4, the structure of the uncertainty block, , is assumed to be known as in (13).

(13)

where with is the dimension of the block .

De finition 1: When isan interconnectedtransfer matrixas in Fig. 4, the structured singular value with respect to isdefined by (14):

(14)

where is the smallest singular value of (i.e., )that makes .

The above definition indicates a frequency dependant stability margin [13], [14]. The robust stability result with regardto structured uncertainties is given in Theorem 2.

Theorem 2: Let be stable, and , the per-turbed system of Fig. 4 is robustly stable with respect to , if and only if .

Theorem 2 gives a suf ficient and necessary condition for robust stabilization. It can be shown that it gives a less conserva-tive stabilization measure as compared to norm minimiza-tion. This can be shown by

(15)

where the equality only holds when is unstructured. There-fore, in case of structured uncertainties, (15) clearly shows that

norm optimization approach leads to more conservative

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controllers as compared to the controller designed based on min-imizing structured singular values (i.e., ).

In addition to robust stability, it is desired that the designedcontrol system can maintain a satisfactory performance leveleven in presence of plant dynamic uncertainties and disturbances. Using -analysis provides a measure to analyze the performance of the closed loop system with the perturbations

occurring. The robust performance requirement can be set as(16) for all [13], [14].

(16)Reference [13] suggests that a fictitious performance block of

can be assumed as shown in Fig. 5, with appropriate di-mensions and . Therefore, based on Fig. 5, the robust performance condition of (16) can be equivalently considered asa robust stabilization problem with the uncertainty block to bereplaced by where

(17)

This is turns out to be a stabilization problem with respect to thestructured uncertainty of , thus yielding to (18)

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C. and -Synthesis Voltage Controller Design

Mixed sensitivity robust design approach along withinner current feedback loop is used in [8] in order to maintainthe stability of the microgrid when PFC capacitor bank isadded. Following the conventional approach, uncertainty inthe effective filter capacitance is assumed to be unstructured

and therefore it is modeled as a single lumped 1 1 full block matrix of defined by (19) where stands for the singular value and and are the nominal and perturbed transfer functions, respectively.

(19)

(20)

Fig. 6 shows the standard configuration adopted for con-troller design. is the plant unstructured uncertainty andthe weighting function is determined from the worst case

and is selected to lie above to normalize the uncer-tainty block (i.e., ). and are the weightingfunctions, penalizing the tracking error and controller effort re-spectively and are suggested to be in form of (21) and (22).The resonant mode in (21) provides internal model dynamics atthe fundamental frequency to achieve zero steady-state trackingerror when the controller is implemented in the stationary ref-erence-frame.

(21)

(22)

Using the schematic provided in Fig. 6 and introducing designweighting functions, the weighted closed loop system can berecast in the standard configuration as shown in Fig. 7

Fig. 6. Schematicof theclosed-loopsystem with conventional Controller.

Fig. 7. Closed loop configuration for robust stability analysis.

where is the robust controller to be designed from solvingthe mixed-sensitivity optimization problem of minimizingnorm of the closed loop system transfer matrix from to .

Considering the design parameters provided in Appendix and by following the provided design approach, is givenin (23). Note that current feedback from the filter capacitor isadopted in order to damp the LC resonant peak.

(23)

Although adopting optimization approach, based on sin-gular values minimization, provides stable operation of thesystem in presence of the unstructured uncertainties, it leads toconservative solutions where the performance of the perturbedsystem is degraded and therefore it fails to meet the robust performance criteria [13], [14]. Therefore, this paper adopts amore detailed model of the system uncertainties which providesfurther knowledge on the structure of the uncertainties. Thismakes it possible to use the -synthesis approach in order to achieve a less conservative robust voltage controller for microgrid applications.

Fig. 8 shows the schematic of the closed-loop system withthe -synthesis controller, where instead of using lumped un-structured uncertainty block, the uncertainties over the effectivefilter capacitor causedby the addition of aswell asthe possible filter inductance variations are modeled individuallyusing multiplicative perturbation method. are theweightings used to normalize the uncertainty blocks assuming

varying up to 5 times its nominal value and 10% deviation

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Fig. 8. Schematic of the closed-loop system with -synthesis controller.

on . and are assumed to have the same form as (21)and (22), respectively.

The schematic of Fig. 8 can be again rearranged in the stan-dard configuration of Fig. 7. Note that, more informationon the structure of the uncertainty block is available by adoptingthe suggested approach. The structure of is provided in (24).

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In this paper, the D-K iteration method provided by Matlab robust control toolbox [17] is adopted to compute the controller.

Based on the weighted open-loop schemes provided inFig. 8 and using the design parameters provided in Appendix,the -synthesis controller is designed. Note that the proposed controller which is based on structured singular anal-ysis provides a direct voltage control solution where no inner current control is needed for plant stabilization purposes. Thecontroller obtained with this method has high order; thereforethe Hankel-norm model reduction method is applied to reduceits order to 6 as shown in (25). In spite of the higher controller order, the proposed controller doesn’t adopt an inductor-currentfeedback control and doesn’t need a capacitor current feedback control for active damping; therefore, it leads to easier design, implementation and also higher controller bandwidthas compared to the conventional multi-loop controller.Further, the sensor requirements are less, as only the outputvoltage is used for feedback. To limit the converter currentduring fault conditions, the inductor current is monitored andused to generate a proportional signal to block the pulse-widthmodulator, which in turns limits the fault current of the con-verter. This protection feature however does not compromisethe advantages of the direct voltage control.

(25)

IV. COMPARATIVE A NALYSIS

Fig. 9 shows the robust stability measure when the con-troller is adopted with active damping loop. Having enoughdamping of the LC filter resonance mode is crucial in this case.Fig. 9 implies that without the inner capacitor-current controlloop, the system stability is not guaranteed in presence of capacitive uncertainties and therefore, direct voltage control using

robust design fails.

Fig. 9. Robust stability analysis of without damping (solid) and withdamping (dashed).

Fig. 10. Nominal performance (dashed) and robust performance (solid) anal-ysis with control.

With inner active damping loop, the nominal and robust per-formance of the closed-loop system with are shown inFig. 10. It can be seen that when there are no perturbations,the closed-loop system achieves nominal performance

, however, it fails to satisfy the robust performance criterionwhich is required to yield satisfactory performance level evenin presence of plant dynamic uncertainties.

The robust stability and performance measures for the closedloop system with are shown in Figs. 11 and 12, respectively.The robust stability of the system is inferred from Fig. 11 wherethe frequency response of is less than 1 over the wholefrequency range. Note that this is achieved without adoptingany inner inductor or capacitor current loop, which indicatesthe robust and inherent damping characteristics of the proposed

-synthesis direct voltage controller. In order to show the dif-ference between the structured and unstructured modeling of theuncertainties, in the same plot, the maximum singular value of the leading 2 2 transfer matrix, , is shown, whichcharacterizes the robust stability with respect to unstructured

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Fig. 11. Robust stability analysis of direct voltage control with structured(solid) and unstructured (dashed) uncertainty.

Fig. 12. Nominal performance (dashed) and robust performance (solid) anal-ysis of proposed controller.

perturbations. It is seen that the latter is greater than 1 over somefrequencies. This means that the robust stability is not preservedif the uncertainty is unstructured. Thisconfirms that if further in-formation is known about uncertainty structure, structured sin-gular values gives less conservative results as compared to theconventional approach where the uncertainties are lumped to-gether as an unstructured matrix of .

Fig. 12 reveals that both nominal and robust performancemeasures are less than 1 when is applied. This implies thatnot only the system remains stable in presence of high uncer-tainties caused by the addition of the PFC capacitor, but alsothe -based controller would provide satisfactory tracking anddisturbance rejection performances in this case.

Fig. 9–Fig. 12 imply that although the controller canmaintain the stability of the closed loop system in presence of PFC capacitor it yields a limited uncertainty rejection range, andfails to maintain a satisfactory level of performance within therobustness range. Moreover, adopting this controller requires

Fig. 13. Dominant modes of the closed-loop resonant transfer function withand when is increased.

applying active damping method. Even then, as was illustratedin Fig. 2, applying filter capacitor current feedback cannot fullycompensate the resonance effect caused by connecting the PFCcapacitors. The -synthesis controller, on the other hand, can

provide both robust stability and performance without any needfor the inner current feedback (damping).

In order to have a better appreciation of the range of the un-certainty that the system remains stable in and also in order tocompare the relative stability of the closed loop poles, the char-acteristic equation of the closed loop system is derived in (26),where is the voltage controller transfer function. (See theequation at the bottom of the page.) Considering the system pa-rameters presented in Appendix, Fig. 13 shows how the closedloop dominant poles change when the PFC capacitor increaseswhen and controllers are used. The locations of the poles suggest that provides more damping yielding to better performance under the occurrence of uncertainties. It should be

noted that is designed to yield best performance available.Performance limitation is inherently associated with unstruc-tured uncertainty construction associated with the controlapproach.

V. SIMULATION R ESULTS

To evaluate the performance of the proposed control schemeunder the operation of a microgrid system, the study systemshown in Fig. 1 is implemented for time-domain simulationunder Matlab/Simulink environment. The nominal circuit pa-rameters are given in Appendix. First, the effect of the commoninductive load at the main feeder is studied; the local load andalso the nonlinear load are assumed to be disconnected. A three

phase capacitor bank is used to provide 17.3 kVAr in order to compensate for the low power factor of the supplied load.This would increase the load power factor from 0.85 laggingto 1.0. In order to have better appreciation of the proposed di-rect controller, its performance is compared to the conventional

(26)

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Fig. 14. (a) Active and reactive power responses of the microgrid setup(b) Output voltage of DG1 when PFC capacitor is added with dual loop

control. (c) Output voltage of DG1 when PFC capacitor is added withconventional PI dual-loop control with feed-forward. (d) Output voltage of DG1 when PFC capacitor is added with proposed direct voltage -control.

dual loop decoupled PI controller with feed-forward adopted in[19] as well as the robust conventional control with activedamping.

Fig. 14(a) shows how each DG unit is supplying active andreactive power via droop control to meet the load demand be-fore and after the connection of the PFC. Fig. 14(b) shows theoutput voltage of DG1 when the PFC capacitor bank is con-nected at with the conventional robust dual-loopcontroller applied (the output voltage of the second DG showssimilar performance). Due to weak robust stability of the con-

ventional controller, the disturbance rejection performanceis very poor as shown in Fig. 14(b). Fig. 14(c)–(d) shows the

performance of the system when the dual-loop conventional de-coupled PI controller with feed-forward [19] and the single-loopdirect-voltage -controller are adopted; respectively. The per-formance comparison reveals that adopting the proposed directvoltage -controller not only can maintain the system stabilitywithout any inner control loop (i.e., active damping); but alsoyields a control performance better than that of the conventional

dual-loop decoupled controller with feed-forward in terms of less voltage oscillation and higher quality of the output voltage.

In order to investigate the performance of the proposed con-troller under the presence of local disturbances, the capacitiveRLC-type local load (residential capacitive load) shown inFig. 1 is connected to DG1 at whereas the inductiveRL-load and the PFC capacitor bank are both connected tothe main feeder. Fig. 15(a) shows how the demanded activeand reactive powers are divided between the two DG units.Because of the capacitive nature of the connected load, thetotal net reactive power generated by DG unit is negative andit is mainly affecting DG1 due to load proximity to DG1.Fig. 15(b), (c), (d) demonstrate the output voltage of DG1 at the

point of common coupling when the conventional robustdual-loop control scheme, conventional PI controller and the proposed direct voltage -controller are adopted, respectively.The proposed controller yields the best performance in termsof the robust stability and voltage quality.

Having a well-designed voltage controller enables the DGunit to contribute to the voltage reliability at the point of common coupling. To test the robustness of the designed con-trol schemes in rejecting unbalanced voltage disturbances, anunbalance fault-ride through scenario is simulated at .Figs. 16 and 17 show the instantaneous voltage and load currentwith dual loop and direct voltage -control, respectivelywhen the unbalanced load is added. Both controllers succeed

in maintaining robust stable voltage operation at the point of common coupling. However, as can be seen, even though noactive damping/inner current loop is applied, the proposeddirect voltage -controller gives robust and high-qualityvoltage control performance as compared to the conventionalmulti-loop controller.

Fig. 18 shows the performance of DG1 when the nonlinear load is switched on at under different controlstructures. Note that the connection of the nonlinear-rectifier load introduces different harmonic distortions which in turncan excite different resonance modes in presence of the PFCcapacitor. Therefore, this scenario can be considered as a usefulmeasure to test the performance of the proposed controller in

rejecting unknown harmonic disturbances. Fig. 18(a) shows theoutput voltage when the conventional PI dual-loop controller with feed-forward is adopted. As can be see, although thesystem remains stable, the voltage quality is highly degraded

. Fig. 18(b) implies that adopting the dual-loopvoltage controller can also help maintaining system sta-

bility and in despite of slight improvement in voltage quality,the voltage THD is still very high . However,the best voltage quality in presence of nonlinear load can beachieved with the proposed direct voltage -controller as shownin Fig. 18(c). The voltage THD in this case is 0.33% and 5.7% prior and after connecting the nonlinear load, respectively.

It should be noted that theproposed contoller is tested without

internal model dynamics at harmonic frequenices to gauge therobustness of both controller under harmonic disturbances. The

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Fig. 15. (a) Active and Reactive power responses of the microgrid setup whencapacitive local load is added. (b) DG1 output voltage with dual loopcontrol (c) DG1 output voltage with conventional PI dual-loop control withfeed-forward (d) DG1 output voltage with proposed direct voltage -control.

THD in the output voltage can be further reduced by embeddinginternal model dynamics in voltage control structure. This can be achieved by including the following resonant dynamics atharmonic frequencies:

where is the fundamental angular frequency, is constant,are damping coef ficient, and is the harmonic order.

VI. EXPERIMENTAL R ESULTS

To validate the effectiveness of the proposed control system,a laboratory-scale microgrid system, shown in Fig. 19, isused. A semi-stack IGBT voltage-source converter is used tointerface a DG unit to the microgrid system. The dSpace1104control system is used to implement the proposed controlscheme in real-time. The pulse-width modulation algorithmis implemented on the slave-processor (TMS320F240-DSP)

Fig. 16. Dynamic response of the system under unbalanced condition with di-rect voltage -control being adopted: Instantaneous load current (a). Output DGvoltage (b).

Fig. 17. Dynamicresponseof thesystem under unbalanced conditionwith dualloop control adopted: (a)Instantaneous load current. (b)Output DG voltage(b).

of the dSPACE controller. The sampling/switching frequencyis 10 kHz, which indicates that the proposed control scheme(voltage and angle controllers) is computationally ef ficient andcan be effectively implemented under high sampling frequency.The current and voltage sensors used are HASS 50-S and LEMV 25-400, respectively. The LC ac-side filter parameters are

and . The performance of the proposedcontrol scheme is tested under different load conditions. For the sake of performance comparison, the robustness of the proposed -controller is compared to the control whensudden filter capacitor increase is adopted.

Fig. 20 shows the power and voltage responses when the mi-crogrid load is connected. As can be seen the voltage dip re-covers swiftly

The detailed voltage waveform at the instance of the loadconnection is also shown in Fig. 20(c) verifying the capa- bility of the proposed method in rejecting load disturbances.Fig. 21(a) shows the output voltage control performance under highly nonlinear load. The voltage quality is slightly degradedunder heavily nonlinear load conditions (3-phase full-wave bridge rectifier with highly-inductive dc-side load). However,the THD in the output voltage is around 5%, which is belowthe standard limits [18].

In order to verify the effectiveness of the proposed -con-troller, in maintaining stable operation of DG units in presence

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Fig. 18. DG1output voltage when thenonlinear load is connected(a) with con-ventional dual-loop control with feed forward (b) with dual-loop control(c) with proposed direct voltage -control.

Fig. 19. A view of the laboratory setup.

of highly capacitive loads and PFC capacitor banks, the nom-inal filter capacitor value is increased by 500% and the responseof the proposed method is presented through Fig. 22. As can be seen, the -controller is well capable of maintaining systemstability by effectively damping the resonance mode changescaused by the filter capacitor increase. On the other hand, how-ever, without active damping, the controller is incapable of maintaining the system stability. Fig. 23 shows unstable systemoperation due to lack of effective damping when controller is adopted without inner active damping loop.

Fig. 20. Control performance with proposed -control. (a) Power response.(b) Phase-a voltage response. (c) Detailed waveform.

Fig. 21. Voltage response with the proposed controller under highly nonlinear load. (a) Voltage waveform. (b) Load current.

Fig. 22. System voltage response to a 500% increase in output filter capacitor when the proposed -controller is adopted.

VII. CONCLUSION

This paper has presented a robust single-loop direct voltagecontrol strategy featuring effective suppression of uncertain res-onant modes generated due PFC capacitors and residential capacitive loads in DG microgrids. An improved uncertainty mod-

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Fig. 23. System voltage response to a 500% increase in output filter capacitor when the controller is adopted w ith .

eling approach has been adopted to facilitate the realization of a robust controller based on structured singular values anal-

ysis. The salient features of the proposed controller are 1) robust stability and robust control performance as compared toconventional multi-loop controller; 2) single-loop directvoltage control performance without dedicated active or passivedamping, which simplifies the control structure and reduces thesensor requirement; and 3) effective mitigation of uncertain andmultiple resonant modes due to PFC or capacitive loads, whichin turns enhances the power quality of the microgrid system.A theoretical comparative analysis, comparative time-domainsimulation studies and experimental results have been presentedto show the effectiveness and robustness of the proposed con-troller in microgrid applications.

APPENDIXThe parameters of the test system shown in Fig. 1 and con-

verter control parameters are given as follows:DG1: 42 kVA, 480 V(L-L), 60 Hz, ,

, , , ,,

DG2: 20 kVA, 480 V(L-L), 60 Hz, ,, , , ,

,: 480 V, : 42 kVA

L1: , L2: , L3:(without d amping): ,

(with damping):

(without damping): , , ,,

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Alireza Kahrobaeian received the B.Sc. and M.Sc.degrees in electrical engineering from University of Tehran, Tehran, Iran, in 2007 and 2010, respectively.He is currently working toward the Ph.D. degree atUniversity of Alberta, Edmonton, Canada.

His research interests include control and stabilityanalysis of microgrids and smart grid systems.

Yasser Abdel-Rady I. Mohamed (M’06–SM’011)was born in Cairo, Egypt, on November 25, 1977. Hereceived the B.Sc. (with honors) and M.Sc. degreesin electrical engineering from Ain Shams University,Cairo, in 2000 and 2004, respectively, and the Ph.D.degree in electrical engineering from the Universityof Waterloo, Waterloo, ON, Canada, in 2008.

He is currently with the Department of Electricaland Computer Engineering, University of Alberta,Canada, as an Assistant Professor. His researchinterests include dynamics and controls of power

converters; distributed and renewable generation; modeling, analysis andcontrol of smart grids; electric machines and motor drives.

Dr. Mohamed is an Associate Editor of the IEEE TRANSACTIONSON I NDUSTRIAL ELECTRONICS. He is also a Guest Editor of the IEEETRANSACTIONS ON I NDUSTRIAL ELECTRONICS Special Section on “Distributed

Generation and Microgrids.” His biography is listed in Marquis Who’s Who inthe World . He is a Registered Professional Engineer in the Province of Alberta.

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