Accurate Reactive Power Sharing in an Islanded
Microgrid Using Adaptive Virtual Impedances Hisham Mahmood,Student Member,IEEE,Dennis Michaelson,Member,IEEE,and Jin Jiang,Senior Member,IEEE
Abstract—In this paper,a reactive power sharing strategy that employs communication and the virtual impedance concept is pro-posed to enhance the accuracy of reactive power sharing in an is-landed microgrid.Communication is utilized to facilitate the tuning of adaptive virtual impedances in order to compensate for the mis-match in voltage drops across feeders.Once the virtual impedances are tuned for a given load operating point,the strategy will result in accurate reactive power sharing even if communication is dis-rupted.If the load changes while communication is unavailable, the sharing accuracy is reduced,but the proposed strategy will still outperform the conventional droop control method.In addition, the reactive power sharing accuracy based on the proposed strat-egy is immune to the time delay in the communication channel. The sensitivity of the tuned controller parameters to changes in the system operating point is also explored.The control strategy is straightforward to implement and does not require knowledge of the feeder impedances.The feasibility and effectiveness of the proposed strategy are validated using simulation and experimental results from a2-kV A microgrid.
Index Terms—Droop control,microgrid control,reactive power control,virtual impedance.
I.I NTRODUCTION
Distributed generation(DG)has recently received a great deal of attention as a potential solution to meet the increased demand for electricity,to reduce stress on the existing transmission sys-tem,and to incorporate more renewable and alternative energy sources.Subsequently,the microgrid concept has emerged as a promising approach to coordinate different types of distributed energy resources effectively by using local power management systems.A microgrid also allows the DG units to work in an islanded configuration,and therefore improves the availability and quality of power supplied to customers[1].However,is-landed microgrids exhibit challenging control problems,such as the difficulty of maintaining generation/load power balance and reactive power sharing.
When a microgrid is operating in the islanded mode each DG unit should be able to supply its share of the total load in propor-tion to its rating.To achieve this,frequency and voltage droop control techniques that mimic the behavior of synchronous ma-Manuscript received November3,2013;revised February17,2014;accepted March17,2014.Date of publication April1,2014;date of current version October15,2014.Recommended for publication by Associate Editor Y.Sozer. The authors are with the
Department of Electrical and Computer Engineer-ing,University of Western Ontario,London,ON N6A5B9,Canada(e-mail: hmahmoo2@uwo.ca;dgm@uwo.ca;jjiang@eng.uwo.ca).
Color versions of one or more of thefigures in this paper are available online at
Digital Object Identifier10.1109/TPEL.2014.2314721chines in conventional power systems are widely adopted in the literature[2]–[8].The reason for the popularity of the droop control technique is that it provides a decentralized control ca-pability that does not depend on external communication links in the control strategy—this enables“plug-and-play”interfac-ing[3]and enhances the reliability of the system.Communi-cation can,however,be used in addition to the droop control method to enhance the system performance without reducing reliability[9]–[15].
Although the frequency droop technique can achieve accu-rate real power sharing,the voltage droop technique typically results in poor reactive power sharing due to the mismatch in the impedances of the DG unit feeders and,also,due to the differ-ent ratings of the DG units[16].Consequently,the problem of reactive power sharing in islanded microgrids has received con-siderable attention in the literature and many control techniques have been developed to address this issue[17]–[30].
reactive drop是什么意思A comprehensive treatment of the virtual impedance con-cept to mitigate errors in reactive power sharing is presented in[17]–[19].The focus has been on the mismatch in the output impedances of the closed-loop controlled inverters that are used to interface the DG units.With proper design of the voltage con-troller,the closed-loop output impedances must be negligible at steady state around the nominal operating frequency.Therefore, the virtual impedance is dominant,which results in accurate re-active power sharing.However,the analysis in[17]–[19]did not consider the mismatch in the physical impedance of the feed-ers,including transformers,cables,and the interface inductors associated with each unit.
A unique approach is proposed in[20]to achieve accurate reactive power sharing.The proposed strategy requires injection of a small ac voltage signal in the system.Overlaying such an ac voltage signal may reduce the quality of the output voltage and line current[21],[24].Also,extracting and processing this signal may result in a complicated implementation,particularly in a noisy environment.
A control strategy employing an inductive virtual impedance is developed in[21]to ensure accurate reactive power sharing. The proposed analysis and design is based on the assumption that the feeder impedance is small and dominated by the virtual impedance,which is a known parameter.Moreover,the feeder physical impedance is estimated to improve the accuracy,and to include the effect of the imped
ance resistive component.The estimation technique requires the system to operate in grid con-nected modefirst,before islanding.The technique is validated for a system with different virtual impedances,but with identical feeder physical impedances.On the other hand,the analysis and the control strategy introduced in[22]requires that the feeder
0885-8993©2014IEEE.Personal use is permitted,but republication/redistribution requires IEEE permission.
See /publications standards/publications/rights/index.html for more information.
impedances are resistive.The analysis and the control strategy results in accurate power sharing if this condition is satisfied. In practice,however,the feeders may have both nonnegligible inductive and resistive components[17].
Control strategies are proposed in[23]and[29]to achieve ac-curate power sharing among the inverters in an islanded micro-grid.When the inverters are in close proximity an instantaneous control interconnection becomes feasible and can be used as an essential component to achieve accurate sharing.In practice, the DG units might be located in different geographic locations making this approach ineffective.
An interesting control strategy is proposed in[24].The con-trol strategy is composed of two stages:An initial conventional droop-based control stage and a synchronized compensation stage.During the synchronized compensation stage,the fre-quency droop is used to control the reactive power sharing. Since this action will also disturb the real power sharing,an integral control term is added to the voltage droop to main-tain real power sharing accuracy.However,load changes during the compensation period or between compensation periods may result in poor power sharing.
Communication is used in[25]to facilitate the estimation of the feeder impedances which are then used to set the vir-tual impedances to ensure accurate reactive power sharing.The feeder impedance is estimated at the local DG controller by uti-lizing the point of common coupling(PCC)voltage harmonic data transferred via a communication link.This is based on the assumption that the phase angle difference between the voltages at the PCC and at the inverter output is negligible.This assump-tion may not hold for long feeders or for higher power levels. The same technique is used in[26]under the same assumption. Communication links are also used in[27]to enhance the performance of conventional droop control.The proposed tech-nique can reduce the sharing error but cannot eliminate it com-pletely.For example,it reduces the maximum sharing error from5.02%to3.05%.Also,the performance of the technique is sensitive to delays in ,a delay of16ms degrades th
e sharing accuracy significantly.A new droop control is proposed in[28]to reduce the power sharing error.As in[27], the sharing error can be reduced but not completely eliminated and the improvement in performance is not significant if local loads are connected at the output of each unit.
A distributed secondary control technique is proposed in[30] to restore the frequency and the voltage,and also to ensure accurate reactive power sharing.In this technique,the controller is implemented in each DG unit instead of implementing it in the microgrid central energy management unit.Communication data drop-outs/packet losses are briefly discussed in the paper, however the scenario of a complete communication failure is not investigated.
In this paper,a control strategy that employs communication is proposed to enhance reactive power sharing accuracy.Com-munication is utilized to tune the adaptive virtual impedances in order to compensate for the mismatch in voltage drops across feeders.Once the virtual impedances are tuned for a given load operating point,the strategy will result in accurate reactive power sharing even if the communication is disrupted.If
the Fig.1.Islanded microgrid with communication links to an energy manage-ment system(EMS).
load changes while communication is unavailable,the proposed strategy will still outperform conventional droop control.The control strategy is straightforward to implement and does not require knowledge of the feeder impedances.Also,the reac-tive power sharing accuracy based on the proposed strategy is immune to time delays in the communication channel.
In Section II of this paper,an overview of the system structure is presented along with an explanation of how reactive power is conventionally shared.The proposed controller is in-troduced in Section III along with a discussion of the controller sensitivity to the operating point and discussion of the commu-nication mechanism.Simulation and experimental results based on the proposed strategy are presented in Sections IV and V, respectively,followed by concluding remarks in Section VI.
II.I SLANDED M ICROGRID S TRUCTURE AND C ONTROL A.Islanded Microgrid Structure
The structure of an islanded microgrid is shown in Fig.1.The microgrid considered in this paper operates at the low-voltage power distribution level(208V l−l).Each DG unit is connected to the microgrid bus through a feeder.The loads connected to the microgrid bus are lumped into a single load.The focus in this paper is on the fundamental real and reactive power sharing,as in[24]and[28],an
d therefore only linear loads are considered. Each DG unit consists of a primary energy source,a three-phase inverter,and an LCfilter.The feeder impedance includes the impedances of the interface inductor,isolation transformer, and the impedance of the feeder cables.
The local controllers can communicate information,such as real power and reactive power measured at the DG unit output, to the central energy management system(EMS)over a com-munication link.Since the proposed strategy only requires that the local controllers exchange data periodically at a slow rate, low-bandwidth communication links are considered adequate for this application.The local controller consists of the power
MAHMOOD et al.:ACCURATE REACTIVE POWER SHARING IN AN ISLANDED MICROGRID USING ADAPTIVE VIRTUAL IMPEDANCES
1607
Fig.2.Simplified model of the microgrid with two inverters. controller,which generates the output voltage reference,and the voltage controller to track the voltage reference.Conven-tional frequency and voltage droop control is implemented in the controller as follows:
ω=ωo−mP m(1)
V∗=V o−nQ m(2) whereωand V∗are the frequency and voltage magnitude refer-ences,respectively.P m and Q m are the real and reactive powers measured at the output of the DG unit,respectively,and arefil-tered to extract the fundamental power components.m is the frequency droop coefficient and n is the voltage droop coeffi-cient.It is worth mentioning that to facilitate the utilization of the droop control concept in low-voltage distribution networks, a physical and/or a virtual interface inductor is commonly added in line at the output of the DG unit in an attempt to reduce the coupling between the real and the reactive powerflows.
B.Reactive Power Sharing Analysis
The effect of the feeder impedance mismatch on the reactive power sharing is examined in this section by analyzing the volt-age drop across the feeders.The voltage drop across the feeder impedance can be approximated as in[24]and[21]
ΔV≈XQ+RP
V o
(3)
where X and R represent the feeder reactance and resistance, P and Q represent the real and reactive powerflowing through the feeder,respectively,and V o is the DG unit nominal output voltage.Without loss of generality,a two unit microgrid as shown in Fig.2is used as a case study in this section.The voltage drops across Feeder1and Feeder2in Fig.2can be approximated by
ΔV1≈X1Q1+R1P1
V o
(4)
ΔV2≈X2Q2+R2P2
V o
.
(5)
The mismatch in the feeder impedances is given by
ΔX=X1−X2(6)
ΔR=R1−R2.
(7)Fig.3.Detailed network model as seen from DG1.
Considering(6)and(7),the network as seen from DG1is shown in Fig.3,where V∗1and V∗2represent the voltage refer-ences generated by the conventional droop controllers.X and R are the reactance and resistance of Feeder2(X2and R2),respec-tively,that are chosen as references to calculate the mismatch between feeder impedances.X v and R v stand for the effect of any virtual impedance that might be implemented in the con-troller.δV∗1represents the net change in the voltage reference that could be added by the controller,as will be seen later,to en-hance the performance of the conventional droop control.Note that with proper design of the voltage controller,the voltages controlled and measured at the outputfilter capacitors of the DG units are assumed to match the references V∗1+δV∗1and V∗2at the steady state.P1,Q1,P2,and Q2are the powers that can be measured at the outputs of the DG units.Based on Fig.3and(3)ΔV1≈
(X+ΔX)Q1+(R+ΔR)P1
V o
=
XQ1+RP1
V o
+
ΔXQ1+ΔRP1
V o
=ΔV1+δV1(8) where as shown in Fig.3,ΔV1is the total voltage drop across the Feeder1impedance represented by X+ΔX and R+ΔR.ΔV1is the voltage drop across Feeder1due to the reference reactance and resistance,X and R.δV1indicates the voltage drop mismatch between Feeder1and Feeder2 due to the mismatch in feeder impedances,ΔX andΔR.This voltage will cause unequal reactive power sharing between the DG units[16],[21],[22],[24].One solution to this problem is to match the feeder impedances by using a virtual impedance of X v=−ΔX and R v=−ΔR,which would result in Q pcc1=Q pcc2.It is important to mention that if the DG units have different ratings then the feeder reactance and resistance must be modified to be inversely proportional to the Q and P ratings,respectively,in order to achieve proper proportional reactive power sharing[16],[25],[26].The drawback of this technique is that it requires knowledge of the feeder impedances which is often not readily available.
The other way to resolve this issue,as proposed in this pa-per,is to employ voltage drop compensation instead of match-ing impedances.Without loss of generality,the case where both units have the same rating is considered in this analysis.
1608IEEE TRANSACTIONS ON POWER ELECTRONICS,VOL.30,NO.3,MARCH2015 When using conventional droop control only,V∗1and V∗2can be
represented as
V∗1=V pcc+ΔV1+δV1(9)
V∗2=V pcc+ΔV2.(10)
The effect of the voltage drop mismatch due toΔX andΔR
on reactive power sharing can be compensated by modifying
the voltage reference V∗1as follows:
V∗1+δV∗1=V pcc+ΔV1+δV1(11)
assuming that a controller can be designed such that at any time
δV∗1=δV1.(12)
Consequently,(11)can be reduced to
V∗1=V pcc+ΔV1.(13)
AlthoughΔV1will still not be equal toΔV2,the effect ofδV1
on the reactive power sharing will be compensated.For exam-
ple,every timeδV1increases due to an increase in load,the con-
troller will increaseδV∗1accordingly.This can be implemented
by using an adaptive virtual impedance and communication as
proposed in the next section.
III.P ROPOSED C ONTROL S TRATEGY
A.Proposed Controller
The feasibility of the condition in(12)can be further in-
vestigated by using the principle of virtual impedance and the
approximation in(3).Considering the use of a virtual impedance
to generate the voltageδV∗1,from Fig.3
−δV v=δV∗1.(14)
Using the approximation in(3),the condition in(12)can be
approximated by
−X v Q1+R v P1
V o ≈ΔXQ1+ΔRP1
V o
.
(15)
Satisfying(15)by matching the impedances is not practical as stated in Section II.However,(15)can be simplified by setting
˜K
v
=X v=R v(16) where˜K v is called the virtual impedance variable.The condition in(16)will result in a feasible controller as will be shown later in this section.Substituting(16)in(15)and rearranging
˜K
v≈−ΔXQ1+ΔRP1
Q1+P1
.(17)
As can be seen from(17),for any given values ofΔX,ΔR, P1,and Q1,there is a corresponding˜K v that m
atches the volt-ages to meet the condition in(12).However,(17)still cannot be used to implement the controller because the feeder discrepan-cies(ΔX andΔR)are unknown.Nevertheless,the main goal of(17)is to show that one value for the virtual reactance and resistance can satisfy the condition in(12).
If the proper reference for Q1is available to the local con-troller,the variable˜K v can be tuned to the required virtual impedance value as proposed in this paper.To achieve this,
each Fig.4.Proposed adaptive virtual impedance controller.
unit shares its actual reactive power load with the microgrid EMS over the communication link.The EMS calculates the proper share for each unit based on its rating and the total load and sends it back to each unit,along with a controller enable signal(EN).Note that the communication link is not used here within the closed loop of the tuning control,but instead it is used to set the reactive power reference that will be used in the tuning process.Therefore,the sharing accuracy at steady state is unaffected by time delays in the communication channels. Consequently,each unit will utilize the received reactive power share reference Q∗to adaptively tune˜K v.The received Q∗value will not vary with transients in the reactive power of each unit caused by the tuning process,since it is calculated based on the total reactive power load.Therefore,Q∗will be a fixed reference until the total reactive power load changes. Once˜K v is tuned for a given load condition,accurate reactive power sharing will continue even if the communication channel becomes unavailable,as long as the load does not change.Even if the load changes while communication is disrupted,there will be a smaller sharing error in comparison to the conventional droop control case,as will be shown in Sections IV and V. The proposed controller to tune the virtual impedance variable ˜K
v
is shown in Fig.4.A simple integral control loop can be used to tune˜K v by regulating Q indirectly to match Q∗.The virtual impedance is implemented in the dq-frame whereθrepresents the phase angle of the unit output voltage.Note that the objective of the controller is not to regulate the reactive power directly but to tune the virtual impedance to a value that compensates for the effect of the feeder mismatch on the reactive power sharing.Therefore,once the virtual impedance is tuned for the current load conditions it will result in accurate sharing,and in reasonable sharing if the load changes and communication is disrupted.More details regarding the communication loss and delay will be discussed in Sections III-C,IV,and V.
For a microgrid of two DG units,the controller can be im-plemented in one unit only or in both units.A similar analysis to that presented in Section II-B can be developed for DG2 considering that the network seen by the second unit can be rep-resented similarly to that in Fig.3.In general,for a microgrid with two or more DG units,the controller implemented at each unit tunes the virtual impedance in the same way as described previously for DG1.
MAHMOOD et al.:ACCURATE REACTIVE POWER SHARING IN AN ISLANDED MICROGRID USING ADAPTIVE VIRTUAL IMPEDANCES
1609
Fig.5.˜K
v sensitivity based on the parameters of DG units 1and 2from Table I (ΔX =0.94Ω,ΔR =0.5Ω).(a)˜K v as a function of the load operating point.(b)S v in the considered operating range.
TABLE 1
S YSTEM P
ARAMETERS
The integral control is chosen such that the integration time is much longer than the information update ,the integration time T i =1/K i is chosen to be 200s ·var/Ω,versus an information update peri
od of 0.2s (see Table I).Therefore,the time delay in the received Q ∗sample,due to the fact that reference Q ∗is updated periodically,will have no effect on the reactive power sharing at steady state.This time delay is called the information update delay.Moreover,the tuning loop is slow enough that the interaction is negligible with the mi-crogrid dynamics,which are dominated by the power low-pass filter dynamics [31],[32].A detailed small-signal model of the virtual impedance tuning loop is developed and presented in the Appendix.
Note that the reference Q ∗is calculated by the EMS based on the total reactive power load in the microgrid,therefore Q ∗stays unchanged during the tuning action unless the total load changes.This part of the strategy can be considered to be a supervisory control system,which reacts only when the total load in the microgrid changes (a disturbance).B.Tuned Controller Sensitivity to Operating Points
The proposed controller is designed so that the tuned virtual impedance is held at its most recent value after a communication failure occurs,as will be illustrated in the following section.If
the operating point remains unchanged after the communication failure,the sharing error will remain zero since the controller is already tuned for that operating point.However,an operating
point change will result in a sharing error because ˜K
v can no longer adapt to the new operating point.The change needed in ˜K
v to adapt to the new operating point defines the sensitivity of ˜K
v with respect to the change in the operating point.To gain insight into the ˜K
v sensitivity,the approximated relation in (17)is used.Rearranging the terms in (17)
˜K
v ≈−ΔX +ΔR (P/Q )1+(P/Q )
.(18)
It is clear from (18)that ˜K
v depends on the ratio P/Q rather than on the value of P or Q separately.Therefore,any new operating point with the same ratio P/Q (the same power factor)
will result in the same ˜K
v .Define the variable K P Q as P/Q .The nonlinear relation in (18)can be linearized around the operating point as follows:
˜K v ≈˜K v o +∂˜K v ∂K P Q K P Q o
ΔK P Q (19)
where ˜K
v o is the virtual impedance variable tuned at the oper-ating point and K P Qo is the associated P/Q ratio.The slope of ˜K
v in (19)is defined as the sensitivity S v around the operating point.Therefore,S v can be written as
S v =−∂∂K P Q ΔX +ΔRK P Q 1+K P Q
K P Q o =
−(1+K P Qo )ΔR +(ΔX +ΔRK P Qo )
(1+K P Qo )2
.
(20)
To gain insight into the sensitivity of ˜K
v to the operating point,feeders 1and 2from Table I are considered,where ΔX =0.94Ωand ΔR =0.5Ω.As can be seen from Fig.5(a)
and (18)when K P Q is zero (PF =0)then ˜K
v equals −ΔX .However,when K P Q approaches infinity (PF =1)˜K
v equals −ΔR .Consequently,for high K P Q values (high power factors)
the sensitivity of ˜K
v is low as shown in Fig.5(b).From Fig.5(b),|S v |is less than 0.1for power factors higher than 0.74and ˜K
v
版权声明：本站内容均来自互联网，仅供演示用，请勿用于商业和其他非法用途。如果侵犯了您的权益请与我们联系QQ:729038198，我们将在24小时内删除。
发表评论