718 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO....

718 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 2, MAY 2013

Autonomous and Adaptive Voltage Control UsingMultiple Distributed Energy Resources

Huijuan Li, Member, IEEE, Fangxing Li, Senior Member, IEEE, Yan Xu, Member, IEEE,D. Tom Rizy, Senior Member, IEEE, and Sarina Adhikari, Student Member, IEEE

Abstract—This paper proposes a plug-and-play control methodto coordinate multiple distributed energy resources (DER or DE)to regulate voltages in future distribution systems with a high DEpenetration. Theoretical analysis shows that there exists a corre-sponding formulation of the dynamic control parameterswithmul-tiple DEs to give the desired responses. Therefore, the proposedcontrol method has a solid theoretical basis. The method is basedon dynamically and adaptively adjusting DE control parametersto ensure that actual voltage responses follow the desired outputs.Also, it is based on local and the other DEs’ voltages without theneed of the full system data and extensive studies to tune the con-trol parameters. Hence, the method is autonomous and adaptivefor variable operational situations, and has the plug-and-play fea-ture with a high tolerance to unavailable or inaccurate system data.Thus, it is suitable for broad utility application. Simulation resultsfrom various conditions, such as asynchronous start of multipleDEs, disappearance of the original disturbance in the middle ofthe control process, and operation in looped distribution systems,confirm the performance, validity, and flexibility of the proposedcontrol method. The possible impact of communication latency onthe performance of the proposed method is also discussed.

Index Terms—Adaptive control, ancillary services, communica-tion latency, distributed energy resources, distributed generation,inverter control, microgrid, PI control, reactive power, smart grid,voltage control.

I. INTRODUCTION

U SING distributed energy resources (DER or DE) ordistributed generators (DG) to supply dynamic voltage

regulation at the load demand side of power systems has re-ceived significant interest in the research community [1]–[28],in U.S. Department of Energy (DOE) programs [1], [29], andby the IEEE Std. SCC21 committee and 1547 working groups[30]–[33].

Manuscript received September 09, 2011; revised January 26, 2012, May11, 2012, and July 20, 2012; accepted August 06, 2012. Date of publicationSeptember 27, 2012; date of current version April 18, 2013. This work wassponsored by the Office of Electricity Delivery & Energy Reliability, U.S. De-partment of Energy under Contract No. DE-AC05-00OR 22725 with UT-Bat-telle and conducted at ORNL and UT Knoxville. This work also made use ofEngineering Research Center Shared Facilities supported by the EngineeringResearch Center Program of the National Science Foundation and the Depart-ment of Energy under NSF Award Number EEC-1041877 and the CURENTIndustry Partnership Program. Paper no. TPWRS-00848-2011.H. Li, F. Li, and S. Adhikari are with the Department of Electrical Engi-

neering and Computer Science, The University of Tennessee (UT), Knoxville,TN 37996 USA (e-mail: [email protected]; [email protected]; [email protected]).Y. Xu and D. T. Rizy are with the Oak Ridge National Laboratory (ORNL),

Oak Ridge, TN 37831 USA (e-mail: [email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPWRS.2012.2213276

Currently, most DEs operate at unity power factor due to theIEEE Std. 1547 Guide [30]. Although Std. 1547 is still the ef-fective standard for utility practices, with the fast growth of PVsystems and the fact that some utilities are experiencing high PVsystem penetration levels on distribution circuits, guidelines forvoltage and reactive power (volt/var) regulation from DE areunderway by the IEEE 1547.8 working group (WG) of SCC 21[31]. The WG is developing recommended practices to identifythe requirements for local volt/var control by DG and renewableenergy.Benefits of providing volt/var control from DE with power

electronics (PE) interface, more specifically, an inverter, havebeen discussed in the literature [3]–[6], [23], and [26]. A note-worthy, but many times underestimated, benefit is that the DEinverter can provide significant var support by utilizing the re-maining DE inverter capacity or via a slight increase of its ca-pacity. For instance, assume that a DE system has a 100 kVArated capacity. If the active power output is 90 kW, the re-maining reactive power capability is up to kVar; a rangeof 87.2 kVar. This characteristic, which is due to the “power tri-angle”, makes volt/var control an attractive service provided byDE with a PE interface.Another important benefit of the PE-based DE is its ability

to provide fast, dynamic and continuous var compensation thatcannot be achieved with conventional capacitor banks at thedemand side. Plus, var output of capacitor banks drops off withvoltage squared and the switch operations produce transients.Various research works in DE control for providing dynamicvolt/var support have been undertaken. Reference [24] pro-poses a power systems and cyber-communications frameworkfor the control of end-user reactive-power-capable DGs forvoltage support at the transmission system level. Reference[25] validates the benefits of voltage control by DG over powerfactor control in terms of maximizing the real power injectionas well as minimizing line losses by using an optimal powerflow (OPF) method. Reference [27] proposes a method usinglocal data history to dynamically set optimal voltage referencesfor the DG to minimize system losses as well as maintainingan acceptable voltage profile. In addition to the research workfrom a steady-state viewpoint, some of the work focuses ondynamic study. References [9]–[15], [19], and [20] illustratethat grid-connected DE using a PE interface is capable ofsupplying voltage regulation service dynamically, in particularwith the application of proportional-integral-differential (PID)controllers in [12]–[15], [19], and [20] because of their sim-plicity and robustness. However these papers focused on thecontrol method structure design with little effort on exploringhow to set the PID controller parameters systematically.

U.S. Government work not protected by U.S. copyright.

LI et al.: AUTONOMOUS AND ADAPTIVE VOLTAGE CONTROL USING MULTIPLE DISTRIBUTED ENERGY RESOURCES 719

PI controller parameters greatly affect the DE dynamic re-sponse for voltage regulation [17], [22]. As stated in [22], acontrol logic question is: “How to ensure that control param-eters for voltage-regulating DE work efficiently and effectivelyusing a systematic approach?” Our previous work in [22] pro-vides such a solution for a single voltage-regulating DE case ina distribution system.However, when multiple DEs with voltage regulating capa-

bility are deployed in the system, their control could possiblychase against each other in achieving their individual controlgoals. It is a challenging task to coordinate their voltage reg-ulation. The droop control method has addressed the reactivepower sharing among DEs [28]. However, for voltage referencetracking DEs, the coordination issue remains unsolved. Thiswork proposes an autonomous and adaptive control method,which demonstrates the plug-and-play feature to coordinatemultiple DEs to regulate voltages in distribution systems, whichdoes not require the full system data and extensive studies totune the control parameters. The proposed method requireslimited communication only at the beginning of the regula-tion and does not impose a heavy burden on communicationsystems.The DE response speed is much faster than other mechan-

ically-switched devices like transformer load tap changers(LTCs), voltage regulators, and capacitor banks. DE can sta-bilize in the scope of 0.5 s versus tens of seconds or evenlonger for these other devices. Thus, in this paper it is assumedthat the DE regulation process has been completed beforethe other devices respond to the voltage sag or dip. It is alsoanticipated that the DEs will provide voltage regulation moreoften than LTCs, voltage regulators, and capacitor banks; andthese system-level devices will respond to larger changes thatcannot be addressed by DEs. However, the optimal order ofoperating DEs with system-level voltage regulation via LTCs,voltage regulators and capacitor banks is another interestingand future research topic.The paper is organized as follows. Section II briefly reviews

the control model for voltage regulating DEs. The control chal-lenges are discussed in Section III. Section IV presents the the-oretical analysis of the new control method. The implemen-tation details of the method are discussed in Section V fol-lowed by a step-by-step example to demonstrate the implemen-tation in Section VI. The simulation results for three additionalcase studies are presented in Section VII. Section VIII discussesthe impact of communication latency on the proposed method.Section IX provides a conclusion and possible future work.

II. REVIEW OF ADAPTIVE VOLTAGE CONTROL METHOD

A simplified PE inverter interfaced with a DE connected inparallel with the distribution system through a coupling inductoris shown in Fig. 1. The distribution system is simplified as

an infinite voltage source (utility) with a system impedance of. The voltage at the point of common coupling (PCC)

is denoted as . By generating or consuming vars, the DE reg-ulates .An adaptive voltage regulation method is developed based on

the system configuration in Fig. 1 with a PI feedback controller

Fig. 1. Parallel connection of a DE with PE inverter to the distribution system.

Fig. 2. Control diagram for DE voltage regulation.

[22]. The control diagram is shown in Fig. 2. The PCC voltage(or terminal voltage), , is measured and its RMS value, , iscalculated. The RMS value is then compared to a voltage ref-erence, (which could be a utility specified voltage scheduleand possibly subject to adjustment based on load patterns likedaily, seasonal, on-and-off peak, etc.). The error between the ac-tual measurement and reference is fed back to adjust the refer-ence DE output voltage , which is the reference for generatingthe pulse-width modulation (PWM) signals to drive the inverter.In this manner, the DE output voltage, , is controlled to reg-ulate to match the PCC reference voltage, . The controlscheme can be specifically expressed as

(1)

where and are the proportional and integral gain param-eters of the PI controller, respectively; is the time duration/pe-riod for the implementation of the control. Note, the subscriptsuch as in stands for “terminal”.Conventionally, the PI controller has fixed control gains forand . This has been advanced with the adaptive control

approach in [22] that adaptively adjusts and in real time(dynamically) based on the comparison of the desired and theactual responses. The desired response is defined as an expo-nential decay curve as presented in [22].Previous research in [22] has demonstrated the validity of this

method for the case of a single voltage-regulating DE. How-ever, in many cases, there could be more than one voltage-reg-ulating DE connected to a feeder. The interactions among thesevoltage-regulating DEs further complicate the voltage controlprocess. Thus, the previous work needs to be extended to de-velop an enhanced algorithm to ensure that the adaptive voltagecontrol with multiple DEs properly functions to prevent un-wanted control interaction between the DEs.In this paper, although the principal behind adaptive

adjustment of control parameters remains, the adjustmentmethod is different based on the calculation of the needed


Fig. 3. Base case—a radial test distribution feeder.

Fig. 4. Voltage responses of DE2 for different DE1 voltage reference settings.

adjustment of DE output voltages. Details are provided in therest of this paper.

III. CHALLENGES OF MULTIPLEDES FOR VOLTAGE REGULATION

The impact of voltage regulation by multiple DEs on one ofthe DEs is tested in a distribution system model. The systemdiagram is shown in Fig. 3 with two DEs connected to Bus 3and Bus 6, respectively. Also, both DE controllers are set withfixed control gains. The paper refers to this as the Base Case.The reference setting of DE1 is varied while that of DE2 is heldfixed to test the impact on DE2. The results are shown in Fig. 4.The simulation results in Fig. 4 clearly show that voltage reg-

ulation of DE1 affects DE2’s regulation speed. Therefore, inthe case of multiple voltage-regulating DEs, each DE needs totake into consideration the impacts from the other DEs in deter-mining its own regulation output.Besides the impact on the response speed, multiple voltage-

regulating DEs complicate the var compensation direction. Forinstance, assume that initially, a DE’s local voltage is under itsreference setting, which usually requires var injection. How-ever, due to the simultaneous var injection from the other DEs,eventually this DE may be required to absorb vars to offsetthe local overvoltage. With the voltage profile along a feederchanged by the dispersed real power injections of DEs, thisphenomenon would become common. Hence, it is important todraw the following conclusion:With the case of multiple voltage-regulating DEs, the local

voltage w.r.t. voltage reference may be a false indicator of ab-sorption or injection of vars in regulating local voltage.As shown in Fig. 5, the dashed curve shows the terminal

voltage response of DE2 when only DE1 regulates its own

Fig. 5. Voltage overshoot of DE2 caused by DE1.

Fig. 6. Schematic diagram of a network and with multiple DE sources.

terminal voltage. It exceeds the voltage reference (i.e., the flatline). Hence, DE2 needs to control voltage to reduce it to thevoltage reference, if DE2 also participates in the regulation.However, the blue dotted curve shows that when both DE1and DE2 regulate their voltages, DE2 injects vars to increasethe voltage before reaching the reference. It starts to reducethe voltage after the overshoot occurs. The reason is that itstarts to absorb vars to bring the terminal voltage down onlywhen the terminal voltage is higher than the reference voltage.Therefore, in this case, the error sign between the referenceand actual voltages, which works well in a single DE case, failsto provide the right information about whether the DE shouldincrease or decrease its var output. Accordingly, the voltageovershoot may occur.In short, the interaction among the DEs raises additional chal-

lenges for voltage control. The control algorithm needs to con-sider the impact from the other DEs. Otherwise, local voltageinformation (i.e., voltage error signal w.r.t. voltage schedule)may give misleading information

IV. ANALYTICAL FORMULATION OF THE ADAPTIVE METHODIN THE PRESENCE OF MULTIPLE VOLTAGE-REGULATING DES

The analytical formulation of the adaptive method when asingle DE regulates voltage has been derived in previous work[22]. Questions arise in the presence of multiple voltage-reg-ulating DEs: Can the adaptive control algorithm still be ap-plied to each voltage-regulating DE? This section will answerthe question and present a theoretical formulation of the time-varying controller parameters for multiple DEs with an adaptivealgorithm.Assume that the DEs are connected at Bus 1 to Bus , as

shown in Fig. 6, where only DEs are shownwhile the controllers


are not drawn for simplicity. The nodal voltage equation can beexpressed as

...

...

...

...

...

...

(2)

where is the admittance matrix of the system; isthe impedance matrix, i.e., is the voltage at bus

is the voltage source at bus ( to ), excludingthe DE source; is the equivalent impedance for theelectrical connection from the voltage source to the terminalbuses is the output voltage of the DE source connectedat bus ( to ); and is the inductance for the DE tothe terminal bus connection.From (2), we can obtain the vector of the regulated voltage

as follows:

...

...

...

...

...

...

(3)

From (3), the vector of the DE output voltages can be ex-pressed as

...

...

...

...

...

...

(4)

where is the sub-matrix of , i.e., , formed byrows 1 to is another sub-matrix of formed by

rows 1 to and columns 1 to ; and is the diagonal ma-trix defined as ;and is the diagonal matrix defined as

.From (4), we can conclude that the vector of the DE output

voltages can be determined exclusively by the desired voltageresponse vector. For any bus ( to ), where the DE isconnected, we have

(5)

where is the element at row and column in andis the element at row and column of .Based on the assumption of exponential voltage decay we

have

(6)

where is the RMS of the voltage at bus ; is the ref-erence voltage at bus ; and is decay time constant.At any time instant, we have

(7)

where equals , assuming a linear relation betweenand .By substituting (5) and (6) into (7), we have

(8)

and

(9)where

(10)

is the phase angle of the voltage at the , which can be ob-tained by the steady-state power flow calculation in the simula-tion; and , is the fundamental frequency.Equation (8) and (9) provide the formulations to calculate

the parameters of the adaptive voltage controller when multipleDEs participate in voltage regulation. If only one voltage-reg-ulating DE exists in the system and we assume it is connected


at bus , should be equal to , then (8) and (9) wouldbe identical to the formulations which have been derived in thecase when only one DE regulates voltage [22].Thus, we have theoretically proved that the adaptive control

algorithm, with time-varying and , can still be ap-plied to each voltage-regulating DE. This also shows that withthe independently defined voltage response desired for each DEcontroller, there exists a set of corresponding, unique, time-varying controller parameters, and , for each DE,although the actual implementation of the control method, asdiscussed next, differs from the previous approach in [22].

V. IMPLEMENTATION OF ADAPTIVEMETHOD FOR DE CONTROLLER

The dynamic control parameters and can be theo-retically calculated with the availability of the feeder data, in-cluding accurate load consumption and feeder line parameters.However the required information is usually difficult to obtainor inaccurate if indeed available. The implementation methodproposed in this section does not require these parameters andit is able to plug-and-play by utilizing real time voltages infor-mation to automatically adjust the controller parameters. Theproposed method assumes the availability of communicationsbetween the voltage-regulating DEs or with a control center toprovide the real time information of DE operational conditions,including the terminal or PCC voltage at the other DE buses andthe output voltage of every DE. However, the proposed methodonly requires limited communication at the beginning of the reg-ulation and does not impose a large burden in terms of band-width on the communication systems.Considering fundamental frequency only, at any given time

instant , we have

...

...

...

...

(11)

where is the admittance matrix and, ( to ).

Considering the buses 1 to are connected with a DE andthe buses from to are not, we can obtain the followingequation based on (11):

.

(12)Also, the active power output of DEs is given by

(13)

Note that the DE active power output is assumed to followa given schedule. That is, is a constant value during avoltage regulation period.Since each equation in (12) is complex, we have a total of

with the consideration of (12) and (13).In the adaptive control method, the terminal voltage response

of each DE, , to , is predefined, so we haveunknown variables remaining, which are:• phase angles of the bus voltage , to ;• magnitudes of the voltage at the buses other than the DEterminal buses , to ;

• phase angles of the DE output voltages , to ;and

• magnitude of DEs output voltages, , to .The number of the unknown variables matches the

number of equations. The relationship between andis expressed as function , i.e.,, which can be implicitly de-

rived from (12) and (13) if all system parameters are accuratelyand readily available.Next, a control approach independent of system parameters is

proposed based on measured terminal and DE output voltages.Note, although (11)–(13) contain network parameters, they areused here only for the illustration of needed measurements tosolve the sensitivity , which is the key in the proposedadaptive control. The details of the proposed approach are elab-orated in the following discussion.From to , if is very small, a linear approx-

imation of can be acquired as

(14)

where is assumed to be constant over this small rangeand can be calculated from real-time data measurements.As previously mentioned, the key of the proposed method is

to obtain the needed DE output voltages, for to ,to ensure the terminal voltages, for to , follow thedesired voltage responses. The discussion can be grouped intotwo scenarios:• when the actual voltage responses do not follow the desiredcurves; and

• when the actual voltage responses follow the desiredcurves.

1) Actual Voltage Responses Do Not Follow the DesiredCurvesAssume the time under consideration is . Typically, this sce-

nario is around the startup or a re-start time due to the change inthe disturbance (e.g., disappearance of the original disturbanceor an asynchronous start of a new DE) during a voltage regula-tion process.At , , , we can set the output

voltages of DE at bus to be , ,, respectively, where to . The

corresponding terminal voltages at these buses can bemeasured.


Hence, for any bus which has a DE connection, we have thefollowing equations:

...

(15)

where ,to .Equation (15) could be rewritten in matrix form as follows:

...

......

......

...(16)

From (16), the coefficient vector is derived as

......

......

...

...

...(17)

Equation (17) gives the linearized relation in a small rangebetween all DE output voltages and the voltages at all DEterminals.

In the adjustment process, once the coefficient vectors havebeen calculated with (17), we can easily calculate the DEoutput voltage needed for the next adjustment step by (14)in order to achieve the voltage response matching the desiredresponse.2) Actual Voltage Responses Follow the Desired CurvesThis is the scenario when the voltage responses match well

with the desired ones, especially after the initial startup periods.By intuition, it appears that we may use the approach in the

previous scenario, calculating the coefficient using themeasured results from the previous steps based on (17) andthen applying (14). However, since the voltage responses matchwell with the desired ones in the previous steps, the matrixis a singular matrix so (17) cannot be performed. The reason ofthe singularity is shown next.Again, without losing generality, assume the time instant to

consider is . In the previous time step ( to ), sincethe terminal voltages follow the desired ones, the voltage changeshould be as follows:

(18)

Similarly, for the time step from to , we have

(19)

For two consecutive voltage changes, we can obtain the ratioof the two by dividing (19) by (18)

(20)

Since the step size, , is fixed during the adjustment process,the ratio between two consecutive voltage changes can be as-sumed to be a constant value and remains the same for eachDE terminal voltage when the actual performance is almostthe same as the desired response. As a result, the row vectors,

, in matrix in (16) will be linearlyrelated such that is singular.Thus, (17) cannot be directly used in this scenario. However,

since the actual voltages have been very close to the desiredresponses, we can use the previous coefficients directly, whichcan further simplify the calculation of the needed DE outputvoltage. This is shown next.


Combining (20) and (14), we have

(21)

Thus, the DE output voltage required to generate the desiredresponse can be simply calculated as the previous voltagechange multiplied by , which is a constant ratio between twosteps if the actual voltage responses follow the desired curvesvery closely.Certainly, if something happens during the regulation process

such that the actual responses do not follow the desired onesvery well, we may have a restart to use (17) and (14) to calculatethe needed DE output voltage.After the needed output voltage at each DE is determined in

either scenario, the new and can be calculated based onthe time-domain format of (7).These two scenarios can be flexibly repeated if needed such as

when a new perturbation occurs. The actual steps to implementthe control method are described as follows:1) The desired exponential response curve is calculated.2) In the first steps, the DEs voltage output is increased ordecreased by a fixed step in order to calculate the coeffi-cient vector .

3) In the step, iscalculated according to (17) and the DE voltage output isset based on (14) to bring each DE terminal voltage closeto the desired response at and steps. The new

and are calculated based on (7).4) From the step and onward, if the voltage re-sponses are close enough to the desired curves, the DEsvoltage output is updated with (21) to continue followingthe desired curves, and the new and are calculatedbased on (7). Otherwise, if the accumulation of error oranother change (new disturbance, disappearance of distur-bance, etc.) leads to a large deviation from the desired re-sponse, go to Step 1 as a re-start.

Note that the key (7), (14), (17), and (21) in the proposedadaptive control are all based on measured terminal and DEoutput voltages and do not require system parameters. Thus, theproposed control has the self-learning and plug-and-play fea-tures for broad utilities deployment.

VI. STEP-BY-STEP EXAMPLE TO DEMONSTRATETHE IMPLEMENTATION FOR THE BASE CASE

A step-by-step example on two voltage-regulating DEs isshown in the following to illustrate the implementation pro-cedures. The Base Case in Fig. 3 is used for illustration. The

line-to-line voltage at the consumer side of the infinite bus isassumed to be 480 V (RMS). The total load of the system is70.18kVA (59 kW, 38kVar). The active power injection of DE1and DE2 is 10 kW and 20 kW, respectively, and they remainconstant. The voltage references for Bus 3 and Bus 6 are 275.80V and 275.60 V. Assume after a load increase, the voltages atBus 3 and Bus 6 drop to 271.66 V and 271.76 V, respectively.The adjusting frequency is 60 Hz, aligned with the system fre-quency.1) Calculate the Coefficient VectorInitially, we have

and . IncreaseDE output voltage by and

in two consecutive adjustmentprocesses. Then, we haveand . The correspondingterminal voltages are and

. According to (17), for DE1we have

Similarly, for DE2, we have

2) Adjusting DE Output Voltages to Make Terminal VoltageMatch the Desired ResponseThe desired voltage at Bus 3 and Bus 6 are

V. Ac-

cording to (14), the voltage adjustments need to be

After the adjustments, the output voltages of two DEs are


The corresponding terminal voltages are, which are very close to the desired

response.For the next adjusting process, we have the desired response

as

To match the desired response, the DEs output voltages needto be at the following values:

The actual voltages are . Thevoltage responses at both buses follow the desired response.3) AdjustingDEOutput Based on the Ratio of Voltage Change

Between Two Consecutive Adjusting StepsThe ratio of the two consecutive voltage changes can be cal-

culated theoretically by (20):

The actual needed ratio can be calculated as. For multiple DEs, we can take

the average value of all the DEs to neutralize the random errors.For this adjustment, we have

Hence, the DE output for this step should be

The corresponding terminal voltages are. The actual voltages closely follow

the desired responses. The adjusting process will be repeateduntil the actual responses reach the voltage references.Fig. 7 shows the comparison of the actual and desired voltage

responses in the entire process. At the beginning of the regula-tion process, the voltage responses of both DEs do not followthe desired responses very well because the DEs’ output volt-ages are intentionally increased by a small fixed step size withvery conservative initial control parameters in order to calculatethe coefficients between the DEs’ output and terminal voltagechanges. After obtaining the coefficients, the voltage responses

Fig. 7. Voltage responses of DE1 and DE2. (a) Voltage response of DE1. (b)Voltage response of DE2.

Fig. 8. Comparison of values of generated in control versus the analyticalresults for both DEs. (a) of DE1. (b) of DE2.

successfully reach the desired responses and follow the desiredresponses very closely until reaching the reference voltages.The theoretical values of are calculated by the analytical

(8) for both DEs. The results are shown in Fig. 8 in comparisonwith the results generated in the adaptive control algorithm. As


Fig. 9. Ratio of the two consecutive voltage changes.

observed in Fig. 8, after initial calculation of coefficients vector,the value of generated by the adaptive control algorithm isvery close to the theoretical value. Note is proportional to. One interesting observation is that the values of of DE2

reduce to negative. The overvoltage problem, shown in Fig. 5and discussed in Section III, explains this phenomenon. Thevoltage support of DE1 results in overvoltage at the terminalof DE2. Hence, negative control parameters are generated forDE2 to absorb reactive power, even when the actual voltage islower than the reference voltage to prevent voltage overshoot.Fig. 9 shows the average value of , the ratio of two consecutivevoltage changes, which is close to the theoretical value 0.8465.It is very important to note that the theoretical values are

obtained with the assumption that all system parameters, i.e.,feeder data and load changes, are known and accurate, whilethe actual autonomous and adaptive control algorithm presentedin Section V uses real-time sensitivities to calculate the time-varying control gains. Since the system parameters are usu-ally not readily available or accurate in real operation, the the-oretical calculation (with all system parameters) is for bench-marking purpose only and not highly suitable for practical use,while the proposed autonomous and adaptive control algorithmin Section V is more meaningful in practice and can lead to aplug-and-play application, regardless of which system it is de-ployed in.

VII. SIMULATION RESULTS ON THREEADDITIONAL CASE STUDIES

In this section, the applications of the adaptive control methodare further demonstrated with more detailed results for threecase studies to demonstrate the flexibility of the control method:• Case 1: two DEs starting voltage regulation asynchro-nously;

• Case 2: disturbances disappearing in the middle of voltageregulating process; and

• Case 3: three voltage-regulating DEs in a looped system.

A. Case 1—Two DEs Starting the Regulation Asynchronously

In actual system operations, the voltage-regulating DEs maystart their voltage regulation at different times. When this hap-pens, the DEs already in service will synchronize with the newDEs coming into operation by restarting its regulation processto achieve coordination among all the DEs. To feature this phe-nomenon in Case 1, the Base Case is reconfigured by starting

Fig. 10. Voltage responses of DE1 and DE2 in Case 1. (a) Voltage response ofDE1. (b)Voltage response of DE2.

DE1’s voltage regulation first and then starting DE2. Fig. 10(a)and (b) shows the voltage responses at the two DEs terminalbuses for this case. Before 0.35 s, only DE1 regulates its ter-minal voltage and follows the desired response. However, theterminal voltage of DE2 exceeds its reference starting at 0.3 s.At 0.35 s, DE2 starts to regulate its terminal voltage and as a re-sult, DE1 recalculates the coefficients and redefines its desiredresponse to synchronize with DE2. In the case of voltage over-shoots, regulation can be speeded up by reducing the time con-stant of the desired response curve such that the voltage will bequickly decreased. In this case, within the next 0.15 s, the ter-minal voltage of DE2 is back to its reference and that of DE1reaches the reference as well.

B. Case 2—Disturbances Disappearing in the Middle ofVoltage Regulating Process

The Base Case shows the scenario of disturbances (load in-creases) persisting in the whole regulation process. However,some disturbances may last for only a very short time and dis-appear before the regulation process is completed. If the disap-pearance of the disturbances results in a large enough deviation,as stated in Section V, the regulation process will start all overto recalculate the coefficients and re-track the new desired re-sponse curve Fig. 11(a) and (b) shows the voltage responses insuch a case where the disturbances disappear before the initialvoltage regulation process is completed. In this case, the systemconditions and initial disturbances are identical to those in theBase Case; however, at 0.05 s, the disturbances disappear re-sulting in voltage rise at both DEs terminals.Since the voltage for either DE deviates from the initial de-

sired response substantially, the voltage regulation process starts


Fig. 11. Voltage responses of DE1 and DE2 in Case 2. (a) Voltage response ofDE1. (b)Voltage response of DE2.

all over. The desired response curves for both DEs are updatedusing the new starting points, as shown by the dash curves after0.05 s in both Fig. 11(a) and (b). The response speed of both isspeeded up and within the next 0.15 s, the voltages of both DEsare brought back to their references.The simulation results in this case demonstrate that by

restarting the control cycle when detecting the deviation fromthe desired response curve, the proposed method is able tohandle the disappearance of disturbances in the middle of theregulation process.Both the simulation results of Cases 1 and 2 verify that the

flexible recalculation of the coefficients of the proposed con-trol successfully addresses a wide range of disturbances (e.g.,the startup of another voltage-regulating DE or another loadchange) which can occur in the middle of the original voltageregulation activity.

C. Case 3—Three Voltage-Regulating DEs in a Looped System

Some distribution systems are meshed such as urban distri-bution networks. Thus, the Base Case is modified with a loopas shown in Fig. 12 to demonstrate the application of the pro-posed adaptive control method in a meshed system. A new loadof 10 kW and 2 kVar is connected at the new bus 7. Also, thiscase study considers three voltage-regulating DEs connected atbuses 3, 4, and 6, respectively, to further demonstrate the ap-plication of the proposed method. The active power injectionsof the three DEs are 20, 20, and 10 kW, respectively. Voltagereferences are 280.63, 280.60, and 280.30 V, respectively. Weassume that load increases at bus 3 and bus 6 cause the voltagesat the three DEs’ buses to drop to 273.20, 273.11, and 272.84 V,respectively. Fig. 13(a)–(c) shows the voltage responses of thethree DEs after the load change in comparison with the desired

Fig. 12. System with loop connection and three voltage regulating DEs.

Fig. 13. Voltage responses of DE1, DE2 and DE3 in Case 3. (a) Voltage re-sponse of DE1. (b) Voltage response of DE2. (c). Voltage response of DE3.

responses. As can be seen, voltage responses of the three DEsmatch the desired responses after the calculation of initial coef-ficients is finished.These results verify that the proposed control can track the

desired response very closely in loop systems and is scalable todistribution systems with more than two DEs. The response can


track the desired response very well under different systems ordifferent operating conditions due to the autonomous learningcapability in the control algorithm. This demonstrates the plug-and-play feature which makes the control highly suitable forfuture utility applications.

VIII. DISCUSSIONS: IMPACT OF COMMUNICATION LATENCY

A communication system is required by the proposed methodto achieve the real-time coordination among the voltage-regu-lating DEs. A distribution-level monitoring system, having thesame structure as the wide area monitoring system [34], is ableto meet the requirement for real-time data exchange. Also, withthe development of the smart grid, more communication tech-nologies are being applied in power systems which will providefaster communications (in the order of milliseconds) for systemmonitoring and real-time control [35].In this section, a preliminary study considering communi-

cation latency is performed with the assumption that the un-derlying communication system has similar latency to a wide-area monitoring system (WAMS). InWAMS, the typical latencyassociated with one-way communication propagation is 2 cy-cles, and data concentrator processing is also 2 cycles [34]. Thevoltage measurement delay is 1 cycle. This gives a round tripdelay of cycles. In terms of a distribu-tion monitoring system with a much smaller area and much lessnodes, the latency should be much less. Here, a latency of 9 cy-cles is chosen to perform a simulation which gives conservativeresults.It should be noted that the communication delay affects only

two steps of the whole control process described in Section V,which are the and steps. Only local measure-ments are involved in the first steps. At the step,the local DE has to wait for the information of the other DEsto calculate the coefficient vector and accordingly the neededoutput to match the desired response. In order to calculatethe of the two consecutive points of the desired responsecurve, the DE’s output has to be calculated in the same wayby using the same coefficients and other DE’s updated informa-tion, which is performed in the step. After that, theDE’s output is updated based on (21), which only requires localvoltage measurements and local historical data. Thereafter, thecommunication delay does not affect the response speed.Fig. 14(a)–(c) shows the simulation results of Case 3 with

the impact of the communication delay, assumed to be 9 cycles.Again, this is a conservative assumption. In the first 3 cycles (0to 0.05 s), each DE adjusts its output by a fixed step size andmeasures its local voltage. Then, during the next 9 cycles (from0.05 s to 0.2 s) local data are collected and transmitted to all theother voltage-regulating DEs. Meanwhile, each DE adjusts itsoutput based on its initial and settings. At 0.2 s, each DEreceives the other DEs information and its output is set based onthe calculation method described earlier and the values ofand are updated as well. As can be seen, in the next step,voltage matches the desired response. From 0.2 s to 0.35 s, eachDE adjusts its output based on the and settings updatedat 0.2 s while waiting for the other DEs voltage information. At

Fig. 14. Voltage responses of DE1, DE2 and DE3 of Case 3 including commu-nication latency. (a) Voltage response of DE1. (b) Voltage reponse of DE2. (c)Voltage response of DE3.

0.35 s, each DE receives the others DEs’ information and ad-justs its output according to the calculation to catch the desiredresponse. After 0.35 s the DEs only need local and past datato track the desired response, and the communication delay nolonger affects the voltage regulation performance.It should be noted that during the communication latency, theand values initially set or updated in previous steps are

used to track the reference, which are also used in the case ofcommunication system failure due to severe weather or otherreasons.Communication latency only has a minor effect on the perfor-

mance of the DE voltage regulation. The voltage tracking is notas smoothly as the ideal one. However, in terms of the overallresponse speed, because the proposed method requires commu-nication data only in two steps, it is capable to respond in theperiod around twice the communication latency, which is still


much faster than any mechanically switched devices such as ca-pacitor banks. With the industry-acceptable 0.5 s response timesetting, the communication latency does not impair the overallcontrol response speed. In the near future, while the communi-cation and smart grid technologies are deployed and further de-veloped, faster and more efficient communication will be avail-able in power systems to ensure low communication latency tofurther enhance the proposed method.

IX. CONCLUSION AND FUTURE WORK

In this paper, the contribution and findings of this paper canbe summarized as follows:• When multiple DEs participate in voltage regulation, theterminal voltage response of each DE is the result of theaggregated regulation behavior of all DE’s, and the localmeasurement of one DE’s terminal voltage can reflect theaggregated impact. Thus, it can still be used as feedbackinformation to adjust the controller parameters.

• The voltage correction of the other DEs may result in over-voltage at another DE’s terminal bus. In this case, the flatreference voltage fails as a good indicator of injecting orabsorbing reactive power and thus fails to provide a timelyregulation direction signal and overshoot of voltage is in-evitable with fixed gains. A more dynamic reference, likethe desired response curve, is preferred.

• Theoretical analysis proves that a unique, time-varyingsolution for the gain parameters does exist for multiplevoltage-regulating DEs. The gains may be negative in thecase that one DE needs to absorb reactive power even ifits reference voltage is higher than its terminal voltage.The theoretical analysis is model-based and requires de-tailed system data, so it is not likely preferred for practicingutility engineers. However, the analytical formulation doesverify that the proposed adaptive control approach has asolid theoretical foundation.

• With communication present among all voltage-regulatingDEs, the voltage regulation process can be better controlledto avoid voltage overshooting. A regulation method is pro-posed, which can calculate how much DE output voltageis required for adaptive adjustment of voltage regulationcontrol parameters, based on the real-time voltage mea-surements without load or feeder data. Hence, the methodis autonomous and adaptive for variable operational situa-tions, and has a high tolerance to unavailable or inaccuratenetwork parameters. This plug-and-play feature makes theproposed method suitable for broad utility application.

• Simulation shows that this method can track the idealvoltage response very closely under various operatingconditions such as asynchronous start of regulating DEs,disappearance of the disturbance in the middle of theregulating process, operation under looped systems, andoperation with more than two DEs.

• Communication latency does slightly impact the perfor-mance of the proposed control. However, since the pro-posed method only requires limited communications at thevery beginning, the communication latency does not im-pair the overall response speed, as shown by a preliminarystudy in this paper considering communication delay.

In future work, additional research needs to focus on moreadvanced active power control for frequency regulation in Mi-crogrids or Smart Grid applications. Also, the optimal numberof DEs to participate in voltage regulation may be investigatedin the future from the optimization viewpoint. Finally, coordi-nation of the voltage regulation of DEs with system level regu-lating equipment, such as under load tap changing transformersand voltage regulators, needs to be studied.

ACKNOWLEDGMENT

The authors would like to thank C. Vartanian (formerly ofSouthern California Edison and currently of A123 Systems),R. Dugan (EPRI), R. Boroughs (TVA), J. D. Kueck (retiredfrom ORNL), M. Young II (ORNL), and J. Gracia (ORNL) fortheir comments on how to make this work practical, useful, andtheoretically sound. The authors would also like to thank E.Lightner, D. Ton, and M. Smith from DOE Office of ElectricityDelivery and Energy Reliability for the program support to com-plete this research.

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Huijuan Li (S’07–M’11) received the Ph.D. degree from The University ofTennessee (UT) at Knoxville in 2010.She is presently a postdoc research associate with Oak Ridge National Lab-

oratory (ORNL), Oak Ridge, TN.Ms. Li won the First Place Prize award at the Student Poster Contest during

the IEEE PES General Meeting, Calgary, AB, Canada, in July 2009.

Fangxing (Fran) Li (M’01–SM’05) received the Ph.D. degree from VirginiaTech, Blacksburg, in 2001.He is presently an Associate Professor at The University of Tennessee (UT) at

Knoxville and the Director of the Education Program of the CURENT researchcenter. He was a principal consulting R&D engineer at ABB Consulting priorto joining UT.Dr. Li a registered Professional Engineer in North Carolina, an Editor of the

IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, and a Fellow of IET.

Yan Xu (S’02–M’06) received the Ph.D. degree in electrical engineering at TheUniversity of Tennessee (UT) at Knoxville in 2006.She is presently a research staff member in the Power & Energy Systems

Group at Oak Ridge National Laboratory (ORNL), Oak Ridge, TN.

D. Tom Rizy (SM’87) received the BSEE and MSEE from the University ofVirginia, Charlottesville, and Virginia Tech, Blacksburg, respectively.He is a senior research engineer at Oak Ridge National Laboratory (ORNL),

Oak Ridge, TN, in the Power & Energy Systems Group. He is a cofounder ofORNL’s DECC Laboratory and PCAT Facility. He has over 34 years of experi-ence in power systems R&D.Mr. Rizy is the recipient of an IEEE Prize Paper in 1990, chair of the IEEE

PES Volt/Var Control Task Force, and member of the IEEE PES Smart Distri-bution, Distributed Energy Resources Integration and Distribution ReliabilityWorking Groups. He is an editor for the IEEE TRANSACTIONS ON POWERSYSTEMS.

Sarina Adhikari (S’08) received the B.E. degree in electrical engineering fromthe Institute of Engineering, Pulchowk Campus, Pulchowk, Lalitpur, Nepal, in2002 and the M.E. degree in electrical power systems management from theAsian Institute of Technology, Pathumthani, Thailand, in 2005. She is pursuingthe Ph.D. degree in electrical engineering at The University of Tennessee atKnoxville.She worked as a Research Associate in Energy Field of Study, Asian Insti-

tute of Technology, after completing her M.E. degree. Her research interestsare voltage stability, distributed energy resources, and distribution system reli-ability.

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