From Each According to its Ability: Distributed Grid Regulation With Bandwidth and Saturation Limits in Wind Generation and Battery Storage

384 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 21, NO. 2, MARCH 2013

From Each According to its Ability: Distributed GridRegulation With Bandwidth and Saturation Limits

in Wind Generation and Battery StorageChaitanya A. Baone, Student Member, IEEE, and Christopher L. DeMarco, Member, IEEE

Abstract—The problem addressed here is motivated by dis-tributed control for frequency regulation in the electric powergrid, and by the characteristics of new technologies contributing tothis control objective: wind generation and battery energy storage.In the large scale, coupled dynamical system of the power grid, weseek a distributed control design approach that can successfullyshare control effort among two classes of actuators: one classhaving low bandwidth, but broader actuation limits (controllablepower output from wind turbines); and a second class, havingnarrow actuation limits, essentially zero gain at dc, but muchbroader bandwidth actuation possible at high frequencies (poweroutput from battery energy storage). In this context, we extendthe “saturation-respecting” design methodology developed bySaberi and his co-workers, adapting their low-high gain methodwith partitioning of slow acting actuator input channels (e.g.,wind turbine power changes) from fast acting actuators (batterypower delivery). The design methodology, resulting frequencyregulation performance, and characteristics of control actuationfrom individual wind generators and batteries is demonstrated inrepresentative test power system models.

Index Terms—Battery storage, distributed control, distributedobservers, frequency regulation, saturation, wind power.

I. INTRODUCTION

G OVERNOR feedback loops on generators have long beenthe primary actuators by which frequency control is ex-

ercised in the electric power grid. On the relatively fast timescale of seconds, governor action is an entirely distributed con-trol, acting on the locally measured signal of frequency, yetimpacting the coupled electromechanical dynamics of all ma-chines in the entire synchronous network. Wider area automaticgeneration control and economic set-point changes then act onslower time scale, as supplementary signals to these local con-trol loops. Yet recent studies suggest the effectiveness of this tra-ditional governor control is declining [1]. Moreover, the rapidlyexpanding role played by wind generation, and the prospect ofincreasing grid penetration of electrical energy storage pose new

Manuscript received March 10, 2011; revised September 22, 2011; acceptedDecember 10, 2011. Manuscript received in final form January 06, 2012. Dateof publication January 31, 2012; date of current version February 14, 2013.Recommended by Associate Editor N. H. El-Farra. This work was supportedby U.S. National Science Foundation Award 0968833, through the PSERC In-dustry University Collaborative Research Center.The authors are with the Department of Electrical and Computer Engi-

neering, University of Wisconsin-Madison, Madison, WI 53706 USA (e-mail:[email protected]; [email protected]).Digital Object Identifier 10.1109/TCST.2012.2183596

challenges to this long-standing philosophy of frequency con-trol in the grid [2], andmotivate a new perspective on distributedcontrol to be explored in the work here. In 2007, the Federal En-ergy Regulatory Commission (FERC) issued Order No. 890 [3]which creates a framework for the provision of regulation ser-vices by non-generation technologies in regulation markets.From a control systems perspective, two features of these

emerging grid technologies motivate a new approach. First isthe characteristic of modern wind turbines, and second is the im-pact of their increasing percentage of the generation fleet. Whilewind turbines do have the capability to vary their power outputto help regulate frequency, their capacity to do so is limited bothby the loss of energy production inherent in leaving “headroom”for control, and by the potential for life-shortening fatigue ontheir drive train if rapid control actions are required. The keypremise here is that power control from wind turbines, if exer-cised at all, is best limited to a very low frequency control ac-tion. Electric energy storage, particularly as might be providedthrough batteries, has the potential to provide a complemen-tary characteristic. Recognizing that power output is the “ac-tuation signal” in grid regulation, it is clear that any device withmodest energy storage benefits from a high pass characteristicin its control actuation. In particular, to prevent feedback controlfrom driving a battery to excessive charge or discharge, a nat-ural constraint is to require that the loop gain determining thepower output has zero dc gain. Moreover, on the scale of elec-tric grid needs, the magnitude of maximum power output avail-able from an individual battery installation will be quite small.Therefore, control design that respects the saturation limits onthis new class of “actuator” will be important.Another class of problems where such a complementary na-

ture of saturation-bandwidth limits would exist is in the pro-posed hybrid power management systems in electric vehicles(EVs), where the use of ultra-capacitors is being considered [4],[5]. The idea is to use ultra-capacitors for short duration tran-sients and use the batteries for steady state type situations. Thebatteries in this case would form the slow actuators with broadersaturation limits, while the ultra-capacitors would form the fastactuators limited in the amount of power that they could pro-vide.With this motivation in the specifics of new grid technologies,

the general framework motivating our approach can be stated asfollows. In a large scale, coupled dynamical system (the powergrid), we seek a distributed control design approach that can suc-cessfully share control effort among two classes of actuators:one class having low bandwidth, but broader actuation limits

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BAONE AND DEMARCO: DISTRIBUTED GRID REGULATION WITH BANDWIDTH AND SATURATION LIMITS 385

(wind turbines); and a second class, having narrow actuationlimits, essentially zero gain at dc, but much broader bandwidthactuation possible at high frequencies (battery energy storage).Most of the solutions proposed in the literature seek to mimicthe inherent inertial response of traditional synchronous genera-tors by adding a control loop that feeds (or draws) active powerin response to a decline (or rise) in the time derivative of fre-quency. For example, in [6], Morren et al. propose a methodutilizing stored kinetic energy in the wind turbine blades to em-ulate inertia by having additional control paths. In [7], Vittalet al. demonstrate a modification to the torque control loop ofthe wind system by having an additional control loop that re-flects inertial emulation. Similar ideas of inertial emulation canbe found in [8]–[10], and [11]. While the idea of inertial em-ulation is intuitively appealing, it neglects the bandwidth andsaturation limitations of the additional control loop. Apart fromhaving control systems on the wind systems, various strategieshave been proposed for frequency regulation in power systemswith wind power using different energy storage systems such asbattery systems, superconducting magnetic energy storage sys-tems (SMES), flywheels and others in [12]–[14].Over the past decade or more, model predictive control

(MPC) has emerged as an effective method across severalindustrial sectors, expanding beyond its original focus inchemical process control applications. Effective treatment ofprocess constraints is among the attractive attributes of MPC.In broad terms, an MPC approach can be roughly summarizedas follows. At each time step, the plant model is used to predictthe future system trajectories using past measurements andinputs. Using the estimated state information, a constrained op-timization problem is solved to determine an open-loop controllaw. At the next time step, the system state is re-estimated usingnew measurements. The optimization problem is once againsolved and the optimal control law is recomputed. Electricpower systems control is among the application areas to whichMPC has been applied in recent literature. In [15], Venkat et al.propose distributed MPC strategies for automatic generationcontrol. Various distributed MPC strategies have been consid-ered in their work. In [16], Hiskens and Gong propose the useof MPC in non-disruptive load control. They approximate theoptimal control problem as a linear time-varying discrete-timecontrol problem through the use of trajectory sensitivities. Theoptimization objective is to minimize the amount of load shedwith constraints on the voltages and the amount of load that isavailable for control at each location. The trajectory sensitivi-ties-based approximation of the optimal control problem leadsto a very tractable linear programming problem. In [17], Qi etal. develop MPC methods to treat the integration of renewablegeneration resources into the power grid, examining controldesign for a hybrid standalone wind-solar energy generationsystem. In their optimization problem, the cost function to beminimized is a quadratic function that is the difference betweenthe power generated by the hybrid system and the total powerdemand and a small penalty on the solar generator output. Theconstraints include limits on the power output during eachinterval, as well as limits on time rate of change of power(termed “ramp rate” in the power literature). The algorithm

developed yields the control inputs of commanded power forthe wind and solar generation.The work cited above makes clear that MPC offers a control

design methodology to treat limits on available power outputfrom individual generators in the electric grid control problem.In this respect, the work to be presented here is an alternativeapproach to treating these limits in control design. However, anovel feature of our approach lies in its objective of exploitingthe complementary saturation-bandwidth characteristics of thetwo classes of actuators to be examined (i.e., wind turbine andbattery energy storage). That is, the design maintains the com-mand signal within the narrow saturation limits on power outputavailable from an energy storage device, while taking advantageof its higher bandwidth. Similarly, the design seeks to take ad-vantage of the broader saturation limits of the blade pitch powercontrol, while respecting its low bandwidth of operation. Themodeling framework also includes an explicit representation ofan unforced model to represent exogenous disturbance signals.This unforced system can be used to capture the spectral con-tent of wind power variations that drive variations in electricgrid frequency, against which our control design seeks to regu-late.In this work, we tailor the saturating controller design tech-

nique of Saberi et al. [18] to exploit the complementary rela-tion between the bandwidth and saturation limits between twoclasses of actuators contributing to stable regulation of grid fre-quency. Section II describes the saturation accommodating con-trol design method of [18] and a modification of this method toexploit the complementary relation between the bandwidth andsaturation limits of the two classes of actuators. In Section III,models for various components of the system are presented.Also, an observer-based distributed control scheme is presentedin this section to demonstrate a control implementation utilizinga very small number of remote measurements. In Section IV,simulation results for the control design methods applied ontwo test power systems are presented. Section V summarizesthe contributions of this paper.

II. CONTROL DESIGN METHOD

Saberi et al. [18] have demonstrated optimal control designmethods to form controllers for linear systems subject to inputamplitude limits (i.e., actuator saturation). We recall their “low-high gain” design method that is obtained via solution of an al-gebraic Riccati equation (ARE). The method yields a familyof state feedback gains, parameterized in a low gain param-eter and a high gain parameter . One of the conceptuallyattractive features of this design approach, as it relates to thewind energy control application, is the adoption of an exogenoussystem (“exosystem”) model to represent input disturbances. Inparticular, typical designs using this method adopt an unforcedlinear system with all purely imaginary eigenvalues as the ex-osystem. Over the bounded set of initial conditions, its outputthen yields families of weighted sinusoidal responses as the dis-turbance signals; in essence, the choice of the exosystem repre-sents a choice of allowable spectra for periodic disturbances.


This is well suited to typical wind variation models in the liter-ature [19]. Consider the linear system

(1)

(2)

(3)

Equation (1) describes the plant with state and controlinput , subject to the effect of an exogenous distur-bance represented by , where is the state of anexosystem. Equation (2) describes the state space realization ofthe autonomous exosystem. The output is , and is anormalized vector-valued saturation function defined as

(4)

with

ififif .

(5)

Because of the presence of the saturation function, , the systemis nonlinear. Conditions to ensure solvability for this regulationproblem are given in [18] and are summarized as follows:(i) if all the eigenvalues of lie in the closed left-half planeand the pair is stabilizable;

(ii) there exist matrices and such that they solve the reg-ulator equation

(6)

(7)

(iii) there exists a and a time such thatfor any allowable initial condition on

the exosystem.The solvability conditions are independent of the set of initialconditions of the plant. As long as has eigenvalues in theclosed left-half plane and the pair is stabilizable, the un-forced closed-loop system is asymptotically stable [18]. Withrestrictions on initial conditions of the exosystem, and if a so-lution to the regulator equations exists, the problem is solvable(internal stability and regulation).For the class of exosystem to be employed here, that is simply

a set of undamped second-order oscillators with integer multiplefrequencies (i.e., basis functions for a truncated Fourier repre-sentation of a periodic disturbance signal), the set of allowableinitial conditions on the exosystem state can be taken simply asa norm ball. In this scenario, the conditionis guaranteed satisfiable if a sufficiently small norm ball of ini-tial conditions is selected; i.e., the magnitude of the disturbancesignal is controlled by the size of its initial condition set. Hence,one intuitive measure of the quality of the control design herecan be judged as follows: how large a disturbance magnitudecan the system regulate, without exceeding the saturation limitson the actuators. The conditions (i) and (ii) above form the solv-ability conditions in the absence of any saturating elements,and thus form the necessary conditions for the output regulationproblem with saturating elements. The condition (iii) above is

the crucial condition for solvability with amplitude saturatingactuators and forms the sufficient conditions for solvability.Under the above conditions, an approach based on a linear

quadratic regulator problem with associated cost function

(8)

is adopted. It is well known that the solution of this problem isobtained via solution of the ARE

(9)

where is a continuously differentiablematrix-valued function such that , for any

, and .The solution of (9) is a unique positive definite that is

continuously differentiable with respect to , is monotonicallyincreasing with , and .The state feedback gain matrix is given by

(10)

where, in the terminology of [18],

is the high gain control parameter;

is the low gain parameter.

Feedback using yields an asymptotically stable undis-turbed system for any . The feedback control law isgiven by

(11)

For a system subject to input amplitude saturation, this design,with an appropriate choice of results in exact output regulationwith the system operating in the linear regions of the saturationelements as long as the previously stated conditions hold true.A key feature in the problem considered in this work is the

complementary nature of the saturation-bandwidth limits ofthe two classes of actuators—the wind power actuators and theenergy storage actuators. It is typical for energy storage devicesto offer fast control action (high bandwidth) while havingnarrow limits on the magnitude of power and energy suppliedor absorbed. In contrast, varying the mechanical input power toa wind turbine by varying its blade pitch or nominal rotationalspeed, is a relatively slow control action (low bandwidth), butone which can have fairly broad limits before saturation isreached. We tailor the low-high gain design method to enhancecontroller utilization and regulation performance when actua-tors fall into these two classes. To do so, we partition thematrix according to the characteristics of the input channels. Todo so, the system is first transformed into its modal coordinates.The transformation square matrix is formed such thatevery real eigenvector of the matrix forms a column of

and every complex eigenvector of , , results in twocolumns of such that one column is the real part of andthe other column is the imaginary part of . Then, the statematrix in the modal coordinate frame is given by

(12)


The matrix thus formed has all the real eigenvalues ofon the diagonal, and each of the complex eigenvalues result inblocks of size 2 2 with the real part of the eigenvalues on thediagonal and the imaginary part appearing as skew symmetricterms on the off-diagonal [20]. For example, for a matrix witha real eigenvalue and a pair of complex conjugate eigen-values , the corresponding matrix in its modal formis

(13)

Typically, is chosen as . But here, to exploit the comple-mentary nature of saturation-bandwidth limits of the two classesof actuators, we partition the matrix parameterized in twodifferent ’s. The influence of each class of the input channelson the states can be quantified by looking at the modal degreesof controllability. In particular, for each input channel and eachmode of the system define the scalar given by

(14)

Here, is the normalized left eigenvector of correspondingto the mode ( ), is the th column of . Thisprovides a way to rank pairs of modes that are most control-lable through a particular input channel. Once this is known,corresponding 2 2 diagonal blocks of the matrix can beweighted with appropriate ’s. So, for the high bandwidth, lowsaturation limits channels, the resulting diagonal blocks ofmatrix are weighted with higher values of as compared tothose chosen for the diagonal blocks associated with the lowbandwidth channels. This modal-based tailoring of the low-highgain design method complements the characteristics of the twoclasses of actuators considered in this work. Initial results of thismethod applied on simple power system models are shown in[21].

III. SYSTEM MODEL

The system under consideration consists of the power net-work including wind generation systems, energy storage de-vices at some of the nodes in the network and an exosystemmodel governing the wind power variation. Variation in windspeed gets reflected at the output of the wind generator as vari-ation in power generated, which in turn gets reflected onto thepower system as variation in frequency. We seek to constructthe autonomous exosystem in such a way that it approximatesperiodic wind variation.We apply the control design method de-scribed in the previous section on two test power systems, andstudy the performance of the system with the controller undervariations in wind power. Models of various components of thesystem are described below.

A. Model of Wind Variation

As a simple proof of principle in modeling periodic varia-tion in wind power, we construct the exosystem such that it cangenerate a periodic disturbance as a band limited approxima-tion to a square wave. The matrix governing the dynamicsof the exosystem in (2) is chosen such that it has purely imagi-nary pairs of eigenvalues. With an appropriate choice of initial

conditions, , an unforced system that approximates a periodicsquare wave can be constructed. More specifically, we choose amatrix of size 10 10, given by

. . .

(15)

where is the frequency of the periodic square wave. Here,has along its diagonal, 2 2 blocks of anti-diagonal matrices

with odd harmonics of forming the entries on the anti-diag-onal. All the other entries of are zero. This choice of resultsin purely imaginary eigenvalues of the exosystem, the eigen-values being For the specific initialconditions of

(16)

direct calculation confirms that trajectories will containsinusoids at and its odd harmonics to order 9. The matrix

is chosen such that each row corresponding to eachwind generator is of the form

(17)

The remaining rows of are set to zero, so that the periodicsquare wave affects only the input channels of the system asso-ciated with the wind generators.

B. Model of Wind Generation System

To model the wind generator system, we consider the stan-dard doubly-fed induction generator (DFIG)-based model. Thespecific representation used is known as Type-3 Wind TurbineGenerator (WTG) Western Electricity Coordinating Council(WECC) generic model per classification of the WECC WindGenerator Modeling Group (WGMG) [22]. Fig. 1 shows theblock diagram of this system. The model is described in detailin [22]. One of the key features of this model is the way inwhich the drive train is represented. A two-mass torsionalmodel is used to represent the behavior of the turbine-rotorsystem. This feature allows us to study the incremental differ-ence in the turbine speed and the rotor speed during transients.This represents torsional flexing of the drive shaft, and hence isan indicator of mechanical stress on the drive train. One of theobjectives of our control method is to minimize this differencein speeds during transients so that the stress on the drive trainshaft is reduced.The generator/converter model is the equivalent of the gen-

erator and the field converter and provides the interface be-tween the WTG and the network. The generator is modeled asa controlled-current source. This current controller delivers theamount of current that must be injected into the grid in responseto the flux and active current commands which are generated bythe converter control model.


Fig. 1. Type-3 WTG system.

The converter control model determines the amount of ac-tive and reactive power that must be delivered by the generatorto the grid. It compares the measured active power withthe ordered active power from the turbine model and themeasured reactive power with the ordered reactive powerfrom the reactive power control model , and provides cur-rent and voltage commands to the generator model.The wind turbine model calculates the mechanical power and

speed of the wind turbine. It includes a simplified model ofthe turbine aerodynamic characteristics and the WTG rotor me-chanical equations. The rotor mechanical equations represent atwo-mass model as mentioned earlier.The pitch control model provides blade pitch command to

the wind turbine model according to the rotor speed and con-verter torque command. A change in blade pitch angle changesthe aerodynamic power at the wind turbine. State space modelsof each of these sub-systems are formed according to the re-spective model descriptions. The overall wind system model isconnected at a bus in the power system with the bus voltage andangle as the algebraic variables at that bus. Since one of the ob-jectives of the control is to minimize the stress on the drive train,the states of the wind system model are transformed so that thespeed difference between the turbine and the rotor forms one ofthe states.

C. Power System Model

The state space formulation of the power system is assembledas follows. The electromechanical behavior of each of the tradi-tional synchronous generators in the system can be captured bystandard swing equation models [23]. The frequency and theangle are related by definition

(18)

The differential equation governing the dynamics of a generator,the swing equation, is given by

(19)

where

is the rotational inertia of the generator;

is the damping constant;

is the mechanical shaft power input to the generator;

is the electrical power output of the generator.

can be assumed to be zero for the generator, as we areonly interested in variation in frequency arising due to wind

power variation. is the change in power generated by thegenerator at that bus. This must also match with the change inpower injected into the system at that bus. As is typical in powersystems practice, the feedback control design is based on a lin-earization about the operating point.We consider a power system consisting of traditional syn-

chronous generators at some of the buses, wind generation sys-tems at some of the buses and constant loads at some of thebuses. The state equations governing the traditional generatorsand those governing the wind generator systems can be writtentogether with the network power balance equations in the form

(20)

(21)

where are the net system dynamic states, are algebraic vari-ables, and are the inputs. The dynamic states consist of thestates of the WECC wind system model, and the ’s and ’sof the traditional generators. The algebraic variables consist ofthe voltage magnitudes and angles at the wind generator busesand at the load buses, and the real power injections at the tradi-tional generator buses. These are standard power flow variablesat the respective buses in the network. Equation (21) is a setof algebraic equations that represents the power flow Jacobianrelation of the network. For a linearization about the operatingpoint, the Jacobian relates various bus powers and the bus volt-ages according to a linear set of equations. The number of theseequations must match the number of algebraic variables

D. Model of Energy Storage

Battery energy storage systems have very high bandwidths,but are limited in the amount of power that they can provide.Typical Bode plots of R-C circuit linearized models repre-senting batteries [24] resemble high-pass filter characteristics.So, we model the high bandwidth, low saturation limitationcharacteristics of energy storage devices, the fast set of ac-tuators in the system, using standard fourth order high-passButterworth filters. We add energy storage devices at someof the traditional generator buses, as has been done for somecurrent grid scale energy storage prototypes [25]. A standardstate space representation of the filter can be modeled to repre-sent an energy storage device and this can be augmented withthe overall model of the system described above. The statefeedback output is fed as an input signal to the energy storagedevice. Since the actuator associated with the wind generationsystem, the blade pitch controller, is already part of the WECCwind system model, we avoid adding any external feedbacksignal to the wind generation systems. The schematic of thenet system model along with the full state feedback-basedcontroller is shown in Fig. 2.

E. Observer-Based Implementation

Even with the advances in communications and smart gridtechnologies, centralized real-time feedback control on thepower grid remains an impractical proposition. In order tomake the control technique described in the previous sectionpractically feasible, a distributed observer-based feedbackcontrol scheme, also presented in [26], is demonstrated here. In


Fig. 2. Block diagram of the full state feedback-based system.

Fig. 3. Block diagram of the observer-based system.

this proposed scheme, the control input to each battery storagesystem is generated by a local observer-fed controller. Thisscheme utilizes a small subset of available measurement signalsfrom the system to form estimates of the system states that arethen fed to each of the local controllers. A schematic of theproposed system is shown in Fig. 3. This approach overcomesthe limitations of traditional centralized control, where largecommunication bandwidth is required for exchanging informa-tion between various sub-systems.The local observers are designed according to the following

technique. The technique is described for one of the local ob-servers. The observer-based control design is performed on thesystem in its modal coordinates, , so thatthe complementary nature of saturation-bandwidth limits of theactuators is exploited

(22)

(23)

The dynamic equation of the observer is given by

(24)

which can be written as

(25)Define

(26)

Substituting (23) in (25) and subtracting resulting equation from(22), we obtain

(27)

This equation governs the estimation error. The choice of thematrix determines the eigenvalue/eigenvector placement of thissystem.Next, a method to form the matrix that takes advantage

of the degrees of freedom in choosing not only the eigenvaluesbut also the eigenvectors of this system is described. Given acomplex scalar (such as an eigenvalue), the Hautus matrix isdefined as

(28)

Suppose is an eigenpair of such that is fullrank, i.e., mode is observable, the matrix is chosen such that

is an eigenpair of for arbitrarily chosen. The choice of the matrix is made as follows.From the basic definition of eigenpair of a matrix

(29)

(30)

Let , and . Also, let beof size . Then, , can be formed for number ofobservable modes.Let

(31)

(32)

Then, (30) leads to

(33)

(34)

Thus, for each observer, the matrix can be formed. This matrixcould be different for different observers, since it depends onthe choice of the matrix at that particular bus. The controllaw (11) is modified such that the state feedback acts on theestimated states, . So

(35)


Fig. 4. Four bus test system.

Fig. 5. Wind power variation.

IV. RESULTS OF IMPLEMENTATION

We simulate themodel described in the previous section usingtwo test power systems—a four bus system and a fourteen bussystem. We first show the results of the simulation without anycontroller. Next, we apply the control design method describedin Section II on these systems and analyze the results.

A. Four Bus System Without Controller

We first consider a simple four bus test system as shown inFig. 4. As can be seen in the figure, there is one wind generatorsystem at bus 1, one traditional synchronous generator at bus4, and one load at bus 3. Bus 2 is considered as theswing bus. The wind variation modeled by the exosystem isshown in Fig. 5. The four bus system is simulated accordingto the model described in Section III. The variation in windpower gets reflected on to the system as variation in frequencyat the traditional generator bus. The resulting frequency inhertz is shown in Fig. 6. As can be seen from the figure,the variation in frequency does not settle to zero and has anamplitude of 0.03 Hz varying about the nominal 60 Hz value.The resulting difference in wind system turbine speed androtor speed is shown in Fig. 7.

Fig. 6. Frequency—4 bus system.

Fig. 7. Wind turbine speed, rotor speed difference—4 bus system.

B. IEEE 14 Bus System Without Controller

Next, we consider the standard IEEE 14 bus system whosesingle line diagram is shown in Fig. 8. In this system, we re-place the traditional synchronous generators at buses numbered2 and 8 with wind generator systems. Also, we have traditionalsynchronous generators at buses numbered 3 and 6. Bus number1 is considered as the swing bus. The remaining buses havestandard loads connected at their locations. Here again, wesimulate the system, including variations in wind power at eachof the two wind systems according to the model described inSection III. To monitor one single frequency, we look at theweighted average of the frequencies at each of the traditionalgenerator locations (each frequency weighted by the respectivegenerator inertia). Here we consider the two traditional genera-tors to be identical, so, the frequency to be monitored is simplythe average of the two frequencies. The resulting frequency isshown in Fig. 9. Again here the frequency deviations do not godown to zero. The resulting speed difference in the turbine androtor speeds of each of the wind systems (labeled and )is shown in Figs. 10 and 11, respectively.

C. Four Bus System With Controller

Now, we implement the full state feedback-based control de-sign method described in Section II on the four bus examplesystem. The aim of the controller is to bring the frequency de-viations down to zero while utilizing power available via theenergy storage device and at the same time reducing the stress


Fig. 8. IEEE 14 bus test system.

Fig. 9. Frequency—14 bus system.

on the drive train of the wind system. The resulting plot of fre-quency after inclusion of the controller is shown in Fig. 12. Ascan be seen from the figure, the frequency deviation goes downto zero due to the inclusion of the controller. The resulting plotof difference in the wind system turbine speed and rotor speedafter the inclusion of the controller is shown in Fig. 13. Com-paring this with the corresponding plot without any control inFig. 7, it can be seen that there is a significant reduction in the

Fig. 10. Wind turbine speed, rotor speed difference for —14 bus system.

speed difference, thereby reducing the stress on the drive trainsignificantly.

D. IEEE 14 Bus System With Controller

Next, we implement the full state feedback-based control de-sign method on the fourteen bus system. The resulting plot offrequency is shown in Fig. 14. As can be seen from the figure,the frequency deviations go down to zero due to the inclusion of



Fig. 12. Frequency with controller—4 bus system.

Fig. 13. Wind turbine speed, rotor speed difference with controller—4 bussystem.

the controller. The resulting plots of the speed differences in theturbine and rotor speeds for each of the wind systems are shownin Figs. 15 and 16. Here again, comparing these plots with thecorresponding plots for the case without controller in Figs. 10and 11, it is very clear that the introduction of the energy storagedevices in the system not only brings down the frequency devi-ations to zero, but also reduces the stress on the drive train, thusrespecting the saturation-bandwidth complementary relations.The resulting plots of the battery power outputs (in p.u.) of thetwo batteries are shown in Figs. 17 and 18, respectively.

Fig. 14. Frequency with controller—14 bus system.



E. Observer-Based Implementation on IEEE 14 Bus System

Next, we implement the observer-based feedback control asdescribed in Section III on the fourteen bus system.We have oneobserver-based controller at each of the two traditional gener-ator buses. Apart from using the local generator frequency, eachof the observers use the other traditional generator’s frequencymeasurement to form the state estimate. The resulting plot offrequency is shown in Fig. 19. The resulting plot of differencein speeds of the turbines and rotors of the two wind systems


Fig. 17. Battery 1 power output—14 bus system.

Fig. 18. Battery 2 power output—14 bus system.

Fig. 19. Frequency with observer-based controller—14 bus system.

are shown in Figs. 20 and 21. Comparing these with the corre-sponding plots for the state feedback-based control scheme inFigs. 14–16, it can be seen that the observer-based scheme per-forms almost as good as the full state feedback-based scheme.The resulting plots of the battery power outputs (in p.u.) of thetwo batteries are shown in Figs. 22 and 23, respectively.

V. CONCLUSION

This work has proposed a distributed control design method-ology suited to emerging problems in the electric power grid:that of maintaining stable regulation of grid frequency with thenew technologies of wind generation and battery energy storage.

Fig. 20. Wind turbine speed, rotor speed difference for —Observer-basedcontrol.

Fig. 21. Wind turbine speed, rotor speed difference for —Observer-basedcontrol.

Fig. 22. Battery 1 power output—Observer-based control.

The approach has addressed two new challenges inherent inthese technologies, and indirectly, exploited opportunities in thenew measurement technology of phasor measurement units. Inparticular, the work here has built on the existing literature ofso-called low-high gain controllers for systems with saturation,to treat the narrow range of power (by grid standards) that bat-teries can practically deliver or absorb. To extend the existingdesignmethods for keeping individual actuators within their sat-uration limits under expected ranges of disturbances, this work


Fig. 23. Battery 2 power output—Observer-based control.

has exploited a modal decomposition in the grid and controllerdynamics.In particular, we have demonstrated an effective approach

to “share” the control action among distributed actuators thathave very different control bandwidth characteristics: low band-width, extending down to dc for controllable wind power vari-ation, versus high bandwidth, but zero dc gain, for the actuatorresponse characterizing power variation allowable from batterystorage units. The proposed design methodology has been il-lustrated on a four bus system model and a standard 14 bustest power system model, with results that confirm the designobjectives are achieved: stable regulation of frequency, whilerespecting the saturation and bandwidth limitation of each ofthe classes of (power) controllable equipment available to con-tribute to this objective.

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Chaitanya A. Baone (S’09) received the B.Tech. de-gree in electrical engineering from Visvesvaraya Na-tional Institute of Technology, Nagpur, India, in 2006,and the M.S. degree in electrical engineering fromthe University of Wisconsin-Madison, Madison, in2009, where he is currently pursuing the Ph.D. degreefrom the Department of Electrical and Computer En-gineering.His research interests include power system dy-

namics, control, and optimization.

Christopher L. DeMarco (M’85) received the B.S.degree from the Massachusetts Institute of Tech-nology, Cambridge, and the Ph.D. degree from theUniversity of California, Berkeley, both in electricalengineering and computer sciences, in 1980 and1985, respectively.He joined the faculty at the University of Wis-

consin-Madison, Madison, in 1985, where hecurrently holds the position of Professor of electricaland computer engineering. At the University ofWisconsin-Madison, he has served as Electrical and

Computer Engineering Department Chair, and currently serves as GraingerProfessor of Power Engineering and Site Director for the Power SystemsEngineering Research Center (PSERC). His research and teaching interestscenter on dynamics and control of electrical energy systems.

Documents

From Each According to its Ability: Distributed Grid Regulation With Bandwidth and Saturation Limits in Wind Generation and Battery Storage