1

Distributed Automatic Generation Control usingFlatness-Based Approach for High Penetration of

Wind GenerationM. H. Variani, Student Member, IEEE, K. Tomsovic, Fellow,IEEE

Abstract—To allow for high penetration of distributed gen-eration and alternative energy units, it is critical to minimizethe complexity of generator controls and the need for closecoordination across regions. We propose that existing controlsbe replaced by a two-tier structure of local control operatingwithin a global context of situational awareness. In local control,individual components and individual loads operate in a mannerto follow some desired trajectory based on local observations.The global control, on the other hand, refers to the desiredtrajectory which is determined by the context of the overallsystem needs for reliability, speed, and robustness. Flatness asan extension of controllability for non-linear systems is a key toenable planning and optimization at various levels of the grid inthis structure. In this study, flatness-based control for AutomaticGeneration Control (AGC) of a multi-machine system with highpenetration of wind energy is investigated. The local controltracks the reference phase which is obtained through economicdispatch at the global control level. As a result of applyingthe flatness-based method, the n machine system is decoupledinto n linear controllable systems in canonical form. Therefore,the control strategy results in a distributed AGC formulationwhich is significantly easier to design and implement compared toconventional AGC. Practical constraints such as generator ramp-ing rates can be considered in designing the local controllers.The proposed strategy demonstrates promising performance inmitigating frequency deviations and the overall structure couldfacilitate operation of other non-traditional generators.

Keywords— Frequency Regulation, Automatic GenerationControl (AGC), Flatness, Trajectory Tracking, Trajectory Gen-eration, Wind Power.

NOMENCLATURE

δi Rotor electrical angle, in rad (subscript i denotesthe ith generator).

ωi Rotational speed of rotor, in rad/s.ωs Machine electrical synchronous speed, in rad/s.Pgvi Governor power, in p.u..Pmi Mechanical power, in p.u..P refi Speed changer position.Ei Voltage behind reactance, in p.u..Vi∠θi Machine terminal voltage, in p.u. and rad.x′di Direct axis transient reactance, in p.u..Hi Inertia constant, in seconds.Di Damping constant, in p.u..Ri Slope of the machine speed-droop characteristic,

in p.u.τgi,τTi Governor and turbine time constants in second.

M. H. Variani and K. Tomsovic are with the Min H. Kao Department ofElectrical Engineering and Computer Science, The University of Tennessee,Knoxville, TN 37996 USA (e-mail: mhassani@utk.edu).

Bf The frequency bias setting, in MW/0.1 Hz.

I. INTRODUCTION

THE rapid introduction of wind power has begun toimpact overall power system control, and particularly

frequency control. As a fundamental characteristic of electricpower operations, frequency of the system deviates from itsnominal value due to generation-demand imbalance. Conven-tional generators, in which the turbine rotational speed isnearly constant, provide inertia and governor response againstfrequency deviations; however, the speed of a wind turbineis not synchronous with the grid and is usually controlledto maximize active power production. Therefore, wind plantpower production is not inherently coupled to the systemfrequency, and historically, wind plants have not been requiredto participate in frequency regulation. Still, modern windplants offer limited ability to contribute in frequency regulationwithin few seconds after loss of generation [1].

With increased penetration of wind energy, system operatorshave begun to study the performance of the primary frequencyresponse. The California ISO frequency response study showsthat the reduced system inertia due to penetration of wind unitshas an impact on the initial rate of change of frequency butit has little impact on the severity of the frequency excursionand settling frequency. Inertia controls from wind generationcan significantly improve the frequency nadir but they dorelatively little to correct a shortage in the amount of availableresponse. Unlike inertial response, wind plant governor likecontrol will significantly improve frequency nadir and settlingfrequency. This control requires the wind plants to work belowavailable power [2]. According to the investigation of windgeneration penetration in the ERCOT market, the percentageincrease in regulation requirements has been found to be equalto the percentage wind penetration on a capacity basis. Theregulation needs increase much more for certain times of theyear [3]. Another assessment of frequency control consid-ered changing a fraction of the on-line turbine capacity thatprovides primary and secondary control. This study showedthat adequate reserve to cover expected variations of windpower is not sufficient on its own. In fact, proper dynamiccharacteristics and control capabilities are as important as thelevel of reserves [4].

The amount of secondary control response capability re-quired and the rate at which it must be delivered havehistorically been functions of the daily load forecast, allowance

2

for error in the forecast, and provision for contingencies. Theintroduction of variable resources clearly adds a new andpotentially large component to the requirement for secondaryresponse with respect to both amount and rate of delivery.The correct operation of the system for load frequency control(LFC) to handle as much as possible of the imperfectionresults in minimizing the use of primary response capability[4]. If secondary control is exhausted due to wind, solar orload variability, the actions of primary frequency control willreduce primary frequency response capability for respondingto the faults [2]. Secondary control action is based on theassumption that frequency error throughout a balancing au-thority is identical. This assumption may not be well suited forsystems with high wind penetration because larger imbalancesmay occur at locations with high installed wind capacity [5].On the other hand, improvements in wide area measurementsallow for more distributed secondary control. Thus, a highproportion of wind powered generation will require renewedattention to secondary control capability.

AGC, secondary frequency control, has been conventionallyperformed by integrating the Area Control Error (ACE), whichacts on the load reference settings of the governors. Theintegral of square error (ISE) is used in [6] to find theoptimum gain for the controller. Performance of other classicalcontrol methods such as Proportional-Integral (PI), Integral-Derivative (ID), Proportional-Integral-Derivative (PID) andIntegral-Double Derivative (IDD) controllers is investigatedin [7]. All these approaches are adequate for the traditionalcentralized system controls but suffer from the need forcareful coordination of local controllers with overall systemobjectives.

In the present study, a flatness-based approach is appliedto multi-machine AGC. The performance of the proposedcontrol system is investigated in presence of penetration ofwind generation. Flat systems were first introduced by Fliess[8] using the formalism of differential algebra. In differentialalgebra, a system is viewed as a differential field generatedby a set of variables. The system is said to be flat if onecan find a set of variables, called the flat outputs, such thatthe system is algebraic over the differential field generatedby the set of flat outputs. The flatness-based approach iswell adopted to control systems in two levels of planning,trajectory generation, and tracking the desired trajectories. Inthe proposed structure, the n-machine system is split into nlinear controllable systems. Consequently, the control strategyis significantly easier to implement relative to conventionalAGC. This work is an extension of the work in [9] thatestablished a two-tier structure in a multi-machine system tocontrol the frequency and tie-line power flow considering theoverall system reliability, speed, and robustness.

II. FLAT SYSTEMS

When a system is flat, it is an indication that the non-linear structure of the system is well characterized and onecan exploit that structure in designing control algorithms formotion planning, trajectory generation, and stabilization. Onemajor property of differential flatness is that the state and input

variables can be directly expressed in terms of the flat outputand a finite number of its derivatives. In other words, a systemis flat if we can find a set of flat outputs (equal in number tothe number of inputs) such that all states and inputs can bedetermined from these outputs without integration [10].

Consider

x = f (x, u) (x ∈ Rn, u ∈ Rm) (1)

The dynamic feedback linearizability of (1) means the exis-tence of a regular dynamic compensator{

z = a (x, z, v)

u = b (x, z, v) (z ∈ Rq, v ∈ Rm)(2)

and a diffeomorphism

ξ = Ξ (x, z)(ξ ∈ Rn+q

)(3)

such that (1) and (2), whose (n+ q) dimensional dynamics isgiven by {

x = f (x, b (x, z, v))

z = a (x, z, v)(4)

becomes, according to (3), a constant linear controllablesystem ξ = Fξ +Gv.

Up to a static state feedback and a linear invertible changeof coordinates, this linear system may be written in Brunovskycanonical form,

y(α1)1 = v1

...y(αm)m = vm

(5)

Then it can be deduced that:{x = A(y, y, ..., y(α−1))

u = B(y, y, ..., y(α))(6)

where (y, y, ..., y(α−1)) corresponds symbolically to(y1, ..., y

(α1−1)1 , ..., ym, ..., y

(αm−1)m

)and the same for

(y, y, ..., y(α)) [8], [11].The dynamic feedback (2) is said to be endogenous if and

only if, the converse holds, i.e., if and only if, any componentof y can be expressed as a real-analytic function of x and uand a finite number of its derivatives:

y = C(x, u, u,..., u(γ)) (7)

A dynamics (1) which is linearizable via such an endoge-nous feedback is said to be (differentially) flat; y is called alinearizing or flat output.

The flatness property may be very useful when dealing withtrajectories: from the y trajectories, x and u trajectories areimmediately deduced. These properties permit a straightfor-ward open loop path tracking. The equivalence of the flatsystem with a controllable linear system via an endogenousfeedback yields a feedback stabilization of the desired trajec-tory. Precisely, according to the flat output properties, system

3

trajectories joining a collection of points with given velocities,acceleration, jerks, etc., are easily generated. This replacesdifficult dynamical computations by statistical interpolationtechniques [12].

A. Trajectory Generation

Due to flat outputs properties, all trajectories (x(t), u(t))satisfying the system differential equation can be interpretedin terms of the flat output and its derivatives (6). Consideringthe problem of steering from an initial state to a final state, thecomponents of the flat output yi, i = 1, ...m are parameterizedby:

yi(t) :=∑j

Aijλj(t) (8)

where λj(t), j = 1, ..., α are basic functions. Thus, theproblem of steering from an initial state x(ti) to x(tf ) reducesto find the coefficient Aij in the following system of equations:

yi(t0) =∑j Aijλj(t0)

.

.

.

y(αi−1)i (t0) =

∑j Aijλ

(αi−1)j (t0)

yi(tf ) =∑j Aijλj(tf )

.

.

.

y(αi−1)i (tf ) =

∑j Aijλ

(αi−1)j (tf )

(9)

It is observed that the problem reduces to solving simplealgebraic equations. The multi-dimensional case follows byrepeatedly applying the one-dimensional case, since the algo-rithm is decoupled in the component of the flat output [10],[13].

B. Trajectory Tracking

In a flat system, tracking the desired trajectory is ensuredusing the fact that the flat system is equivalent to a trivialsystem y(α) = v by endogenous dynamic feedback. By setting(y∗)(α) = v∗, it suffices then to set :

v = v∗ −α−1∑j=1

Kje(j) (10)

with appropriate gain matrix K = [K1, ...,Kα−1] and e =y− y∗ the error term in this equation. Linear control methodssuch as pole-placement and Linear Quadratic Regulator (LQR)can be applied to find the K coefficients. Similar to trajectorygeneration for multi-dimensional case, trajectory tracking fol-lows by repeatedly applying the one-dimensional case [10],[13].

III. FREQUENCY REGULATION

System frequency deviates from the nominal setting when-ever there is imbalance between generation and load. Theimbalance will be drawn from the kinetic energy stored in therotating masses of the generators. Local governor control is theprimary control loop to ensure balance. In order to maintainsystem frequency at the nominal value and schedules betweencontrol areas, a secondary control loop, AGC, coordinates theunit raise and lower signals.

A. Conventional AGC

The supplemental control serves several functions, includ-ing: restoration of the nominal frequency, maintenance of thescheduled interchanges between authority areas and provisionfor the economic dispatch of units. The coordination amongareas is achieved by defining the so called ACE. A frequencybias setting, 10Bf , is multiplied by the frequency deviation,∆f , which is subtracted from the deviation of tie flowsto obtain ACE. The ACE is integrated over time and thissignal is used to determine the generator set points. Thecontrol center gathers the relevant frequency and power flowinformation, calculates the ACE and sends the appropriate setpoint adjustments for each of the units on AGC. Therefore,set point controls are discrete. In North America, the AGCsignals are fed to the units typically, about once every 2-4 sec[14]. Economic dispatch is performed once every 5 minutesto calculate plant based points and participation factors forplants on secondary control. Conventionally, each control areaof an interconnected system is controlled in a similar manner,but independently of the other control areas. That is, thecontrol of generation in the interconnected system is “area-wise decentralized” [15].

B. Governor-Turbine-Generator Model

Considering the governor-prime-mover-rotating mass/loadmodel block diagram in [16], a multi-machine system toanalyze AGC performance can be described by a fourth-ordermodel in (11-14). Since the focus of this study is only onfrequency response, it is appropriate to assume that the voltageregulator and other dynamics within the machine are fastcompared to the phenomena of interest [17].

δi = ωi − ωs (11)

ωi =1

2Hi

[Pmi − EiVi

x′disin(δi − θi)−Di (ωi − ωs)

](12)

Pgvi =1

τgi

(P refi − ωi − ωs

Riωs− Pgvi

)(13)

Pmi =1

τTi

(Pgvi − Pmi) (14)

In this model, the active power output at the generatorinternal nodes is stated as a function of terminal voltage,voltage behind the reactance and x′d [18]. Terminal voltage

4

magnitude and angle depend on the network equations. Sincethe flux decay dynamics are neglected, terminal voltage canbe calculated using algebraic equations.

Speed changer position, P refi , is conventionally calculatedthrough integration of ACE. The main challenge in this methodis the design of the integral controller and the coordinationacross areas. This becomes more challenging in the presenceof wind farms in the system as the energy generated by theseunits varies rapidly, which may result in misleading ACEsignals.

IV. FLATNESS-BASED AGC

Based on (11)-(14) and considering δ = [δ1, ..., δi, ..., δn]′

as the flat output set, the flat outputs and their derivative upto degree four for a multi-machine system can be derived asfollows:

δi = ωi − ω0 (15)

δi =1

2Hi

[Pmi − EiVi

x′disin(δi − θi)−Di (ωi − ωs)

](16)

...δ i =

1

2Hi

[1

τTi(Pgvi − Pmi)−Diδ −

EiVix′di

δicos(δi − θi)]

(17)

δ(4)i =

1

2Hi

1τTiτgi

(P refi − δiRωs− Pgv)− 1

τ2Ti

(Pgvi − Pmi)−EiVi

x′di

(δicos(δi − θi)− (δi)2sin(δi − θi))

−Di

...δ i

(18)

The algebraic relations between the state variables, input,flat outputs and their derivatives, verify that δ is the flat outputin this system as stated in (15)-(18). The algebraic functionsA, B and C can be defined as follows:{

xi = A(δi, δi, ..., δ(3)i )

ui = B(δi, δi, ..., δ(4)i )

(19)

δi = C (xi, ui) (20)

where xi = [δi, ωi, Pgvi, Pmi]′and ui = P refi . Therefore,

the compensator for the system in each area can be definedas:

zi1 = zi2zi2 = zi3zi3 = zi4zi4 = vi

(21)

where zi1 = δi and δ(4)i = vi. According to (21), one sees thatthe dynamics of a multi-machine system can be split into nlinear controllable subsystems. The trajectory generation andthe asymptotic tracking of the desired trajectory, rotor angle,is studied in the following to find the control input, vi, foreach subsystem.

A. Trajectory generation for multi-machine AGC system

An important role of AGC is to allocate generation sothat each power source is loaded most economically [15].In this study, economic dispatch is performed to find thedesired operating points. Note that this can be replaced byother methods depending on the system’s overall needs. Thedesired operating point has to be updated at frequent intervalsin order to follow load changes and wind generation variations.Here, intervals of five minutes are considered for economicdispatch as it is used in conventional AGC. The referencepoints and participation factors are sent to generators every5 minutes and a smooth trajectory is then planned locally.The planning method described in section II-A is deployedto generate the optimum path to be followed by trajectorytracking control. Within the five minute intervals, the referencevalues for rotor angle are updated such that each generatorcontributes in frequency regulation based on its participationfactor. The desired operating point determines the participationfactors.

Although the operating points in the system are updatedevery five minutes, significant wind power changes may occurin the interval and cause the system to deviate from the desiredtrajectory. In this situation, the trajectory can be updated lo-cally by solving simple algebraic equations to keep the systemat the new desired trajectory. The trajectory can be updatedregularly, e.g., approximately every minute or whenever thedeviation from trajectory is larger than a specific value.

B. Trajectory tracking for multi-machine AGC system

The gain matrix, K, in (10) should be designed to restorethe nominal frequency and track the scheduled net inter-change with desired performance characteristics. Individualunits tracking the desired trajectory generated in section IV-Awill guarantee overall system performance. The trivial systemof (21) for each area is the key to achieve tracking of thedesired trajectory. In general any simple linear control methodcan be applied to find the gain. In this work, the LQRmethod is employed which allows consideration of practicalconstraints related to AGC [19].

The obtained K leads to asymptotic tracking of the desiredtrajectory. The practical constraints considered in this studyare:• Generator ramping rate constraint (GRC) which limits the

rate of generation increase/decrease. In LQR method, thisconstraint can be considered by choosing a large value forR, which is representative of cost of the control.

• Raise/lower signals are sent to the governor every 2seconds. Therefore, continuous optimal control may notbe optimal for the system in practice. In order to designthe digital control law for this continuous time systems,the flat system is discretized using 2 second samples.The discretization process assumes that the control inputv(t) to the continuous plant is switched only at times2k and it is held constant between switchings [19]. InNorth America, AGC is typically executed once every2 to 4 seconds. However, the control action in flatnessapproach is based on local measurements and due to a

5

Fig. 1. Flatness-Based control block diagram

large sampling rate of modern units, measurement doesnot restrict the frequency of sending controller signal. Inthe other words, the control signal can be sent to governoras frequent as the governor limits allow.

C. Summary of Approach

Fig. 1 shows the schematic control diagram of the proposedapproach. Desired operating points are determined at theglobal level control using the economic dispatch or othermethods, while the trajectory is generated at the local controllevel. Rotor angle and frequency are the quantities requiringmonitoring in this scheme. Due to the lack of a direct measure-ment of rotor angle, this parameter is assumed estimated usingthe measurements of a Phasor Measurement Unit (PMU) [20].In this study, rotor angle is estimated based on the terminalvoltage angle and generator active and reactive powers asshown in (22) and (23).

Ii = IDi + jIQi = (PGi − jQGi)/Vie−jθi (22)

δi = ∠(Viejθi + jx′di(IDi + jIQi)) (23)

The measured and estimated quantities are compared withthe reference values and the control signal is generated througha trajectory tracking approach at the generator level. In sum-mary, the planning is performed at the global level and thetrajectory is generated and tracked locally using closed loopcontrol.

V. SIMULATION RESULTS

In this section, the proposed flatness-based AGC is evalu-ated on a 3 area, 10-machine and the 39-bus system shownin Fig. 2 and is compared with conventional AGC [21]. Thetotal load in this system is assumed to be 5.483 GW andeconomic dispatch is performed to find the scheduled activepower generation. In order to evaluate the performance of thecontroller in presence of penetration of wind energy, the windpower profile shown in Fig. 3 is applied to the test system.The wind power has an average value of 500 MW and thefluctuations are about ±5% of the average power. Frequencydeviation in frequency domain, considering spatial filtering ofgeographically dispersed wind turbines in a wind farm, is usedto generate this wind power profile [22]. Two scenarios arestudied:

• Scenario 1: 10% penetration of wind power generation inarea 2.

• Scenario 2: 20% penetration of wind power generation inareas 1 and 2.

Fig. 2. 10 Generator, 39 Bus Test System

0 1 2 3 4 50

2

4

6

Time(min)

Pwin

d(pu

)

Fig. 3. Wind Power (pu) - Base is 100 MVA

Based on the Western Wind and Solar Integration Study(WWSIS) results, the addition of every 3MW of wind gener-ation was accomplished with a 2 MW de-commitment and a1 MW reduction in other generation. Therefore for 500 MWadditional wind production, the 2/3 de-commitment objectiveis 333 MW and the 1/3 re-dispatch objective is 167 MW. De-commitment of the thermal units reduces the contribution of

6

these units in frequency regulation, while dispatching downgives more headroom for secondary control [1]. The originaldispatching, the updated dispatching related to scenarios 1 and2 and generator data are displayed in Table I.

Note in the flatness approach the control areas would notnecessarily be the same as today’s balancing areas. Smallerbalancing areas can be selected to improve the controllerperformance in presence of large scale wind generation at noadditional cost of monitoring. The changes in the planning andtrajectory generation are investigated in section V-C.

Table IGENERATOR DISPATCH IN PU (BASE IS 100MVA)

Area GenOriginal Scenario 1 Scenario 2 Inertia x′

d

Dispatch Dispatch Dispatch H(sec) (pu)

11 5.620 5.620 5.620 70.0 0.0202 3.727 3.727 2.454 30.3 0.0703 3.727 3.727 0 35.8 0.053

2

4 7.481 7.481 7.481 28.6 0.0445 7.796 7.796 7.796 26.0 0.1326 5.796 5.092 5.092 34.8 0.0507 4.296 0 0 26.4 0.049

38 4.296 4.296 4.296 24.3 0.0579 4.296 4.296 4.296 34.5 0.057

10 7.797 7.797 7.797 20.0 0.044

A. Scenario 1

In this scenario, the wind power profile is added in area2, which is about 10% of the total load. Fig. 4 displaysthe average frequency deviations in each area. The totalmechanical power values in each area are shown in Fig.5. Tie line flow deviations from the scheduled values aredisplay in Fig. 6. As observed, the flatness approach resultsin improved performance in mitigating both the frequency andtie flow deviations while the mechanical power changes do notexcess the ramping rate limits of the generators. Comparisonof frequency deviations and tie flow deviations in three areasshows that, with flatness-based approach the control actionsoccur primarily in the area where the wind farm is located. Inother words, the wind power fluctuations are damped locally.It is worth mentioning that in the flatness-based approach,the average of the frequency in areas is only calculated forclear presentation. As stated in section IV-C, the frequencyis measured locally and compared with a reference value foreach generator.

B. Scenario 2

In this scenario, a wind farm is in both areas 1 and 2. Theaverage frequency deviations in each area, total mechanicalpower values in each area and tie flow fluctuations are shownin Fig. 7, Fig. 8 and Fig. 9. The first observation is that higherpenetration of wind power results in greater frequency and tieflow deviations in the system. Also, comparison of the twoscenarios shows that the effectiveness of the flatness-based

0 1 2 3 4 5−0.2

0

0.2 Area1

Fre

q de

viat

ion(

Hz)

0 1 2 3 4 5−0.2

0

0.2 Area2

Fre

q de

viat

ion(

Hz)

0 1 2 3 4 5−0.2

0

0.2Area3

Time (min)

Fre

q de

viat

ion(

Hz)

Fig. 4. Frequency Deviation with Conventional (red dash line) and flat-tness_based (solid blue) with 10% Penetration

0 1 2 3 4 512.5

13

13.5Area1

Pm(p

u)

0 1 2 3 4 520

20.5

21Area 2

Pm(p

u)

0 1 2 3 4 516

16.5

17Area 3

Time (min)

Pm(p

u)

Fig. 5. Mechanical Power with Conventional (red dash line) and flat-tness_based (solid blue) with 10% Penetration

approach is more noticeable with the higher penetration ofwind power.

C. Planning

Simulation results shown in sections V-A and V-B areassumed to be performed in 5 minutes intervals with aconstant desired operating point. In this section, the concept

7

0 1 2 3 4 5−0.5

0

0.5Area1

Ptie

dev

iatio

n (p

u)

0 1 2 3 4 5−0.5

0

0.5Area2

Ptie

dev

iatio

n (p

u)

0 1 2 3 4 5−0.5

0

0.5Area3

Time (min)

Ptie

dev

iatio

n (p

u)

Fig. 6. Tie Flow with Conventional (red dash line) and flattness_based (solidblue) with 10% Penetration

0 1 2 3 4 5−0.2

0

0.2Area1

Fre

q de

viat

ion(

Hz)

0 1 2 3 4 5−0.2

0

0.2Area2

Fre

q de

viat

ion(

Hz)

0 1 2 3 4 5−0.2

0

0.2Area3

Time (min)

Fre

q de

viat

ion(

Hz)

Fig. 7. Frequency Deviation with Conventional (red dash line) and flat-tness_based (solid blue) with 20% Penetration

of trajectory generation that reflects the system needs isdemonstrated. Two generators in area 2 are re-dispatched sothat the scheduled value for generator 5 is decreased by 0.2pu and the scheduled value for generator 7 is increased bythe same amount. Fig. 10 shows two different trajectories,one with a step change in the rotor angle trajectory andthe other one based on generating a smooth trajectory. Theactual rotor angles are also shown in the same figure. Fig.11 displays the frequency deviations in two generators relatedto two trajectories. It is observed that the smooth trajectoriesresult in improved frequency and rotor angle deviations andthe controller tracks the desired trajectories well. The lower

0 1 2 3 4 57.5

8

8.5Area1

Pm(p

u)

0 1 2 3 4 520

20.5

21Area2

Pm(p

u)

0 1 2 3 4 516

16.5

17Area3

Time (min)

Pm(p

u)

Fig. 8. Mechanical Power with Conventional (red dash line) and flat-tness_based (solid blue) with 20% Penetration

0 1 2 3 4 5−0.5

0

0.5Area1

Ptie

dev

iatio

n (p

u)

0 1 2 3 4 5−0.5

0

0.5Area2

Time(min)

Ptie

dev

iatio

n (p

u)

0 1 2 3 4 5−0.5

0

0.5Area3

Time (min)

Ptie

dev

iatio

n (p

u)

Fig. 9. Tie Flow with Conventional (red dash line) and flattness_based (solidblue) with 20% Penetration

deviations decrease the control effort required to keep thesystem at the desired operating point.

VI. CONCLUSIONS

This paper presents a flatness-based method to controlfrequency and power flow for multi-area power systems.The two level control consisting of trajectory generation andtrajectory tracking replaces conventional AGC. This approachcan also replace conventional area based frequency control.As an important feature of the proposed approach, the set ofnonlinear equations corresponding to an n-machine system isdecoupled into n linear controllable sub-systems. Therefore,

8

the proposed AGC is easier to design and implement. Locallinear controllers are designed for each sub-system to maintainthe frequency at nominal value and to keep power flows nearscheduled values. The main requirement is the availabilityof PMU measurements. The flatness-based control methoddemonstrates promising performance in mitigating frequencyand tie-line flow deviation. This approach also provides aplatform for non-conventional units to contribute to loadfollowing and frequency control.

1 2 3 4 50.2

0.4

0.6

0.8

1

Time(min)

Del

ta(r

ad)

Gen5−trajectory

Gen7−trajectory

Gen5

Gen7

0 1 2 3 4 50.2

0.4

0.6

0.8

1

Time(min)

Del

ta(r

ad)

Gen5−trajectory

Gen7−trajectory

Gen5

Gen7

Fig. 10. Rotor Angles and Trajectories in Area 2

1 2 3 4 5

−0.2

−0.1

0

0.1

0.2

Time(min)

Fre

q de

viat

ion(

Hz)

Gen5− Step TG

Gen7− Step TG

Gen5− Smooth TG

Gen7− Smooth TG

Fig. 11. Frequency Deviation in Area2

VII. ACKNOWLEDGEMENT

This work was supported in part by the Engineering Re-search Center Program of the National Science Foundation andthe Department of Energy under NSF Award Number EEC-1041877 and the CURENT Industry Partnership Program.

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