Predictive Frequency Stability Control Based on Wide-Area Phasor Measurements

8/10/2019 Predictive Frequency Stability Control Based on Wide-Area Phasor Measurements

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Predictive Frequency Stability Control based onWide-area Phasor Measurements

Mats Larsson, Christian Rehtanz

Abstract Wide-area phasor measurements provide a dy-namic view of the power system in short-term intervals. Thetime synchronization and concentration of these measure-

ments opens up a range for wide area applications for pro-tection and control. For each kind of instability, relateddetection and action schemes can be defined to limit or pre-

vent the system from severe disturbances or even collapses.

This paper proposes a novel predictive method for emer-

gency frequency control to be used on such occasions. Theproposed method avoids the drawbacks of local underfre-quency load shedding schemes, such as delayed response

and overshedding, by basing control on synchronized pha-sor measurements. A single machine equivalent for each

power system island including the frequency sensitivity ofloads, is computed online using phasor measurements. Us-ing this model the progression of frequency stability after

a contingency is predicted and stabilizing load shedding isdetermined in a co-ordinated way for the supervised area ofthe power system.

Keywords Power Systems, Frequency Control, Stability.

I. Introduction

POWER supply has become so important for the en-tire society that large efforts must be made to prevent

power systems from collapse [1]. One way is to provide asystem wide protection complementary to the conventionallocal equipment and SCADA/EMS system [2]. Increasingdemand on the power system increases the likelihood ofsystem problems such as instabilities and collapses. Whileit is not possible to predict or prevent all contingenciesthat may lead to power system collapse, a wide area pro-tection system that provides a reliable security predictionand optimized coordinated actions is able to mitigate orprevent large area disturbances. The main tasks are earlyrecognition of instabilities, increased power system avail-ability, operation closer to the physical limits, increasedpower transmission capability with no reduction in secu-rity, better access to low-cost generation and minimizationof load shedding. Pre-calculations of the stability for one ora combination of two contingency events address a part of

the problem. This requires a huge calculation effort and thesystems state for which a case is calculated must fit mostexactly to the actual systems state. For unexpected con-tingency cases this approach is not useful. Conclusively, themajor drawbacks of all these approaches are due to that theinformation that can be obtained from steady-state viewis limited. The solution for this is a departure from theSCADA-based approach to an on-line measurement sys-tem using synchronized Phasor Measurement Units (PMU)

M. Larsson ([email protected]) and C. Rehtanz([email protected]) both are with ABB SchweizAG, Corporate Research, 5405 Baden-Dattwil, Switzerland.

[3]. Together with the stability assessment and stabiliza-tion algorithms such a system is called wide area protectionsystem in the following. PMUs offer phasors of voltage,currents and frequency together with a satellite triggeredtime stamp in time intervals down to 20 ms. Single in-stallations of such units are in an experimental stage atmany utilities [4]. Previously, methods for voltage stabilitymonitoring [5,6] and corrective control [7] based on phasormeasurements have been presented.

This paper contributes further on the topic of instabil-ity detection and control with methods for monitoring andcontrol of frequency stability.

II. Frequency Stability

Frequency stability denotes the ability of a power systemto operate with the (average) system frequency within nor-mal operating limits. Failure to do so may cause damageto generation and/or load side equipment.

Underfrequency load shedding (UFLS) is the mostwidely used protection against frequency instability. Typi-cally, load is shed based on a local frequency measurementin several steps of 5-20 % (of the total feeder load) each.Typical threshold values are 57-58.5 Hz for 60 Hz systemsor 48-48.5 Hz for a 50 Hz system [2]. Usually there is alsoa time-delay intended for noise rejection. The main draw-

back of these schemes is their delayed response since theymust wait for the frequency to decline before taking action.

It is well known (see e.g., [8]) that the power mismatchfollowing the outage of a generator or a tie-line can becalculated from the initial rate-of-change of the frequencyand the system inertia constant according to the formula

P = d

dtHsystem (1)

This value can be used as an indication of the amount ofload that has to be shed to arrest further frequency de-cline. Many authors have proposed UFLS relays based on

the frequency rate-of-change [912]. These schemes avoidthe delayed response of the relays of traditional type andare decentralized and therefore cheap and easy to imple-ment. There are however significant drawbacks also to thisapproach:

The system inertia constant is assumed to be known The load frequency sensitivity is assumed to be known. The voltage sensitivity of the load is assumed to beknown.

The above assumptions make this type of relays difficultor perhaps impossible to tune so that they operate reli-ably. Particularly the system inertia constant is difficult to

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know in advance, since it may change drastically for exam-ple due to islanding of the system. The method proposedhere avoids the above mentioned assumptions by insteadextracting the relevant information from wide-area mea-surements as follows:

The inertia constants of on-line generators are suppliedby the wide-area measurement system. The frequency and voltage sensitivities of the load areestimated on-line, during the initial stage following a dis-turbance, and are included in the system model on whichthe control is based. The actual load distribution is measured, and the effectof disconnecting a certain feeder is therefore exactly known.This knowledge can also be used to fine-tune the amountof shedding employed or to use other criteria such as loadpriorities or post-shedding power-flows. The proposed method needs only a few tuning parame-ters that are easy to choose.

III. The Test System

In order to illustrate the method, simulations are car-ried out using the simple two-area test system shown inFig. 1. It is based on data given in reference [13]. Eachload is assumed to consist of five identical feeders that canbe switched out independently when there is a need for loadshedding. The generators are modelled using standard 6thorder models with first order fast excitation systems andconstant power governors.

To simulate the effect of measurement noise, random 0.01Hz additive errors have been introduced on the generatorspeed measurements and 0.02 % multiplicative errors onthe amplitudes and phase angles of the voltage and cur-rent phasors. These assumptions correspond to about twice

the noise levels specified by manufacturers of PMUs, e.g.[14]. Communication delays of 0.25 s in either directionbetween the PMUs and the central processing unit and acomputational delay of 0.25 s have also been included inthe employed simulation model.

IV. Proposed Predictive Control Strategy

The execution of the proposed method consists of sepa-rate steps. First, a single-machine equivalent model of thesystem is formed based on the collected measurements. Inthe next step, the model is employed to estimate the activepower imbalance in the system and subsequently a pre-

dicted steady-state frequency. Using the same model, theamount of load shedding required to keep the frequencyabove some target value is calculated. In the final step,the calculated amount is allocated to different feeders us-ing a simple iterative method considering the actual loadon the feeders.

A. System Modelling

The method is based on a single generator model of eachpower system island as proposed by [8]. However, the con-servative assumption that the effect of governors can beneglected is made. The frequency dynamics can then be

described by the differential equation

d

dt =

1

2Hsystem(Pm Pe) (2)

whereHiis the inertia constant of generator i andHsystemis the system inertia constant defined as follows

Hsystem =1..N

Hi (3)

Pm =

1..N

Pm,i (4)

Pe = Ploss+

1..M

Pl,i (5)

The constants N and Mis the number of generators andloads, respectively. The active power losses are denotedPloss, the load consumed at bus i is denoted Pl,i, the me-chanical power delivered to the shaft of generator i is de-noted Pm,i, and the system average frequency is denoted.

Each load is modelled using a static load model

Pl,i = (1 ki)P0,i(ViV0,i

)as,i(1 + ci( s)) (6)

Ql,i = (1 ki)Q0,i(ViV0,i

)bs,i(1 + di( s)) (7)

where ki is an input signal modelling load shedding foreach load, V0,i is the nominal voltage, P0,i the nominalload and s is the synchronous frequency. Linearizing theload model and writing on vectorized form yields

PL = AV + C+ Gk (8)

QL = BV + D+ Hk (9)

whereA = diag(a1 . . . aM), B = diag(b1 . . .bM) etc.To account for the effect of voltage variations on the load,

the model proposed by [8] is augmented with matrices ofsensitivity coefficients

V = EPL (10)

V = FQL (11)

After combining (2) and (8)-(11) to eliminate the variablesV, PL and QL, the model can be written on the or-dinary differential equation form

dxdt

= Aodex + Bodek+ Eoded (12)

y = Codex (13)

where x is the dynamical state vector. In the applicationin this paper, the state vector contains only the system av-erage frequency and is thus a scalar. Also other dynamicstates can be included, such as the states of an equivalentgovernor models or dynamic load models. k is a vec-tor of the load shedding inputs and d is a disturbanceinput, modelling for example generator trippings. Notethat all equation are now written on incremental form, that

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G1

Pg=6.4

G2

Pg

=5

G3

Pg

=2

G4

Pg

=2

G5

Pg

=5

G6

Pg=7.1N1

N2

N3

N4

N5

N6N7 N8

N9

N10

N11

N12

3.

5 0

+

j

0.

5

1

. 5

+

j

0.

3

3.

5 0

+

j

0.

5

3

+

j

0.

5

8

+

j

3

8

+

j

2

j2

PMU

PMU

PMU

PMU

PMU

PMU

PMU

PMU

PMU

PMU

PMU

PMU

Fig. 1. The employed test system.

is, relative to the current operating point. x = x x0,y = y y0 and k= k k0 wherex0, y0 andk0 are thevalues of the respective variables at the linearization point.In postcontingency cases it is not unlikely that the networkhas been split into two or more separate islands. In those

cases, a single machine equivalent according to (12)-(13) isformed for each island.

B. Estimation of Average Frequency

The frequency estimate provided by a PMU is an esti-mate of the local frequency at the site of the PMU. There-fore for each generator, the signal from a PMU as close aspossible to that generator is selected. In the control of fre-quency stability, it is the average frequency (in each powersystem island) that is of interest. This is commonly definedusing the center-of-inertia method [15, pp.946].

avg =

i=1..NHii

i=1

..N

Hi(14)

The frequency derivative is then approximated using abackward difference approximation

avg (k) avg (k) avg (k h)

h (15)

whereh is the selected sample interval. Note that the ap-proximation error in the frequency derivative increases withincreasingh. Ideally, the derivative should be computed lo-cally by each PMU and transmitted to the central point.This would enable the use of a shorter sampling time andthereby a more exact derivative approximation. To reducethe effect of measurement noise and transients related to

rotor angle swings and excitation systems on the frequencyderivative estimate, a first order exponential filter is appliedto to the estimate as follows

avg f ilt(k) = avg (k) + (1 )avg f ilt(k h) (16)

The effect of the filter is illustrated in Fig. 2. It is ap-parent that a tradeoff between unwanted oscillations andspeed of convergence of the estimate must be made whenthe value of the parameter is selected. If it is chosentoo large, the magnitude of the oscillations may be unac-ceptable and if the value is chosen too small, the conver-gence of the frequency derivative estimate may be too slow.

0 5 10 15 20 25 30 35 400.4

0.2

0

df/dt(Hz/s)

=1

0 5 10 15 20 25 30 35 400.4

0.2

0

df/dt(Hz/s)

=0.5

0 5 10 15 20 25 30 35 400.4

0.2

0

df/dt(Hz/s)

Time (s)

=0.1

Fig. 2. Filtered frequency derivative estimate for different values ofthe filtering parameter . The estimate is computed using wide-areameasurements by the center-of-intertia method.

0 5 1 0 15 20 25 30 35 400.4

0.2

0

df/dt(Hz/s)

=0.5

Fig. 3. Filtered frequency derivative estimate for = 0.5. Theestimate is computed using a single measurement point.

In the remaining simulations, the value = 0.5 has beenused. Note that a similar filter is necessary also for localUFLS relays based on the frequency derivative. By aver-aging the derivative estimated over all measurements, theeffect of electromechanical oscillations can be reduced [10]

and a filter with less delay can be used when the frequencyderivative estimate is calculated using the center-of-inertiamethod than when only local measurements are applied.As shown in Figs. 2-3, there are considerably more oscil-lations when only a single local measurement is used, andtherefore a slower filter must be used.

C. Estimation of Load Parameters

Fig. 4 shows a typical frequency response following theloss of a generator (when no governor control is providedby the remaining generators). The parameters ai, bi, ciand di in the load model (8)(9) can be determined from

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0 50 10047

48

49

50

51

Time(s)

Frequency

(p.

u.

)

10 11 12 13

49.8

49.9

50

Time(s)

Frequency

(p.

u.

)

Close-up View

Data Range

Fig. 4. Illustration of the data range used for load estimation.

measurements taken at (at least) three different samples.The method triggers when the system average frequencydeviation is greater than 0.1 Hz or a frequency derivativegreater than 0.3 Hz/s. Measurement samples are then col-lected until a sufficiently large frequency variation has oc-curred, and the load parameters are then estimated in aleast-squares manner according to [16]. In this paper wecollect data for parameter estimation during the first 0.2Hz of frequency decline.

D. Frequency Stability MonitoringTiming of SheddingOnce the load parameters have been determined, the sys-

tem model can be written on the ODE form (12)-(13).For the case with no governor control the response ismonotonous and the steady-state frequency is equal to theminimum frequency. The current power mismatch can beestimated as

d= 2Hsystem avg filt(k) (17)

This power mismatch will change due to load frequencyand voltage sensitivity as well as applied control actions.Thus, it is only at the instant of disconnection that the

power mismatch is equal the amount of generation or loadlost. Using the remaining power mismatch as estimated by(17), the predicted steady-state output can be estimatedas

y =CodeA1

ode(Bodek+ Eoded) (18)

At this stage, it is assumed that no load shedding controlis made, i.e, k = 0, so the predicted steady-state outputis written

y =CodeA1

odeEoded (19)

Subsequently, the predicted actual output is found using

y = y + y0 (20)

Fig. 5 illustrates the accuracy of the estimated minimumfrequency without load shedding for a case with sequentialtripping of generators G3 at 10.1 s, G4 at 85.2 s and G5 at160 s. This corresponds to one third of the pre-disturbancegeneration. Note that the last tripping is an unrealisticallylarge disturbance that is used only to illustrate that thereis some inexactness in the method due to the assumptionthat the network is linear. For the two previous trippings,the method accurately predicts the final frequency in 1-2

seconds, however this time is highly dependent on the valuechosen for the parameter . Quicker convergence can beachieved but this results in oscillations in the steady-statefrequency prediction.

Fig. 6 shows the steady-state frequency prediction errorin the same scenario. We can see a sharp increase in theprediction error for the first few samples after each trip.This is due to a one sample time delay before the planttrips are noticed and subsequently to the time it takes forthe frequency derivative estimate to converge. Followingthis initial spike, there is then a slower transient due tothe errors introduced by the linearization of the networkequations. As the frequency approaches its steady-statevalue this error component also converges to zero.

E. Calculation of Required Amount of Shedding

Assume that a certain steady-state frequency y =y + y0 has been calculated using (19) and that thispredicted frequency is found to be unacceptable. The re-quired amount of load to shed can be found by setting

Bode = 1/(2Hsystem), thus assuming that all load is shedin a single point. The power step that needs to be appliedto keep the steady-state frequency estimate at a certaintarget value yrefcan then be determined from (18) where

P= (yref y0) + CodeA

1

odeEoded

CodeA1

odeBode(21)

Fig. 7 shows the frequency response following disconnec-tion of the two units G3 and G4. At time 60 s, (21) suggeststhat 1.16 p.u. of active load needs to be shed to restore thefrequency to a target value of 49 Hz. Following shedding,

the frequency reaches a new steady-state at about 48.95Hz. To illustrate the accuracy of the prediction also forcases where the system frequency dynamics have not yetsettled, a second trip is applied at 86.5 s. At time 90 s, anamount of 2.15 p.u. is shed, and the frequency reaches anew steady-state at about 48.8 Hz.

On both occasions, the shedding is emulated by a fic-titious generation unit (PQ-node) at bus 8 which injectsthe required amount of active power. As shown in the fig-ure, the calculated amount is reasonably accurate on bothoccasions.

F. Compensation for Communication and Filtering Delays

Note that there is a delay before ordered controls are car-ried out and their effect can be noticed in the measurementsfrom the power system. There are several sources of thisdelay: for example the communication delay to the sub-station where the control is carried out, the actual time ittakes to apply the control, the communication delay of thenext set of measurements and the time constant of the filteron the measurement signal. During this time, the steady-state frequency estimates provided by (18) and (19) are un-reliable. This unreliabilty, in combined with the integratorinherent in the control loop, may cause excessive controlaction and frequency overshoot as a result. Therefore it is

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0 50 100 150 20040

42

44

46

48

50

52

Time (s)

Frequency

(p.u.)

Actual FrequencySteadyState Frequency Prediction

Fig. 5. Frequency response and steady-state frequency prediction inthe simulation with disconnection of the three units G3, G4 and G5at 10.1 s, 85.2 s and 160 s, respectively.

0 50 100 150 2001

0

1

2

3

4

5

6

Time (s)

EstimationError(Hz)

Fig. 6. Steady-state frequency frequency prediction error followingthe three unit trippings.

0 50 100 150 20046.5

47

47.5

48

48.5

49

49.5

50

50.5

Time (s)

Frequency

(p

.u.)

Actual FrequencySteadyState Frequency Prediction

Fig. 7. Application of power steps calculated according to (21).

necessary to model and compensate for these delays whencomputing the new control to apply. A compensation termis therefore defined as

ucomp(k) = ucomp(k)(1 ) + Pactual(k 1) (22)

where Pactual(k 1) is the shedding amount executed atthe previous sample and is a tuning parameter that is

used to control the speed of forgetting old control actionsapplied. In this paper we have use the value = 0.5. Thecontrol to actually apply is then corrected as

Pactual(k) = P(k) ucomp(k) (23)

where P(k) is the amount of shedding calculated by (21).The compensation mechanism is similar to anti-windupwhich is often implemented in digital PID controllers.

G. Choice of Shedding Locations

The last step is to assign the calculated amount of shed-ding to the feeders where load is available for shedding.

The very basic, yet efficient, algorithm we employ in thispaper is:1. Calculate the amount of load required for shedding using(21).2. Find loads with available steps, and calculate their ac-tual step size, that is, taking the actual load on the feedersinto account.3. Allocate one step of load shedding at the load with thestep size closest to the remaining amount to shed.4. Repeat step 3 until at least the amount of load calcu-lated in step 1 has been shed.

V. Closed Loop Operation

The simulations in the previous sections have been pre-sented as illustrations of the various aspect of the proposedmethod, such as its inaccuracy and computational proce-dure. In this final section of simulation results we presentclosed loop simulation results to illustrate the method. Forcomparison we present simulation results with local under-frequency load shedding (UFLS) relays employing the samecontrol step sizes at each load bus. The local relays havebeen tuned to shed 20 % of the load at the frequencies 48,47.8, 47.6 Hz with a random time delays between 0.1-0.2 s.

Fig. 8 shows the frequency response following the dis-connection of the three units, with local UFLS and theproposed scheme. We see that when the two small units

are tripped at 10 and 86 s, respectively, the local UFLSscheme reacts later since is has to wait for the frequencyto decline sufficiently before ordering corrective action. Onthe other hand, the proposed scheme applies stabilizing ac-tions as soon as they can be accurately calculated and thefrequency decline is therefore arrested earlier. Another ob-servation that can be made is that the reaction time, andthereby the frequency decline, is slightly smaller at the sec-ond trip since no time is spent estimating the load param-eters. When the large unit is tripped, the frequency de-cline is actually larger with the proposed scheme than withthe local scheme because of the time-delays introduced by

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0 50 100 150 200 250

47.5

48

48.5

49

49.5

50

50.5

51

51.5

52

52.5

53

Time (s)

Frequency(Hz)

Local UFLSProposed Scheme

Fig. 8. Comparison of frequency response with local UFLS and theproposed scheme.

communication and centralized calculation. However, thelocal scheme uses an excessive amount of shedding and aconsiderable frequency overshoot is present.

VI. Future Work

In a real system, the load model (12)-(13) will not bean exact model of the load demand. The impact of var-ious load types on the proposed method is a subject forfurther study. Also dynamic models could be used if thestate vector in (12) is extended. The effect of governor con-trols could be included in a similar manner. Note however,that the parameters for these dynamic load and governormodels may be difficult to to obtain since they require es-timation over a prolonged time window. In this paper weuse perhaps the simplest possible approach to the selectionof which loads to shed. Since the location of the shedding

is not critical from a frequency stability point of view, theselection could be done based on other criteria, such as tominimize overvoltages or steady-state angle differences, orto consider prioritization or shedding rotation.

VII. Conclusion

A novel approach to frequency stability control has beenpresented. A single-machine model of each power systemisland and its connected load and generation is formedbased on wide-are phasor measurements. This model isused to monitor frequency stability and determine the cor-rect amount of load or generation to shed in order to restorethe frequency to a target value. Since control determina-

tion is based on a predictive strategy, the proposed methodavoids the delayed response of traditional underfrequencyload shedding relays.

References

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[4] T W Cease and B Feldhaus, Real-time monitoring of the TVApower system, IEEE Computer Applications in Power, pp.4751, 1994.

[5] K T Vu et.al, Voltage instability predictor and its applications,in Power System Computation Conference, PSCC, 1999, pp.5605.

[6] C Rehtanz and J Bertsch, A new wide area protection system,

in Bulk Power System Dynamics and Control V, August 26-31,2001, Onomichi, Japan, 2001.[7] M Larsson and D Karlsson, System protection scheme against

voltage collapse based on heuristic search and predictive con-trol, IEEE Transactions of Power Systems, to appear, 2002.

[8] P M Anderson and M Mirheydar, A low-order system frequencyresponse model), IEEE Transactions on Power Systems, vol.5, no. 4, pp. 7209, August 1990.

[9] P M Anderson and M Mirheydar, An adaptive method for set-ting underfrequency load shedding relays), IEEE Transactionson Power Systems, vol. 7, no. 2, pp. 64755, May 1992.

[10] D Novosel, K T Vu, D Hart, and E Udren, Practical protectionand control strategies during large power-system disturbances,in 1996 IEEE Transmission and Distribution Conference Pro-ceedings, 1996, pp. 5605.

[11] S-J Huang and C-C Huang, An adaptive load shedding methodwith time-based design for isolated power systems, ElectricalPower and Energy Systems, vol. 22, pp. 518, 2000.

[12] V N Chuvychin, N S Gurov, S S Venkata, and R E Brown,An adaptive approach to load shedding and spinning reservecontrol during underfrequency conditions, IEEE Transactionson Power Systems, vol. 11, no. 4, pp. 180510, November 1996.

[13] D Prasetijo, W R Lachs, and D Sutanto, A new load shed-ding scheme for limiting underfrequency, IEEE Transactionson Power System, vol. 9, no. 3, pp. 137178, August 1994.

[14] Arbiter Systems, Model 1133A Power SentinelData Sheet,www.arbiter.com.

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Mats Larsson received his Masters degree(Computer Science and Engineering), Licen-tiate (Industrial Automation), and PhD (In-dustrial Automation) Degrees from Lund Insti-tute of Technology, Sweden in 1993, 1997 and2001, respectively. Since 2001 he has been em-ployed by ABB Corporate Research, Switzer-land working on the research and developmentof wide-area stability controls for power sys-tems. His research interests are p ower systemstability, optimal control and artificial intelli-

gence applications in power systems.

Christian Rehtanz was born in Germany

in 1968. He received his diploma degree inElectrical Engineering in 1994 and his Ph.D.in 1997 at the University of Dortmund, Ger-many. He is now with ABB Corporate Re-search Ltd., Baden, Switzerland. His researchactivities include the stability assessment, widearea protection and integrated control of ad-vanced power systems, information technologyapplications and questions of distributed powergeneration.

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Predictive Frequency Stability Control Based on Wide-Area Phasor Measurements

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