Determ Bias

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904 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 2, MAY 2003

Estimation of for Adaptive Frequency Bias Settingin Load Frequency Control

Le-Ren Chang-Chien, Student Member, IEEE, Naeb-Boon Hoonchareon, Member, IEEE,Chee-Mun Ong, Senior Member, IEEE, and Robert A. Kramer

AbstractUtilities in the U.S. use tie-line bias control to sharegenerationand frequency support in the interconnection. To ensurethat the reliability and the responsibility of frequency supportare maintained, NERC guidelines specify that the frequency biascoefficient

1 0

that a control area uses in its tie-line controlbe set as close as practical to the areas frequency responsecharacteristic . This paper presents an algorithm to estimate

online using variables commonly available from existing AGCsystem. Results showing the algorithms performance in simulatedconditions and on actual field data are presented. Issues relatedto using the estimated in an adaptive frequency bias-settingcontrol are examined.

Index TermsAdaptive frequency bias control, frequency re-sponse characteristic, tie-line bias control.

I. INTRODUCTION

MOST utilities in the U.S. still operate with a conventional

load frequency control (LFC) that is based on tie-line

bias control. The fast-acting governor on a regulating unit

serves as the primary control in load-generation balance, sup-

plemented by a higher level, slow-acting automatic generation

control (AGC), whose other functions are to ensure the area

absorbs its own load change, and to maintain net interchange

and frequency at their schedule values.

The conventional wisdom in tie-line bias control is to use thefrequency bias coefficient, , to offset the areas frequency

response characteristic, . Supposedly, with , the

area control error (ACE) would only react to internal distur-

bances [2], [3]. Unnecessary AGC action to external distur-

bances not only results in extraneous regulation effort but also

inter-area tie-flow oscillations. When matches of the

control area, unnecessary control actions could be reduced and

the control becomes more efficient [3]. NERCs Policy 1 rec-

ommends that a control area sets its frequency bias coefficient

as close as practical to the areas frequency response

characteristic [4].

Presently , which is not easily obtained on a real time basis,

is approximated [1]. The object of getting a good estimate of the

areas to improve the load-frequency control performance has

motivated this work on estimation.

Manuscript received October 15, 2002.L.-R. Chang-Chien andC.-M. Ongare with theSchool ofElectricaland Com-

puter Engineering, Purdue University, West Lafayette, IN 47907 USA.N.-B. Hoonchareon is with the Department of Electrical Engineering, Chula-

longkorn University, Ba ngkok, 10330, Thailand.R. A. Kramer is with NiSource Energy Technologies, Merrillville, IN 46410

USA.Digital Object Identifier 10.1109/TPWRS.2003.810996

The proposed estimation algorithm is based on the ACE

model given in [5]. When implemented online, the algorithm

can provide estimates of the areas in real-time. Since

the estimation scheme uses commonly available variables in

existing AGC system, it does not require additional SCADA

measurements.

In this paper, we first present an online estimation method

for determining the of a control area. Following which, we

examine some practical issues of implementing the algorithm

and how should be set relative to the estimated for ac-

ceptable control areas response to tie-line bias control. Resultsshowing the performance of the estimation algorithm on simu-

lated condition and on actual field data are presented.

II. MATHEMATICAL MODEL FOR ESTIMATION

The per unit equation of the electromechanical power balance

for the local control area may be expressed as

pu (1)

where and are the total generation excluding units pri-

mary control effort and total demand within the local control

area in per unit, respectively. is defined as the net tie flow

from the local to the external areas in per unit; is the areasfrequency response characteristic in per unit.

As the actual response of regulating units to the LFC

controller depends on the status of the equipment and their

operating constraints, the actual may not track the desired

generation command. A slack term is introduced in

the model to account for the difference between desired and

actual generation

pu (2)

where and are the regulation and basepoint com-

ponents in per unit, respectively. Note that includes the

scheduled tie flows.

In many of the ACE controllers, the regulating component,, in (2) is expressed as a proportional-integral function

of the filtered ACE

pu (3)

Replacing in (2) by (3) and substituting in (1)

with (2), we obtain

pu (4)

0885-8950/03$17.00 2003 IEEE
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Fig. 2. Sensitivity of to local areas bias setting B .

C. Effect of Nonlinearities on Estimate

Within the LFC loop are many nonlinearities, some of whichcan affect the value of . Here, we will examine the impacts of

the following nonlinearities on control areas .

5 MW ACE deadband in the AGC control logic of the

five control areas;

30-MHz speed governor deadband on all online units;

rate and range limits apply on units under regulation con-

trol in local control area

The dynamic 30-MHz governor deadband is implemented in

the simulation using a backlash function given in reference [7].

Units rate and range limits are included in the model of the

governor and prime mover as described in [8]. The result of esti-

mating for the same inputs and interval as those used in Fig. 1

but with the above nonlinearities included is given in Fig. 3.With nonlinearities, the estimated islower than the cal-

culated using a value of computed from the dc loop gains

in (10).

It is known that the effective speed droop in transient

operation with governor backlash can be less than the speed

droop based on steady-state dc gains [6]. Changes in effective

speed droop is most noticeable in hydraulic units, followed by

reheat units, and is the least in nonreheat units. The effective

speed droop with or without nonlinearities for all the units in

the local area over the simulation run may be determined from

the dotted-line major axes of the versus trajectories in

Fig. 4. Superimposed on the trajectories, are solid lines which

represent equivalent steady-state or dc droop characteristics ofthe online governors in the whole control area computed from

MW/Hz (11)

where the summation is over all regulating units in the control

area and is the speed droop of the th unit. For a unit with

5% regulation

rating of th unit (MW)Hz/MW (12)

The dashed line, with slope , is the first order approximation

of the major axis for the elliptical envelope containing the tra-

Fig. 3. and with nonlinearities.

Fig. 4. Effective governing characteristics of local area.

jectories of the governor response with deadband and rate limits.

With nonlinearities, the slope of is steeper than that of .

Thus, the effective gain of governor control loop, , is less

than that of its dc loop gain, . Much of this difference

between and may be traced to the governors dead-

band. When the frequency deviation is within the governors

deadband, the governors response is inhibited. The higher ef-

fective slope with deadband is also collaborated by the steep ini-

tial slope of the System Response Characteristic (SRC) curve at

low frequency deviation given in [3], [9]. For larger frequency

excursions outside the deadband of the governors, the dash-line

in Fig. 4 will be rotated counter clockwise. In other words, the

effective slope will decrease further, as is evident by the flat-

tening of the SRC at higher frequency deviation.

Thus, the estimated in Fig. 3 is less than because of

the effective droop, , with deadband nonlinearities is higher

than the dc droop, .

IV. PERFORMANCE OF ALGORITHM ON FIELD DATA

The usefulness of the estimation algorithm can be deter-

mined from its performance on actual field data taken from a
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CHANG-CHIEN et al.: ESTIMATION OF FOR ADAPTIVE FREQUENCY BIAS SETTING IN LOAD FREQUENCY CONTROL 907

Fig. 5. Estimated of utilitysystem between 19:0024:00 P.M. on 02/15/2001.

utility company. A sample result from such a test is given in

Fig. 5. The period between 19:00 and 22:00pm corresponded tothe on-peak hours when large loads were active. After 22:00pm,

the areas demand went from high to low. This condition is re-

flected by smaller variation in the estimated . The actual bias

setting used by the utility for its tie-line bias control

during the operating period was 600 MW/Hz.

V. USING THE ESTIMATED FOR ADAPTIVE FREQUENCY BIAS

CONTROL

The ability to estimate online naturally raises the possi-

bility of using the estimated value to adjust the value of

to suit the prevailing system condition. For each control areain an interconnection, may be viewed as its share of in-

ternal power imbalance to compensate for the deviation in fre-

quency. When its frequency bias setting is set equal to its , that

is , the control areas LFC would be responding to

the appropriate internal power imbalance. When ,

the control areas LFC not only compensate for the deviation in

frequency but also assist other areas in frequency support. But

when , the control areas LFC does not fully meet

its share of frequency support even though the disturbance is

external. The degree of supplementary control response and the

amountof tie flow oscillationswill depend on the frequency bias

setting in relation to its .

The variable bias setting scheme described in [9], [10] usesa two-segment bias setting characteristic for different operating

conditions. The nonlinear bias curve is kept between the SRC

and horizontal axis in the vs. plane. In the assist mode,

for the security of the interconnection, upon detecting a large

frequency deviation, as in an emergency, a control area should

use a larger bias value.

In this section, we will explore how the frequency bias set-

ting affects the AGC response and the tie flows oscillations to

understand the dynamics and to establish some rationale for ad-

justing .

Fig. 6 shows the two-area system simulated to represent a

local control area and its external equivalent. The capacity ratio

Fig. 6. Model of internal and external areas.

Fig. 7. Response to an external disturbance at t = 1 0 0 sec followed by a stepchange in 0 1 0 B after t = 3 0 0 s.

of the external area to internal equivalent is arbitrarily set to

6:1 for the base case. For clarity, the subscript will be used

to denote variables of the local control area and subscript for

those of the external area.

A. Dynamics Introduced by a Change in

Tests were first conducted to establish the response in fre-

quency and tie flow to a change in frequency bias setting of

the local areas LFC following a load disturbance applied tothe external area, with the LFC of the external area deactivated.

Fig. 7 shows the changes in frequency response, , and tie

flow, , when the of the local area was switched from

to and 200 seconds after the change in external

load. Following the disturbance applied at the 100th second, the

response with is as expected from theory. When

was subsequently raised to at the 300th second,

there was an increased tie flow out to the external area accom-

panied by a decrease in the frequency deviation. The changes

in tie flow and frequency deviation were opposite when

was lowered to at the 300th s, as indicated by the dotted

traces.
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Fig. 8. Response plots for first three cases in Table I.

B. Control Interaction

Tests were also conducted to gauge the interaction between

the two areas LFCs, as evident in , , , and .

Throughout this second set of tests, the frequency bias setting

of the external areas LFC is set equal to the external areas

, when that of the local control areas LFC is varied. The

disturbance is applied either inside or outside of the local control

area.

A sample of the kind of transient response is given in Fig. 8.

It shows the , , and response to an internal

step disturbance for the three values of given in the first

half of Table I for AGC proportional and integral gains of 0.065.

It is representative of the dynamic response obtained for the

other cases in Tables I and II.

A summary of the RMS errors of the four variables for a rel-

atively high and a relatively low value of AGC gains about the

nominal value is given in Tables IIII. Here, RMS error is de-fined as the root mean square (RMS) difference between mea-

sured and steady state values over the observed time interval.

The RMS errors in Table I for all four variables decrease with

higher ratiofor a disturbance within the localcontrol

area. Note also that the RMS errors of and with high

AGC gains are lower than those obtained with lower AGC gains.

Thus, a higher bias setting is beneficial in limiting the frequency

deviation and tie-line oscillations when the load disturbance is

inside the local control area.

Tables II and III are for a load disturbance applied outside the

local control area. For an external load disturbance, the RMS

errors of and decrease with lower ratio in

TABLE IRMS ERROR FOR STEP DISTURBANCE IN INTERNAL AREA GENERATING

CAPACITY RATIO OF AREAS EXTERNAL:INTERNAL = 6:1

TABLE IIRMS ERROR FOR STEP DISTURBANCE IN EXTERNAL AREA GENERATING

CAPACITY RATIO OF AREAS, EXTERNAL:INTERNAL = 6:1

TABLE IIIRMS ERROR FOR STEP DISTURBANCE IN EXTERNAL AREA GENERATING

CAPACITY RATIO OF AREAS EXTERNAL:INTERNAL = 1:1

high AGC gains. The benefit of using a is good for

a limited period under the above condition.

The above test results with different ratios and

AGC gains indicate potential benefits in adjusting the frequency

bias setting to suit different system conditions. For example,

when a local area detects that a disturbance is inside the localcontrol area, the results in Table I show that temporarily raising

its above would limit the frequency deviation and

bring about faster frequency regulation without excessive oscil-

lations in tie flow.

When the disturbance is external, the results in Table II show

that using a higher ratio of does not seem to have

significant adverse impact in , , and when the

size of the external area is six time larger than the local area.

However, when the size of the internal area is comparable to

that of the external area, the results in Table III show that there

is advantage in reducing the frequency bias setting when the

AGC gains are high for an external disturbance.


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Fig. 11. Trace of adaptive 0 1 0 B setting with respect to the trace of forthe local control area, concurrent external and internal load disturbances.

are results from using the different fixed bias setting relative

to . For purpose of comparison, the value of the

(mean) is set at the mean value of the used by the

logic throughout the simulation run.

In Table IV, slightly smaller RMS values of and

were obtained with compared to those with

(mean), indicating that the adaptive bias logic yielded smaller

oscillations in tie flow and local areas power output. In this

case,using resultedin smalleroscillationsthanusing

MW/Hz, which is larger than . Note also

that the MW/Hz case gave smaller oscillations

in tie flow and power generation than using , but has

a larger frequency deviation.

C. Case II: Internal Load Disturbance

A second set of tests was conducted with a load disturbance

applied inside the local control area. It can be seen from Table V

that the RMS values of and with are still

less than those with . The result of higher RMS

values of and with MW/Hz, which

is less than , confirms the previous observation that using a

that is smaller than would result in larger tie flow

and generating output oscillations when the load disturbance is

internal.

D. Case III: Simultaneous External and Internal Load

Disturbances

In practice, disturbances could simultaneously occur inside

and outside the local control area. Although setting

or MW/Hz in previous two cases gave less

RMS error in and than using for external

or internal load disturbance, the results for simultaneous internal

and external disturbances could be different. The results with

simultaneous external and internal load disturbances are given

in Table VI. The RMS errors in and with

are smaller than those using various settings.

TABLE IVRMS ERRORS WITH DIFFERENT FREQUENCY BIAS SETTINGS FOR THE LOCAL

CONTROL AREA, EXTERNAL LOAD DISTURBANCE

TABLE VRMS ERROR WITH DIFFERENT FREQUENCY BIAS SETTINGS FOR THE LOCAL

CONTROL AREA, INTERNAL LOAD DISTURBANCE

TABLE VIRMS ERROR WITH DIFFERENT FREQUENCY BIAS SETTINGS FOR THE

LOCAL CONTROL AREA, CONCURRENT EXTERNAL, AND INTERNALLOAD DISTURBANCES

VII. CONCLUSION

Our observations of tie-line bias control response behavior

under different system conditions support NERCs recommen-

dation to control areas to use a frequency bias setting close to

. Since the of an area is a function of the effective speed

droop, which in turn is dependent on the number and type of

regulating units online and the nonlinearities present, its value

will be time-varying.

In this paper, we have presented a method to estimate the of

a control area continually using inputs which are readily avail-

able in most conventional automatic generation control using

tie-line bias. Presented are test results on simulation and on fielddata indicating that the algorithm is performing as desired.

Also presented in this paper are simulation and analytical

results on the transient behavior of , and that

suggest potential benefits of using a variable bias setting under

certain operating conditions. Results fromour simulation studies

of an adaptive frequency bias setting logic do confirm such

benefits in reducing unit movements and tie flow oscillations.

The estimation algorithm can be used in conjunction with

the ACE model described in [5] to realize a model reference,

adaptive bias setting control. We are currently working on the

design of such an adaptive tie-line bias controller. Our plan is

to implement the estimate algorithm online in the near future,
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CHANG-CHIEN et al.: ESTIMATION OF FOR ADAPTIVE FREQUENCY BIAS SETTING IN LOAD FREQUENCY CONTROL 911

gather experience and data with it to help us design an adaptive

bias control that will operate more efficiently under the new

NERCs CPS1 and CPS2 criteria.

ACKNOWLEDGMENT

This work was performed under a research contract from

NiSource Energy Technologies and the U.S. Department of

Energy.

REFERENCES

[1] N. Jaleeli, L. S. VanSlyck, D. N. Ewart, L. H. Fink, and A. G. Hoffman,Understanding automatic generation control, IEEE Trans. PowerSyst., vol. 7, pp. 11061122, Aug. 1992.

[2] N. Cohn, Control of Generation and Power Flow on InterconnectedPower Systems. New York: Wiley, 1966.

[3] T. Kennedy, S. M. Hoyt, and C. F. Abell, Variable, nonlinear tie-linefrequency bias for interconnected system control, IEEE Trans. PowerSyst., vol. 3, pp. 12441253, Aug. 1988.

[4] Policy 1 Generation Controland Performance, Version 1a, North Amer-ican Electric Reliability Council, 2000.

[5] N.-B. Hoonchareon, C.-M. Ong, and R. A. Kramer, Feasibility of de-composing A C E to identify the impact of selected loads on CPS1 and

CPS2, IEEE Trans. Power Syst., vol. 17, pp. 752756, Aug. 2002.[6] N.-B. Hoonchareon, Feasibility of Decomposing One-Minute Average

Area Control Error for Apportioning Load-Frequency RegulationCosts, Ph.D. dissertation, Purdue University, West Lafayette, IN, 2000.

[7] Dynamic modelsfor fossilfueled steam units in powersystem studies,IEEE Trans. Power Syst., vol. 6, pp. 753761, May 1991.

[8] Dynamic models for steam and hydro turbines in power systemstudies, IEEE Trans. Power Apparat. Syst., vol. PAS-92, pp.19041915, Nov./Dec 1973.

[9] L. S. VanSlyck, N. Jaleeli, and W. R. Kelly, Implication of frequencycontrol bias settings on interconnected system operation and inadvertentenergy accounting, IEEE Trans. Power Syst., vol. 4, pp. 712723, May1989.

[10] N. Jaleeli and L. S. VanSlyck, Tie-line bias prioritized energy control,IEEE Trans. Power Syst., vol. 10, pp. 5159, Feb. 1995.

[11] Chee-Mun Ong, Dynamic Simulation of Electric Machinery UsingMATLAB/SIMULINK. Englewood Cliffs, NJ: Prentice-Hall, 1998.

[12] L.-R. Chang-Chien, An Automatic Generation Control With AdaptiveFrequency Bias Setting for Current NERC Performance Standard,Ph.D., Purdue University, West Lafayettte, IN, 2002.

Le-Ren Chang-Chien (S00) received the B.S. degree in Engineering Sciencefrom National Cheng Kung University, Tainan, Taiwan, R.O.C., in 1993, theM.S.E.E. degree from the University of Wisconsin-Madison in 1998, and thePh.D. degree from Purdue University, West Lafayette, IN, in 2002.

He joined the Department of Electrical Engineering at National Cheng KungUniversity, Tainan, Taiwan, R.O.C., as an Assistant Professor in 2003. His re-search interests include electric machines, power system operation, and control.

Naeb-Boon Hoonchareon (M01) received the B.Eng.(Hons) degree in elec-trical engineering from Chulalongkorn University, Bangkok, Thailand, in 1993,the M.S.E.E. and Ph.D. degrees from Purdue University, West Lafayette, IN, in1996 and 2000, respectively.

Currently, he is with the Department of Electrical Engineering, Chula-longkorn University in Bangkok, Thailand. He was a Post-Doctoral ResearchAssociate at Purdue University on the DOE/NIPSCo project. His researchinterests include interconnected power systems operation, modern automaticcontrol, and optimization.

Chee-Mun Ong (SM80) received the B.E.(Hons) degree in electrical engi-neering from the University of Malaya in 1967, and the M.S. and Ph.D. degrees

from Purdue University, West Lafayette, IN, in 1968 and 1974, respectively.During the periods, 19681973 and 19761978, he was a Lecturer in the Uni-versity of Malaya. In l969/70 he spent a year as an UNESCO Fellow with theCentral Electricity Generating Board and the English Electric in England. In1978 he joined the School of Electrical Engineering at Purdue University as anAssistant Professor and in 1985 became a Professor. His interests are in powersystems and electrical drives.

Dr. Ong is a Fellow of the Institution of Electrical Engineers, and a registeredProfessional Engineer of Indiana.

Robert A. Kramer received the M.S. and Ph.D. degrees in nuclear engineeringfrom Purdue University, West Lafayette, IN, and the B.S. and M.S. degrees inphysics, also from Purdue University.

Currently, he is Vice-President and Chief Scientist of NiSource Energy Tech-

nologies, Merrillville, IN. In this position, he is responsible for the introductionof new technology into the gas and electric functions of the utility as well asproviding support on various technical and competitive issues.

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