A simulation model for AGC studies of hydro–hydro systems

Electrical Power and Energy Systems 27 (2005) 335–342 www.elsevier.com/locate/ijepes

A simulation model for AGC studies of hydro–hydro systems K.C. Divya, P.S. Nagendra Rao* Department of Electrical Engineering, Indian Institute of Science, Bangalore 560012, India Received 19 March 2003; revised 25 November 2004; accepted 29 December 2004

Abstract AGC studies pertaining to hydro–hydro systems have received little attention. In this paper a simulation model for AGC studies of such systems has been proposed. The difficulty in extending the traditional approach [Elgerd OI. Electric energy systems theory. New York: McGraw Hill; 1983.] for such systems is overcome by assuming that all areas in a system operate at the same frequency. The proposed simulation model is obtained by ignoring the difference in frequency between control areas, unlike the traditional approach, where in each area is assumed to operate at a different frequency. The features of the proposed model have been demonstrated through simulation studies. q 2005 Elsevier Ltd. All rights reserved. Keywords: Automatic generation control; Simulation models; Hydro systems

1. Introduction The normal operation of an interconnected multi-area power system requires that each area maintain the load and generation balance. This is normally achieved by means of an automatic generation controller (AGC). AGC tries to achieve this balance by maintaining the system frequency and the tie line flows at their scheduled values. The AGC action is guided by the area control error (ACE), which is a function of system frequency and tie line flows. The ACE represents a mismatch between area load and generation taking into account any interchange agreement with the neighboring areas. The ACE for the ith area is defined as ACE Z DPtie C Bi Df

(1)

where DPtie Z Ptie actual K Ptie scheduled and Ptie is the net tie line flow; DfZfactualKfscheduled and f is the system frequency; Bi is referred to as the frequency bias factor This control philosophy is widely used and is generally refered to as the tie line bias control. AGC studies are generally carried out using simulation models. The origin of the simulation model that has been * Corresponding author. Tel.: C91 80 22932365; fax: C91 80 2360444. E-mail addresses: [email protected] (K.C. Divya), [email protected] (P.S. Nagendra Rao).

0142-0615/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2004.12.004

widely used [1] for AGC studies can be traced to [2]. Subsequently, the state space and discrete versions of this model have also been used [3,5]. In [1,3] this model has been used for AGC studies of a two-area non-reheat thermal system. Later, this model has been used to study the AGC for two area reheat thermal system [4–6] and hydro thermal system [7]. Further, it has been extended for multi-area systems, which comprises of three [8] as well as four area systems [9,10]. It appears that the studies carried out so far are limited to only thermal or hydrothermal systems. Even though the interconnected hydro systems are quite common, AGC of such systems does not seem to have been studied so far. This paper presents a study of the AGC for a two area hydro system. As an attempt to extend the conventional model [1] turned out to be unsuccessful, an alternate simulation model for AGC studies of such a system has been proposed here. The AGC performance of a two area test system has been studied using the proposed model with an integral controller.

2. The proposed model The primary requirement of the power system model in the context of AGC studies is that it should enable the computation of deviations in frequency and area tie line flows. In the traditional models, each area with in a system is assumed to be operating at a different frequency. The frequency deviation in each area is obtained by

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considering the area dynamics (aggregate dynamics of the governors, turbines, generators and loads present in the area). The tie line flow deviations between the areas is computed as the product of the tie line constant and the angular difference between the two areas. The proposed model adopts a different approach. Here, the entire system is considered to be operating at a single frequency (all area frequencies are equal). This approach though uncommon, is not unjustified. In fact, the IEEE task force on AGC [11] explicitly recommends this approach. In [11] it has been stated that ‘in AGC studies, the momentary difference between the frequency of different areas can be ignored. For all AGC purposes the frequency used for one area to compute ACE should be the same as used in the other areas so long as they remain interconnected’. A conceptual frame work of such a simulation model (common system frequency approach) had also been outlined earlier by Athay [12] in his comprehensive review of AGC. In the proposed model, the frequency (system frequency common to all areas) is determined by integrating the net system accelerating/decelerating power (i.e. difference of total system generation and load). Since the difference between the area frequencies is neglected, the traditional approach cannot be used to compute the tie line flow deviations. In order to obtain the tie line flows the area power balance equations has been used. The power balance equation for the ith area is written as Ptie C Pgi K Pli ðf Þ Z Hi

dfsys dt

(2)

where Ptie is the tie line power flow; Pgi is the actual total area generation; Pli(f) is the total area load, which is a function of frequency; Hi ðdfsys =dtÞ is accelerating or decelerating power of each area; Hi is the total generator inertia of the area and fsys is the system frequency. It may be noted that the concept of common system frequency and power balance equation based tie line flow computation have been incorporated in a power system simulator developed to verify the long term dynamic behaviour as well as AGC performance of the Pacific Northwest system [13]. It is claimed in [13] that with some

fine tuning of the prime mover parameters (based on system measurements) the simulator response matched closely with the measured responses. However, this approach does not seem to have been adopted by others for AGC studies subsequently. It can be seen that the proposed model has two distinct advantages as compared with the traditional approach. The first is that, this model does not require the computation of the tie line constant. This calculation is not straight forward for systems wherein two areas are connected by more than one tie line. The other advantage is that this model does not require the use of a composite prime mover model representing the entire area. Thus, this model can preserve the identity of each unit and non-linearities like dead band and generation rate constraint (GRC) of different units can be separately incorporated.

3. Simulation results Results of simulation studies of two systems are presented here in order to illustrate the performance of the proposed model. The first test system (Test system-1) corresponds to a two area hydro–hydro system with each area being represented by a composite model. The other test system (Test system-2), having six hydro units, is derived from the IEEE 30 bus test system. 3.1. Test system-1 The choice of this test system (with composite hydro unit model) is prompted by the following considerations: (i) Representing area dynamics through a composite turbine model is an extensively used practice in AGC literature [2–7] over the last 50 years. (ii) This choice facilitates the comparison of the primary response obtained using the proposed model with that obtained using the conventional model. (iii) The parameters for the composite hydro unit model of an area are readily available from earlier work [7]. Pa 1

1 R

Pl 1 1 + s t2 1 + s tR

Pc1

1 1 + s t1

Pgv1 1 – s tw/2 1 + s tw

Tie line flow computation block

1 + s t2 1 + s tR

Pc2

1 R

1 1 + s t1

Pgv2

Kp 1 + s Tp

Pm1

1

1 – s tw/2 1 + s tw

2π T12 s

Kp 1 + s Tp

Pm 2

Pl 2

Fig. 1. Conventional model—block diagram.

f1

Pa 2

f2

K.C. Divya, P.S. Nagendra Rao / Electrical Power and Energy Systems 27 (2005) 335–342 Table 1 Parameter values: two area hydro system Parameters

Elgerd’s model

Proposed model

Kp Tp t1 t2 tR tw R (Hz/puMW) T12 Kpsys Tpsys B1 (puMW/Hz) B2 (puMW/Hz)

120 20 48.7 0.513 5 1 2.4 0.0867 – – – –

– – 48.7 0.513 5 1 2.4 – 60 20 0.425 0.425

First, the responses of both the models (conventional and proposed) have been obtained and compared in the absence of AGC (primary response). Later, the response of the proposed model has been studied with an integral controller. 3.1.1. AGC models for test system-1 Fig. 1 shows the block diagram representation of the conventional model for the two area hydro system considered here. The parameters of each of the areas are identical and are given in Table 1. They correspond to the hydro area model used in [7]. The value of the tie line constant is also identical to that used in [7], which is the same as that used for two area non-reheat thermal system in [3] and the two area reheat thermal system in [4–6]. The block diagram representation of the proposed model for this system is shown in Fig. 2. Comparing Fig. 2 with Fig. 1 it can be seen that the tie line flow computation block is absent in the proposed model. Further, a single system frequency is obtained by integrating the net system accelerating power (DPasys). However, in the conventional model shown in Fig. 1, two different area frequency deviations (Df1, Df2) are obtained by integrating the individual area accelerating powers (DPa1, DPa2).

3.1.2. Primary response The responses of the proposed and conventional models, in the absence of AGC, have been studied for a step load disturbance in one of the area. This response essentially shows how a new load is shared by the two interconnected areas in the absence of AGC. The variation in frequency and tie line power flow deviations obtained using the conventional and the proposed model (with out the controller) for a 0.01 pu step load increase in area-2 have been shown in Figs. 3 and 4, respectively. From these plots, it is evident that the response obtained with the proposed model is stable and does not contain any high frequency oscillations and that obtained with the conventional model contains high frequency oscillations whose magnitude increases with time. It is obvious that the conventional model response is unstable. This inference is further reinforced by the location of the poles of the conventional model given in Table 2. From Table 2 it is seen that a pair of complex poles are situated in the right half of the s-plane. However, it is well known that a number of hydro units can operate in parallel in a very stable manner, even when there is no AGC. This implies that the traditional model is incapable of capturing the right dynamics of a hydro–hydro system for AGC studies. A perusal of Figs. 3 and 4 also shows that the response obtained from the proposed model appears to retain only the slow varying components, filtering out some of the high frequency components seen in the response of the conventional model. This feature of the proposed model conforms to the views of the IEEE task force [11], which states that ‘As a central control process AGC is neither able nor can be expected to play any role in damping electromechanical transients including inter-machine oscillations. Therefore, system models developed for AGC studies need not represent phenomena having time constants shorter than a few seconds’. 3.1.3. Response with controller The AGC response of this system is studied using the proposed model with a simple integral controller.

1 R

1 + s t2 1 + s tR

Pc1

1 1 + s t1

Pgv1 1– s tw/2 1 + s tw

Pm1 Pasys Pl

1 + s t2 1 + s tR

Pc2

1 R

1 1 + s t1

337

Pgv2 1– s tw/2 1 + s tw

Pm2

Pl2

Fig. 2. Proposed model—block diagram.

Kpsys 1 + s Tpsys

fsys

K.C. Divya, P.S. Nagendra Rao / Electrical Power and Energy Systems 27 (2005) 335–342

frequency deviation (Hz)

338

0.2 Conventional model area2 Conventional model area1 Proposed model

0.1 0

–0.1 –0.2 0

5

10

15

20

25

30

time(sec)

Tie line flow deviation(pu)

Fig. 3. Frequency deviation for a 0.01 pu step load change.

0.04 0.02

Proposed model Conventional model

0

–0.02 –0.04 –0.06 0

5

10

15

20

25

30

time(sec) Fig. 4. Tie line power flow deviation for a 0.01 pu step load change.

A comparison with the conventional model is not made as this model is unstable and AGC, being only a supplementary control, is not expected to stabilize an unstable system. Considering the proposed model, an integral controller can be designed by considering a suitable performance index. Here, the performance index J is chosen so as to minimize the excursions in the ACE signal and J is defined as, ðN J Z ACE2 dt (3) 0

The variation of J with Ki, the controller gain is tabulated in Table 3 and is also plotted in Fig. 5, considering a 0.01 pu step load disturbance in area-2. From the plot and the table it can be seen that the integral square error is minimum for a controller gain of about 0.04. Further, it can also be seen that for gain values between 0.02 to 0.04 the value of J remains substantially constant (J changes only by about 4%). Hence, any value of gain between 0.02 to 0.04 will result in a value of J which is close to the minimum. In order to choose a particular gain value, in this range, the qualitative guidelines suggested in [11,14] have been used. In [11] it has been stated that ‘the strategy which accumulates lower cost associated with the wear and tear of regulation for all units combined is preferred. This strategy, therefore, is expected to avoid unnecessary rapid maneuvering of unit generation’. Hence, the controller output (governor set point variation) for various values of gain, from 0.02 to 0.04, were obtained. It was observed that as the value of gain reduces, from 0.04 to 0.02, the overshoots seen in the control action also reduce. Fig. 6 shows the variation in the set point for two extreme values of gain, i.e. KiZ0.04

and 0.02. From this it can be seen that KiZ0.04 corresponding to minimum J, causes overshoots in the control actions. However, with a gain of 0.02 such overshoots in the controller settings are not seen. Consequently, the controller gain of 0.02 was chosen as it can not only reduce the integral square error but also reduce futile and counter productive control actions. The response of the system with the integral controller (KiZ0.02) is obtained for a step load disturbance of 0.01 pu in area-2. Fig. 7 shows the variation in ACE for a 0.01 pu step load disturbance in area-2. From this it can be seen that the ACE remains with in a band around zero (5% of the disturbance) after about 100 s. This slow response can be attributed to the low values of the controller gain chosen as well as to the inherently slow response of the hydro system. A significant increase in the controller gain is seen to affect the stability of the system and it becomes unstable for a gain value of 0.6. It is to be noted that this gain value (KiZ0.02) turns out to be quite small as compared to the optimal gain values reported for two area thermal (0.6 in [3]) and hydrothermal (0.2 in [7]) systems. Table 2 Poles of the conventional model of two area hydro system 0.1008C2.5622i* 0.1008K2.5622i* K3.1004 K2.8128 K1.3882 K0.1899C0.2932i K0.1899K0.2932i K0.5396 K0.0204

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339

Table 3 Variation of J with Ki: test system-1 Ki J!105 Ki J!105

0.0 3768 0.05 1383

0.005 2094 0.06 1429

0.007 1852 0.07 1494

0.01 1647 0.08 1580

0.015 1487 0.09 1691

3.2. Test system-2

0.02 1394 0.10 1834

0.025 1377

0.03 1359

3.2.1. AGC model for test system-2 The schematic representation of the proposed model for this test system is shown in Fig. 8. Each of the hydro unit indicated in Fig. 8 is represented by a detailed model as shown in Fig. 9. This hydro model includes the dead band as well as GRC. The parameter values as well as the participation factor (PF) for each of the units and the area in which they are located are given in Table 4.

This test system has been derived from the IEEE 30 bus test system [15]. The IEEE 30 bus test system, consisting of 6 generating units is considered to represent a two area system. All the generators are considered to be hydro units. The system is divided into two areas such that each area has 3 generating units. The two areas are connected by 7 tie lines and buses 1–16 except bus# 10 belong to area-1 and buses 10 and 17–30 belong to area-2. In the quiescent operating condition (prior to the load disturbance) the total generation of area-1 and area-2 are 123.94 and 67.7 MW, respectively. In this operating condition of the system, area1 exports 9.065 MW of power to area-2. Since each area consists of more than one unit, the participation factor of each unit is chosen here. This is normally available as the units participating in AGC is decided apriori.

3.2.2. Primary response The primary response of this test system has been obtained using the proposed model, for a 0.02 pu step load disturbance applied in area-1. The system base is 100 MVA and the tie line power flow as well as the load disturbance are given in pu, while the frequency variations are given in Hz. The variation in frequency and tie line flows for this system, are shown in Fig. 10. From Fig. 10 it can be seen

J

0.03

0.02

0.01 0

0.02

0.04

0.06

0.08

0.1

0.12

Ki

change in set point (pu)

Fig. 5. Variation of J with Ki: test system-1.

0.015 0.01 Ki = 0.02 Ki = 0.04

0.005 0

0

50

100

150

200

time (sec)

Fig. 6. Response of the integral controller: test system-1.

ACE (pu)

0.01 0 –0.01 –0.02 –0.03 –0.04 –0.05 0

50

0.04 1357

100

150

200

250

time (sec) Fig. 7. Variation in ACE with integral controller (controller gainZ0.02): test system-1.

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Fig. 8. Schematic diagram of the proposed AGC model: test system-2.

Fig. 9. Hydro unit model.

that the system frequency falls considerably immediately after the disturbance, rises as the generators pick up the load and finally settles down at 59.9920 Hz. As the load disturbance is in area-1, the tie line flow deviation of area-1 is negative. Further, from this plot, it can be seen that the tie line flow deviations of the two areas oscillate around 0.01 and then settle down at this value (in the absence of supplementary control). However, from the tie line flow variation obtained (using the proposed model) shown in Fig. 4, it is seen that the tie line flow immediately settles down to its final value without any oscillations. This is because the test system-1 both the areas are chosen to be identical, while in test system-2, each unit is different and the corresponding dynamics of the two areas are different.

3.2.3. Response with controller The AGC response of test system-2 is obtained using the proposed model with an integral controller. The design procedure followed here is identical to that used earlier for test system-1. The performance index J has been obtained for various values of gain and KiZ0.01 is seen to minimize J. The response of the controller, for this value of gain is shown in Fig. 11. From this it can be seen that the governor set point increases almost monotonically and finally settles down at a value equal to the load disturbance in area-1; no futile control actions are seen. Hence, a value of KiZ0.01 has been chosen as the integral controller gain for this system. The response of test system-2 with the integral controller (KiZ0.01) has been obtained. Fig. 12 shows the variation in ACE for a 0.02 pu step load disturbance in area-1. From this

Table 4 Hydro generator unit data Gen.

Gen. bus no.

Area no.

tp

Ks

tG

tR

s

d

tw

H

PF

A B C D E F

1 2 13 22 23 27

1 1 1 2 2 2

0.05 0.02 0.04 0.02 0.03 0.04

5.0 5.0 4.85 5.1 4.9 5.2

0.20 0.15 0.20 0.19 0.24 0.18

5.0 5.5 5.0 5.0 5.0 4.5

0.04 0.04 0.04 0.04 0.04 0.04

0.4 0.4 0.4 0.4 0.4 0.4

1.0 1.1 1.0 1.0 1.0 0.9

2.5 2.5 2.5 4.5 2.5 2.0

1/4 1/3 5/12 1/6 1/3 1/2

∆fsys (Hz)

K.C. Divya, P.S. Nagendra Rao / Electrical Power and Energy Systems 27 (2005) 335–342

341

0.04 0 –0.05 –0.1 0

10

20

30

40

50

60

70

80

90

100

∆ Ptie1 (pu)

Tie line flow variation : Area-1 0

time (sec)

–0.005 –0.01 –0.015 0

10

20

30

40

50

60

70

80

90

100

80

90

100

time (sec)

∆ Ptie2 (pu)

Tie line flow variation : Area-2 0.015 0.01 0.005 0

0

10

20

30

40

50

60

70

time (sec)

change in set point (pu)

Fig. 10. Primary response: test system-2.

0.025 0.02 0.015 0.01 0.005 0

0

50

100

150

200

250

300

time (sec) Fig. 11. Response of the integral controller (controller gainZ0.01): test system-2.

ACE (pu)

0 –0.02 –0.04 –0.06 –0.08 0

50

100

150

200

250

300

time (sec) Fig. 12. Variation in ACE with integral controller (controller gainZ0.01): test system-2.

it can be seen that the magnitude of the ACE of area-1 (area in which load increases) reaches a value which is about four times the magnitude of load disturbance immediately after the load disturbance. While this rise in ACE appears to be large, it is to be noted that in the absence of the supplementary control the overshoot seen in ACE signal is 0.16 pu. Consequently, the integral control action has not only reduced the steady-state error to zero, but also reduced the overshoot in ACE signal. In this case also, similar to test system-1, the ACE signal remains in a band around zero (5% of the disturbance magnitude) after about 100 s.

4. Conclusions In this paper a simulation model has been proposed for AGC studies of a hydro–hydro system. It has been shown that this model, unlike the conventional model, provides a stable representation for an interconnected multi-area hydro system. An additional feature of this model is that it filters out the fast varying components—a desirable feature according to the IEEE task force on AGC [11]. The AGC response of two different test systems obtained using the proposed model have been studied. In this study,

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an integral control strategy has been used and a suitable controller gain has been obtained.

References [1] Elgerd OI. Electric energy systems theory. New York: Mc-Graw Hill; 1983. [2] Concordia C, Kirchmayer LK. Tie-line power frequency control of electrical power systems. Part I. Trans AIEE 1953;562–72. [3] Elgerd OI, Fosha CE. Optimum megawatt-frequency control of multiarea electric energy system. IEEE Trans Power Apparatus Syst 1970;PAS-89(4):556–62. [4] Tripathy SC, Hope GS, Malik OP. Optimization of load frequency control parameters for power systems with reheat steam turbines and governor dead band non-linearity. IEE Proc—Part C 1982;129:10–16. [5] Kothari ML, Satsangi PS, Nanda J. Sample data automatic generation control of interconnected reheat thermal systems considering generation rate constraint. IEEE Trans Power Apparatus Syst 1981; PAS-100(4):2334–42. [6] Kothari ML, Nanda J, Kothari DP, Das D. Discrete mode agc of a two area reheat thermal system with new area control error. IEEE Trans Power Syst 1989;4(2):730–8.

[7] Nanda J, Kothari ML, Satsangi PS. Automatic generation control of interconnected hydro-thermal systems in continuous and discrete mode considering generation rate constraint. IEE Proc—Part D 1983; 130(1):17–27. [8] Lim KY, Wang Y, Zhou R. Robust decentralized load frequency control of multiarea power systems. IEE Proc—Part C 1996;143: 377–86. [9] Malik OP, Kumar A, Hope GS. A load frequency control algorithm based on generalized approach. IEEE Trans Power Syst 1988;3: 375–82. [10] Chang CS, Fu W. Area load frequency control using fuzzy gain scheduling of PI controllers. Electr Power Syst Res 1997;42: 145–52. [11] Jaleeli N, Vanslyck LS, Ewart DN, Fink LH, Hoffmann AG. Understanding automatic generation control. IEEE Trans Power Syst 1992;7(3):1106–21. [12] Athay TM. Generation scheduling and control. Proc IEEE 1987;75: 1592–606. [13] Taylor CW, Cresap RL. Real-time power system simulation for automatic generation control. IEEE Trans Power Syst 1976;PAS95(1):375–84. [14] NERC. Policy 1—generation control and performance. Oper Manual 1996;Dec.:1–14. [15] http://www.pserc.cornell.edu