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Effects of load modelling on the behaviour of power systems
Effects of load modelling on the behaviour of power systems G P T Roelofs
Electrical Research Department, NV Kema. Arnhem, The Netherlands
This paper describes the influence of the electrical load model on the behaviour of an electrical power system. Seven different load models have been selected and the impact of these models on four aspects of the behaviour of the network has been investigated. The investigation has been performed on the 220 and 110 kV FGO grid, which forms part of the Dutch high-voltage network. If, for a specific study, the nature of the load is unknown, it is recommended to use a load model in which the active and reactive parts are represented by a constant admittance.
II. N o t a t i o n P active power (p.u.) Q reactive power (p.u.) Po active power at nominal voltage and frequency (p.u.) Qo reactive power at nominal voltage and frequency (p.u.) V voltage (p.u.) Af frequency deviation (p.u.) ai, ni parameters for a load model
Keywords: modelling of energy systems - global, load modelling, dynamic stability
I. I n t r o d u c t i o n Performing stability studies on electric power systems requires adequate modelling of the components of such systems. During the past few years most of the work of Kema's Electrical Research Department has been dedicated to the modelling of power plants 1, while less attention has been paid to load modelling. From the literature and from individual studies it becomes evident that load modelling is important. Complete knowledge of the load model leads to more reliable calculation results. However, sometimes there is no or little information available on the load model. The aim of this study is to investigate the influence of different load models on the behaviour of the power system and to establish a load model which can be used in studies where no data on these models are available. This paper describes the investigation of the influence of the electrical load model on the behaviour of part of the Dutch high-voltage (FGO) grid. Calculations have been performed for seven load models, and the following three system disturbances have been investigated:
III. M o d e l o f t h e F G O n e t w o r k The FGO network consists of 91 buses, 184 branches and six generators with a nominal output power of 2100 MVA. For the generators a round rotor model is used with rotor mechanical dynamics and full representation of transient and subtransient rotor flux linkages. For two of the investigated load models the induction motor load is used, with a model representing rotor mechanical dynamics and transient rotor flux linkages. For the generators there is a detailed model of voltage- and turbine-regulating systems. Data concerning the power plants and the network are presented in Reference 2. The static active and reactive powers of the load on a bus are represented by the following relations:
P = Po(azV nt + a2 Vn2 + a3V"3)(1 + aTAf) Q = Qo(a4V"" + asV "s + a6V6)(1 + aaAf) In the investigation seven load models have been used. 1 Constant power P=Po 2
Constant current
P=Po V •
calculation of the duration of the critical faultclearing time for three-phase short-circuits on a number of buses in the network;
• calculation of the maximum safe power transfer from one part of the grid to another, maintaining the dynamic stability after a fault and successful clearance; • calculation of the voltage and frequency deviations after tripping a generator. Received:8 July 1987 accepted2 March 1988
Vol 11 No 4 October 1 989
Q=Qo Q=Oo V
3 Constant admittance P=Po V2 4
Q=Qo V2
50% constant current, 50% constant admittance P = Po(0.5 V + 0.5V 2)
5
Q = Qo(0.5v + 0.5v z)
25% motor load, 75% constant admittance. On some buses the load is replaced by an induction motor, while the load on the other buses is a constant impedance load.
0142-0615/89/040289-04/$03.00 © Butterworth Et.Co (Publishers) Ltd
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Short circuit on bus A a Short-circuit on bus B C Short-circuit on bus C 1 2 3 4 5 6
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123456
1 2 3
Load condition 1 Load condition 2 Load condition 3
Constant power Constant current Constant admittance 50% const, current, 50% const, admittance 25% motor load, 75% const, admittance As load model 5 with LV motor trip
Figure 1. Critical clearing time
123456
A
1 23456
Short-circuit on bus A
1 23
56
1 Load condition 1
C Short-circuit on bus C
2
D E
3 Load condition 3
Short-circuit on bus D
Load condition 2
Short-circuit on bus E 1 2 3 4 5 6
Constant power Constant current Constant admittance 50% const, current, 50% const, admittance 25% motor load, 75% const, admittance As load model 5 with LV motor trip
Figure 2. Maximum safe power transfer level 6 This load model is the same as load model 5 but induction motors are tripped when the bus voltage drops below 0.7 p.u. 7
Frequency-dependent load
P=PoV2(1 +2Af)
Q=QoV2(1+2Af)
IV. C a l c u l a t i o n s The investigation of the influence of load modelling on
290
the behaviour of the FGO power system has been performed under four different load conditions (1, 2, 3 and 4) covering a wide range of operating points of the FGO network, including island operation. Rough data on these load conditions are given in Table 1; for detailed data see Reference 2. In the transient calculations, short-circuits have been applied to five different buses, denoted A, B, C, D and E. In the FGO power system, generators have been connected to buses A, C, D and E.
Electrical Power EtEnergy Systems
Table 1. Data concerning the load conditions Swing bus (MW)
Q (Mvar)
Line losses R X (MW) (Mvar)
C (Mvar)
98 -337 -674 -337
327 -- 156 1 -- 156
20 16 16 16
- 312 -335 - 321 -335
Generation Load P condition (MW)
Q (Mvar)
Load P (MW)
Q (Mvar)
P
1 2 3 4
195 613 305 613
1300 1300 963 1300
639 639 430 639
1222 1653 1653 1653
0.15
010
i.i.......... :i 0.10
A,,.:50.05 ~ F "~ 0.00t_. g "~ 0.10
0.05
0.00 0.10
0.05
0.00
123457
123457
123457
123457
Figure 3. Voltage deviation after a generator trip (symbols as for Figure 4)
195 153 197 153
IV.2 Maximum safe power transfer level When planning the addition of new power plants to a power system, it is important to know the maximum amount of power which can be transferred safely from a generator bus to the grid in such a way that transient stability is maintained after a three-phase short-circuit and successful fault clearance. The influence of load modelling on this maximum safe power transfer level has been investigated. The calculations have been performed for the generators on buses A, C, D and E. Under load condition 1 there are no generators in operation on buses A and D and therefore no results are presented. The calculation procedure is as follows. The generator on a bus is replaced by a large 1200 MVA generator with matching parameters. For a fixed short-circuit time of 200 ms, the maximum output power is calculated on condition that the power system remains stable after fault clearance. The results of the calculations are presented in Figure 2. No results are given for the short-circuit on bus E under load conditions 1 and 3 because the maximum output power of the generator on this bus is so low that other generators have to supply power exceeding their maximum.
IV.3 Voltage and frequency deviations after a generator trip When a generator is tripped, the voltage and the frequency in a power system will temporarily drop. Under load conditions 1, 2 and 3 the F G O grid is connected to the swing bus and consequently the frequency will remain almost constant, so only the voltage deviation is calculated. Under load condition 4 the F G O grid is an island, and both voltage and frequency deviations are calculated. Under this load condition only half of the generator power is tripped, because otherwise the power shortage would be so extensive that no equilibrium could be reached. The calculations have been performed for the generators on buses A, C, D and E. Under load condition 1 there are no generators in operation on buses A and D and therefore no results are presented. The results of the voltage and frequency deviations are given in Figures 3 and 4.
V. Analysis IV.1 Critical clearing time The influence of the load models on the critical clearing time has been investigated. Short-circuits have been applied to buses A, B and C, after which one or more lines have been tripped. The results are presented in Figure 1.
Vol 11 No 4 October 1989
On the basis of the results described in Section 4, the following analysis can be made. Load model 1, 100% constant power, results in the shortest critical clearing time, whereas load model 6, 25% motor load with undervoltage trip, results in the longest critical clearing time. The critical clearing time for load
291
0.020
0.015
A
Generator trip on bus A
C Generator trip on bus C D Generator trip on bus D
0.010
E Generator trip on bus E
iiili E 0.005
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D. 0.0O5~
Load condition 1
2 Load condition 2
3 4
D
model 6 is about twice as long as it is for load model 1. The differences in critical clearing time for the other load models are relatively small. Load model 1 results in the lowest and load model 6 in the highest maximum safe power transfer level. For load model 6 the maximum safe power transfer level is about twice as high as for load model 1. Again the differences in the maximum safe power transfer level for the other load models are small. The smallest voltage deviation occurs with a load model with a large contribution of constant admittance, and the largest voltage deviation with load model 1, 100% constant power. The difference between the largest and smallest voltage deviations is about a factor of 3. Load model 8, frequency-dependent load, results in the smallest frequency deviation, whereas load model 1, 100% constant power, results in the largest frequency deviation. The difference is about 85%.
Load condition 3 Load condition 4
8 "o
~ 0.000 0.010
0.005
C 0.000 0.010 -
1 2 3 4
Constant power Constant current Constant admittance 50% const, current, 50% const. adm ittance 5 25% motor load, 75% const. admittance 7 As load model 5 with LV motor trip
VI. Conclusions The load model in which the active and reactive parts are represented by a constant power independent of voltage and frequency (load model 1) leads to the most pessimistic calculation results, i.e. the shortest critical clearing time, the lowest maximum safe power transfer level and the largest voltage and frequency deviation when tripping a generator. If, for a specific study, no data are available on the nature of the load, it is recommended to use a load model where the active and reactive parts are represented by a constant admittance (load model 3).
0.005
A
VII. R e f e r e n c e s 1
0.000
1 23457 2
Figure 4. Frequency deviation after a generator trip
292
Roelof$, G P T, van der Veer, J H C and W i c h e r n , P H M "Determination of the dynamic model of electric power plants' Kema Scientific & Technical Reports ISSN 0167-8590; 3-11 (November 1985) pp 139-149 Roelof$, G P T 'Onderzoek naar de modellering van electrische belasting" KEMA 51971 -EO 87-3014 (1987)
Electrical Power Et Energy Systems
Electrical Research Department, NV Kema. Arnhem, The Netherlands
This paper describes the influence of the electrical load model on the behaviour of an electrical power system. Seven different load models have been selected and the impact of these models on four aspects of the behaviour of the network has been investigated. The investigation has been performed on the 220 and 110 kV FGO grid, which forms part of the Dutch high-voltage network. If, for a specific study, the nature of the load is unknown, it is recommended to use a load model in which the active and reactive parts are represented by a constant admittance.
II. N o t a t i o n P active power (p.u.) Q reactive power (p.u.) Po active power at nominal voltage and frequency (p.u.) Qo reactive power at nominal voltage and frequency (p.u.) V voltage (p.u.) Af frequency deviation (p.u.) ai, ni parameters for a load model
Keywords: modelling of energy systems - global, load modelling, dynamic stability
I. I n t r o d u c t i o n Performing stability studies on electric power systems requires adequate modelling of the components of such systems. During the past few years most of the work of Kema's Electrical Research Department has been dedicated to the modelling of power plants 1, while less attention has been paid to load modelling. From the literature and from individual studies it becomes evident that load modelling is important. Complete knowledge of the load model leads to more reliable calculation results. However, sometimes there is no or little information available on the load model. The aim of this study is to investigate the influence of different load models on the behaviour of the power system and to establish a load model which can be used in studies where no data on these models are available. This paper describes the investigation of the influence of the electrical load model on the behaviour of part of the Dutch high-voltage (FGO) grid. Calculations have been performed for seven load models, and the following three system disturbances have been investigated:
III. M o d e l o f t h e F G O n e t w o r k The FGO network consists of 91 buses, 184 branches and six generators with a nominal output power of 2100 MVA. For the generators a round rotor model is used with rotor mechanical dynamics and full representation of transient and subtransient rotor flux linkages. For two of the investigated load models the induction motor load is used, with a model representing rotor mechanical dynamics and transient rotor flux linkages. For the generators there is a detailed model of voltage- and turbine-regulating systems. Data concerning the power plants and the network are presented in Reference 2. The static active and reactive powers of the load on a bus are represented by the following relations:
P = Po(azV nt + a2 Vn2 + a3V"3)(1 + aTAf) Q = Qo(a4V"" + asV "s + a6V6)(1 + aaAf) In the investigation seven load models have been used. 1 Constant power P=Po 2
Constant current
P=Po V •
calculation of the duration of the critical faultclearing time for three-phase short-circuits on a number of buses in the network;
• calculation of the maximum safe power transfer from one part of the grid to another, maintaining the dynamic stability after a fault and successful clearance; • calculation of the voltage and frequency deviations after tripping a generator. Received:8 July 1987 accepted2 March 1988
Vol 11 No 4 October 1 989
Q=Qo Q=Oo V
3 Constant admittance P=Po V2 4
Q=Qo V2
50% constant current, 50% constant admittance P = Po(0.5 V + 0.5V 2)
5
Q = Qo(0.5v + 0.5v z)
25% motor load, 75% constant admittance. On some buses the load is replaced by an induction motor, while the load on the other buses is a constant impedance load.
0142-0615/89/040289-04/$03.00 © Butterworth Et.Co (Publishers) Ltd
289
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1 23
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Short circuit on bus A a Short-circuit on bus B C Short-circuit on bus C 1 2 3 4 5 6
A
50o
6
123456
1 2 3
Load condition 1 Load condition 2 Load condition 3
Constant power Constant current Constant admittance 50% const, current, 50% const, admittance 25% motor load, 75% const, admittance As load model 5 with LV motor trip
Figure 1. Critical clearing time
123456
A
1 23456
Short-circuit on bus A
1 23
56
1 Load condition 1
C Short-circuit on bus C
2
D E
3 Load condition 3
Short-circuit on bus D
Load condition 2
Short-circuit on bus E 1 2 3 4 5 6
Constant power Constant current Constant admittance 50% const, current, 50% const, admittance 25% motor load, 75% const, admittance As load model 5 with LV motor trip
Figure 2. Maximum safe power transfer level 6 This load model is the same as load model 5 but induction motors are tripped when the bus voltage drops below 0.7 p.u. 7
Frequency-dependent load
P=PoV2(1 +2Af)
Q=QoV2(1+2Af)
IV. C a l c u l a t i o n s The investigation of the influence of load modelling on
290
the behaviour of the FGO power system has been performed under four different load conditions (1, 2, 3 and 4) covering a wide range of operating points of the FGO network, including island operation. Rough data on these load conditions are given in Table 1; for detailed data see Reference 2. In the transient calculations, short-circuits have been applied to five different buses, denoted A, B, C, D and E. In the FGO power system, generators have been connected to buses A, C, D and E.
Electrical Power EtEnergy Systems
Table 1. Data concerning the load conditions Swing bus (MW)
Q (Mvar)
Line losses R X (MW) (Mvar)
C (Mvar)
98 -337 -674 -337
327 -- 156 1 -- 156
20 16 16 16
- 312 -335 - 321 -335
Generation Load P condition (MW)
Q (Mvar)
Load P (MW)
Q (Mvar)
P
1 2 3 4
195 613 305 613
1300 1300 963 1300
639 639 430 639
1222 1653 1653 1653
0.15
010
i.i.......... :i 0.10
A,,.:50.05 ~ F "~ 0.00t_. g "~ 0.10
0.05
0.00 0.10
0.05
0.00
123457
123457
123457
123457
Figure 3. Voltage deviation after a generator trip (symbols as for Figure 4)
195 153 197 153
IV.2 Maximum safe power transfer level When planning the addition of new power plants to a power system, it is important to know the maximum amount of power which can be transferred safely from a generator bus to the grid in such a way that transient stability is maintained after a three-phase short-circuit and successful fault clearance. The influence of load modelling on this maximum safe power transfer level has been investigated. The calculations have been performed for the generators on buses A, C, D and E. Under load condition 1 there are no generators in operation on buses A and D and therefore no results are presented. The calculation procedure is as follows. The generator on a bus is replaced by a large 1200 MVA generator with matching parameters. For a fixed short-circuit time of 200 ms, the maximum output power is calculated on condition that the power system remains stable after fault clearance. The results of the calculations are presented in Figure 2. No results are given for the short-circuit on bus E under load conditions 1 and 3 because the maximum output power of the generator on this bus is so low that other generators have to supply power exceeding their maximum.
IV.3 Voltage and frequency deviations after a generator trip When a generator is tripped, the voltage and the frequency in a power system will temporarily drop. Under load conditions 1, 2 and 3 the F G O grid is connected to the swing bus and consequently the frequency will remain almost constant, so only the voltage deviation is calculated. Under load condition 4 the F G O grid is an island, and both voltage and frequency deviations are calculated. Under this load condition only half of the generator power is tripped, because otherwise the power shortage would be so extensive that no equilibrium could be reached. The calculations have been performed for the generators on buses A, C, D and E. Under load condition 1 there are no generators in operation on buses A and D and therefore no results are presented. The results of the voltage and frequency deviations are given in Figures 3 and 4.
V. Analysis IV.1 Critical clearing time The influence of the load models on the critical clearing time has been investigated. Short-circuits have been applied to buses A, B and C, after which one or more lines have been tripped. The results are presented in Figure 1.
Vol 11 No 4 October 1989
On the basis of the results described in Section 4, the following analysis can be made. Load model 1, 100% constant power, results in the shortest critical clearing time, whereas load model 6, 25% motor load with undervoltage trip, results in the longest critical clearing time. The critical clearing time for load
291
0.020
0.015
A
Generator trip on bus A
C Generator trip on bus C D Generator trip on bus D
0.010
E Generator trip on bus E
iiili E 0.005
il;ii Ei!i: 1
iiiii !:!:!
0.000
D. 0.0O5~
Load condition 1
2 Load condition 2
3 4
D
model 6 is about twice as long as it is for load model 1. The differences in critical clearing time for the other load models are relatively small. Load model 1 results in the lowest and load model 6 in the highest maximum safe power transfer level. For load model 6 the maximum safe power transfer level is about twice as high as for load model 1. Again the differences in the maximum safe power transfer level for the other load models are small. The smallest voltage deviation occurs with a load model with a large contribution of constant admittance, and the largest voltage deviation with load model 1, 100% constant power. The difference between the largest and smallest voltage deviations is about a factor of 3. Load model 8, frequency-dependent load, results in the smallest frequency deviation, whereas load model 1, 100% constant power, results in the largest frequency deviation. The difference is about 85%.
Load condition 3 Load condition 4
8 "o
~ 0.000 0.010
0.005
C 0.000 0.010 -
1 2 3 4
Constant power Constant current Constant admittance 50% const, current, 50% const. adm ittance 5 25% motor load, 75% const. admittance 7 As load model 5 with LV motor trip
VI. Conclusions The load model in which the active and reactive parts are represented by a constant power independent of voltage and frequency (load model 1) leads to the most pessimistic calculation results, i.e. the shortest critical clearing time, the lowest maximum safe power transfer level and the largest voltage and frequency deviation when tripping a generator. If, for a specific study, no data are available on the nature of the load, it is recommended to use a load model where the active and reactive parts are represented by a constant admittance (load model 3).
0.005
A
VII. R e f e r e n c e s 1
0.000
1 23457 2
Figure 4. Frequency deviation after a generator trip
292
Roelof$, G P T, van der Veer, J H C and W i c h e r n , P H M "Determination of the dynamic model of electric power plants' Kema Scientific & Technical Reports ISSN 0167-8590; 3-11 (November 1985) pp 139-149 Roelof$, G P T 'Onderzoek naar de modellering van electrische belasting" KEMA 51971 -EO 87-3014 (1987)
Electrical Power Et Energy Systems