Short-Circuit Calculation in Distribution Networks with Distributed Induction Generators
Abstract
:1. Introduction
2. Sequence Component Current Model of Induction Generators (IGs)
2.1. Stator and Rotor Flux of IGs during Grid Faults
2.2. Sequence Component Current Model of Fixed-Speed IGs
2.3. Sequence Component Current Model of Variable-Speed IGs
3. Coupling Relationship between Short-Circuit Current of IGs and the Distribution Network
4. Short-Circuit Calculation of the Multi-IG Network
4.1. Initial Value Calculation for Short-Circuit CurrentSequence Components of IGs
4.2. Short-Circuit CurrentSequence Components of IGs during Grid Faults
4.3. Procedure of Short-Circuit Calculation
- Step 1: Form the original matrixes Z1 and Z2 of the pre-fault network without IGs, determine the pre-fault voltage and stator current of each IG according to the mechanical torque during normal operation, and solve Equation (16) to obtain .
- Step 2: Add and to Z1 and Z2 to form the matrixes Z1′ and Z2′, obtain by Equation (17) and , and then determine and according to the fault node and type.
- Step 3: Solve Equation (19) to obtain and , determine and , and solve Equation (20) to obtain and .
- Step 4: Solve Equation (8) for a fixed-speed IG, Equation (12) for a variable-speed IG with and si(1) to obtain , determine the RMS of the positive and negative sequence components and , set = , = , = and = , and then go to Step 5.
- Step 5: Solve Equation (24) by calculating of using Equation (23) to obtain the slip vector s(k).
- Step 6: Solve Equation (25) with Z1 and Z2 to obtain the voltage and of the normal network, calculate and , substitute them into Equation (27) to obtain and of the fault component network, and determine the voltages and of each IG.
- Step 7: Solve Equations (8) and (9) for a fixed-speed IG, Equations (12) and (13) for a variable-speed IG with , s(k) and to obtain and , substitute = and into (22) to obtain , and = .
- Step 8: If k ≤ N (N = 20), set k = k + 1 and go to Step 5; otherwise, stop the iteration and output the RMS of sequence components of the short-circuit current of each IG.
5. Simulation Studies
5.1. Three-Phase Short Circuit of Fixed-Speed IGs
5.2. Two-Phase Short Circuit of Fixed-Speed IGs
5.3. Two-Phase Short Circuit of Variable-Speed IGs
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A
Appendix B
- (1)
- The IG parameters:
- (a)
- Rated power = 3 MW, Rated AC voltage = 0.69 kV;
- (b)
- Rs = 0.004843 p.u., Xls = 0.1248 p.u.;
- (c)
- Rr = 0.004347 p.u., Xlr = 0.1791 p.u.;
- (d)
- Xm = 6.77 p.u., H = 5.04 s;
- (e)
- Capacitor rated voltage = 0.69 kV, Rated power = 0.75 Mvar for a fixed-speed IG;
- (f)
- Rated DC voltage = 1.5 kV, Crowbarresistance = 0.1043 p.u. for a variable-speed IG.
- (2)
- Transformer T1, T2, T3 and T4 have the same parameters:
- (a)
- Rated capacity = 3.5 MVA;
- (b)
- VI/VII (Yn/Δ) = 0.69/10.5 kV;
- (c)
- XT = 0.06 p.u., RT = 0.02 p.u..
- (3)
- The length of lines and impedance of per km are:
- (a)
- L1 = L2 = L3 = L4 = 0.5 km, L5 = 3.5 km;
- (b)
- ZL = j0.300 Ω/km.
- (4)
- The parameters of substation:
- (a)
- Rated Voltage = 10 kV, Es = 1.05 p.u.;
- (b)
- Short circuit level = 240 MVA, X/R = 10.
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Induction Generators | IG1 | IG2 | IG3 | IG4 | |
---|---|---|---|---|---|
Analytical I1sp (pu) | 1.642 | 2.079 | 2.605 | 1.317 | |
I1sp | Simulation I1sp (pu) | 1.745 | 2.187 | 2.716 | 1.369 |
Relative error (%) | −5.90 | −4.93 | −4.09 | −3.80 | |
Analytical I1ss (pu) | 1.426 | 1.363 | 1.297 | 1.308 | |
I1ss | Simulation I1ss (pu) | 1.434 | 1.414 | 1.321 | 1.361 |
Relative error (%) | −0.56 | −3.61 | −1.82 | −3.89 |
Induction Generators | IG1 | IG2 | IG3 | IG4 | |
---|---|---|---|---|---|
Analytical I1sp (pu) | 0.727 | 0.911 | 1.116 | 0.582 | |
I1sp | Simulation I1sp (pu) | 0.765 | 0.947 | 1.151 | 0.587 |
Relative error (%) | −4.97 | −3.80 | −3.04 | −0.85 | |
Analytical I1ss (pu) | 0.645 | 0.712 | 0.789 | 0.573 | |
I1ss | Simulation I1ss (pu) | 0.644 | 0.712 | 0.789 | 0.575 |
Relative error (%) | 0.16 | 0 | 0 | −0.35 | |
Analytical I2sp (pu) | 0.813 | 1.042 | 1.283 | 0.55 | |
I2sp | Simulation I2sp (pu) | 0.822 | 1.052 | 1.292 | 0.552 |
Relative error (%) | −1.09 | −0.95 | −0.70 | −0.36 | |
Analytical I2ss (pu) | 0.790 | 1.012 | 1.244 | 0.537 | |
I2ss | Simulation I2ss (pu) | 0.793 | 1.021 | 1.248 | 0.538 |
Relative error (%) | −0.38 | −0.88 | −0.32 | −0.19 |
Induction Generators | IG1 | IG2 | IG3 | IG4 | |
---|---|---|---|---|---|
Analytical I1sp (pu) | 0.856 | 1.093 | 1.196 | 0.715 | |
I1sp | Simulation I1sp (pu) | 0.937 | 1.104 | 1.308 | 0.765 |
Relative error (%) | −8.62 | −1.03 | −0.81 | −6.53 | |
Analytical I1ss (pu) | 0.418 | 0.444 | 0.489 | 0.395 | |
I1ss | Simulation I1ss (pu) | 0.412 | 0.439 | 0.485 | 0.396 |
Relative error (%) | 1.37 | 1.09 | 0.86 | −0.21 | |
Analytical I2sp (pu) | 0.436 | 0.596 | 0.746 | 0.278 | |
I2sp | Simulation I2sp (pu) | 0.456 | 0.634 | 0.806 | 0.307 |
Relative error (%) | −4.39 | −5.99 | −7.44 | −9.45 | |
Analytical I2ss (pu) | 0.159 | 0.185 | 0.219 | 0.102 | |
I2ss | Simulation I2ss (pu) | 0.158 | 0.183 | 0.208 | 0.103 |
Relative error (%) | 0.36 | 1.22 | 5.29 | −0.65 |
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Zhou, N.; Ye, F.; Wang, Q.; Lou, X.; Zhang, Y. Short-Circuit Calculation in Distribution Networks with Distributed Induction Generators. Energies 2016, 9, 277. https://doi.org/10.3390/en9040277
Zhou N, Ye F, Wang Q, Lou X, Zhang Y. Short-Circuit Calculation in Distribution Networks with Distributed Induction Generators. Energies. 2016; 9(4):277. https://doi.org/10.3390/en9040277
Chicago/Turabian StyleZhou, Niancheng, Fan Ye, Qianggang Wang, Xiaoxuan Lou, and Yuxiang Zhang. 2016. "Short-Circuit Calculation in Distribution Networks with Distributed Induction Generators" Energies 9, no. 4: 277. https://doi.org/10.3390/en9040277