Figure 1.
Topological structure. (a) Configuration of the hybrid type DC superconducting fault current limiter (H-SFCL); (b) high-speed controlled switch S1; (c) the breaking characteristics of S1.
Figure 1.
Topological structure. (a) Configuration of the hybrid type DC superconducting fault current limiter (H-SFCL); (b) high-speed controlled switch S1; (c) the breaking characteristics of S1.
Figure 2.
Principles of the H-SFCL. (a) Normal; (b) current limiting stage I; (c) current limiting stage II.
Figure 2.
Principles of the H-SFCL. (a) Normal; (b) current limiting stage I; (c) current limiting stage II.
Figure 3.
Schematic diagram of DC short-circuit fault. (a) DC short-circuit fault of VSC-based DC system. (b) Short-circuit current path of pole-to-pole DC fault in a pseudo bipolar VSC-based system.
Figure 3.
Schematic diagram of DC short-circuit fault. (a) DC short-circuit fault of VSC-based DC system. (b) Short-circuit current path of pole-to-pole DC fault in a pseudo bipolar VSC-based system.
Figure 4.
Unipolar line equivalent circuit.
Figure 4.
Unipolar line equivalent circuit.
Figure 5.
Two typical high voltage DC circuit breakers (DCCBs): (a) hybrid DCCB (H-DCCB); (b) coupling mechanical DCCB (CM-DCCB).
Figure 5.
Two typical high voltage DC circuit breakers (DCCBs): (a) hybrid DCCB (H-DCCB); (b) coupling mechanical DCCB (CM-DCCB).
Figure 6.
Action sequence of H-SFCL and H-DCCB.
Figure 6.
Action sequence of H-SFCL and H-DCCB.
Figure 7.
Action Sequence of H-SFCL and CM-DCCB.
Figure 7.
Action Sequence of H-SFCL and CM-DCCB.
Figure 8.
The diagram of three-terminal detailed VSC-based DC system simulation model.
Figure 8.
The diagram of three-terminal detailed VSC-based DC system simulation model.
Figure 9.
Comparison of the effects of different R1 values. (a) DC-side voltage; (b) DC line current; (c) the current of freewheel diode; (d) the current of superconducting coil; (e) the overvoltage of superconducting coil; (f) the magnetic energy of superconducting coil; (g) current limiting impedance; (h) the overvoltage of S1; (i) the current of S1.
Figure 9.
Comparison of the effects of different R1 values. (a) DC-side voltage; (b) DC line current; (c) the current of freewheel diode; (d) the current of superconducting coil; (e) the overvoltage of superconducting coil; (f) the magnetic energy of superconducting coil; (g) current limiting impedance; (h) the overvoltage of S1; (i) the current of S1.
Figure 10.
Comparison of the effects of different LSC: (a) DC-side voltage; (b) DC line current; (c) the current of freewheel diode; (d) the current of superconducting coil; (e) the overvoltage of superconducting coil; (f) the magnetic energy of superconducting coil; (g) current limiting impedance; (h) the overvoltage of S1; (i) the current of S1.
Figure 10.
Comparison of the effects of different LSC: (a) DC-side voltage; (b) DC line current; (c) the current of freewheel diode; (d) the current of superconducting coil; (e) the overvoltage of superconducting coil; (f) the magnetic energy of superconducting coil; (g) current limiting impedance; (h) the overvoltage of S1; (i) the current of S1.
Figure 11.
Comparison of the effects of different R2: (a) DC-side voltage; (b) DC line current; (c) the current of freewheel diode; (d) the current of superconducting coil; (e) the overvoltage of superconducting coil; (f) the magnetic energy of superconducting coil; (g) current limiting impedance; (h) the overvoltage of S1; (i) the current of S1.
Figure 11.
Comparison of the effects of different R2: (a) DC-side voltage; (b) DC line current; (c) the current of freewheel diode; (d) the current of superconducting coil; (e) the overvoltage of superconducting coil; (f) the magnetic energy of superconducting coil; (g) current limiting impedance; (h) the overvoltage of S1; (i) the current of S1.
Figure 12.
The basic requirements of parameter matching and optimization in H-SFCL.
Figure 12.
The basic requirements of parameter matching and optimization in H-SFCL.
Figure 13.
The model in MTALAB/Simulink. (a) The equivalent short-circuit model of a VSC single-terminal system. (b) The detailed model of SFCL1.
Figure 13.
The model in MTALAB/Simulink. (a) The equivalent short-circuit model of a VSC single-terminal system. (b) The detailed model of SFCL1.
Figure 14.
Capacitor discharging circuit: (a) t1 ≤ t < t2, S1 is in on state; (b) t2 ≤ t, S1 is in off state.
Figure 14.
Capacitor discharging circuit: (a) t1 ≤ t < t2, S1 is in on state; (b) t2 ≤ t, S1 is in off state.
Figure 15.
The simulation comparison: (a) the DC-side voltage, UDC; (b) the DC-line current, IDC; (c) the current of R1, i1; (d) the current of LSC, IL.
Figure 15.
The simulation comparison: (a) the DC-side voltage, UDC; (b) the DC-line current, IDC; (c) the current of R1, i1; (d) the current of LSC, IL.
Figure 16.
Basic implementation frameworks of parameter matching and optimization methods. (a) Basic frameworks based on hybrid model; (b) basic frameworks based on single model.
Figure 16.
Basic implementation frameworks of parameter matching and optimization methods. (a) Basic frameworks based on hybrid model; (b) basic frameworks based on single model.
Figure 17.
The optimization Workflow 1 based on genetic algorithm (GA).
Figure 17.
The optimization Workflow 1 based on genetic algorithm (GA).
Figure 18.
The optimization Workflow 2 based on GA.
Figure 18.
The optimization Workflow 2 based on GA.
Figure 19.
The optimization Workflow 1 based on particle swarm optimization (PSO).
Figure 19.
The optimization Workflow 1 based on particle swarm optimization (PSO).
Figure 20.
The optimization Workflow 2 based on PSO.
Figure 20.
The optimization Workflow 2 based on PSO.
Figure 21.
The variation trend of current limiting rate with R1.
Figure 21.
The variation trend of current limiting rate with R1.
Figure 22.
All calculation results in search space: (a) maximum transient magnetic energy; (b) ratio of designed critical current to rated current of superconducting coil; (c) maximum overvoltage of S1.
Figure 22.
All calculation results in search space: (a) maximum transient magnetic energy; (b) ratio of designed critical current to rated current of superconducting coil; (c) maximum overvoltage of S1.
Figure 23.
All feasible solutions of grid search in search space.
Figure 23.
All feasible solutions of grid search in search space.
Figure 24.
Convergence comparison of different methods: (a) Hybrid model + GA/PSO + Workflow 1; (b) Hybrid model + GA/PSO + Workflow 2; (c) Single model + GA/PSO + Workflow 1; (d) Single model + GA/PSO + Workflow 2.
Figure 24.
Convergence comparison of different methods: (a) Hybrid model + GA/PSO + Workflow 1; (b) Hybrid model + GA/PSO + Workflow 2; (c) Single model + GA/PSO + Workflow 1; (d) Single model + GA/PSO + Workflow 2.
Figure 25.
Optimization efficiency between different methods. (a) The number of possible solutions; (b) average running time of parameter matching and optimization methods.
Figure 25.
Optimization efficiency between different methods. (a) The number of possible solutions; (b) average running time of parameter matching and optimization methods.
Figure 26.
Ten rounds of optimization results for each method. (a) The optimization results of Emax; (b) the optimization results of R1; (c) the optimization results of LSC; (d) the optimization results of R2.
Figure 26.
Ten rounds of optimization results for each method. (a) The optimization results of Emax; (b) the optimization results of R1; (c) the optimization results of LSC; (d) the optimization results of R2.
Figure 27.
Simulation verification of optimization results. (a) DC line current; (b) the current of superconducting coil; (c) current limiting impedance; (d) the overvoltage of S1.
Figure 27.
Simulation verification of optimization results. (a) DC line current; (b) the current of superconducting coil; (c) current limiting impedance; (d) the overvoltage of S1.
Figure 28.
Comparison simulation results for VSC-based DC system. (a) DC side voltage; (b) DC line current; (c) the current of freewheel diode.
Figure 28.
Comparison simulation results for VSC-based DC system. (a) DC side voltage; (b) DC line current; (c) the current of freewheel diode.
Figure 29.
Comparison simulation results for DCCB. (a) The voltage of CM-DCCB; (b) the breaking current of CM-DCCB; (c) the absorbed energy of CM-DCCB; (d) the voltage of H-DCCB; (e) the breaking current of H-DCCB; (f) the absorbed energy of H-DCCB.
Figure 29.
Comparison simulation results for DCCB. (a) The voltage of CM-DCCB; (b) the breaking current of CM-DCCB; (c) the absorbed energy of CM-DCCB; (d) the voltage of H-DCCB; (e) the breaking current of H-DCCB; (f) the absorbed energy of H-DCCB.
Figure 30.
Comparison simulation results for H-SFCL. (a) The overcurrent of superconducting coil; (b) the overvoltage of superconducting coil; (c) the magnetic energy of superconducting coil; (d) equivalent current limiting impedance; (e) the overvoltage of S1; (f) the breaking current of S1.
Figure 30.
Comparison simulation results for H-SFCL. (a) The overcurrent of superconducting coil; (b) the overvoltage of superconducting coil; (c) the magnetic energy of superconducting coil; (d) equivalent current limiting impedance; (e) the overvoltage of S1; (f) the breaking current of S1.
Table 1.
Studies on the parameters of fault current limiters in HVDC.
Table 1.
Studies on the parameters of fault current limiters in HVDC.
HVDC System | DC FCL/SFCL | Study on Parameters of SFCL/FCL | Method | Year |
---|
Influence | Matching | Optimization |
---|
VSC | Resistive Type [20] | Yes | No | No | Enumeration, Comparison | 2015 |
VSC | Resistive, Inductive Type [18] | Yes | No | No | Enumeration, Comparison | 2016 |
VSC | Hybrid Type [33] | Yes | Yes | No | Enumeration, Comparison | 2017 |
MMC | Hybrid Type [13] | Yes | Yes | No | Analytical Formula, Graphical method | 2017 |
Hybrid | Resistive Type [25] | Yes | No | No | Enumeration, Comparison | 2018 |
MMC | Inductive type [34] | Yes | Yes | No | Analytical Formula, Comparison | 2019 |
MMC | Resistive, Inductive, Hybrid Type [35] | Yes | Yes | No | Enumeration, Comparison | 2019 |
Table 2.
Main system parameters.
Table 2.
Main system parameters.
Parameters | Value | Parameters | Value |
---|
The type of converter station | Two-level | DC-link capacity, C (mF) | 0.5 |
Rated capacity (MVA) | 100/50/150 | Resistance, R (Ω) | 0.08 |
AC voltage (kV) | 110 | Smoothing inductance, L (mH) | 20 |
Frequency, f (Hz) | 50 | Resistance per unit length of cable, Ω (km) | 0.0139 |
DC voltage, UDC (kV) | ±100 | Inductance per unit length of cable, H (km) | 0.159 × 10−3 |
Rated DC current, IDC (A) | 500/200/700 | Capacitance per unit length of cable, F (km) | 12.74 × 10−9 |
Current limit of IGBT and diode (kA) | 2 | Prospective maximum fault current (kA) | 16.4 |
Table 3.
The influence of main parameters of H-SFCL.
Table 3.
The influence of main parameters of H-SFCL.
| Affected Indicators | Main Influence Factors |
---|
R1↑ | LSC↑ | R2↑ |
---|
VSC-based DC system | UDC | + | / | / |
IDC | − | / | / |
ID1 | − | / | / |
H-SFCL | IL | + | − | − |
UL | + | + | − |
E | + | + | − |
ZSFCL | + | / | + |
US1 | + | − | + |
IS1 | + | − | / |
Table 4.
Comparison of short-circuit calculation models.
Table 4.
Comparison of short-circuit calculation models.
Model | Implementation Method | Precision | Effective Scope of Precision | Calculation Speed |
---|
Hybrid model | Simulink model + State Matrix Codes | High | The whole process | General |
Single model | State Matrix Codes | Medium | Within 10 ms after fault | Fast |
Table 5.
The main settings of GA Workflows 1 and 2.
Table 5.
The main settings of GA Workflows 1 and 2.
| Workflow 1 | Workflow 2 |
---|
Time Step Ts | 5 × 10−5 s | 5 × 10−5 s |
Optimization variables | R1, LSC, R2 | LSC, R2 |
Number of variables | 3 | 2 |
Type of variables | Integer | Integer |
Population size | 40 | 40 |
Mutation rate | 0.9 | 0.9 |
Crossover ratio | 0.08 | 0.08 |
Generations | 300 | 300 |
Stall generations | 50 | 50 |
Function tolerance | 1 × 10−6 | 1 × 10−6 |
Optimization variables range | R1 (Ω) | 5–50 | 9 |
LSC (mH) | 10–200 | (10–200 |
R2 (Ω) | 10–100 | (72–100 |
Constraint conditions | K | ≥50% | / |
α | ≤3 | ≤3 |
Rrequired | ≥8 Ω | / |
Urated | ≤80 kV | ≤80 kV |
Table 6.
The main settings of PSO workflow 1,2.
Table 6.
The main settings of PSO workflow 1,2.
| Workflow 1 | Workflow 2 |
---|
Time Step Ts | 5 × 10−5 s | 5 × 10−5 s |
Optimization variables | R1, LSC, R2 | LSC, R2 |
Type of variables | Integer | Integer |
Dimension, N | 3 | 2 |
Number of particles | 10 | 10 |
Maximum velocity of particles | 20 | 20 |
learning factors, c1, c2 | 1, 2 | 1, 2 |
Initial inertia weight | 0.9 | 0.9 |
Final inertia weight | 0.4 | 0.4 |
Maximum iteration number | 300 | 300 |
Minimum global error gradient | 1 × 10−6 | 1 × 10−6 |
Iterations before error gradient criterion terminates run | 50 | 50 |
The range of particles | R1 (Ω) | 5–50 | 9 |
LSC (mH) | 10–200 | 10–200 |
R2 (Ω) | 10–100 | 72–100 |
Constraint conditions | K | ≥50% | / |
α | ≤3 | ≤3 |
Rrequired | ≥8 Ω | / |
Urated | ≤80 kV | ≤80 kV |
Table 7.
The optimization results of different methods.
Table 7.
The optimization results of different methods.
Method | Optimization Workflow | Optimal Parameters Combination | Number of Possible Solutions | Number of Iterations | Average Time (s) |
---|
R1 (Ω) | LSC (mH) | R2 (Ω) | Emax (kJ) | US1max (kV) |
---|
Grid search | / | 9 | 111 | 72 | 61.65590843 | 75.888 | 5539 | 5539 | 23,239 |
Hybird + GA | Workflow 1 | 9 | 111 | 72–75 | 61.65590843 | 75.8–79.1 | 799,526 | 71 | 9310 |
Workflow 2 | 9 | 111 | 72 | 61.65590843 | 75.888 | 5539 | 54 | 7934 |
Hybird + PSO | Workflow 1 | 9 | 111 | 72–75 | 61.65590843 | 75.8–79.1 | 795,526 | 114 | 7577 |
Workflow 2 | 9 | 111 | 72 | 61.65590843 | 75.888 | 5539 | 56 | 3748 |
Single + GA | Workflow 1 | 9 | 113 | 72–76 | 62.05086515 | 75.5–79.7 | 795,526 | 70 | 152 |
Workflow 2 | 9 | 113 | 72 | 62.05086515 | 75.454 | 5539 | 55 | 105 |
Single + PSO | Workflow 1 | 9 | 113 | 72–76 | 62.05086515 | 75.5–79.7 | 795,526 | 109 | 121 |
Workflow 2 | 9 | 113 | 72 | 62.05086515 | 75.454 | 5539 | 66 | 62 |
Table 8.
The characteristics’ evaluation of parameter matching and optimization methods.
Table 8.
The characteristics’ evaluation of parameter matching and optimization methods.
Method | Accuracy | Average Time Consuming | Search Range | Convergence Rate | Stability of Results |
---|
Grid search | ★★★★★ | ★☆☆☆☆ | ★★★☆☆ | / | ★★★★★ |
Hybird + GA | Workflow 1 | ★★★★☆ | ★★☆☆☆ | ★★★★★ | ★★★☆☆ | ★★☆☆☆ |
Workflow 2 | ★★★★★ | ★★★☆☆ | ★★★☆☆ | ★★★★☆ | ★★★★★ |
Hybird + PSO | Workflow 1 | ★★★★☆ | ★★☆☆☆ | ★★★★★ | ★★★★☆ | ★★☆☆☆ |
Workflow 2 | ★★★★★ | ★★★☆☆ | ★★★☆☆ | ★★★★☆ | ★★★★★ |
Single + GA | Workflow 1 | ★★★☆☆ | ★★★★☆ | ★★★★★ | ★★★☆☆ | ★★☆☆☆ |
Workflow 2 | ★★★★☆ | ★★★★★ | ★★★☆☆ | ★★★★☆ | ★★★★☆ |
Single + PSO | Workflow 1 | ★★★☆☆ | ★★★★☆ | ★★★★★ | ★★★★☆ | ★★☆☆☆ |
Workflow 2 | ★★★★☆ | ★★★★★ | ★★★☆☆ | ★★★★★ | ★★★★★ |
Table 9.
The effects of comparison between unoptimized and optimized H-SFCL.
Table 9.
The effects of comparison between unoptimized and optimized H-SFCL.
| Parameters | Unoptimized H-SFCL | Optimized H-SFCL | Improvement | Influence Degree |
---|
Optimization variable | R1 | 9 Ω | 9 Ω | 0% | / |
LSC | 140 mH | 111 mH | 20.71%↓ |
R2 | 20 Ω | 72 Ω | 250%↑ |
VSC-based DC system | Minimum UDC | 15.1 kV | 28.8 kV | 90.73%↑ | ★★☆☆☆ |
Maximum IDC | 8.37 kA | 8.04 kA | 3.9%↓ |
Maximum ID1 | 4.59 kA | 4.37 kA | 4.79%↓ |
DCCB | M-DCCB | Maximum UDCCB | 132.2 kV | 130.0 kV | 1.66%↓ | ★☆☆☆☆ |
Maximum IDCCB | 8.22 kA | 8.18 kA | 0.49%↓ |
Absorbed Energy | 0.83 kJ | 0.77 kJ | 7.22%↓ |
H-DCCB | Maximum UDCCB | 143 kV | 143 kV | 0% |
Maximum IDCCB | 8.23 kA | 8.04 kA | 2.31%↓ |
Absorbed Energy | 0.77 kJ | 0.70 kJ | 9.09%↓ |
H-SFCL | Superconducting coil | Maximum IL | 1.88 kA | 1.06 kA | 43.62%↓ | ★★★★★ |
Maximum UL | 54.1 kV | 51.9 kV | 4.07%↓ |
Duration of Overvoltage | 7 ms | 4 ms | 42.86%↓ |
Maximum E | 248 kJ | 62 kJ | 75%↓ |
ZSFCL | Transient ZSFCL | 7.8 Ω | 7.8 Ω | 0% |
Steady ZSFCL | 5.9 Ω | 8.06 Ω | 36.61%↑ |
S1 | Maximum US1 | 37.6 kV | 74.1 kV | 97.07%↑ |
Maximum IS1 | 0.98 kA | 1.04 kA | 6.12%↑ |