Metaheuristic Based Solution for the Non‐Linear Controller of the Multiterminal High‐Voltage Direct Current Networks
Abstract
:1. Introduction
2. Control of Voltage-Source Converters (VSC) Based Multiterminal High Voltage Direct-Current (MT-HVDC) Grids
2.1. Inner Current Control Loop
2.2. Outer Current Control Loop
2.3. Voltage-Droop Control
3. Optimization Technique Based Artificial Bee Colony Algorithm
3.1. Initial Population
- represent parametric numbers,
- indicate the lower limit of the initial population’s parameters,
- indicate the upper limit, respectively.
3.2. Employee Bees
- is a random number between [−1, 1],
- is the new source position,
- is the previous source position.
3.3. On-Looker Bees
- where shows the improved fitness of the solution and can be written as:
- shows the fitness value of the solution.
3.4. Scout Bees
3.5. Tuning of Inner-Current Control Loop (ICC-L)
- whereas represent corresponding d-axis current,
- represent referenced-axis current.
3.6. Tuning of Outer-Current Control Loop (OCC-L)
4. Execution of the Multiobjective Functions
- shows the nonzero weights. Here, the user-defined set of values describe the preferred criteria of weights.
- , represent the allocated weights and associated with each other as , whereas variate between 0 and 1.
4.1. Comparative Analysis of the Controller’s Efficiency
4.2. Tuning of ICC-L Based on the Classical Optimization Method
- The ICC-L’s closed-loop bandwidth must be 1/5 times lower than the angular switching- frequency to attain adequate efficiency.
- The inner current controllers must be ten times faster than outer controllers to achieve a closed-loop system free from the oscillating response.
4.3. Tuning of ICC-L Based on the Classical Optimization Method
4.4. Multiobjective Optimization of ICC-L and OCC-L Based on ABC Algorithm
5. Simulation Results
- Unbalance wind power,
- Unbalanced power demand at the AC grids side,
- Eventual VSC disconnection.
5.1. Unbalance Wind Power
5.2. Unbalanced Load Demand at AC Grids
5.3. Eventual VSC Disconnection
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
ABC Algorithm Pseudo-Code |
Initialization (1) C (cycle number) = 1 (2) Initialize a random population (solutions) (Wi,j), , (3) Evaluate the population (fitness function based on Equation (12) (4) Repeat (5) Employee Bee Phase For each employee bee Generate a new population (food source) Calculate the fitness values and If new solution is better than the previous solution Then memorize the new solution and apply the greedy selection End for. (6) Evaluate the probability of the solution (7) On-looker Bees Phase For each on-looker bee Select a solution depends on Generate the new solution Evaluate the fitness values and If new solution is better than the previous solution Then memorize the new solution and apply greed selection End for (8) Scout Bees Phase If there is an employee bee becomes a scout Then replace it with a new random population (9) Memorizing the best solution (10) C = C +1 (11) Until C = Maximum cycle number (i.e., 120 in our case) and satisfy minimization of objective function = |
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Specifications | Number of Food-Source | Bees (Employeed + On-Looker Bees) | Iterations |
---|---|---|---|
Values | 20 | 20 | 60 |
Controllers | CL P-I | ABC P-I | ||
---|---|---|---|---|
ICC-L | 0.48 | 16.7500 | 0.87 | 21.6535 |
OCC-L | 0.12 | 35.0050 | 0.87 | 76.2550 |
Controllers | ITAE | |
---|---|---|
CL P-I | ABC P-I | |
ICC-L | 4.82208 × 10−4 | 9.5642 × 10−5 |
Active power | 1.6402 × 10−3 | 4.8640 × 10−4 |
MO-F | 5.1532 × 10−5 |
Component | Nominal-Voltage (kV) | Impedance | Description |
---|---|---|---|
Wind-farms | 33 | 0.002 + j0.012 (p.u) | 1000 MVA |
AC grids | 220 | 0.001 + j0.0125 (p.u) | 1000 MVA |
Phase-reactor | 180 | 0.02 + 0.15 (p.u) | |
DC-capacitor | ±250 | 1200 µF, two capacitors in series | |
DC link | ±250 | R = 0.20 × 10−2 10 Ω/km L = 0.55 × 10−4 H/km C = 2.2 × 10−7 F/km | 100 km b/w all terminals |
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Khan, M.A.; Li, X.; Yousaf, M.Z.; Mustafa, A.; Wei, M. Metaheuristic Based Solution for the Non‐Linear Controller of the Multiterminal High‐Voltage Direct Current Networks. Energies 2021, 14, 1578. https://doi.org/10.3390/en14061578
Khan MA, Li X, Yousaf MZ, Mustafa A, Wei M. Metaheuristic Based Solution for the Non‐Linear Controller of the Multiterminal High‐Voltage Direct Current Networks. Energies. 2021; 14(6):1578. https://doi.org/10.3390/en14061578
Chicago/Turabian StyleKhan, Muhammad Ahmad, Xiaocong Li, Muhammad Zain Yousaf, Ali Mustafa, and Mingshuo Wei. 2021. "Metaheuristic Based Solution for the Non‐Linear Controller of the Multiterminal High‐Voltage Direct Current Networks" Energies 14, no. 6: 1578. https://doi.org/10.3390/en14061578