Survey and Comparison of Optimization-Based Aggregation Methods for the Determination of the Flexibility Potentials at Vertical System Interconnections
Abstract
:1. Introduction
1.1. Motivation
1.2. Related Work
1.3. Contributions of this Article
2. Formulation of the FOR Determination as Non-Linear Optimization Problem
2.1. Determination of Vertical Active and Reactive Power Flows
2.2. Constraints of the Optimization Problem
2.3. Determination of Initial Sampling Points
3. Sampling Strategies for the Determination of the FOR
3.1. Angle-Based Sampling Strategies
3.2. Set-Point-Based Sampling Strategies
4. Formulation of FOR Determination as Sequential Linear Constrained Quadratic Programming
4.1. General Formulation of a Quadratically Constrained Linear Program
4.2. Linear Objective Function with Quadratic Constraints
5. Formulation and Modification of the Particle Swarm Optimization for the FOR Determination
5.1. Solution Process of the Classic Particle Swarm Optimization
5.2. Compliance of Technical Constraints
5.3. Modifications of the Classic Particle Swarm Optimization for an Improved FOR Determination
5.3.1. Return Operator
5.3.2. Limitation and Inversion of Particle Velocities
5.4. Algorithm and Parameterization of the Modified Particle Swarm Optimization
- Step 1:
- Initialization of the particle positions and velocities by Equation (51) at iteration step .
- Step 2:
- Evaluation of the particle swarm objective values by the objective function in Equation (1) based on the results of a power flow calculation for each swarm particle.
- Step 3:
- Update of and .
- Step 4*:
- Update of and .
- Step 5:
- Update of the particle velocities for the next iteration step by Equation (53).
- Step 6*:
- Step 7:
- Update of the particle positions for the next iteration step by Equation (54).
- Step 8:
- Set-to-limit operator.
- Step 9*:
- Return operator.
- Step 10:
- Repeat steps 2 to 10 until .
6. Benchmark System and Comparison Scenario
7. Convergence Behavior of the Modified Particle Swarm Optimization
8. Comparison of FOR Sampling Strategies
9. Comparison of the Optimization Methods Regarding the FOR Determination
10. Discussion
11. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
Cigré | Conseil International des Grands Réseaux Électriques |
CMA-ES | Covariance Matrix Adaptation Evolution Strategy |
DER | Decentral energy resource |
DSO | Distribution system operator |
ENTSO-E | European Network of Transmission System Operators for Electricity |
FOR | Feasible operation region |
FPU | Flexibility providing unit |
GAMS | General algebraic modeling system |
HV | High voltage |
ICPF | Interval constrained power flow |
ICT | Information and communication technology |
IPOPT | Interior point optimizer |
LV | Low voltage |
MV | Medium Voltage |
NLP | Non-linear programming |
OLTC | On load tap changing transformer |
OPF | Optimal power flow |
PQ | Active and reactive power |
PSO | Particle swarm optimization |
PV | Photovoltaic |
QCLP | Quadratically constrained quadratic programming |
REvol | Evolutionary Training Algorithm for Artificial Neural Networks |
TSO | Transmission system operator |
Appendix A. Cigré MV Benchmark Grid
Type | Vector Group | High Voltage in kV | Low Voltage in kV | Rated Loading in MVA | Short Circuit Voltage in % | Copper Loss in kW | Open Circuit Current in % | Iron Loss in kW |
---|---|---|---|---|---|---|---|---|
HV/MV | Yyn0 | 110 | 20 | 25 | 12 | 25 | 0.2 | 0 |
MV/LV | Dyn0 | 20 | 0.4 | 2 | 8 | 16.7 | 0.2 | 4 |
Maximum Thermal Current Limit in | Primary LINE constant For The loop resistance in | Primary Line Constant for the loop Inductance in | Primary Line Constant for the Insulator Capacitance in |
---|---|---|---|
680 | 0.501 | 2.2790988 | 0.1511759 |
Bus i | Nominal bus voltage in kV | Active Power Loads in MW | Reactive Power Loads in Mvar | Active Power Wind Turbines in MW | Active Power PV Units in MW | Bus Voltage V in p.u. | Phase Angle in |
---|---|---|---|---|---|---|---|
1 | 110 | 0 | 0 | 0 | 0 | 1.0000 | 0 |
2 | 20 | 7.644 | 1.552 | -3.211 | 0 | 0.9849 | 0.32 |
3 | 20 | 0 | 0 | 0 | 0 | 1.0027 | 2.45 |
4 | 20 | 0 | 0 | −0.535 | 0 | 1.0327 | 5.65 |
5 | 20 | 0 | 0 | −3.479 | 0 | 1.0356 | 5.94 |
6 | 20 | 0 | 0 | −1.070 | 0 | 1.0363 | 6.02 |
7 | 20 | 0 | 0 | −0.535 | 0 | 1.0370 | 6.09 |
8 | 20 | 0 | 0 | −0.535 | 0 | 1.0358 | 5.98 |
9 | 20 | 0 | 0 | −0.535 | 0 | 1.0351 | 5.90 |
10 | 20 | 0 | 0 | 0 | 0 | 1.0354 | 5.93 |
11 | 20 | 0 | 0 | −0.535 | 0 | 1.0360 | 6.00 |
12 | 20 | 0 | 0 | −0.535 | 0 | 1.0362 | 6.02 |
13 | 0.4 | 0.374 | 0.068 | 0 | −0.272 | 0.9817 | 0.09 |
14 | 0.4 | 0.369 | 0.067 | 0 | −0.272 | 0.9817 | 0.10 |
15 | 0.4 | 0.340 | 0.062 | 0 | −0.272 | 0.9821 | 0.17 |
16 | 0.4 | 0.386 | 0.070 | 0 | −0.272 | 0.9815 | 0.07 |
17 | 0.4 | 0.380 | 0.069 | 0 | −0.272 | 0.9816 | 0.08 |
18 | 0.4 | 0.369 | 0.067 | 0 | −0.272 | 0.9817 | 0.11 |
19 | 0.4 | 0.385 | 0.070 | 0 | −0.272 | 1.0295 | 5.42 |
20 | 0.4 | 0.339 | 0.062 | 0 | −0.272 | 1.0329 | 5.81 |
21 | 0.4 | 0.374 | 0.068 | 0 | −0.272 | 1.0325 | 5.74 |
22 | 0.4 | 0.369 | 0.067 | 0 | −0.272 | 1.0326 | 5.75 |
23 | 0.4 | 0.340 | 0.062 | 0 | −0.272 | 1.0329 | 5.81 |
24 | 0.4 | 0.386 | 0.070 | 0 | −0.272 | 1.0331 | 5.80 |
25 | 0.4 | 0.380 | 0.069 | 0 | −0.272 | 1.0332 | 5.80 |
26 | 0.4 | 0.369 | 0.067 | 0 | −0.272 | 1.0340 | 5.90 |
27 | 0.4 | 0.385 | 0.070 | 0 | −0.272 | 1.0326 | 5.75 |
28 | 0.4 | 0.339 | 0.062 | 0 | −0.272 | 1.0324 | 5.77 |
29 | 0.4 | 0.374 | 0.068 | 0 | −0.272 | 1.0330 | 5.80 |
30 | 0.4 | 0.369 | 0.067 | 0 | −0.272 | 1.0332 | 5.82 |
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Max. Inertia | Min. Inertia | Max. Iteration | Swarm Size n | Acceleration Coefficients |
---|---|---|---|---|
0.9 | 0.4 | 200 | 100 | 2 |
GAMS | Modified PSO | Benchmark FOR GAMS | QCLP |
---|---|---|---|
105 s | 640 s | 10910 s | 164 s |
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Sarstedt, M.; Kluß, L.; Gerster, J.; Meldau, T.; Hofmann, L. Survey and Comparison of Optimization-Based Aggregation Methods for the Determination of the Flexibility Potentials at Vertical System Interconnections. Energies 2021, 14, 687. https://doi.org/10.3390/en14030687
Sarstedt M, Kluß L, Gerster J, Meldau T, Hofmann L. Survey and Comparison of Optimization-Based Aggregation Methods for the Determination of the Flexibility Potentials at Vertical System Interconnections. Energies. 2021; 14(3):687. https://doi.org/10.3390/en14030687
Chicago/Turabian StyleSarstedt, Marcel, Leonard Kluß, Johannes Gerster, Tobias Meldau, and Lutz Hofmann. 2021. "Survey and Comparison of Optimization-Based Aggregation Methods for the Determination of the Flexibility Potentials at Vertical System Interconnections" Energies 14, no. 3: 687. https://doi.org/10.3390/en14030687