A Flexible Envelope Method for the Operation Domain of Distribution Networks Based on “Degree of Squareness” Adjustable Superellipsoid
Abstract
:1. Introduction
2. Feasible Domain Modeling Based on Network Operational Constraints
2.1. Rewriting of the Power Flow Model of the Distribution Network
2.2. Distribution Network Constraints
3. Construction and Improvement of Flexible Operational Domain Models
3.1. Distribution Network Operating Envelope Definition
3.2. Tunable Superellipsoid Running Envelope Solution Model Based on “Degree of Squareness”
4. Experimental Verification
4.1. Total Operational Domain Envelope Security Assessment
4.2. Active Node Independent Regulatory Scope Analysis
4.3. Operational Domain Envelope Time Analysis
4.4. Operational Domain Envelope Security Validation
5. Conclusions
- (1)
- The method adopted in this paper uses an improved convex inner approximation approach, providing a convex solution space that is strictly contained within the original feasible region of the system for subsequent envelope construction of the distribution network operation domain.
- (2)
- This paper employs a “degree of squareness” adjustable superellipsoid envelope method with high network adaptability, capable of dynamically adjusting parameters to change its size and adapt to different operating states of the system, achieving p-q decoupling operation among various active nodes in the distribution network. Compared with traditional methods, the proposed method significantly enhances the range of the operation envelope while ensuring the feasibility of solution decomposition.
- (3)
- In response to the high penetration of DERs, compared with traditional convex envelope methods, this paper’s method adds a penalty term to the model to penalize unknown states of each node during the calculation of the operation domain, effectively mitigating the adverse effects brought by the uncertainty and complexity of resources such as DERs.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Symbol | |
Mathematical expression of feasible domain | |
The set of all run constraints | |
Mathematical expression of hyperrectangle | |
L | The length of all axes of a hyperellipsoid |
Hyperellipsoid with adjustable “square” | |
Built-in hyperrectangular volume | |
Introduced relaxation variable | |
The input/output quota to be allocated by each node | |
Abbreviations | |
DERs | Distributed energy resources |
DFR | Decoupled feasibility region |
UTOPF | Unbalanced three-phase optimal power flow |
DOEs | Dynamic operation envelopes |
CDOEs | Convex DOEs |
RDOEs | Rectangular DOEs |
HDOEs | Hyperellipsoidal DOEs |
MHDOEs | Modified HDOEs |
Appendix A
No. | DG Type | Quantity | Location | Active Power/MW |
---|---|---|---|---|
DG1 | PV cell | 1 | 6, 9, 13, 24 | 0~0.5 |
DG2 | WTG | 1 | 30 | 0~0.35 |
DG2 | WTG | 1 | 33 | 0~0.65 |
No. | DG Type | Quantity | Location | Active Power/MW |
---|---|---|---|---|
DG1 | PV cell | 1 | 4, 8, 21, 25, 36, | 0~0.35 |
DG2 | WTG | 1 | 40, 45, 48, 52, 60 | 0~0.25 |
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RDOEs | HDOEs | MHDOEs | |
---|---|---|---|
IEEE 33 | 0.21 | 0.09 | 0.01 |
IEEE 69 | 0.23 | 0.13 | 0.02 |
RDOEs | HDOEs | MHDOEs | |
---|---|---|---|
IEEE 33 | 0.039 s | 16.154 s | 18.674 s |
IEEE 69 | 0.055 s | 24.564 s | 28.389 s |
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Wang, K.; Huang, Y.; Xu, J.; Liu, Y. A Flexible Envelope Method for the Operation Domain of Distribution Networks Based on “Degree of Squareness” Adjustable Superellipsoid. Energies 2024, 17, 4096. https://doi.org/10.3390/en17164096
Wang K, Huang Y, Xu J, Liu Y. A Flexible Envelope Method for the Operation Domain of Distribution Networks Based on “Degree of Squareness” Adjustable Superellipsoid. Energies. 2024; 17(16):4096. https://doi.org/10.3390/en17164096
Chicago/Turabian StyleWang, Kewei, Yonghong Huang, Junjun Xu, and Yanbo Liu. 2024. "A Flexible Envelope Method for the Operation Domain of Distribution Networks Based on “Degree of Squareness” Adjustable Superellipsoid" Energies 17, no. 16: 4096. https://doi.org/10.3390/en17164096