Efficient Computation of Sensitivity Coefficients of Node Voltages and Line Currents in Unbalanced Radial Electrical Distribution Networks (1203.6798v2)

Abstract: The problem of optimal control of power distribution systems is becoming increasingly compelling due to the progressive penetration of distributed energy resources in this specific layer of the electrical infrastructure. Distribution systems are, indeed, experiencing significant changes in terms of operation philosophies that are often based on optimal control strategies relying on the computation of linearized dependencies between controlled (e.g. voltages, frequency in case of islanding operation) and control variables (e.g. power injections, transformers tap positions). As the implementation of these strategies in real-time controllers imposes stringent time constraints, the derivation of analytical dependency between controlled and control variables becomes a non-trivial task to be solved. With reference to optimal voltage and power flow controls, this paper aims at providing an analytical derivation of node voltage and line current flows as a function of the nodal power injections and transformers tap-changers positions. Compared to other approaches presented in the literature, the one proposed here is based on the use of the [Y] compound matrix of a generic multi-phase radial unbalanced network. In order to estimate the computational benefits of the proposed approach, the relevant improvements are also quantified versus traditional methods. The validation of the proposed method is carried out by using both IEEE 13 and 34 node test feeders. The paper finally shows the use of the proposed method for the problem of optimal voltage control applied to the IEEE 34 node test feeder.

• The paper presents an analytical method to compute sensitivity coefficients for node voltages and line currents, optimizing real-time control in unbalanced networks.
• It leverages the sparsity of the Y compound matrix and generalizes to multiple slack busses while incorporating transformer tap-changer sensitivities.
• Tests on IEEE 13 and 34 node feeders demonstrate up to threefold computational speed improvements over traditional Jacobian-based approaches.

Overview of "Efficient Computation of Sensitivity Coefficients of Node Voltages and Line Currents in Unbalanced Radial Electrical Distribution Networks"

The paper addresses the increasingly important challenge of optimal control in power distribution systems due to the growing integration of distributed energy resources (DERs). Specifically, the focus is on computing sensitivity coefficients for node voltages and line currents in unbalanced radial distribution networks. This is highly relevant as distribution systems are undergoing significant transformation, incorporating more active elements and requiring sophisticated control strategies to ensure efficient and reliable operation.

Key Contributions

The authors present a method for analytically deriving sensitivity coefficients of node voltages and line currents in response to changes in nodal power injections and transformer tap-changer positions. Unlike traditional approaches, this method employs the [Y] compound matrix, which is particularly advantageous due to its sparsity, to handle the multi-phase unbalanced configuration of distribution networks effectively. Unique aspects of the proposed method include:

1. Generalization to Multiple Slack Busses: The approach accommodates a generic number of slack busses, enhancing its applicability to a wide range of network configurations.
2. Inclusion of Tap-Changer Sensitivities: It extends computations to include transformer tap-changer positions, an aspect often neglected in conventional methods.
3. Accounting for Unbalance: By leveraging the complete admittance matrix, the paper addresses the often significant impact of phase imbalances in distribution systems.
4. Computational Efficiency: Compared to methods reliant on repeatedly updating and inverting the Jacobian matrix, this approach proves significantly more computationally efficient, as validated through tests on IEEE 13 and 34 node test feeders.

Theoretical Underpinnings and Methodology

At the core of this work is the construction of analytical expressions for voltage and current sensitivities. This is achieved by solving a series of linear equations, inspired by the Gauss-Seidel approach but adapted for distributed network scenarios with potentially numerous slack nodes and phase imbalances. The theoretical framework guarantees a unique solution for radial networks, a critical feature for dependable real-time control applications.

Numerical Validation and Practical Implications

The authors validate the proposed method using IEEE standard test feeders, demonstrating its equivalence to traditional Jacobian-based approaches yet achieving a factor of up to three in computational time reduction. Such efficiency enhancements have profound implications for real-time controls and other applications such as contingency analysis and network optimization.

Future Directions

The demonstrated capability to handle the complexities of unbalanced networks with greater speed suggests potential extensions of this method to more dynamic control scenarios. For instance, integrating the proposed computation of sensitivity coefficients into a real-time optimization framework for active distribution networks could substantially enhance grid flexibility and resilience. Moreover, as distribution networks continue to evolve with more DERs and smart grid technologies, the outlined method may play a vital role in supporting advanced control schemes.

In conclusion, while the paper builds on existing knowledge of sensitivity analysis in power systems, it offers a refined and highly applicable method tailored to contemporary challenges in distribution network operations. It effectively bridges the gap between theoretical derivation and practical implementation, paving the way for robust and timely control strategies in the face of ever-evolving grid demands.