Thévenin's theorem

Summary

As originally stated in terms of direct-current resistive circuits only, Thévenin's theorem states that "Any linear electrical network containing only voltage sources, current sources and resistances can be replaced at terminals A–B by an equivalent combination of a voltage source Vth in a series connection with a resistance Rth."

The equivalent voltage Vth is the voltage obtained at terminals A–B of the network with terminals A–B open circuited.
The equivalent resistance Rth is the resistance that the circuit between terminals A and B would have if all ideal voltage sources in the circuit were replaced by a short circuit and all ideal current sources were replaced by an open circuit.
If terminals A and B are connected to one another, the current flowing from A and B will be \tfrac{V_\mathrm{th} }{R_\mathrm{th} }. This means that Rth could alternatively be calculated as Vth

Official source

https://en.wikipedia.org/wiki/Th%C3%A9venin's_theorem

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Decentralized voltage control of clustered active distribution network by means of energy storage systems

Maryam Bahramipanah, Mario Paolone

The paper presents a network partitioning strategy for the optimal voltage control of Active Distribution Networks (ADNs) actuated by means of a limited number of Distributed Energy Storage Systems (DESSs). The proposed partitioning uses a linear programming approach by means of the known concept of voltage sensitivities. Then, two decentralized optimal control algorithms are proposed relying, respectively, on the Thévenin equivalents and a recursive approach. These algorithms are developed using the Multi- Agent System (MAS) concept. With respect to a centralized control algorithm, the aim of the network clustering is to reduce the number of exchanged messages among the clusters when one of the two proposed decentralized control algorithms is adopted. The effectiveness of the two proposed controls is assessed with respect to the performances of the equivalent centralized control using numerical examples composed by the IEEE 13 and IEEE 123 buses distribution test feeders adapted to include stochastic generation and DESSs.

Elsevier2016

Network clustering for voltage control in active distribution network including energy storage systems

Maryam Bahramipanah, Mostafa Nick, Mario Paolone

This paper presents a network partitioning strategy for the optimal voltage control of Active Distribution Networks (ADNs) by means of Dispersed Energy Storage Systems (DESSs). The proposed partitioning is based on the concept of voltage sensitivity coefficients and is adopted for a decentralized voltage- control strategy specifically developed for radial ADNs. The aim of the partitioning is to decompose the network into quasi- autonomous areas and to limit the information exchange only at the interfacing nodes between adjacent areas. The information exchange relies on Thévenin equivalents to represent the external grids of each cluster/area. The effectiveness of the proposed decentralized control approach is assessed with respect to an equivalent centralized control approach. Such an assessment is carried out using a numerical example referring to IEEE 123 buses distribution test feeder suitably adapted to include stochastic generation and DESSs.

IEEE2015

This paper proposes a Voltage Stability Index (VSI) suitable for unbalanced polyphase power systems. To this end, the grid is represented by a polyphase multiport network model (i.e., hybrid parameters), and the aggregate behavior of the devices in each node by Thévenin Equivalents (TEs) and Polynomial Models (PMs), respectively. The proposed VSI is a generalization of the known L-index, which is achieved through the use of compound electrical parameters, and the incorporation of TEs and PMs into its formal definition. Notably, the proposed VSI is capable of handling unbalanced polyphase power systems, explicitly takes into account voltage-dependent behavior (represented by PMs), and is computationally inexpensive. These features are valuable for the operation of both transmission and distribution systems. Specifically, the ability to handle the unbalanced polyphase case is of particular value for distribution systems. In this context, it is proven that the hybrid parameters required for the calculation of the VSI do exist under practical conditions (i.e., for lossy grids). The proposed VSI is validated against state-of-the-art methods for voltage stability assessment using a benchmark system which is based on the IEEE 34-node feeder.

2019