Talk:Nodal admittance matrix

Merge this article with Admittance parameters?
It has been proposed that Nodal admittance matrix be merged with Admittance parameters.
 * oppose as these appear to refer to different entities:
 * The nodal admittance matrix in the context of power engineering is not clearly defined by this page, but [now it is ] seems to coincide with my understanding of this term in network theory - that is, it's the coefficients of the equations to be solved in nodal analysis. So Kirchhoff's current law is 0 = YV where Y is the nodal admittance matrix and V is a vector of voltages, being the voltage of each circuit node with respect to a common ground.
 * The matrix of admittance parameters relates port currents and port voltages in a black-box representation of a network (whose internal nodes are not considered). Each port consists of a pair of terminals carrying equal and opposite currents into and out of the box. There is no concept of a common ground.
 * Of course, both are square matrices of admittances. --catslash (talk) 23:09, 14 December 2011 (UTC)
 * oppose I agree.  The nodal admittance matrix is an N x N matrix used in general circuit analysis of electronic circuits (networks).  The admittance parameters are a 2 x 2 matrix used with the two-port network model.  They're related, but not enough to merge into the same article -- Chetvorno TALK 01:16, 3 April 2012 (UTC)

The (albeit meagre) response to this proposal over the last 18 months has been entirely negative. I shall therefore remove the merge templates. --catslash (talk) 23:59, 28 September 2012 (UTC)

Editing the "Context" Section
I thought the "Context" Section of the article was very brief and could use some elaboration in order to make the purpose and origins of the admittance matrix more clear to readers without much background in electrical engineering. I expanded on why the admittance matrix is a useful tool and why computers are needed to solve these systems, as well as where the principles used to construct the admittance matrix come from, to hopefully give readers a better understanding of the concept.

S.ham2015 (talk) 16:51, 25 November 2013 (UTC)

Construction of the Admittance Matrix in the "Design" Section
Using the subscript $$i$$ in the summation $$\sum_{i \neq j} y_{ij}$$ in the case where $$i = j$$ is confusing, as the variable $$i$$ is also used in the index of $$Y_{ij}$$. Replacing $$i$$ in the summation with another variable may be helpful. For instance

$$Y_{ij} = \begin{cases} y_{ii} + \sum_{k \neq i} {y_{ik}}, & \mbox{if } i = j \\ -y_{ij}, & \mbox{if } i \neq j. \end{cases} $$

— Preceding unsigned comment added by Gkaf (talk • contribs) 21:37, 24 February 2015 (UTC) Gkaf (talk) 21:51, 24 February 2015 (UTC)


 * Yes, it's clearer if the bound variable of the summation is distinct from the matrix row-number. I have changed it, but please be bold and do it yourself next time (also please sign your posts on talk pages by typing four tildes ~ or by pressing the signature button on the edit box tool bar).


 * The parameter $$y_{ii}$$ is also confusingly named; would $$y_{i0}$$ or $$y_{i \, \mathrm{ground}}$$ be better? --catslash (talk) 00:06, 26 February 2015 (UTC)

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The construction of Ybus matrix is usually done choosing the neutral as reference
The building algorithm of the Ybus matrix described in this article for power systems, is done assuming the neutral node (whether real or ficticious) of the single-phase impedance diagram is chosen as reference node. I think we should clarify this.

In some scenarios, for example in economic dispatch, it is desired to choose a bus (and not the neutral) as reference node. Alej27 (talk) 02:14, 25 December 2020 (UTC)


 * I suspect that power dispatch is related to voltage angles rather that the voltage reference. The power injection in the busses is
 * S = VI^{*} = V Y^{*} V^{*} = \sum_{k=1, \ldots, N} \sum_{m=1, \ldots, N} V_{k} Y_{mk}^{*} V_{m}^{*} = \sum_{k=1, \ldots, N} \sum_{m=1, \ldots, N} Y_{km}^{*} \vert V_{k} \vert \vert V_{m} \vert e^{j (\phi_{k} - \phi_{m})},
 * so the power injection depends on the angles $\phi$. However, multiple angles can result in the same power injection. For instance, assume that
 * S(\vert V \vert, \phi) = \sum_{k=1, \ldots, N} \sum_{m=1, \ldots, N} Y_{km}^{*} \vert V_{k} \vert \vert V_{m} \vert e^{j (\phi_{k} - \phi_{m})},
 * then for $$\theta_{i} = \phi_{i} + a$$,
 * S(\vert V \vert, \theta) = \sum_{k=1, \ldots, N} \sum_{m=1, \ldots, N} Y_{km}^{*} \vert V_{k} \vert \vert V_{m} \vert e^{j (\phi_{k} + a - \phi_{m} - a)} = \sum_{k=1, \ldots, N} \sum_{m=1, \ldots, N} Y_{km}^{*} \vert V_{k} \vert \vert V_{m} \vert e^{j (\phi_{k} - \phi_{m})} = S(\vert V \vert, \phi).
 * In the power dispatch problem we should also specify a reference bus from which all angles are measured to avoid this ambiguity, and the reference bus is independent from the ground, our zero voltage reference.
 * Does this resolve the ambiguity regarding the selection of the ground as voltage reference? Gkaf (talk) 17:03, 3 November 2023 (UTC)
 * then for $$\theta_{i} = \phi_{i} + a$$,
 * S(\vert V \vert, \theta) = \sum_{k=1, \ldots, N} \sum_{m=1, \ldots, N} Y_{km}^{*} \vert V_{k} \vert \vert V_{m} \vert e^{j (\phi_{k} + a - \phi_{m} - a)} = \sum_{k=1, \ldots, N} \sum_{m=1, \ldots, N} Y_{km}^{*} \vert V_{k} \vert \vert V_{m} \vert e^{j (\phi_{k} - \phi_{m})} = S(\vert V \vert, \phi).
 * In the power dispatch problem we should also specify a reference bus from which all angles are measured to avoid this ambiguity, and the reference bus is independent from the ground, our zero voltage reference.
 * Does this resolve the ambiguity regarding the selection of the ground as voltage reference? Gkaf (talk) 17:03, 3 November 2023 (UTC)
 * In the power dispatch problem we should also specify a reference bus from which all angles are measured to avoid this ambiguity, and the reference bus is independent from the ground, our zero voltage reference.
 * Does this resolve the ambiguity regarding the selection of the ground as voltage reference? Gkaf (talk) 17:03, 3 November 2023 (UTC)

The context section is out of scope
The context section does not help the presentation of the main topic at the moment. Some applications that are discussed in the context section could be moved to the dedicated section after the definition of the nodal admittance matrix. Also, some of the theoretical discussions in the context section about Kirchhoff's laws are useful in the introduction. If all of the remaining material can be replaced by links to relevant topics, the content section can be removed.

Gkaf (talk) 18:19, 31 October 2023 (UTC)


 * I removed the context section, as it is better suited for the power flow problem article. I quote the removed text here in case you would like to propose any modification:
 * ''Electric power transmission needs optimization in order to determine the necessary real and reactive power flows in a system for a given set of loads, as well as the voltages and currents in the system. Power flow studies are used not only to analyze current power flow situations, but also to plan ahead for anticipated disturbances to the system, such as the loss of a transmission line to maintenance and repairs. The power flow study would determine whether or not the system could continue functioning properly without the transmission line. Only computer simulation allows the complex handling required in power flow analysis because in most realistic situations the system is very complex and extensive and would be impractical to solve by hand. The admittance matrix is a tool in that domain. It provides a method of systematically reducing a complex system to a matrix that can be solved by a computer program. The equations used to construct the admittance matrix come from the application of Kirchhoff's current law and Kirchhoff's voltage law to a circuit with steady-state sinusoidal operation. These laws give us that the sum of currents entering a node in the circuit is zero, and the sum of voltages around a closed loop starting and ending at a node is also zero. These principles are applied to all the nodes in a power flow system and thereby determine the elements of the admittance matrix, which represents the admittance relationships between nodes, which then determine the voltages, currents and power flows in the system.
 * Gkaf (talk) 14:53, 3 March 2024 (UTC)
 * Gkaf (talk) 14:53, 3 March 2024 (UTC)