Electrical admittance¶
The complex current-to-voltage coefficient of a linear electrical branch or load at a stated frequency, equal to reciprocal impedance and separable into conductance and susceptance.
Core Idea¶
Electrical admittance says how much electrical current a specified linear branch or load takes per unit voltage at a stated frequency. For matched current and voltage phasors, with current into the branch counted positive, \(I=YV\) and, when the quotients are defined, \(Y=I/V=1/Z\). It is a complex quantity: \(Y=G+jB\). The real part \(G\) is conductance and the imaginary part \(B\) is susceptance.[^ref-a0f5ac8467d0]
An admittance belongs to a stated component or modeled load and a stated terminal pair, reference, current arrow and frequency. Change one of those conditions and the relevant coefficient may change. In particular, a source that counts current injected into a node uses the opposite sign from current absorbed by a load.[^ref-0e4cbef84a81]
Scope of Application¶
The entry covers a scalar electrical coefficient in a linear branch, port or one phase of a constant-impedance load. A model may specify \(Y\) even when its applied voltage is zero; calculating \(I/V\) at zero voltage is still invalid. A nonlinear element may require a declared local model rather than one constant admittance over all amplitudes. A whole network Y-bus is a matrix built from many coefficients, not one scalar admittance.[^ref-0e4cbef84a81]
Clarity¶
Admittance and impedance describe the same eligible response with reciprocal quotients; substituting \(Z\) for \(Y\) without taking the reciprocal changes the calculation.[^ref-a0f5ac8467d0] Conductance alone is not the full response when susceptance is present. Likewise, a minus sign in a load's node-injection equation can record current direction rather than a negative physical admittance.[^ref-0e4cbef84a81]
Manages Complexity¶
At one frequency, the coefficient compresses a modeled terminal response into one complex number. NBS converts a lumped component's series impedance into equivalent parallel conductance and susceptance.[^ref-a0f5ac8467d0] A power-system model uses a scalar phase-load coefficient before assembling network equations.[^ref-0e4cbef84a81] The shortcut still needs the original frequency, connection and reference, and it does not reveal a unique internal circuit.
Abstract Reasoning¶
First identify the electrical carrier and its voltage and current phasors. State the current arrow, frequency and linear model. NBS gives the reciprocal-impedance relation and the \(G\)/\(B\) component split.[^ref-a0f5ac8467d0] Find the coefficient from a supported current-voltage relation, use \(I=YV\) to predict current, and examine \(G\) and \(B\) separately. When the grid source reports node-injection current for a consuming load, reverse that current before comparing with the absorbed-load convention.[^ref-0e4cbef84a81]
Knowledge Transfer¶
The same questions work for component metrology and for a modeled power-grid phase load: which carrier, which matched phasors, which direction and which coefficient? NBS discusses measurements and converts an assumed component response; the grid paper stipulates a phase-load coefficient for its model.[ref-a0f5ac8467d0][ref-0e4cbef84a81] That shared diagnostic does not make a calibration bridge and a feeder the same system.
Examples¶
Lumped inductor calculation. The NBS guide works a hypothetical high-Q inductor, converting series impedance at a stated frequency into equivalent parallel \(G\) and \(B\).[^ref-a0f5ac8467d0] The inductor terminals identify the carrier; voltage and entering current are matched phasors; \(Y=1/Z\) is the coefficient; \(G\) and \(B\) expose its two complex components. This is a worked calculation, not an observed specimen.
One phase of a power-grid load. Bazrafshan and Gatsis model a wye constant-impedance load with node-injection term \(i_{Z,n}^{\phi}=-y_{L,n}^{\phi}v_n^{\phi}\).[^ref-0e4cbef84a81] The load's absorbed current is \(I_{\mathrm{load}}=-i_{Z,n}^{\phi}\), so \(I_{\mathrm{load}}=y_{L,n}^{\phi}v_n^{\phi}\). One modeled phase is the carrier, \(v\) and \(I_{\mathrm{load}}\) are matched phasors, and the scalar \(y_L\) is its admittance. The later Y-bus assembly is a separate matrix operation; the paper does not claim both parts of this particular \(y_L\) are nonzero.
Relationships to Other Abstractions¶
Current abstraction Electrical admittance Domain-specific
Parents (1) — more general patterns this builds on
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Electrical admittance is a kind of Ratio Prime
Electrical admittance is the ordered current-to-voltage ratio for a specified linear electrical response, with a nonzero reference voltage for direct division.
Hierarchy path (1) — routes to 1 parentless root
- Electrical admittance → Ratio → Comparison
Neighborhood in Abstraction Space¶
Electrical admittance sits in a sparse region of the domain-specific corpus (91st percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (2721 abstractions)
Nearest neighbors
- Equivalent impedance transforms — 0.81
- Three-phase electric power — 0.79
- Star-mesh transform — 0.79
- Inductive circuit model of transformer — 0.79
- Electrical network — 0.78
Computed from structural-signature embeddings · 2026-10-17
Not to Be Confused With¶
- Impedance: \(Z=V/I\), the reciprocal of eligible \(Y=I/V\).[^ref-a0f5ac8467d0]
- Conductance alone: \(G\) is only the real component of complex \(Y\).[^ref-a0f5ac8467d0]
- Characteristic admittance: a transmission-line characteristic quantity, not the general branch or load coefficient.
- Y-bus: a network matrix assembled from coefficients and connections.[^ref-0e4cbef84a81]
- A non-electrical analogue: similar mathematical language does not supply electrical voltage, current or Siemens units to another field.
References¶
[^ref-a0f5ac8467d0]: R. N. Jones, The Measurement of Lumped Parameter Impedance: A Metrology Guide, National Bureau of Standards Monograph 141 (June 1974), especially Section 2 (printed pp. 11, 13–14), Section 3.2 (printed p. 22) and Appendix I (printed pp. 181, 184). https://nvlpubs.nist.gov/nistpubs/Legacy/MONO/nbsmonograph141.pdf [^ref-0e4cbef84a81]: Mohammadhafez Bazrafshan and Nikolaos Gatsis, "Comprehensive Modeling of Three-Phase Distribution Systems via the Bus Admittance Matrix," arXiv:1705.06782v2 (2017), especially Sections II–V and Table I. https://arxiv.org/html/1705.06782