zmVault/voltage-drop.md

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aliases	title	tags	up
voltage drop	Voltage Drop	type/encyclopedia-entry	electricity

Voltage Drop

Voltage drop is an observed decrease in voltage as measured between a source and load.

[!info] Ohm's Law

V = I \times R, \quad R = \frac{V}{I}, \quad I = \frac{V}{R}

Step 1: Effective Impedance Z

The formula for effective impedance Z is given by

Z = R \cos(\theta) + X \sin(\theta)

where

• R = AC resistance
• X = Reactance
• \theta = Power factor angle = \arccos(\text{PF})

|Z| = \sqrt{ R^{2} + X^{2} }

[!info] Inverse Trig Function Notation \arccos(x) \equiv \cos^{-1}(x)

\sin(\cos^{-1}(x)) = \sqrt{ 1 - x^{2} }

Parallel Runs

The equivalent resistance of parallel resistances is given by

\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots + \frac{1}{R_n}

For n parallel resistances of value R

\begin{align*}
\frac{1}{R_{\text{eq}}} &= n \times \left(\frac{1}{R}\right) \\
&= \frac{n}{R} \\
R_{\text{eq}} &= \frac{R}{n}
\end{align*}

Step 2: Voltage Drop

Important

This section assumes a 3-phase 208Y/120V or 480Y/277V voltage system

[!info] 3-Phase Voltage

V_{L} = \sqrt{3} \times V_{P}, \quad V_{P} = \frac{V_{L}}{\sqrt{3}}

3% allowable voltage drop for a 120V line-to-neutral load:

\text{Max}\ \Delta V = 0.03 \times 120 \text{V}_{P} = 3.60 \text{V}_{P}

3% allowable voltage drop for a 208V line-to-line load:

\text{Max}\ \Delta V = 0.03 \times 208 \text{V}_{L} = 6.24 \text{V}_{L}

Line to Neutral Loads

\Delta V_{P} = I \times Z \times 2L

Line to Line Loads

\Delta V_{L} = I \times Z \times 2L

3-Phase Loads

\Delta V_{3\phi} = \sqrt{3} ( I \times Z \times L )

where

• \Delta V = Voltage drop in volts (V)
• I = Current in amperes (A)
• Z = Effective impedance in ohms
• L = Length of wire one way in feet (\text{ft})

Important

"Current" is not the OCPD rating, but the actual load.

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When exact length is unknown, it is often most useful to calculate the maximum length a certain wiring configuration is suitable for.

L = \frac{ \Delta V }{ I \times M } \times \frac{1}{Z}

where

• M is the "phase multiplier" (2 for single phase, \sqrt{3} for 3-phase)
• Z is the linear resistance of the wiring configuration

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When exact length is known, it is often most useful to calculate the linear resistance that will result in a specified voltage drop. That is, the maximum linear resistance for a specific feeder.

Z = \frac{ \Delta V }{ I \times M \times L }