138 lines
2.6 KiB
Markdown
138 lines
2.6 KiB
Markdown
---
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aliases:
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- voltage drop
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title: Voltage Drop
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tags:
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- type/encyclopedia-entry
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up: "[[electricity]]"
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---
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# Voltage Drop
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**Voltage drop** is an observed decrease in voltage
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as measured between a source and load.
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> [!info] Ohm's Law
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>
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> $$
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> V = I \times R, \quad R = \frac{V}{I}, \quad I = \frac{V}{R}
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> $$
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## Step 1: Effective Impedance $Z$
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The formula for effective impedance $Z$ is given by
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$$
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Z = R \cos(\theta) + X \sin(\theta)
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$$
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where
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* $R$ = AC resistance
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* $X$ = Reactance
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* $\theta$ = Power factor angle = $\arccos(\text{PF})$
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$$
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|Z| = \sqrt{ R^{2} + X^{2} }
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$$
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> [!info] Inverse Trig Function Notation
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> $\arccos(x) \equiv \cos^{-1}(x)$
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$$
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\sin(\cos^{-1}(x)) = \sqrt{ 1 - x^{2} }
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$$
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### Parallel Runs
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The equivalent resistance of parallel resistances is given by
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$$
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\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots + \frac{1}{R_n}
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$$
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For $n$ parallel resistances of value $R$
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$$
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\begin{align*}
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\frac{1}{R_{\text{eq}}} &= n \times \left(\frac{1}{R}\right) \\
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&= \frac{n}{R} \\
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R_{\text{eq}} &= \frac{R}{n}
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\end{align*}
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$$
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## Step 2: Voltage Drop
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> [!important]
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> This section assumes a 3-phase
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> 208Y/120V or 480Y/277V voltage system
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> [!info] 3-Phase Voltage
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>
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> $$
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> V_{L} = \sqrt{3} \times V_{P}, \quad V_{P} = \frac{V_{L}}{\sqrt{3}}
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> $$
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3% allowable voltage drop for a 120V line-to-neutral load:
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$$
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\text{Max}\ \Delta V = 0.03 \times 120 \text{V}_{P} = 3.60 \text{V}_{P}
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$$
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3% allowable voltage drop for a 208V line-to-line load:
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$$
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\text{Max}\ \Delta V = 0.03 \times 208 \text{V}_{L} = 6.24 \text{V}_{L}
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$$
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### Line to Neutral Loads
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$$
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\Delta V_{P} = I \times Z \times 2L
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$$
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### Line to Line Loads
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$$
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\Delta V_{L} = I \times Z \times 2L
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$$
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### 3-Phase Loads
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$$
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\Delta V_{3\phi} = \sqrt{3} ( I \times Z \times L )
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$$
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where
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* $\Delta V$ = Voltage drop in volts (V)
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* $I$ = Current in amperes (A)
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* $Z$ = Effective impedance in ohms
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* $L$ = Length of wire one way in feet ($\text{ft}$)
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> [!important]
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> "Current" is not the OCPD rating,
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> but the actual load.
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***
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When exact length is unknown,
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it is often most useful to calculate the maximum length
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a certain wiring configuration is suitable for.
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$$
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L = \frac{ \Delta V }{ I \times M } \times \frac{1}{Z}
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$$
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where
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* $M$ is the "phase multiplier" (2 for single phase, $\sqrt{3}$ for 3-phase)
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* $Z$ is the linear resistance of the wiring configuration
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***
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When exact length is known,
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it is often most useful to calculate the linear resistance
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that will result in a specified voltage drop.
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That is, the maximum linear resistance for a specific feeder.
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$$
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Z = \frac{ \Delta V }{ I \times M \times L }
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$$
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