Warning: The following information is not a substitute for knowledge or experience
The purpose of this document is to familiarize the uninitiated with conventions of electrical design used at #Riveer and some of the underlying physics that affect choices made in the creation of electromechanical systems.

Riveer conventions

technique only.

typical wire colors

N.B. - These are not regulatory; the NEC only prescribes the color of ground (green or bare copper).

International projects will comply with the best practices of the host nation. E.g. - 415V 3$\varphi$ power in Australia is indicated with Brown, Black, and Grey for 3 line voltages with a Blue wire included for the neutral return path.

electrical drawings

drawings are created in AutoCAD Electrical and are numbered by pages and by lines:

wire numbering conventions

• The hexagons on each side of the page are drawn with a page number over a line number.
• Wire numbers are derived from the line number and page number on which they originate.
  • e.g. on page 1, line 09, wire 1040 connects to a circuit breaker and then wire 1090 connects the circuit breaker to the motor's control relay and overload heater. From there, wire 1091 connects the heater to one of 3 inputs to the three-phase motor
    • wire 1040 is L1 of the 3-phase 480VAC input, which originates from the terminal block on page 1, line 04.
    • wire 1090 is the first unique node on page 1, line 09.
    • wire 1091 is the second unique node on page 1, line 09

sheet numbering conventions

drawing sheets are non-consecutively numbered. There is no single standard, two examples are #Brian's convention and #Steve's conventions, as shown below:

Characteristics applicable to both Systems:

• Page groups which do not apply are omitted.
  E.g. a 208 VAC system would start with 208 VAC input lines (L1, L2, and L3) on pg. 1 and all other page number groups would decrement by 10.
• If only 2 pages of 24 VDC distribution are required, the pages would number: $\dots 20,21,30,31\dots$ and skip the unused page numbers.

Brian's convention

From the mind of Brian Matheny:

Steve's conventions

Chart below as created by Steve Kalmar

AWG

American Wire Gauge is a logarithmic stepped standard wire gauge used in North America.

• It is distinct from and implicitly superior to British Standard Wire Gauge (SWG).
• Other standards include IEC 60228 which defines metric wire sizes in terms of cross-sectional area (in units of $m{m}^2$).
  American Wire Gauge Chart and AWG Electrical Current Load Limits table with ampacities, wire sizes, skin depth frequencies and wire breaking strength

AWG sizes

• AWG is mechanically similar to the Brown & Sharp (B&S) sheet metal gauge.
• larger numbers indicate a smaller diameter conductor.
• Stranded AWG have the same electrical properties as the equivalent solid AWG (although stranded wire will occupy a larger space than an equivalent solid wire)
  • stranded AWG is sometimes expressed as $A$ AWG $B/C$ :
    $A=$ overall AWG size
    $B=$ number of strands
    $C=$ AWG of the strands
  • E.g. a 22 AWG 7/30 refers to a 22 AWG wire composed of 7 strands of 30 AWG wire.
• There are 40 defined sizes ranging from 0000 to 36.
  • 0000 AWG = 0.46 inches in diameter
    N.B. - 0000 AWG is also written as 4/0 AWG
  • 36 AWG = 0.005 inches in diameter

convenient coincidences

• the ratio between the diameter of any two adjacent sizes is $\sqrt[39]{92}\approx 1.229$
  • therefore 3 AWG wire is $\approx D_{2AWG}÷1.229$
  • knowing that $D_{2AWG}=0.2576$ (about $\frac{1}{4}$ inch), then $D_{3AWG}=0.2294$ inch
• The ratio of diameters between any wires that are two gages apart is $(\sqrt[39]{92}{)}^2\approx (1.229{)}^2\approx 1.261$
  E.g. 20 AWG wire has a diameter which is 1.261 times larger than 22 AWG wire

AWG rules of thumb

since $(\sqrt[39]{92}{)}^6\approx 2$

doubling the cross-sectional area

• Doubling the cross-sectional area of a wire corresponds to a change of 3 in AWG
  E.g. a 6 AWG wire has nearly the same cross-sectional area as 2 x 9 AWG wires
  which means that two 9 AWG wires can carry around the same current as a single 6 AWG wire.

doubling the diameter

Doubling the diameter of a solid round wire decreases the AWG by 6
A 14 AWG wire has a diameter of 0.0641 inches $(\approx \frac{1}{16}\text{"})$ and a 20 AWG wire has a diameter about half of that: $D_{20AWG}=0.0320\text{ in}\approx \frac{1}{32}\text{"}$

power of 10 AWG

A decrease of 10 AWG increases the area, weight, and conductance by an order of magnitude.
20 AWG wire is 10x heavier and larger (and can carry 10x more current) than 30 AWG.

resistance rule of thumb

For an arbitrary gage $n$, the resistance $(R)$ of a copper wire is approximately

E.g. for 20 AWG, $R\approx {10}^{\frac{20}{10}}\frac{\mathrm{\Omega }}{1000ft}$
$R_{20AWG}\approx 100\frac{\mathrm{\Omega }}{1000ft}\approx 10\frac{m\mathrm{\Omega }}{ft}$

Aluminum has a conductivity which is $\approx 61\mathrm{\%}$ the conductivity of copper, so an aluminum wire has the same resistance as a copper wire which is two sizes smaller (and $\therefore$ has about half the cross-sectional area)

table of AWG characteristic

How to use this chart:
1. find the required wire gauge - if you know your thermal limit (defined by the lowest rating of all components in the circuit) and your design specified maximum current, you can read the maximum wire gauge off the left column.
2. For a given wire gage, use the lowest temperature rating on the circuit to determine the maximum continuous current that the system can support.
3. To find voltage drop, use #Ohm's Law to solve for the voltage difference given the length of the wire (in ft) and the maximum/intended current through it.

ephemera

footnotes for the AWG table

• source: NEC Table 310.15(B)(16), data applies to copper conductors only
• Breakers are made to protect wires.
• circuit breakers are for short-circuit protection, not to protect equipment (that would be an overload heater) or you (GFCI).

ampacity

• per the US NEC, ampacity is defined as, "the maximum current, in amperes, that a conductor can carry continuously under the conditions of use without exceeding its temperature rating."
  • you have to derate conductors if you have multiples in a single conduit.
  • For the purposes of rating conductors in a conduit, a ground is not counted (because in normal operation, it carries no current).
• ampacity is determined by the thermal characteristics of the insulation on the conductor.
  i.e. the temperature rating for the type of wire under consideration dictates which column in the above table applies.

wire types

• Tray Cable
  per NEC, “a factory assembly of two or more insulated conductors, with or without associated bare or covered grounding conductors under a nonmetallic sheath, for installation in cable trays, in raceways, or where supported by a messenger wire.”

• Machine Tool Wire (MTW) is resistant to heat, moisture, oil, and gasoline. This type of wire almost always has a voltage rating of 600V and a maximum temperature of 105°C.

• Thermoplastic High Heat resistant Nylon-coated wire (THHN) wire has a voltage rating of 600V. It has a temperature range of up to 90°C in dry locations and 75°C in wet locations.

resistance

• applies to copper conductors and DC current or AC current of $\approx 60Hz$.
• Other materials have different resistivity $(\rho )$. Per a common #resistance rule of thumb for AWG, the resistance of an aluminum wire is approximately the same as a copper wire two sizes smaller than the aluminum wire.

max frequency

The frequency listed in the table shows the frequency at which the calculated skin depth is equal to the radius of a solid copper wire, and is an indication that above this frequency you should start considering the #skin effect when calculating the wire's resistance.

• This data is useful for high frequency AC engineering. When high frequency AC is conducted by a wire there is a tendency for the current to flow along the outside of the wire.
• This increases the effective resistance.

tables of voltage drop

The resistance of a wire increases linearly as a function of its length. The table below gives expected resistances for a wire of $x$ AWG and $l$ length based on specifications for copper conductors.

physics

The following information is essential only if you want to understand how and why it works.

Ohm's Law

Where
$V=$ voltage, in volts
$I=$ current, in Amps
and $R=$ Resistance in Ohms $(\mathrm{\Omega })$

said another way, Resistance is the voltage loss per Amp $(R=\frac{V}{I})$ for some material.

3 phase power

Sometimes abbreviated as $3\varphi$

Three-phase power uses between 3 and 5 wires to transmit alternating current. Each phase is a sinewave of voltage which is offset by $120\mathrm{°}$ (or $\frac{2\pi }{3}$ radians) from either other phase.

In a $3\varphi$ system, the current in any line is equal to the sum of currents in the other lines:

This means that a 3 phase system does not require a neutral wire to return current - as in a single-phase AC system - provided that all 3 phases have a balanced load.

All else being equal, a 3 phase system (without a neutral wire) supplies the same power as a single-phase AC system (with a line and a neutral wire) using 25% less wire, by mass.

3 phase power simplifies the wiring of electric motors. If all 3 lines are wired to a motor in sequence, the resulting rotating magnetic field will cause the motor to start and run at the line frequency without any additional circuity (as is typically required for a single-phase AC motor or a DC motor).

3 phase voltages

Each phase is carried on an individual wire - a line conductor - and the voltage measured between any two lines is called the line-to-line voltage or just line voltage.

In a setup that includes a neutral wire, the electric potential measured between a line and the neutral is the line-to-neutral voltage or the phase voltage.

As depicted here, the line voltage is equal to the phase voltage multiplied by $\sqrt{3}$,

• In a typical US 480 VAC $3\varphi$ system this equates to a line to line voltage of 480 VAC and a line to neutral voltage of 277 VAC.
• Likewise, using a Wye configuration with phase voltage of 120 VAC results in a line voltage of 208 VAC. This means that a single 3 phase transformer can provide 3 sources of 120 VAC / 208 VAC from 4 wires.

3 phase wiring

Wiring for a 3 phase system requires a minimum of 1 wire per phase. A ground conductor (indicated by either bare copper or green insulation) can be added to any 3 phase system. In normal operation, the ground carries no current.

3 phase systems are wired in either a delta or a wye configuration. Because of conservation of energy, both systems will transfer the same power at different voltages and currents. With respect to line voltage $(v_{line})$ and line current $(i_{line})$ those equations are:

Aside from current draw, they have other advantages and disadvantages, such as the potential for multiple output voltages or fault tolerance.

3 wire delta

A transformer wired in this manner (called a Delta or $\mathrm{\Delta }$ configuration) provides only line-to-line voltages.
$\therefore v_{line}=v_{phase}$ for a $\mathrm{\Delta }$.

In this configuration, current from one phase is returned by the other two phases. All else being equal, the 3 wires required to connect a $\mathrm{\Delta }$ setup will cost 75% of what a #4 wire wye will cost.

Another advantage is the fault tolerance of a $\mathrm{\Delta }$: If one of the windings in the transformer fails (i.e. the wire breaks and it's now an open circuit) then the remaining 2 phases will provide the same voltage albeit with an increased current draw to compensate.

• However, a $\mathrm{\Delta }$ is only suited for balanced 3 phase loads - where all each phase will have a symmetrical current draw - such as a 3 phase motor.
• The line current for a $\mathrm{\Delta }$ configuration is greater than that of an equivalent Wye. Line voltage and phase voltage are the same, but the currents differ:

4 wire wye

By changing the wiring from the transformer windings (as shown), a neutral wire can be provided to allow for split phases, or to balance an asymmetrical load: if one of the loads is turned off or of a vastly different magnitude than the others, the return current is routed through the neutral with no change in the current draw on the other two phases.

A transformer configured in a Wye or Y configuration can provide both line-to-line and line-to-neutral voltages: a 208 VAC $3\varphi$ system will have a phase voltage of 120 VAC (as measured from the neutral to Phase A, B, or C).

The line voltage is equal to the phase voltage multiplied by $\sqrt{3}$ and since electrical power is equal to the product of current and voltage:

skin effect

Most of the AC current in a conductor travels along the skin of conductor, with about 37% of the current density at a distance of $\delta$ from the edge of the conductor. This depth ($\delta$) is dependent on the resistivity ($\rho$) and the magnetic permeability ($\mu$) of the material and varies based on the angular frequency ($\omega$) of the AC current flowing through it.

skin effect explanation

A main current $I$ flowing through a conductor induces a magnetic field $H$. If the current increases, as in this figure, the resulting increase in $H$ induces separate, circulating eddy currents $I_W$ which partially cancel the current flow in the center and reinforce it near the skin.

skin depth equation

This equation is only accurate for frequencies below $\frac{1}{\rho ϵ}$, which is $\approx {10}^{18}$ Hz in copper wire.

where
$\delta =$ the depth at which about 37% $\text{or}\left(\frac{1}{e}\right)$ of the current in the conductor is concentrated, as measured from the outer edge.
$\rho =$ the resistivity of the material
$\mu =$ the magnetic permeability of the material
$ϵ=$ the permittivity of the conductor
The angular frequency of the current, $\omega =2\pi f$ where $f$ is the frequency in Hz.

practical limitations from the skin effect

the impedance $(Z)$ of a wire increases dramatically with an increase in the frequency of an AC current. For a conductor with a diameter $(D)$ which is much greater than the skin depth $(\delta )$, the effective cross sectional area of is approximately that of a hollow tube with a wall thickness of $\delta$.

$\therefore$ you can approximate the effective resistance $(R)$ of a wire a given length $(l)$ and resistivity $(\rho )$ as:

The last column in the table below shows the approximate frequency for which the skin depth in a solid core AWG annealed copper wire radius of the wire.
I.e. at or above the ${\delta }_{max}$ frequency, the #skin effect becomes a factor in the impedance (or effective resistance) of the wire.
Below this frequency, the skin effect will have a negligible impact on the observed resistance.

The ${\delta }_{max}$ equation and constants (as derived from the approximate #skin depth equation):

where:
$d=$ wire diameter
${\rho }_{cu}={(58\cdot {10}^6\frac{S}{m})}^{-1}$ the resistivity of annealed copper
${\mu }_0=4\pi \cdot {10}^{-7}$ vacuum permeability
${\mu }_r=0.999994$ the relative permeability of copper