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Wire Sizing and Voltage Drop in Low Voltage Power Systems
John Davey and Windy Dankoff
Properly sized wire can make the difference between inadequate and full charging of your energy system, between dim and bright lights, and between feeble and full blast
performance of your tools and appliances. Even wiring that is slightly undersized can cheat you out of a major portion of your system's energy.
Designers of low voltage systems are often confused by the implications of voltage drop and wire size. In conventional home electrical systems (120/240 volts ac), wire is sized according to its safe amperage carrying capacity know as "ampacity". The overriding concern here is fire safety. However in low voltage (12/24/48 volts DC) systems, sizing for larger wire is usually necessary to minimize power loss due to voltage drop before increased wire size is required for amperage safety.
Typically, low voltage systems are seen in Alternative Energy (AE) home systems and Recreational Vehicle (RV) systems. The heart of these systems is DC power, because DC electrical power can be stored in batteries. With photovoltaic systems, the electrical power produced is also DC. DC systems are primarily low voltage because most of the DC lights and appliances have traditionally been built for the vehicular market, which is typically 12 or 24 volts. There is also increased fire danger with high voltage DC because of the high potential for arcing in switches and in poor electrical connections. DC at high voltage also has high shock hazard (more than at equivalent ac voltages).
Voltage Drop is caused by a conductor's electrical resistance (Ohms) and may be calculated according to Ohm's Law--
(1) Voltage Drop (Volts) = Electrical Resistance (Ohms) X Current (Amps)
Power Loss is calculated by--
(2) Power Loss (Watts) = Voltage Drop (Volts) X Current(Amps)
By substituting the Voltage Drop Equivalence from equation (1) into equation (2), we find--
Power Loss (Watts) = Ohms X Amps2
If we have a 12V system with a 100 ft. wire run of 12 gauge wire (0.33 Ohms) and a 72 watt load, there will be a 6 amp current (Amps = Watts/Volts) and a power loss of 12 watts (0.33 Ohms X 6 Amps2). If we converted this system to 24V, we would have a current of 3 amps and a power loss of 3 watts. The implication here is that by DOUBLING the system voltage, power loss is reduced by a FACTOR OF FOUR. Or for no increase in power loss, we can use ONE FOURTH the wire size by doubling the voltage. This is why the trend in AE full home systems with DC circuits is towards 24V instead 12V systems. It is also why it is important to reduce the current by using efficient loads and putting fewer loads on the same circuit. Likewise, reducing wire resistance by using large wire and shorter wire runs is important. All of these are particularly critical with AE systems, where cost per kilowatt of electrical power may be several times that of "Grid" supplied electrical power.
32 Home Power #13 • October/November 1989
Wire Size Chart
Because of the significance of voltage drop in low voltage electrical systems, we have developed an easy-to-use wire sizing chart. Most such charts published assume a 2% or 5% voltage drop for 12 and 24 volt systems and result in pages of numbers. This new chart works for any voltage and accommodates your choice of percentage voltage drop. You'll find it the handiest chart available. The chart applies to typical DC circuits and to simple ac circuits (refer to footnote on Wire Size Chart).
We recommend sizing for a 2-3% voltage drop where efficiency is important. We shall discuss this as it applies to specific loads in greater detail in Part II of the article.
ac/DC Wire Size Chart
❶ Calculate Voltage Drop Index (VDI) VDI = AMPS X VOLTS
% VOLT DROP X VOLTAGE
FEET=One-way Wire distance
% VOLTAGE DROP= Percentage you are willing to accept (e.g. use 2 for 2%) VOLTAGE=Line voltage
❷ Calculate Voltage Drop Index (VDI)
a. Compare the "calculated VDI" with the VDI values for the American Wire Gauge (AWG) sizes in the chart to determine the appropriate wire size.
b. Amperage must not exceed the indicated fire hazard AMPACITY for the wire gauge (set by the National Electric Code).
Aluminum Wire Ampacity
OOOO OOO OO O 2 4 6 8 10 12 14 16
Information applies to DC circuits and ac circuits where Power Factor =1.0 and line reactance is negligible.
For 2-wire circuits. For more complex circuits, refer to an electrical engineering handbook.
We recommend sizing for a 2% to 3% voltage drop where efficiency is important.
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