Wire Sizing and Voltage Drop in Low Voltage Power Systems- Part 1 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. 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 % 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. INSERT CLIP & SAVE AC/DC WIRE SIZE CHART Sizing Example We have a 12 volt system with a total one-way wire run of 40 ft. servicing three 13 watt fluorescent lights and one 20 watt quartz halogen light. Sizing for a 2% voltage drop, what wire size is needed for this circuit? INSERT EQUATION The "calculated VDI" 8.2 is between VDI values 8 and 12 on the Chart. This calls for #8 gauge wire (#12 gauge wire could be used in a 24V system). Since the "calculated VDI" is not much greater than 8, we may consider sizing-down and accepting a slightly greater voltage drop. This would be sensible because #8 gauge wire is expensive and difficult to work with. Or we might consider putting these loads on two circuits--compare wire and labor costs. If on the average only one of the fluorescents and the quartz halogen are on at the same time, we could size for this load, being sure not to exceed the wire ampacity for the total of all loads. In this case #12 gauge wire would be adequate. This is an example of some of the considerations and tradeoffs that will be discussed in Part II of the article. Determining Voltage Drop In Existing Circuits You may wish to know how efficient an already existing circuit is in terms of voltage drop. There is an easy way to measure this. With a "multi-tester" or voltmeter, measure the "source voltage" for the circuit and the "load Voltage" at the end of the line, then compare the difference. Do this while the circuit is powered and all the loads are on: INSERT GRAPHIC Now calculate the % voltage drop for the circuit by-- INSERT EQUATION This method will total ALL voltage drops in the circuit caused by wire, connections, and switches. Because the amperage is diminished beyond each load in the circuit, the true % voltage drop will be somewhat less than is calculated in the above equation. An easy way to calculate the wire voltage drop WITHOUT any measurements, if you have the information needed about the circuit, is to solve for % Voltage Drop using the VDI equation-- INSERT EQUATION Look for Part II of the article in the next issue dealing with: PRACTICAL APPLICATIONS OF VOLTAGE DROP AND WIRE SIZE. NERD'S CORNER Wire Size Chart Derivation Voltage drop is caused by the electrical resistance (Ohms) of a conductor. This in turn is determined by resistance of the conductor material and the cross sectional area and length of the conductor. The nominal resistance for copper wire is 10.7 Ohms (17.0 Ohms for aluminum wire) per foot of wire one circular mil in cross sectional area. Therefore the resistance of a copper wire run may be determined by-- INSERT EQUATION From Ohm's Law, the voltage drop in a conductor is E = I X R. Upon substituting equation (a) for R, the voltage drop in a circuit may be calculated by-- INSERT EQUATION Percent voltage drop can be calculated by-- INSERT EQUATION By rearranging this equation we can calculate the appropriate wire size (circular mils) for a given % voltage drop and current-- INSERT EQUATION This equation may be reduced to-- INSERT EQUATION We use the American Wire Gauge (AWG) system which has 40 gauges ranging from the largest gauge 0000 (0.4600 in. diameter) to the smallest #36 (0.005 in. diameter). The ratio of any gauge diameter to the diameter of the next smallest gauge is-- INSERT EQUATION Using this relationship we can calculate the diameter (inches) of every gauge. The cross sectional area of the gauges in circular mils is calculated by-- INSERT EQUATION Now, recalling the equation-- INSERT EQUATION and rearranging it we obtain-- INSERT EQUATION If we solve c-mils/2140 for each gauge we come up with a value, which we shall denote the Voltage Drop Index (VDI), for each gauge. Now, to size wire for a particular circuit, we calculate VDI for this circuit using-- INSERT EQUATION and compare this "calculated VDI" to the VDI's for the standard gauges in the Chart and come up with the appropriate wire gauge for the acceptable % voltage drop. END OF DERIVATION Access Dr, John Davey is a biology/ecology professor and jack-of-all-trades at Flowlight Solar Power. He is a graduate of the Colorado Mountain College Solar/PV program. Windy Dankoff is owner of Flowlight Solar Power. Flowlight supplies remote home PV systems and manufactures "Flowlight Solar Pumps". Windy began working with wind generators in 1975 and PV in 1979. He has contributed 12 articles to Home Power since issue #2.