When I installed a Enphase microinverter based ground-mount PV system for my home, I had to be keenly aware of the voltage drop (really voltage rise) from my array to my main load center. My array is in my back yard, approximately 150 feet from my load center. A run of wire this long will have significant resistance and corresponding voltage drop. This post details what voltage drop is and how to perform calculations to quantify and control voltage drop.

What is voltage drop (or voltage rise)? All real-world conductors, including copper, have electrical resistance (R) which is defined as the ratio of voltage divided by current (V/I). This relationship is called Ohm’s law.

`R = V/I`

The SI units of resistance, voltage, and current are ohms (Ω), volts (V), and amperes (A), respectively. Resistance is caused on the microscopic level by collisions between drifting electrons (the current) and the atoms in the conductor. This causes some of the energy of the electrons to be dissipated as heat. Over a wide range of temperatures, the resistance of a copper wire is fairly constant so the more current, the more heat dissipated. Too much current and the wire’s insulation will melt and a fire can be started. This is why household wiring has over-current protection supplied by circuit breakers.

Using Ohm’s law, the voltage drop along a wire can be calculated if the resistance supplied by the wire and the current flowing through the wire are known.

`V = IR`

In most situations, the maximum current to be generated by a PV system is known. For example, my system is designed to output 240 V and is composed of 10 235 watt panels connected to 10 Enphase M215 microinverters. According to the Enphase datasheet, each inverter produces a nominal current of 0.9 A at peak generation. Therefore, my entire system will produce up to approximately 9 A.

When designing a microninverter PV system, it is important to realize that the microinverters are designed to sense and match the grid-supply voltage at the point-of-entry to the home, which is usually your main load center. At the same time, the microinverters are current sources that are designed to generate current over a range of voltages to compensate for voltage drop from the panels to the grid-power point-of-entry. However, the range of achievable voltages is limited. For my 240 V system, the microinverters can produce up to 10% more voltage (264 V) to 12% less voltage (211 V). If to compensate for voltage drop the inverters have to produce more than 264 V to match the grid voltage at the point of entry, they will not function. They will automatically turn themselves off and you will have a really expensive lawn sculpture. This is why being aware of voltage drop is so important.

Now that you know what voltage drop is (again, we are really dealing with voltage rise since the microinverter is a current source outputing higher voltage then the voltage at the point-of-entry) the goal is to select a conductor that minimizes this voltage change from panel to load center in a cost effective way. The amount of resistance supplied by a wire depends on three things, what material it is made of, how long it is, and it’s diameter. Resistance increases as length increases and decreases as diameter increases. Therefore, in general, you will need a thicker wire the longer the run. But of course, the thicker the wire, the more expensive it is.

Wire size is represented by a number called gauge or AWG for american wire gauge. Gauge is like shoe size in that the gauge number has no direct relationship to the diameter in standard units. In fact, the larger the gauge the smaller the diameter. The table below summarizes the properties at 75 degrees centigrade of the five gauges of coated copper wires (both solid and stranded) most often encountered in household wiring. This data is taken from the 2008 edition of the national electrical code (NEC 2008, Chapter 9, Table 8). The NEC code is updated every few years but this data is unlikely to every change significantly.

Size (AWG) | Type | Diameter (in) | Resistance/Length (ohms/ft) |

14 | Solid | 0.024 | 0.00319 |

14 | Stranded | 0.024 | 0.00326 |

12 | Solid | 0.030 | 0.00201 |

12 | Stranded | 0.030 | 0.00205 |

10 | Solid | 0.038 | 0.00126 |

10 | Stranded | 0.038 | 0.00129 |

8 | Solid | 0.049 | 0.000786 |

8 | Stranded | 0.049 | 0.000809 |

6 | Stranded | 0.061 | 0.000510 |

As a rule of thumb, the voltage rise from the point-of-entry to your inverters due to the resistance of your wires should be no more than about 2%. This leaves an adequate margin for other system components like AC safety switches circuit breakers and trunk cables that will also contribute electrical resistance. For my system I decided to use 8 gauge stranded copper wire. Below is an example calculation showing why I arrived at this decision.

Eight gauge stranded copper wire has a resistance per length of 0.000809 ohms/ft. The run to my panels from my main load center is 150 ft so the total length of the circuit (both ways) is twice this distance (300 ft). This is an important fact. The total length of the circuit is what matters and this is double the length of the run. Based on these parameters the total resistance of my run is as follows.

```
Total Resistance = Resistance/Length x Length =
0.000809 ohms/ft x 300 ft = 0.2427 ohms
```

The maximum current flowing through my PV circuit (as discussed above) is 9 A. Therefore, ohms law tells me the voltage rise from my load center to panels is a follows.

` Voltage Rise = Current x Resistance = 9 A x 0.2427 ohms = 2.184 V`

This is well within 2% of my system voltage of 240 V. I could have probably gotten away with a 10 gauge run but choose to use thicker copper even though it costs more copper because I wanted to maximize the amount of solar power reaching my house. I didn’t want my free solar energy heating the ground. The amount of power wasted in transmission to my house is easily calculated using the following formula.

` Power Wasted = Voltage Rise x Current = 2.184 V x 9 A = 19.66 W`

When my system is running at peak capacity, this is less 1 % of the power my PV system generates.

I hope this post help explain the basics of voltage drop/rise and why it is important to consider when designing your home PV system. Good luck.