How to apply Kirchoof’s laws in Solar Design

In this blog I am going to explain how to apply Kirchoff’s laws to solar design. I will assume you are familiar with Ohm’s Law. These are powerful tools applicable to small residential systems as well as to utility scale projects.

They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of Maxwell.

Kirchoff’s Current Law (KCL): The algebraic sum of currents in a network of conductors meeting at a point is zero.

Image result for kirchoff's laws

Kirchoff’s Voltage Law (KVL): The directed sum of the electrical potential differences (voltage) around any closed network is zero.

figure535

These laws may sound very fancy in the beginning so I will try to explain them with a small commercial real world application.

Lets assume that we have the folowing PV system

  • 2 arrays of 266 modules each using Solarworld 230 Watts poly
  • System size is 266 x 2 x 230 = 122,360 watts or 122.36 Kw.
  • 1 PVPowered 100Kw transformer base inverter connected to a load side panel at 480V, 3P facility.
  • We will also assume string size of 14 modules, and 19 strings per array. Each array will have one combiner box. The setup is shown in Fig. 1 below.
example
Fig. 1: Single Line Diagram

String Level: Here we will apply the KVL to determine the string size. Since I am not providing temperature information, we will just do a rough calculation using the open circuit voltage (Voc) of one solar module. First we will assume that the inverter is 600Vdc rated and we all know that a string is composed by an specific number of solar modules in series. Checking the data sheet of the SW 230w poly module (Fig. 2), we can see that Voc = 36.9V, if we do the algebraic sum we get a string Voc of 516.6V which is less than 600V (Fig. 3). Again to get the exact string size we need the min ambient temperature where the modules will be installed. This blog is intended how to apply the KVL and KCL, I will discuss string sizing on a different blog.

230poly
Fig. 2: SW 230W Poly data sheet
str
Fig. 3: 1 String of 14 modules

Combiner Box Level: Let’s say we need to determine the Amp rating of the combiner boxes shown in Fig.1. We can apply the KCL using the Isc (8.25A) of the module. As depicted in Fig.1 we have 19 strings on each combiner, so the algebraic current sum is 156.75A, then we need to apply NEC factors:

(Equipment rated for continuous use) 1.25x 156.75A = 195.93A: 200A combiner

(Equipment not rated for continuous use) 1.56x 156.75A= 244.92A: 400A combiner

Inverter Level: Here we will apply the KCL again. The total input current will be algebraic current sum of the 2 combiner boxes output current. Here we will use the current at normal operating conditions which is the Imp. So doing the math for each combiner we get 7.72A x 19 = 146.68A. The total input current is 146.68A x 2 = 293.36A

Note that no fuses are needed at the input of the inverter because 2 identical “big” strings are connected to the same node input. If more than 2 combiners are used then fusing is also required at the inverter.

 

 

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