# DC Collectors

The next step in the analysis is to calculate the power lost to resistive (ohmic) losses in the DC collection network between the strings and inverter, and the effects of this on the system voltage.

The user will input a power effect factor for the string-to-inverter wiring, representing the ohmic power effect in % when the load on the system is equal to the array nameplate capacity (\(P_{\text{array,stc}}\) in kWp), as it is always a loss, this gain percentage should always be negative. This gain factor may be specific to each array. Internally we multiply by -1 to convert it to a loss, scale it to a fraction of 1 and denote it \(L_{\text{r,array,stc}}\). In the calculation this loss factor is converted into an equivalent resistance for each array, denoted \(R_\text{collectors}\), by solving the loss equation:

$$L_{\text{r,array}} = \frac{\text{Voltage loss in collectors}}{\text{Voltage produced by strings}}$$

at STC, this gives:

$$L_{\text{r,array, stc}} = \frac{V_{\text{collectors,stc}}}{V_{\text{array,stc}}} = \frac{I_{\text{array,stc}} * R_{\text{collectors}}}{V_{\text{array,stc}}}$$

$$\implies R_{\text{collectors}} = L_{\text{r,array, stc}} \bullet \frac{V_{\text{array,stc}}}{I_{\text{array,stc}}}$$

It is this collector resistance that is then used on each time-step to calculate the effect of the ohmic loss on the array output. This is done by adding the resistance across the whole the IV curve, before the MPP is found. We map each voltage in the IV curve:

$$V_{\text{array}} \to V_{\text{array}} - I_{\text{array}} \bullet R_{\text{collectors}}$$

$$IV_{\text{array, collectors}}\left( t \right) = \left[ I_{\text{array}}(n), V_{\text{array, collectors}}(n) \right] = \left[ I_{\text{array}}(n), V_{\text{array}}(n) - I_{\text{array}}(n) \bullet R_{\text{collectors}} \right]$$

Where the square brakets denote the collection of I-V points in the curve, and \(n\) denothes the \(n^{\text{th}}\) I-V point in the collection.

The ohmic loss affects the IV curve as seen by the inverter. It affects which voltage is selected by the MPP search algorithm in the inverter, so we recalculate the array MPP:

$$P_{\text{array,collectors}}\left( t \right) = \text{MPP}\left( IV_{\text{array, collectors}}\left( t \right) \right)$$

Note: as the fact that the collector loss affects the MPP voltage, the loss equation used to derive \(R_{\text{collectors}}\) has a small error. The user will find that the collector loss under STC conditions is not exactly the value given by the user.