# Inverter Efficiency

Inverter efficiency is usually the most significant cause of inverter-related energy losses. Inverter efficiency data are supplied in two forms:

**California Energy Commission (CEC) measured efficiency curves.**These are typically measured at three input voltages and at six power levels between 10% and 100% of the rated maximum power.In this case, the voltage at which these efficiencies apply will probably not be specified but can be assumed to be the voltage at which the inverter achieves its highest efficiency.*Maximum*and*Weighted*efficiencies (including whether these are European or CEC values).

A function giving inverter efficiency as a function of DC Power and DC Voltage is fitted through these data as described in Inverter Efficiency Model. We denote the power consumed by the inverter as \(DP_{\text{inv}}(V_{\text{DC}},P_{\text{DC}})\). Note that where maximum and weighted efficiencies only are available, inverter power consumption will be evaluated as a function of \(P_{\text{DC}}\) only. Inverter AC Power is the DC Power minus power consumption, and this is compared to the Inverter rated AC power \(P_{\text{inv,ACmax}}(T_{\text{a}}(t))\).

After the inverter's operational envelope has been considered as described in the first four sub-sections, the power available at the inverter's inputs is equal to \(MPP(IV_{\text{array,PDCmin}}(t))\). If no operating point is available, the inverter will shut down and the efficiency calculation described in this section is not required (see Night Time Tare Loss).

The power output from the inverter at time \(t\) is therefore the input power minus power consumed at that power and the operating voltage:

$$P_{\text{inv}}\left( t \right) = \text{MPP}\left( IV_{array,PDCmin}\left( t \right) \right) - \Delta P_{\text{inv}}(MPP_ V(IV_{array,PDCmin}(t)),\ MPP(IV_{array,PDCmin}(t)))$$

Here, *MPP_V* denotes the voltage at the maximum power point of the specified IV curve.

Hence the Inverter Efficiency Effect for a specific inverter at time *t*:

$$\Delta_{inv,eff}\left( t_{\text{operating}} \right) = \left( \frac{P_{\text{inv}}\left( t_{\text{operat}i\text{ng}} \right)}{\text{\ MPP}\left( IV_{array,PDCmin}\left( t_{\text{operating}} \right) \right)} - 1 \right) \bullet 100%$$

The Inverter efficiency Effect for a PV plant can be averaged over longer periods can be calculated as:

$$\Delta_{inv,eff} = \left( \frac{\sum_{i = 1}^{N_{\text{arrays}}}{\sum_{t}^{}{P_{\text{inv}}(t_{\text{operating}})}}}{\sum_{i = 1}^{N_{\text{arrays}}}{\sum_{t}^{}{MPP(IV_{array,PDCmin}(t_{\text{operating}}))}}} - 1 \right) \bullet 100%$$

The above calculations apply only at times when the inverter can operate, and when calculating average inverter efficiency over longer periods, it is important that **only periods when the inverter is able to operate are included in the calculation**. Excepting faults, reasons the inverter would be unable to operate include:

Night time conditions indicated by \(G_{\text{h}}\) equal to zero. It is not necessary to carry out any of the above modelling under these circumstances.

No available operating point for the array within the inverter's envelope.

In both cases, the inverter will shut down and not generate any power; it will instead consume a constant amount of power, known as the "Night-time Tare Loss", and this is quantified separately, as described in Night Time Tare Loss below.