Driesse et al. 2008 presents an alternative inverter performance model to accurately express the effects of both power level and input voltage on PV inverter efficiency. Its accuracy was evaluated using CEC measurements on inverters of different sizes and designs.
The model is expressed by the following formula:
$$\small p_{loss} = \left (b_{00}+b_{01}\left ( v_{in}-1 \right ) \right )+$$
$$\small \left (b_{10}+b_{11}\left ( v_{in}-1 \right ) \right )\cdot p_{in}+$$
$$\small \left (b_{20}+b_{21}\left ( v_{in}-1 \right ) \right )\cdot{p_{in}}^{2}$$
where:
- $$b$$ is the set of empirical parameters whose values are determined by fitting to test data for each specific inverter model.
- $$p_{in}$$ is the normalized DC power, which is calculated as: $$p_{in}=\frac{P_{dc}}{P_{nom}}$$
- $$v_{in}$$ is the normalized DC voltage, which is calculated as: $$v_{in}=\frac{V_{dc}}{V_{nom}}$$
The nominal values that are used for the normalization are usually the maximum output power rating of the inverter and an input voltage identified as nominal by the manufacturer. The latter may correspond to the voltage where the highest efficiencies are achieved, but this is not a requirement
The Driesse inverter model differs in several ways from the Sandia inverter model:
- It is formulated to calculate power loss rather than efficiency or output power. This leads to smaller relative errors at higher power levels, where accuracy matters most.
- The three main terms of the equation represent measurable physical losses: 1) constant power consumption of auxiliary and drive circuits; 2) switching transition losses and voltage drops in semiconductor junctions; and 3) ohmic or resistive losses. Within each of the three terms the first parameter quantifies the loss when operating at the nominal voltage, and the second parameter specifies the voltage dependency, which is approximated as being linear.
- Normalized power and voltage values are used, which produces parameter values that usually lie in the same numeric range. This allows for meaningful comparison between parameter sets for different inverters, and even makes it possible to reuse parameter sets for inverters that are of the same basic design.
- The recommended form of the model given above uses 6 parameters, but it can be extended to 9 parameters to represent more complex voltage dependencies. On the other hand if no data on voltage dependencies is available it can be used with only 3 parameters.
DOI link to paper.