The Sandia Inverter Model provides a means to predict AC output power ($P_{AC}$) from DC input power ($P{_{DC}}$).

The form of the model is as follows:

$P_{AC}=\left&space;\{&space;\frac{P_{AC0}}{A-B}&space;-C\left&space;(&space;A-B&space;\right&space;)\right&space;\}\left&space;(&space;P_{DC}-B&space;\right&space;)+C\left&space;(&space;P_{DC}-B&space;\right&space;)^{2}$

where

$A=P_{DC0}\left&space;\{&space;1+C_{1}\left&space;(&space;V_{DC}-V_{DC0}&space;\right&space;)&space;\right&space;\}$,

$B=P_{s0}\left&space;\{&space;1+C_{2}\left&space;(&space;V_{DC}-V_{DC0}&space;\right&space;)&space;\right&space;\}$, and

$C=C_{0}\left&space;\{&space;1+C_{3}\left&space;(&space;V_{DC}-V_{DC0}&space;\right&space;)&space;\right&space;\}$

Parameters:

• $V_{DC}$ : DC input voltage (V).  This is typically assumed to be the array’s maximum power voltage.
• $V_{DC0}$ : DC voltage level (V) at which the AC power rating is achieved at reference operating conditions.
• $P_{AC}$ : AC output power (W)
• $P_{AC0}$ : Maximum AC power rating for inverter at reference conditions (W).  Assumed to be an upper limit.
• $P_{DC0}$ : DC power level (W) at which the AC power rating is achieved at reference operating conditions.
• $P_{s0}$ : DC power required to start the inversion process (W)
• $C_{0}$ : Parameter defining the curvature of the relationship between AC output power and DC input power
• $C_{1}$ : empirical coefficient allowing $P_{DC0}$ to vary linearly with DC-voltage input, default value
is zero, (1/V)
• $C_{2}$ : empirical coefficient allowing $P_{s0}$ to vary linearly with DC-voltage input, default value
is zero, (1/V)
• $C_{3}$ : empirical coefficient allowing $C_{0}$ to vary linearly with dc-voltage input, default value is
zero, (1/V)

#### Algorithm to estimate model parameters from inverter efficiency curves

The Sandia inverter model requires eight parameters: $P_{AC0},&space;P_{DC0},&space;P_{s0},&space;V_{DC0},&space;C_0,&space;C_1,&space;C_2,&space;C_3$.

Given measurements of an inverter’s AC power, DC voltage and efficiency, parameters for the Sandia inverter model are determined by the following algorithm. Denote the AC power measurements by $P_{AC,&space;d,&space;r,&space;k}$ where $d&space;\in&space;{min,&space;nom,&space;max}$ is the DC voltage level, $r&space;\in&space;{0,&space;0.2,&space;0.3,&space;0.5,&space;0.75,&space;1.0}$ is the power level, and $k$ indexes the replicated measurements. Similarly denote the DC voltage measurements as $V_{DC,&space;d,&space;r,&space;k}$ and measured efficiency as $\eta_{r,&space;d,&space;k}$.

Step 1: Set $P_{AC0}$ equal to the inverter’s AC rating.

Step 2: Calculate $P_{DC,&space;d,&space;r,&space;k}&space;=&space;\frac{P_{AC,&space;d,&space;r,&space;k}}{\eta_{d,&space;r,&space;k}}$

Step 3: For $d&space;\in&space;{min,&space;nom,&space;max}$ :

Step 3a: Calculate $\bar{V}_{d}&space;=&space;\mathrm{Average}_{r,&space;k}(&space;V_{DC,&space;d,&space;r,&space;k})$

Step 3b: Obtain coefficients $a_d,&space;b_d,&space;c_d$ for a quadratic fit by linear regression using the data indexed by $r,&space;k$ : $P_{AC,&space;d,&space;r,&space;k}&space;=&space;a_d&space;P^2_{DC,&space;d,&space;r,&space;k}&space;+&space;b_d&space;P_{DC,&space;d,&space;r,&space;k}&space;+&space;c_d$

Step 3c: Set $C_{0,d}&space;=&space;a_d$

Step 3d: Solve each of the following equations to obtain $P_{DC0,&space;d},&space;P_{s0,&space;d}$:

$a_d&space;P^2_{DC0,&space;d}&space;+&space;b_d&space;P_{DC0,&space;d}&space;+&space;c_d&space;-&space;P_{AC0}&space;=&space;0$

$a_d&space;P^2_{s0,&space;d}&space;+&space;b_d&space;P_{s0,&space;d}&space;+&space;c_d&space;=&space;0$

Step 3e: Denote $X_d&space;=&space;\var{V}_d&space;-&space;\bar{V}_{nom}$ and use linear regression on the data indexed by $d$  to find coefficients $\beta_1,&space;\beta_0$  for each of

$P_{DC0,&space;d}&space;=&space;\beta_{DC,&space;1}&space;X_d&space;+&space;\beta_{DC,&space;0}$

$P_{s0,&space;d}&space;=&space;\beta_{s,&space;1}&space;X_d&space;+&space;\beta_{s,&space;0}$

$C_{0,d}=\beta_{C,1}X_d+\beta_{C,0}$

Step 4: Extract parameters as:

$P_{DC0}&space;=&space;\beta_{DC,&space;0}$

$V_{DC0}&space;=&space;\bar{V}_{nom}$

$P_{s0}&space;=&space;\beta_{s,&space;0}$

$C_0&space;=&space;\beta_{C,&space;0}$

$C_1&space;=&space;\frac{\beta_{DC,&space;1}}{\beta_{DC,&space;0}}$

$C_2&space;=&space;\frac{\beta_{s,&space;1}}{\beta_{s,&space;0}}$

$C_3&space;=&space;\frac{\beta_{C,&space;1}}{\beta_{C,&space;0}}$