Sandia Inverter Model

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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:

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

where

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

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

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

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: $P_{AC0}, P_{DC0}, P_{s0}, V_{DC0}, C_0, C_1, C_2, C_3$ .

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 $P_{AC, d, r, k}$ where $d \in {min, nom, max}$ is the DC voltage level, $r \in {0, 0.2, 0.3, 0.5, 0.75, 1.0}$ is the power level, and $k$ indexes the replicated measurements. Similarly denote the DC voltage measurements as $V_{DC, d, r, k}$ and measured efficiency as $\eta_{r, d, k}$ .

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

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

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

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

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

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

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

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

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

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