Method of wind farm calculation in energyPRO
The wind farm model in energyPRO covers three different cases.
- Annual production calculated
- Power curve used directly
- Power curve is scaled to another level
- Fixed annual production (wind speed is scaled)
Definitions
| Variable | Units | Description |
|---|---|---|
| \(WS_m (t)\) | (m/s) at time t | Wind speed measured |
| \(WS_C (t)\) | (m/s) at time t | Wind speed calculated |
| \(H_m\) | (m) | Height of measurements |
| \(H_h\) | (m) | Hub Height |
| \(\alpha\) | Hellmann coefficient | |
| \(m_f\) | Wind speed modification factor | |
| \(PC(WS_c (t)\) | then power from the power curve based on the calculated wind speed at hub height and linear interpolation on power curve. | |
| \(P_{MaxPC}\) | Max power value found in power curve | |
| \(P_{Max}\) | Max Power stated | |
| \(P(t)\) | Production at time t | |
| \(P_{annualDesired}\) | (MWh) | Annual production desired |
| \(P_{annualCalc}\) | (MWh) | Annual production calculated |
Mathematical description
Wind speed at hub height
Calculated wind speed at hub height in cases 1a and 1b.
\((1) WS_c (t) = WS_m (t) * \left(\frac{H_h}{H_m}\right)^\alpha\)
Calculated wind speed at hub height in case 2.
\((2) WS_c (t) = WS_m (t) * \left(\frac{H_h}{H_m} \right)^\alpha * m_f,\)
Where the modification factor is found through iterations.
Calculation of production at time t
\((3) P(t) = PC(WS_c (t))\) (Case 1a)
\((4) P(t) = PC(WS_c (t)) * P_{max} / P_{maxPC}\) (Case 1b)
\((5) P(t) = PC(WS_c (t))\) (Case 2)
Where \(PC(WS_c (t))\) return the power from the power curve based on the calculated wind speed at hub height and linear interpolation on power curve.
Calculation of modification factor
\((6) P_{annualCalc} = \sum_{t=0}^{t=H_{Year}} PC(WS_c (t)) * \bigtriangleup T\)
Where
\(WS_c (t) = WS_m (t) * \left(\frac{H_h}{H_m} \right) ^\alpha * m_f\)
Start guess \(m_f = 1\)
In each Iteration is the annual production calculated (6) and compared with the desired value
If \(P_{annualCalc} > P_{annualDesired}\) then decrease \(m_f\)
If \(P_{annualCalc} < P_{annualDesired}\) then increase \(m_f\)
This is repeated until
\(P_{annualCalc} \approx P_{annualDesired}\)
then \(m_f\) is found.