Power Curve Convolution¶

• Power curves only offer a "suggestion" of what a wind turbine should produce for a given wind speed
• In reality, many stochastics effects are affect this output
• RESkit allows for the creation of a convoluted power curve which takes stochastic responses into account
  • Begins with any general power curve
  • Convolves a gaussian distribution with a wind-speed-dependent standard deviation onto the power curve

Workflow:

1. Import required packages
2. Create power curves
3. Create power curves with standard deviation

In [1]:

import reskit as rk

import reskit as rk

In [2]:

# Power curve from a given capacity (kW) and rotor diameter (m)
pc = rk.wind.PowerCurve.from_capacity_and_rotor_diam(capacity=3000, rotor_diam=140)

pc

# Power curve from a given capacity (kW) and rotor diameter (m) pc = rk.wind.PowerCurve.from_capacity_and_rotor_diam(capacity=3000, rotor_diam=140) pc

Out[2]:

In [3]:

# Power curve from a specific capacity (in W/m2)
#  * As an example, standard deviation should be calculated with: std = ws*0.05 + 0.2

pc2 = pc.convolute_by_gaussian(scaling=0.05, base=0.2)

pc2

# Power curve from a specific capacity (in W/m2) # * As an example, standard deviation should be calculated with: std = ws*0.05 + 0.2 pc2 = pc.convolute_by_gaussian(scaling=0.05, base=0.2) pc2

Out[3]:

In [4]:

import matplotlib.pyplot as plt

%matplotlib inline

plt.figure(figsize=(12, 5))
plt.rc("font", size=18)

pc = rk.wind.PowerCurve.from_capacity_and_rotor_diam(capacity=3000, rotor_diam=140)

plt.plot(
    pc.wind_speed,
    pc.capacity_factor,
    label="Raw Power Curve",
    zorder=3,
    c="k",
    ls="--",
    lw=2,
)

# Standard deviation = base * wind_speed + scaling
pc2 = pc.convolute_by_gaussian(scaling=0.00, base=0.2)
plt.plot(pc2.wind_speed, pc2.capacity_factor, label="std=0.2*ws+0.00")

pc3 = pc.convolute_by_gaussian(scaling=0.00, base=2.0)
plt.plot(pc3.wind_speed, pc3.capacity_factor, label="std=2.0*ws+0.00")

pc4 = pc.convolute_by_gaussian(scaling=0.05, base=0.2)
plt.plot(pc4.wind_speed, pc4.capacity_factor, label="std=0.2*ws+0.05")

plt.legend()
plt.grid()
plt.ylabel("Capacity Factor")
plt.ylabel("Wind Speed [m/s]")

plt.show()

import matplotlib.pyplot as plt %matplotlib inline plt.figure(figsize=(12, 5)) plt.rc("font", size=18) pc = rk.wind.PowerCurve.from_capacity_and_rotor_diam(capacity=3000, rotor_diam=140) plt.plot( pc.wind_speed, pc.capacity_factor, label="Raw Power Curve", zorder=3, c="k", ls="--", lw=2, ) # Standard deviation = base * wind_speed + scaling pc2 = pc.convolute_by_gaussian(scaling=0.00, base=0.2) plt.plot(pc2.wind_speed, pc2.capacity_factor, label="std=0.2*ws+0.00") pc3 = pc.convolute_by_gaussian(scaling=0.00, base=2.0) plt.plot(pc3.wind_speed, pc3.capacity_factor, label="std=2.0*ws+0.00") pc4 = pc.convolute_by_gaussian(scaling=0.05, base=0.2) plt.plot(pc4.wind_speed, pc4.capacity_factor, label="std=0.2*ws+0.05") plt.legend() plt.grid() plt.ylabel("Capacity Factor") plt.ylabel("Wind Speed [m/s]") plt.show()