Research on the Derated Power Data Identification Method of a Wind Turbine Based on a Multi-Gaussian–Discrete Joint Probability Model

. 2022 Nov 17;22(22):8891. doi: 10.3390/s22228891

Algorithm 1 Wind turbine derated power operation data outlier detection

Require: the sample set of turbine output power and nacelle wind speed pair

{(x^{(1)}, y^{(1)}), \dots, (x^{(m)}, y^{(m)})}

, discretized wind speed interval number

J = 50

, wind turbine theoretical power curve function

P = f (v)

, probability threshold

θ

.
1. Initialize the model parameters to obtain the optimal power level number

K

and the initial values of the mixed probability model parameters

α^{(0)}, σ^{(0)}, ψ^{(0)}, ϕ^{(0)}

.
2. While

α, σ, ψ, ϕ

have no convergence. Do
3. E-step: For each sample

i

and the derated power

k

,
calculate

w_{k}^{(i)} = \frac{p_{X | Y Z} (x^{(i)} | y^{(i)}, k; α, σ) p_{Y} (y^{(i)}; ψ) p_{Z} (k; ϕ)}{\sum_{k = 1}^{K} p_{X | Y Z} (x^{(i)} | y^{(i)}, k; α, σ) p_{Y} (y^{(i)}; ψ) p_{Z} (k; ϕ)}

.
4. M-step: Update parameters
5.

α_{q} = \frac{\sum_{i = 1}^{m} w_{q}^{(i)} x^{(i)} f (y^{(i)})}{\sum_{i = 1}^{m} w_{q}^{(i)} f^{2} (y^{(i)})}

σ_{p q}^{2} = \frac{\sum_{i = 1}^{m} w_{q}^{(i)} I (y^{(i)} \in V_{p}) (x^{(i)} - α_{q} f {(y^{(i)})}^{2}}{\sum_{i = 1}^{m} w_{q}^{(i)} I (y^{(i)} \in V_{p})}

ϕ_{q} = \frac{1}{m} \sum_{i = 1}^{m} w_{q}^{(i)}

ψ_{p} = \frac{\sum_{i = 1}^{m} \sum_{k = 1}^{K} I (y^{(i)} \in V_{p}) w_{k}^{(i)}}{m}

9. End while.
10. Calculate the posterior probability

p_{Z | X Y} (k | x^{(i)}, y^{(i)})

of each sample

i

under each derated power state

k

according to iterative parameters.
11. Calculate the derated power level

c^{(i)} = \arg \max_{k} p_{Z | X Y} (k | x^{(i)}, y^{(i)})

to which the sample

i

belongs.
12. For each derated power

k

, the sample set whose posterior probability is lower than the threshold

{(x^{(i)}, y^{(i)}) | c^{(i)} = k, p_{Z | X Y} (k | x^{(i)}, y^{(i)}) < θ}

is marked as outlier data.