On-line status assessment of wind turbines based on improved fuzzy comprehensive evaluation method

2.1 Dynamic inferior degree and its calculation method

An equation for calculating dynamic inferior degree of partial small assessment indices is as follows: g ( x ) = { 0 , x p < x min x p - x min x max - x min , x min < x p < x max 1 , x p > x max }(1)

where x_max is the maximum value and x_min is the minimum value within the range of assessment indices, respectively; x _p is the predictive value, which is superposed by the current value and the value of parameters variable trend. Because the calculation of dynamic inferior degree synthetically considers the current value of assessment indices and variable parameter trend, the dynamic inferior degree can describe wind turbine operating conditionsdynamically.

In Equation (1), the key to calculate the dynamic inferior degree is to predict the variable trend of parameter accurately. Considering the amount of measured data is large, both the prediction precision and the computation complexity should be taken into account. The state transfer matrix of Markov chain model can predict the state of the next moment based only on the state of the current moment, which has already been successfully used in data tendency forecasting [2, 9]. Therefore, the Markov chain model was chosen to predict the variable parameter trend.

Two given conditions must be specified when the Markov chain model is used to predict the variable parameter trend. The first one is the variation of the current moment. The second one is the state transfer matrix P . Using the SCADA data of wind turbines, the specific steps of prediction were as follow:

The SCADA historical data series of each assessment index were obtained;

The element p _ij can be calculated as follows: p ij = m ij / m i(3)

where m _ij is the number of state s _i transfer to state s _j ; and m _i is the number of occurrences of state s _i .

The status of s _i was determined based on the current parameter variation x _t . Then, the value of x_t+1 was calculated by multiplying the median of the interval number and transition probability p _ij when s _i transferred into the possible status s _j in the next moment. The x_t+1 was as follows:

As shown in Table 1, the values of dynamic inferior degree and the traditional inferior degree were similar from T1 to T3 due to the continuous and slow changes. However, since T4, the generator drive end bearing temperature increased rapidly and the dynamic inferior degree was higher than that of the traditional inferior degree. Obviously, after synthetically considering the current value and its variable trend, the dynamic inferior degree was more effective in describing the abnormal status of the wind turbine.

U was set as a quantitative domain represented by precise values and X ⊆ U. C was the qualitative concept of domain U. If x ∈ X was a random occurrence of qualitative concept C and it satisfied the following two conditions in the meantime, then the distribution of x on domain U was called a normal cloud.

x ∼ ^N(Ex,En′2), where E n ' ~ N ( E n , H e 2 ) ;

In Equation (5), the E _x is the point which best represents the qualitative concept. Entropy E _n synthetically measures the fuzzy degree and probability of qualitative concept and reflects its uncertainty. The excess entropy He reflects the cohesiveness of cloud drops in the data space and indirectly characterizes the cloud’s discrete degree and thickness [15]. The assessment levels can be divided as S = ( S 1 , S 2 , S 3 , S 4 ), which corresponds to four normal clouds C _i  = (C₁, C₂, C₃, C₄). The calculation method of the numerical characteristics are shown in Table 2.

In Table 2, a, b and c denote the limiting values of dynamic inferior degree intervals. According to the maintenance experiences, the corresponding intervals between dynamic inferior degree and assessment levels were set as S₁[0, 0.2), S₂0.2, 0.5), S₃0.5, 0.8) and S₄0.8, 1.0], which meant a = 0.2, b = 0.5 and c = 0.8 in Table 2. q is generally regarded as a constant and can be adjusted based on fuzziness and randomness. In this paper, q was set as 0.005 after repeated testing.

According to the numerical characteristics shown in Table 2, four normal cloud models of assessment levels were generated, as shown in Fig. 1.

After taking the dynamic inferior degree g of assessment indices into the normal cloud model, the cloud membership degree r i ' of each assessment level was obtained. Its equation was as follows:

r i ' = exp ( − ( g − E x i ) 2 2 E n i ′ 2 )(6)

Although the cloud membership degree obtained had minute random variations, it tended to be stable. As such, the average r _i of ten calculation results of cloud membership degree was taken in this paper. Its equation was as follows: r i = ∑ k = 1 10 r ik ′ / 10(7)

By combining the normal cloud model with the fuzzy comprehensive evaluation method, a novel on-line status assessment method for wind turbines was proposed. The specific flow chart is shown inFig. 2.

The assessment system was divided into three layers. Firstly, the assessment object layer was established, which included the on-line operating conditions of the wind turbines. Then, the subsystems were established, including a generator system (U₁₁, drive end bearing temperature; U₁₂, non-drive end bearing temperature; U₁₃, winding temperature; U₁₄, cooling air temperature; U₁₅, generator speed), gear box system (U₂₁, input shaft temperature; U₂₂, output shaft temperature; U₂₃, oil temperature; U₂₄, spindle temperature), control system(U₃₁, control room temperature; U₃₂, cabinet temperature; U₃₃, tower bottom temperature), environmental factors (U₄₁, wind speed; U₄₂, average wind speed; U₄₃, environment temperature), and grid-connected factors (U₅₁, voltage of phase A; U₅₂, current of phase A; U₅₃, active power; U₅₄, power factor; U₅₅, frequency). Finally, each subsystem was divided into multiple assessment indices based on the SCADA monitoring items.

3.1 Data analysis

The SCADA data of wind turbines were chosen, as shown in Table 3. The current data series were obtained from the SCADA data, and the predicted data series were the predicted value.

In Table 3, the change trend of the generator driving end bearing temperature (U₁₁) increased significantly from moment T3 to moment T4, which gave the appearance of deterioration. And in the following moments, the deterioration also appeared in the generator winding temperature (U₁₃) and the gearbox input shaft temperature (U₂₁). This showed that there was something wrong with the wind turbine since moment T4 and the monitors should heighten their vigilance to discover the problems.

3.2 Status assessment of wind turbines

Moment T4 was taken as an example, and the processes of status assessment were performed, as listed below.

Determination of weights, the analytic hierarchy process was firstly used to determine the fixed weight, and then the variable weight theory was used to calculate the varied weight based on the fixed weight.

Finally, the assessment result vector of the wind turbine were V = A * R = [ 0.24 0.70 0.05 0 ]. However, considering the complexity of the wind turbine structure and the “short board” effect in the failure mechanism of fuzzy comprehensive evaluation, the deterioration of bottom parameters should be paid careful attention to provide advance warning of a wind turbine’s potential failures in a timely manner. In this case, the strategy of selecting the lowest level with a non-zero value was used to directly consider the membership degree of the bottom parameters.

Taking moment T4 as an example, although the membership degree of “good” and “qualified” was both bigger than the membership degree of “abnormal,” the level of “abnormal” was the lowest. As such, the final assessment result of the wind turbine operating condition was abnormal in T4 based on the proposed strategy, which was the same as the actual condition. This means that monitors should take appropriate measures to prevent further deterioration of the wind turbine.

3.3 Comparative analysis of assessment results

In order to verify the validity of the condition assessment method based on dynamic inferior degree proposed in this paper, it was compared to the method based on traditional inferior degree. The condition assessment results are shown in Table 4, and the tendency chart of conditions assessment results is shown in Fig. 3.

As shown in Fig. 3, according to the proposed method, the status level of the wind turbine in T4 was “abnormal”, and then it became “serious” in T5. However, the status level obtained by the traditional method in T6 was still “qualified”, and the warning signal of abnormal status did not appear until T7. This means that the proposed method can accurately reflect the on-line status of wind turbine in time, so it can perform an early warning to the potential failure of wind turbine.