3.1.1. Hierarchical Real-Time Classification Framework
In the actual dynamic monitoring of the power system, the real-time measurement data transmitted by PMUs to the dispatching and communication center is continuously accumulated, which contains a wealth of dynamic trajectory information of the power grid. Based on the recursive structure of LSTM, a sliding time window is constructed to select the sub-sequences of the real-time disturbed trajectory measurements as the inputs of the classifier, which can realize the continuous hierarchical assessment process. As shown in
Figure 3, it is the active power output data set obtained from generator 30 in the New England 39-bus system under various load levels.
Figure 3a,b respectively correspond to the distribution of data in stable and unstable conditions under different response times, and the data have been normalized.
If the distribution of a feature in two different classes is similar, the correlation between the feature and the predicted target variable is weak. It can be seen from
Figure 3a that the data distributions in stable and unstable conditions are highly similar. It can be seen from
Figure 3a that the data distributions under stable and unstable conditions are highly similar, indicating that the feature has a weak correlation with transient stability in the early stage after fault clearance. In contrast,
Figure 3b shows the distributions of data in two different conditions at the 50th cycle after fault clearance. The comparison shows that the electrical features have strong time-varying characteristics, and as time goes by, the correlation between the features and the transient stability of the system will become stronger. Therefore, in the hierarchical assessment process, the reliability of the prediction results output by the ensemble LSTM classifier is improved step by step. Similar to the confidence index proposed by [
11], this paper defines the credibility index
R to measure the reliability of the prediction results, and its expression is
where
is the probability that the classifier predicts that x is an unstable sample,
is the probability that the classifier predicts that
x is an stable sample. Obviously,
.
In order to gradually screen out credible samples, set credible instability threshold and credible stability threshold to and respectively. When , if , the instance is judged to be credible stable, otherwise it is marked as undetermined. When , if , the instance is judged to be credible unstable, otherwise it is marked as undetermined. When entering the next round of assessment cycle, the real-time trajectory measurements corresponding to the undetermined sample are dynamically extended, the time window slides forward to update the time series data, and then the data is input into the ensemble LSTM classifier to determine again until the specified upper limit of response time is reached. The transient information contained in the early response trajectory measurements corresponding to some critical samples is not rich, and it is difficult for the classifier to distinguish them reliably. However, the potential connection between trajectory information and transient stability will continue to strengthen and develop, and the classifier will output more reliable prediction results in the next round of assessment.
3.1.2. Stability Margin Prediction and Risk Quantification
On the one hand, for samples that are still marked as undetermined by the ensemble LSTM classifier after reaching the specified upper limit of response time, they need to be judged again through the second line of defense. On the other hand, for samples that are judged to be credible stable, it is necessary to further obtain their transient stability margins to provide a more targeted reference for subsequent power system dispatching and control. Therefore, for the above two types of samples, this paper constructs an ensemble LSTM regressor to quantitatively predict their transient stability margins. If the assessment result is instability, early warning should be given as soon as possible, and dispatchers can make timely adjustments and decisions.
References [
20,
21] construct the transient stability margin index of the power system based on CCT. However, CCT needs to be tested repeatedly to determine through multiple time-domain simulations, which is cumbersome and extremely time-consuming for a large number of samples, and is difficult to be applied in actual large-scale power grids. The post-disturbance dynamic response curves of generator power angles in a power system under different operation conditions are shown in
Figure 4. It can be seen that the variation of generator power angles can directly and effectively reflect the transient stability status of the power grid.
Therefore, this paper defines TSI [
22] as Equation (13), and employs it as the target variable predicted by the ensemble LSTM regressor.
where
refers to the maximum power angle difference between any two generators in the system. Obviously,
. When
, the system is unstable. When
, the system is stable, and the greater
TSI, the greater the transient stability margin of the system.
Although TSI can quantitatively reflect the stability margin of the system, it is not refined enough in terms of risk indication. Therefore, it is necessary to construct a reasonable risk function and classify the risks so that the dispatcher can take more specific subsequent control measures.
The strong nonlinearity and non-autonomy of the power system determine the nonlinearity of the risk function. As TSI decreases, its corresponding risk indicators should rise faster and faster. Therefore, this paper adopts an exponential utility function to describe the degree of risk. The risk function
S should consider both the system’s transient stability probability and the severity of failure [
23], so this paper defines the risk factor:
. Set the threshold
, when
, the system is considered to be hyperstable,
S = 0. When
, the system is considered to be unstable,
S = 3. When
, the risk function expression is
where
A and
B are coefficients.
Since the risk function is a continuous function, substituting the coordinates (
,0) and (0,3) into Equation (14), the risk function on the domain can be obtained as
In the process of dynamic security monitoring of the actual power grid, dispatchers should not only pay attention to the instability situation, but also pay attention to the high-risk situations near the stability domain boundary, and formulate preventive control measures in time to improve the stability of the system. This paper divides the risk into the following five ranks
where
denotes the risk rank of the power grid, and
and
are the thresholds for grading risk, which need to be set reasonably according to the security risk specification requirements and sample conditions of the actual power grid.
means the system is hyperstable and there is no risk of instability.
means the system is basically stable and the risk of instability is low.
means the system is weak-stable and the risk of instability is moderate.
means the system is critical stable and the risk of instability is high.
means the system will be unstable.