A comprehensive localization and assessment method for SSO in power systems with wind power

Subsynchronous Oscillation (SSO) is a common dynamic stability issue in power systems that integrate wind power. This paper proposes a comprehensive method for assessing the localization of SSO in wind power integrated systems. The localization method applies the transient energy flow approach to identify SSO sources in systems with wind power. Additionally, a relevant SSO index system is established where the value of each index is calculated. By using the Fuzzy Inference System (FIS) to judge the index, the SSO disturbance source contribution rating of each area is obtained. Simulation cases demonstrate that the localization method of the transient energy flow approach can effectively identify the SSO disturbance source. Moreover, the SSO disturbance source contribution rating method based on FIS can determine the SSO contribution degree of each area, thus identifying the dominant oscillation disturbance sources. The proposed method can provide valuable insights for formulating emergency control measures.


Introduction
SSO has a significant impact on wind power grid integration [1].Two main methods to mitigate this problem are SSO suppression and SSO disturbance source localization.Much research has already been conducted to suppress SSO in wind farms.SSO additional damping control for doubly-fed induction wind turbines (DFIGs) is a widely accepted solution by wind farm operators.Still, long-term SSO additional damping control may reduce the efficiency of the original controller.
Due to the above defects, online monitoring and localization of SSO sources is necessary.The most commonly used oscillation source localization method in engineering is the transient branch energy flow method (or energy function method), referred to as the "energy method" [2].The frequency of SSO is much higher than low-frequency oscillation, which cannot be analyzed by low-frequency modulation on the industrial frequency power.In addition, the definition of SSO power is unclear, and the energy function above does not consider an electromagnetic transient process.Therefore, the "energy method" above does not apply to the study of SSO.
Artificial intelligence (AI) methods have been increasingly used to assess power grid risks.Early risk assessment systems can provide response time and reduce the impact of predictable disturbances through systematic data collection and pre-defined risk assessments [3].Artificial intelligence is now used in literature to deal with voltage stabilization [4], weather hazards [5] induced network vulnerability, and different cascade tripping events [6].SSOs in wind farms are mostly instability problems caused by negative damping effects [7,8].Similarly, risk assessment of SSOs can be performed by predicting fluctuations in steady state power [9].Recently, AI neural networks have also been used to build wind speed prediction models or learning models for steady-state power fluctuations [10,11].Based on these, combined with transient energy data, online identification of SSO sources is expected to be realized.
In this paper, the transient energy method is first introduced and applied to the localization of SSO sources in wind power-containing systems.Secondly, to recognize the wind farms that play a dominant role in the whole SSO event, the SSO disturbance source contribution assessment is carried out: 1) A set of SSO index systems is built.2) The indexes are calculated by the neural network-based steady state power fluctuation learning mechanism combining the power and energy data.3) We evaluate the abovecalculated index values using FIS to obtain the SSO source contribution ratings for each region of the power system.Historical power data and SSO data are used to verify the validity of the integrated SSO localization method, and the oscillation detection technique is used to record and verify the oscillation information.

Transient energy flow
Based on the original oscillation energy flow method, oscillation source source localization for lowfrequency oscillations can be performed.The energy flow from node i through the branch L ij is mentioned in [12,13]: In Equation ( 1), P ij , Q ij , and I ij are the active power, reactive power, and current of the branch L ij , respectively.U i is the voltage magnitude of node i.  i is the voltage phase angle of node i. f i is the frequency deviation of node i; and "＊" denotes the conjugate.Equation ( 1) cannot be directly applied to the analysis of SSOs, which have high frequencies and cannot be analyzed by low-frequency modulation on the industrial frequency power.Therefore, another representation of transient energy flow [2], i.e., the instantaneous value form, is used in SSO analysis: The variables in Equation (2) are the voltages and currents in the xy coordinate system, both of which can be converted from the instantaneous values in abc coordinates, avoiding the problems caused by the use of industrial frequency phasors in Equation (1), and can be used for SSO analysis.

Steps to localize SSOs
For SSO, the perturbation source continuously emits energy consumed by the positive damping elements in the system, causing power oscillations so the disturbance source can be localized by transient energy flow.The steps are as follows.
Step 1: Collecting data.At the oscillation frequency, we collect the transient voltage and current values at the component ports over time.
Step 2: Coordinate transformation.We transform the collected data from a three-phase stationary coordinate system to a two-phase rotating coordinate system.The sub-synchronous element with frequency f − in the transient value becomes f N −f − in the xy-axis element after the coordinate system transformation, which is the dominant frequency of the SSO in the active power.
Step 3: We calculate the transient energy flow.We substitute the data into Equation (2) to calculate the transient energy flow at the oscillation frequency and plot the real-time curve.
Step 4: We locate the oscillation source.If the transient energy flow curve of the component (outflow) shows a general upward trend at the oscillation frequency, the component emits energy, i.e., it is the oscillation source.

SSO disturbance source contribution assessment based on fuzzy inference
Multiple SSO sources are often determined in the system using the energy method [14], while the contribution of different regions to the SSO varies.In this paper, the assessment of SSO contribution will be further investigated.Firstly, suitable oscillation indexes are selected for this problem, and an index system is established for index calculation.Based on this, the criteria are set up, and the index assessment is carried out to realize the SSO contribution rating.

Index system for SSO disturbance source contribution assessment
For the actual SSOs with complex mechanisms, 4 indexes are chosen for the research in this paper.Firstly, the frequency is an important index to judge whether the SSOs occur.Secondly, the dynamic damping ratio characterizes the oscillation trend, which is closely related to power system stability.Thirdly, the amplitude can directly reflect the degree of harm to the power grid.Lastly, the transient energy mentioned in the previous section can also be constructed as an index to determine the subsystem's energy interaction with the outside system, which is significant in defining the contribution of the SSO source.The indicators in these four areas have sufficient comprehensiveness, and the SSO localization assessment methodology built on these will have high credibility.

Steady-state power fluctuation value learning based on BP neural network.
The actual power grid is affected by various factors, and there are reasonable fluctuations even in the steady state.This steady state fluctuation value is not known, which makes the calculation of some indexes difficult.Therefore, it is necessary to learn the active power fluctuation value of the power grid in a steady state in advance to facilitate the calculation of the two indexes of amplitude and dynamic damping ratio.
Back Propagation Neural Networks (BPNN) is a model with an excellent combination of network structure and learning algorithms.It has strong generalization ability and strong fault tolerance.
The fluctuation value of the steady state power data during the period is approximated by obtaining the number of inflection points num and the corresponding amplitude a(i), i=1, 2…num contained in the sequence, i.e.:  We divide the above samples into 12 groups, and each group of samples is v 1 ~v9 , v 2 ~v10 , …, v 11 ~v19 and v 12 ~v20 in order. We take the first 11 sets as history data for BPNN's input, with the last data of the latter set serving as the output target value for the former set. We use the last set of samples as input when running the network. The predicted value v21 that yields the next fluctuation value can be obtained by running the network, taking  v 21 as the predicted power fluctuation value for the next 15 minutes.

Index calculations for SSO contribution assessment.
The calculations for each of the previously mentioned indexes are as follows.
 Frequency and amplitude of oscillations Before calculating these two indexes, the location of the start and end points of the oscillation needs to be found first.The sequence should be judged from top to bottom to find the first sampling point greater than the value of the fluctuation , which is the location of the start point.Conversely, the process is carried out from bottom to top to obtain the location of the endpoint.Afterwards, the frequency and amplitude of the oscillations can be easily obtained by finding the two nearest inflection points to the start and end points [9].

 Dynamic damping ratio
In practical engineering, the dynamic damping ratio of the online monitoring time-domain curve can be approximated as Equation ( 4): ln / 2 In which A I is the amplitude of the Ith oscillation, A I+N is the amplitude of the I+Nth oscillation, and N is the number of cycles of the oscillating signal.The dynamic damping ratio is the most important index that reflects the stability of the oscillation.
 Transient energy power ratio To accurately determine the source of oscillation, an index on transient energy, transient energy power ratio, is proposed here, which is an important index for judging the degree of participation in a sub-area about an SSO event and is defined as in Equation ( 5): In Equation (5), n is the total number of regions of the grid, P k represents the steady-state power of the kth region, and W k represents the transient energy difference calculated according to Equation ( 6) for the kth region in the current data window.
p_last p_first W p_last represents the transient energy of the last positive inflection point, and W p_first represents the transient energy of the first positive inflection point in the sequence.If no inflection point is detected or there is no pattern to the inflection points, the difference is recorded as the last value minus the first value in the data window.A normalization method is required to make all  WP fall into the interval [-1, 1] to facilitate index evaluation.The closer this value is to 1, the more contribution this sub-area makes to the SSO process.If the value is less than 0, it indicates that transient energy is flowing in, indicating a non-oscillatory source.

SSO disturbance source contribution assessment method
The assessment of SSO's contribution needs to be qualitative and quantitative, as well as high precision, which is a relatively complex process.Therefore, a FIS is introduced to evaluate the above metrics.FIS is a system that can process fuzzy information based on fuzzy set theory and fuzzy inference methods, etc [15].With the FIS built in this section, the above indexes can be evaluated, and the output of the FIS and SSO contribution can be obtained.The meaning of this output value is twofold.It reflects the probability of being the dominant SSO source and the severity of the SSO.The results obtained can grant more effective guidance to the grid dispatchers.
The fuzzy inference process consists of four parts: fuzzy input, inference engine, fuzzy rule base, and defuzzification.Using the membership function of the output parameters, defuzzification is performed according to the fuzzy language results given by the inference engine, which finally results in a non-fuzzy value.The structure of the FIS-based SSO contribution rating model is shown in Figure 1.

Fuzzy rule base.
Since the FIS above has more than two inputs, which is beyond the scope of binary fuzzy logic, linguistic fuzzy rules are used here to describe the fuzzy rule base in this study.The expert experience method and simulation test method are combined to obtain the fuzzy rules for SSO contribution assessment, and some of the higher weighted rules are shown in Table 1.For SSO contribution assessment, damping ratio and transient energy power are more important, and the remaining two indexes are used as aids.

Fuzzy inference and defuzzification methods.
In this study, the Mamdani method is used for fuzzy inference, and area centered algorithm is used for defuzzification.

Case of transient energy flow method
The simulation is carried out in the IEEE 4-unit-2-area system with DFIG wind turbines.Two symmetrical regions are included in the system, each containing two generators.Detailed power line, electric load, and generator parameters can be referred to [16].Two different-sized doubly-fed wind farms are incorporated in areas 3 and 7, respectively, where each DFIG area already contains series compensation capacitors and short-distance transmission lines.11 important areas of the system are selected for electrical quantity monitoring.The structure of the divided system is shown in Figure 3. Figure 3. System structure of 4-unit-2-area with DFIG wind farm.This scenario uses 5 MW capacity DFIGs, of which 30 units are connected to area 3 with a wind speed of 7 m/s and an equivalent series compensation degree of 34%.The other 50 units are connected to area 7 with a 10 m/s wind speed and an 18% compensation degree.All series compensation capacitors are put into operation at 19 s.Under this condition, the system experiences an SSO caused by wind turbines at a frequency near 43 Hz.The oscillation waveforms of wind farm DFIG1 and DFIG2 are shown in Figure 4.The transient energy of each area at the oscillation frequency is shown in Figure 5.The energy curves show that the wind farms at different locations and operating conditions emit energy, so all the wind turbines in this system are regarded as SSO sources.In addition, the energy curves of G1 and G2 also show an increasing trend.They are also recognized as oscillation sources, which may be because the thermal units and wind turbines are at the same busbar.This can be approximated in circuitry as the same position, which makes sense.To summarize, the example results point to multiple oscillation sources.However, even if all possible oscillation sources participate in the oscillation, it is not possible to directly judge the contribution of each region to the SSO through the energy and power curves.In practice, when multiple wind farms are identified as SSO perturbation sources, in most cases, only one wind farm dominates the SSO.In this scenario, there is value in further research in assessing SSO contribution ratings of each area.

Case of SSO disturbance source contribution assessment
To verify the validity of the comprehensive SSO localization assessment method proposed in this paper, the FIS-based SSO disturbance source contribution assessment method for the above case study scenario is further used to assess the level of SSO contribution in each area.Five hours of historical power data on the central connection line (Area 9) of the system is collected and tested using the BPNN prediction model, and the test results are shown in Table 2. To make the calculation more accurate, all the data units are changed to the famous value MW.Learning and prediction for the 12th sample group gave an output of 0.5846 MW, which can be used as the  value in this analysis.
The FIS-based SSO contribution ratings were then performed, with the length of the sliding window set to 0.6 s and the sliding step set to 0.2 s.A total of 13 data windows (18 s to 20 s) were evaluated during this period of oscillation state.Figure 6 illustrates the SSO contribution ratings for areas 1, 2, 3, and 7, identified as SSO sources by the energy curves.As can be seen in Figure 6, the SSO contribution of Area 3 rises steeply from 5% to 73% at the beginning of the 4th data window.It remains high after that, consistently in the VH-or ExH-dominated bands.Meanwhile, the other areas identified as SSO sources show no significant increase in SSO contribution.Therefore, it can be concluded that DFIG1 contributes the most to the SSO perturbation source.Averaging the contributions of each area during the 19~21 s interval of the oscillation, the visualized graph of the SSO source contributions for this period is shown in Figure 7.
The power data in the 6th, 7th, and 8th data windows of Area 3 are extracted respectively for the HOC-ESPRIT online mode identification described in [17], the results of which are shown in Table 3.  3, the oscillation frequency during the oscillation period is around 42.4 Hz, the attenuation factor is positive, and the amplitude increases slowly with a tendency to diverge, which matches the trend of a slowly increasing contribution rating.Based on the fault recordings and combined with the SSO contribution rating, the power grid dispatcher can quickly take measures to prevent the oscillation from further expanding its impact.After DFIG1 is separated, the output curves of G1~G4 and DFIG2 are shown in Figure 8. From the figure, it can be seen that after eliminating the influence of DFIG1, the system regained stability, so it can be confirmed that DFIG1 is the wind farm that dominates this SSO event.Combining the above cases, the FIS-based SSO disturbance source contribution assessment method proposed in this paper can visually present the contribution ratings of each power system area at each period.When multiple SSO disturbance sources are located by the traditional transient energy flow method, further confirmation of the location of the dominant disturbance source can be realized.

Conclusion
This paper first presents the SSO localization method that utilizes transient energy flow to locate SSO sources in wind power systems accurately.However, it does not provide a direct means to assess the contribution of each oscillation source to the SSO event.To address this, we introduce a FIS-based approach to rate the disturbance sources and identify the dominant one in an SSO event.By computing and evaluating corresponding oscillation indexes, real-time SSO oscillation contribution ratings can be generated for visualizing SSO contribution.This method can offer significant guidance to dispatchers in managing grid incidents.For example, direct separation can be implemented in areas with high SSO contribution to prevent further damage to the power system.
to the low probability of SSO occurrence, BPNN-based learning and prediction of historical volatility values can be performed every 15 minutes.The historical 5-hour volatility values can be counted as v 1 , v 2 …, v 20 .

Figure 2 .
Figure 2. Membership functions of inputs and outputs.
2023 4th International Conference on Electrical Technology and Automatic Control Journal of Physics: Conference Series 2704

Figure 4 .
Figure 4. Active power out of DFIG1 and DFIG2.

Figure 5 .
Figure 5. Transient energy flows in each area.

Figure 8 .
Figure 8. Active power of each unit after separate DFIG1.Combining the above cases, the FIS-based SSO disturbance source contribution assessment method proposed in this paper can visually present the contribution ratings of each power system area at each period.When multiple SSO disturbance sources are located by the traditional transient energy flow method, further confirmation of the location of the dominant disturbance source can be realized.

Table 2 .
Learning results of steady-state power fluctuation.The test results show the prediction error of this BPNN-based time series can be controlled within a small range, showing a good learning mechanism and prediction performance.

Table 3 .
Oscillation mode identification results of area 3 by HOC-ESPRIT.