- SCC: The amount of power that flows through a specified point when a short-circuit fault occurs at that point is expressed by SCC. The value of SCC depends on rated voltage (Vrated) and short-circuit impedance (Zsc) and is given as in (1) .
- SCR: The ratio between the grid’s SCC and the power injected by WPP is given by SCR. At the PCC bus of a distribution system connected to WPP, SCR quantifies the bus strength against the power quality issues caused by the wind power penetration. The value of SCR is calculated, as shown in (2) .
- X/RPCC: The grid impedance angle ratio seen at the PCC bus is defined by the X/RPCC. The value of the X/RPCC is determined by the ratio of Thevenin equivalent reactance and Thevenin equivalent resistance seen from that specified point . The internal reactance of distribution lines is small, making the equivalent X/R value seen at the PCC small. The majority of existing approaches proposed for mitigating the voltage stability issues through reactive power compensation are applicable to power transmission networks where the X/R ratio is large . Hence, these methods are not appropriate for distribution networks.
- Develop a novel voltage stability decision tree algorithm-based model predicting the key power quality components at a given PCC bus, i.e., VPCC and Pwind, based on the values of SCR and X/RPCC seen at that bus;
- Simplify the siting and sizing of IG- and DFIG-based WPPs in weak distribution network;
- Increase the prediction accuracy compared to the voltage stability mathematical model presented in .
- Data collection and extension: In this study, the X/RPCC-dVPCC characteristics were required for test systems with different SCR ratios. For this purpose, the X/RPCC-dVPCC data points were obtained simulating the test systems from authors’ previous work presented in . As discussed earlier, the higher accuracy of the prediction can be achieved by increasing the number of data points. However, the size of simulation data obtained by the test systems is small due to the limited capability of the MATLAB/Simulink solver in providing X/RPCC-dVPCC data points. Hence the obtained simulation data were then extended to obtain large training data set. In this work, the extension of simulation data was conducted using Microsoft Excel.
- Developing decision tree algorithm: The extended data were then trained in the decision tree in the MATLAB (version 2014a developed by MathWorks) to formulate a model for predicting dVPCC using the values of SCR and X/RPCC. Boosted regression decision tree was utilized to predict the voltage profile from given network parameters (SCR and X/RPCC).
2.1. Data Collection and Extension
2.2. Decision Tree Algorithm
3. Results and Discussion
3.1. IG-Based WPPs
3.2. DFIG-Based WPPs
3.3. Comparison of Decision Tree Model and Mathematical Model for Different Ranges of X/RPCC
- N is the number of the Pwind-dVPCC data points;
- ∆Vp expresses the dVPCC value obtained by the predictive models, i.e., the decision tree-based model proposed in this paper and the mathematical model presented in , given the Pwind value;
- ∆Vr expresses the reference dVPCC obtained using the test simulation systems for each level of wind power penetration.
4. Significance of the Proposed Decision Tree-Based Model
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
|DFIG||Double-fed induction generator|
|dVPCC||Voltage variation concerning the voltage value before wind power plant connection at the point of common coupling|
|PCC||Point of common coupling|
|Pwind||Power generated by wind power plant|
|Vinitial||Voltage at distribution feeder before the connection of wind power plant|
|WPP||Wind power plant|
|X/RPCC||Short-circuit impedance angle ratio seen at the point of common coupling|
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|Case Study||Topology||Isc (kA)||SCC (MVA)||Pwind (MW)||SCR|
|Test 1||IEEE 37-bus system||0.95||36||9||4|
|Test 2||IEEE 37-bus system||1.42||54||9||6|
|Test 3||IEEE 37-bus system||1.89||72||9||8|
|Test 4||IEEE 9-bus system||0.71||27||3||9|
|1.||Load IG_data/DFIG_data (extended)||The table that contains extended data (SCR, X/RPCC, dVPCC) is loaded as training data set.|
|2.||Feature variable (input) ← SCR,X/RPCC||Assign feature and response variable|
|response variable (output) ← dVPCC|
|3.||T ← template tree (min leaf size = 5)||Create a template tree having a minimum number of data points in a leaf = 5|
|4.||model ← fit regression tree (SCC, X/RPCC, dVPCC)|
Method ← least square boosting
number of learning cycles ← 100
|The ensemble tree is created from training data set using the least square boosting method and with 100 learning cycles|
|5.||Prompt SCC, X/RPCC||Request input from the user|
|6.||Pwind ← [SCC/SCR]|
Input = (SCR, X/RPCC)
|Find power points for respective SCR values|
|7.||[dVPCC] = predict (Igmodel, Input)||Predict the response variable (dVPCC) from features (SCR, X/RPCC)|
|8.||Plot (Pwind, dVPCC)||Plot variation in voltage profile with the amount of penetrated power|
|∆Vr Related to the Proposed Decision Tree-Based Model|
|∆Vr Predicted by the Mathematical Model Proposed |
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