# Developing a Decision Tree Algorithm for Wind Power Plants Siting and Sizing in Distribution Networks

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## Abstract

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_{PCC}) are the most important parameters, which affect the PCC voltage (V

_{PCC}) stability. Hence, design engineers need to conduct the WPP siting and sizing assessment considering the SCR and X/R

_{PCC}seen at each potential PCC site to ensure that the voltage stability requirements defined by grid codes are provided. In various literature works, optimal siting and sizing of distributed generation in distribution networks (DG) has been carried out using analytical, numerical, and heuristics approaches. The majority of these methods require performing computational tasks or simulate the whole distribution network, which is complex and time-consuming. In addition, other works proposed to simplify the WPP siting and sizing have limited accuracy. To address the aforementioned issues, in this paper, a decision tree algorithm-based model was developed for WPP siting and sizing in distribution networks. The proposed model eliminates the need to simulate the whole system and provides a higher accuracy compared to the similar previous works. For this purpose, the model accurately predicts key voltage stability criteria at a given interconnection point, including V

_{PCC}profile and maximum permissible wind power generation, using the SCR and X/R

_{PCC}values seen at that point. The results confirmed the proposed model provides a noticeable high accuracy in predicting the voltage stability criteria under various validation scenarios considered.

## 1. Introduction

_{PCC}) is significantly impacted by short circuit capacity (SCC), short circuit ratio (SCR) and overall system impedance angle ratio seen at that site expressed by the X/R

_{PCC}. These parameters are explained as follows:

- 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 (V
_{rated}) and short-circuit impedance (Z_{sc}) and is given as in (1) [4].$$\mathrm{SCC}=\frac{3}{2}\times {\mathrm{V}}_{\mathrm{rated}}\times {\mathrm{I}}_{\mathrm{sc}}=\frac{3}{2}\frac{{\left({\mathrm{V}}_{\mathrm{rated}}\right)}^{2}}{{\mathrm{Z}}_{\mathrm{sc}}}$$ - 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) [4].$$\mathrm{SCR}=\frac{\mathrm{SCC}}{{\mathrm{P}}_{\mathrm{wind}}}$$

_{sc}) and small SCC and SCR [1,5]. Typically, the SCR value is less than 10 in distribution grid-connected WPPs. The small range of SCR, in turn, causes high voltage variations and power Quality issues at the PCC [4]. Hence, there is a tradeoff between the value of SCR and the voltage stability in distribution systems connected to WPP.

- X/R
_{PCC}: The grid impedance angle ratio seen at the PCC bus is defined by the X/R_{PCC}. The value of the X/R_{PCC}is determined by the ratio of Thevenin equivalent reactance and Thevenin equivalent resistance seen from that specified point [4]. 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 [6]. Hence, these methods are not appropriate for distribution networks.

_{PCC}ensure the V

_{PCC}stability requirements defined by the grid codes. In addition, given the relation between wind power penetration and SCR, engineers need to define the maximum power that can be injected by WPP, ensuring that V

_{PCC}is maintained within the standard range, i.e., 0.95 pu < V

_{PCC}< 1.05 pu.

_{PCC}and SCR for a test system with 0 ≤ SCR ≤ 2.5. Referring to [5], V

_{PCC}can be taken as a quadratic function of SCR. However, the equation proposed in [5] did not consider the relation between V

_{PCC}and X/R

_{PCC}ratio. Given the significant effect of the X/R

_{PCC}ratio on V

_{PCC}stability, the lack of consideration of the relationship between these parameters adversely impacts the accuracy and validation of the relation proposed in [5]. In addition, in the majority of actual distribution networks, the SCR value is more than 2.5 [16]. Given that the mathematical model has been tested for 0 ≤ SCR ≤ 2.5, the validity of the proposed relation in [5] for a system with SCR > 2.5 is ambiguous. The aforementioned issues concerned with the mathematical relation proposed in [5] were addressed and removed by a more comprehensive mathematical model proposed in our previous work presented in [1]. The model expressed the mathematical relation between the V

_{PCC}variation, SCR and X/R

_{PCC}ratio for various test distribution networks connected to induction generator (IG) and doubly-fed induction generator (DFIG)-based WPPs. For IG-based WPPs, two mathematical relations were developed regarding the range of the X/R

_{PCC}: an exponential function for WPPs with the X/R

_{PCC}< 2 and a quadratic function for WPPs with the X/R

_{PCC}> 2. Furthermore, for DFIG-based WPPs, a mathematical relation was developed considering that the X/R

_{PCC}< 2. The mathematical method presented in [1] is one of the most valuable and comprehensive approaches expressing the relationships between V

_{PCC}and the main PCC parameters of distribution network connected WPPs. Such a mathematical model enables the prediction of the key V

_{PCC}stability criteria, including V

_{PCC}profile, step-V

_{PCC}variation and maximum permissible size of WPP. Taking advantage of the predicted V

_{PCC}parameters, the design engineers can easily find the best bus for the interconnection of a WPP without carrying out complex and time-demanding computational tasks and simulating the test systems. However, the results obtained in [1] demonstrated that the accuracy of the mathematical relations is adversely impacted when SCR and X/R

_{PCC}ratios are small. In addition, for IG-based WPPs, the accuracy of the proposed relations is low when the X/R

_{PCC}is around 2. Hence, although the method proposed in [1] simplifies the WPP siting and sizing process compared to the other existing methods, its accuracy is impacted by small SCR and X/R

_{PCC}ratios, which, in turn, limits the method applicability. To address this issue and increase the prediction accuracy, the mathematical model proposed in [1] was replaced by a decision tree algorithm-based method in this paper. Therefore, in this work, a decision tree algorithm method was developed to model the relation between V

_{PCC}variation (dV

_{PCC}), SCR and X/R

_{PCC}. The input parameters of the proposed decision tree-based model are SCR and X/R

_{PCC,}which are the baseline characteristics of distribution feeders and easily available in any power system network. Using the values of input parameters, the model precisely predicts the P

_{wind}-dV

_{PCC}characteristic, which can then be used for optimal WPP siting and sizing. The decision tree algorithm is one of the supervised learning algorithms and can be implemented for regression and classification problems [17]. The accuracy of the decision tree algorithm in predicting output parameters is enhanced by training decision trees with a large training data set [17]. In this study, the X/R

_{PCC}-dV

_{PCC}data points were initially obtained using simulation test systems with different SCR values. Later on, the simulation results were extended to enlarge the training data set. The extended data were then used to develop the decision tree algorithm-based model. The proposed decision tree-based model enables to plot P

_{wind}versus dV

_{PCC}and provides the design engineer with insightful information to carry out an initial predictive assessment on the key power quality parameters at the PCC of WPPs, including V

_{PCC}profile, and maximum permissible power can be injected into the distribution network (P

_{wind}_max). Taking advantage of the power quality parameters predicted by the proposed decision tree algorithm, WPP planning engineers can easily estimate the optimal size of WPP and select the most appropriate site for the interconnection of WPP to distribution networks where the voltage stability requirements defined by the grid codes are provided with very high accuracy. Hence, the main contribution of this work to the existing knowledge is to simplify the WPP sizing and siting analysis as well as achieving a noticeable higher accuracy compared to the similar methods recently published in the literature. The aims of this study were to:

- Develop a novel voltage stability decision tree algorithm-based model predicting the key power quality components at a given PCC bus, i.e., V
_{PCC}and P_{wind}, based on the values of SCR and X/R_{PCC}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 [1].

## 2. Methodology

- Data collection and extension: In this study, the X/R
_{PCC}-dV_{PCC}characteristics were required for test systems with different SCR ratios. For this purpose, the X/R_{PCC}-dV_{PCC}data points were obtained simulating the test systems from authors’ previous work presented in [1]. 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/R_{PCC}-dV_{PCC}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 dV
_{PCC}using the values of SCR and X/R_{PCC}. Boosted regression decision tree was utilized to predict the voltage profile from given network parameters (SCR and X/R_{PCC}).

#### 2.1. Data Collection and Extension

_{wind}) at a given PCC bus with specific SCC and X/R values. Hence, to develop such a predictive model, it is required to obtain a training data set, which includes X/R

_{PCC}-dV

_{PCC}values for a range of SCR ratios. In this study, the initial training data set was obtained using four simulation test systems considered in the authors’ previous work presented in [1]. The test systems were simulated based on the IEEE 9-bus and IEEE 37-bus distribution network models. Given that the power quality issues in distribution network-connected WPPs are mainly related to the PCC sites with SCR < 10, the SCR range considered in this study is 4 < SCR < 10. In addition, the range of the X/R

_{PCC}considered is based on the analysis results gained using actual distribution systems presented in [19].

_{wind}and the corresponding SCR values are as presented in Table 1.

_{PCC}ratio was changed to monitor the corresponding V

_{PCC}value, while the values of SCC, P

_{wind}and SCR are constant. Having the X/R

_{PCC}-dV

_{PCC}data points, the V

_{PCC}variation was calculated using (3).

_{PCC}signifies the PCC voltage value after the P

_{wind}is generated and injected into the test distribution systems and V

_{initial}is the PCC voltage value before the WPP connection when the P

_{wind}= 0.

_{initial}value at the PCC of test systems was considered to be 0.98 p.u.

_{PCC}-dV

_{PCC}characteristics for the IG and DFIG-based test WPPs, respectively.

_{PCC}-dV

_{PCC}curve characteristics presented in Figure 3 and Figure 4, the mathematical functions of graphs with the best fit were developed in [1]. However, as discussed by the authors in [1], the prediction error of the method presented in [1] is high for interconnection points with a small SCC, SCR and X/R

_{PCC}ratio. In this study, the mathematical model developed in [1] was replaced by a decision tree algorithm to improve the prediction accuracy. The algorithm was developed using the X/R

_{PCC}-dV

_{PCC}data points presented in Figure 3 and Figure 4. As discussed earlier, to obtain the X/R

_{PCC}-dV

_{PCC}data points, in each simulation test system with the characteristics shown in Table 1, the X/R

_{PCC}ratio was changed, and the corresponding dV

_{PCC}was monitored. However, MATLAB/Simulink solver was not able to show the difference in dV

_{PCC}value when the X/R

_{PCC}was slightly changed. For example, when the X/R

_{PCC}was changed by 1%, the dV

_{PCC}value obtained by the simulation models was constant, meaning that the change in the X/R

_{PCC}was not reflected in the dV

_{PCC}value. The limited capability of the MATLAB/Simulink solver in providing exclusive dV

_{PCC}value for each X/R

_{PCC}value resulted in collecting a small number of the X/R

_{PCC}-dV

_{PCC}data points. Hence, only 15 data points were obtained from each simulation test system. On the other hand, the prediction accuracy of the algorithm is increased if the larger data set is used to train the decision tree algorithm [17]. Given that the number of data points obtained by the simulation models is not sufficient for training the decision tree algorithm, the data were extended to obtain large training data set.

_{PCC}and X/R

_{PCC}for each SCR level. Higher-order polynomials were fitted, maximizing R

^{2}value by trial and error method. R

^{2}value represents the goodness of fit and lies between 0 and 1. R

^{2}closer to 1 represents a better fit [20] and can represent more data points. The best-fit polynomial was then utilized to determine dV

_{PCC}from the X/R

_{PCC,}forming a large dataset for each SCR level. Finally, the extended X/R

_{PCC}-dV

_{PCC}data were obtained for both IG- and DFIG-based WPPs, as shown in Figure 5 and Figure 6, respectively.

#### 2.2. Decision Tree Algorithm

_{PCC}-dV

_{PCC}obtained for each SCR value shown in Figure 5 and Figure 6, whereas 10% of extended data were set aside as test data set.

_{PCC}and the ratio between SCC and P

_{wind}, i.e., SCR. The model can predict the P

_{wind}-dV

_{PCC}characteristic curve using the value of input parameters.

## 3. Results and Discussion

_{wind}-dV

_{PCC}characteristic for different test systems. In this regard, the P

_{wind}-dV

_{PCC}characteristics plotted by the proposed model were compared with the reference characteristics given by the IEEE test systems presented in Figure 5 and Figure 6. In addition, the P

_{wind}-dV

_{PCC}characteristics gained by the proposed decision tree algorithm-based model were compared with the results obtained by one of the most efficient methods presented in [1], which is capable of simplifying the WPP sizing and siting. Both IG and DFIG-based WPPs were considered in the verification analysis.

#### 3.1. IG-Based WPPs

_{PCC}values, as shown in Table 3.

_{PCC}for various P

_{wind}values. Having the simulation results, the reference P

_{wind}-dV

_{PCC}characteristic was plotted for each scenario. In addition, the P

_{wind}-dV

_{PCC}characteristics were obtained for each scenario using the decision tree-based model developed in this paper and the mathematical model proposed in [1] considering the SCC and X/R

_{PCC}ratios presented in Table 3. Given that the analysis was carried out for the IG-based WPP, the following equations were depicted from [1] to calculate dV

_{PCC}.

_{wind}-dV

_{PCC}characteristics predicted by the decision tree-based model developed in this paper follow the reference graphs obtained by the simulation test models even when the large wind power generation weakens the PCC feeder. As discussed earlier, at the weak PCC sites, the large wind power penetration makes the SCR value small. Hence, the small SCR values do not adversely impact the accuracy of the proposed model in predicting the P

_{wind}-dV

_{PCC}characteristics. On the other hand, the results demonstrate that the curves predicted by the mathematical relations proposed in [1] largely deviate from the reference graphs, especially when the SCR value is small due to the large wind power generation. Hence, as the authors mentioned in [1], the accuracy of the mathematical model is adversely impacted at weak PCC where the grid’s SCC and SCR are small. For example, referring to Figure 8c,d related to the results for the scenarios with the small grid’s SCC, i.e., Scenario 3 with an SCC of 15MVA and Scenario 4 with an SCC of 18 MVA, the highest error between the reference graphs and the characteristics predicted by the proposed decision tree algorithm is less than 0.5%. However, Figure 8c,d show that the error between the reference curve and the curve predicted by the equations proposed in [1] is more than 1% when the wind power generation is around 4 MW, which corresponds to the SCR of around 4.

_{wind}-dV

_{PCC}characteristic when the X/R ratio is around 2. From the results presented in Figure 8h,i related to the scenarios with X/R ratio close to 2, i.e., Scenarios 8 and 9, it shown that the error between the curves plotted by the decision tree-based model and the corresponding reference curves is negligible. However, the results in Figure 8h,i show that curve characteristics plotted by the mathematical model noticeably deviate from the reference graphs when the X/R

_{PCC}ratio is around 2, and the wind power generation is large.

_{wind}-dV

_{PCC}characteristics plotted by the proposed decision tree-based model follow the corresponding reference graphs for different ranges of the X/R

_{PCC}ratio and wind power penetration, whereas the accuracy of the mathematical model in predicting the characteristics is decreased when wind power generation is increased and/or the X/R

_{PCC}ratio is around 2.

#### 3.2. DFIG-Based WPPs

_{wind}-dV

_{PCC}characteristics for the DFIG-based WPPs. Nine test systems were considered with the SCC and X/R

_{PCC}values shown in Table 4.

_{PCC}is given by:

_{wind}-dV

_{PCC}characteristics using the proposed decision tree-based model has a minimal error, while the error between the reference and predicted results are noticeable in most cases when the graphs are plotted using the mathematical equation. The results shown in Figure 9b related to the scenario with the smallest X/R (Scenarios 2) confirms the discussion presented in [1] regarding the low prediction accuracy of the mathematical equation for weak PCC sites with a small X/R

_{PCC}ratio. From Figure 9b, the error between the reference results gained by the simulation models and the graphs predicted by the mathematical model is over 1% when the wind power penetration is large, whereas the graph plotted using the proposed decision tree algorithm precisely tracks the reference curve characteristic for any level of wind power penetration. From Figure 9e, it can be seen that the highest error of the proposed decision tree-based model in predicting the P

_{wind}-dV

_{PCC}curve characteristic is less than 0.5% in Scenario 5, while the error is greater than 1% in this scenario when the characteristic is predicted using the mathematical relation.

#### 3.3. Comparison of Decision Tree Model and Mathematical Model for Different Ranges of X/R_{PCC}

_{wind}-dV

_{PCC}characteristics, so-called prediction error (PE), was evaluated for the scenarios considered in Table 3 and Table 4. For each scenario, the prediction error is given by (7) [24]:

- N is the number of the P
_{wind}-dV_{PCC}data points; - ∆V
_{p}expresses the dV_{PCC}value obtained by the predictive models, i.e., the decision tree-based model proposed in this paper and the mathematical model presented in [1], given the P_{wind}value; - ∆V
_{r}expresses the reference dV_{PCC}obtained using the test simulation systems for each level of wind power penetration.

_{p}and ∆V

_{r}values, as shown in Table 5.

_{PCC}ratios, whereas the maximum prediction error of the mathematical model is 2.5% when the X/R

_{PCC}ratio is around 2. This confirms the findings discussed in Section 3.1 that the accuracy of the mathematical model is adversely impacted when the X/R

_{PCC}ratio tends to 2.

_{PCC}ratio. However, the maximum P.E value of the mathematical method is 1%, which occurred in the scenario with the smallest X/R

_{PCC}ratio. Therefore, as mentioned in the previous section, the accuracy of the mathematical model in predicting the P

_{wind}-dV

_{PCC}characteristics is low at the interconnection sites with a small X/R

_{PCC}ratio, while the proposed decision tree algorithm overcomes this issue.

## 4. Significance of the Proposed Decision Tree-Based Model

_{wind}-dV

_{PCC}characteristic for any X/R

_{PCC}ratio and SCC and SCR values. Consequently, for a potential WPP interconnection site, design engineers can calculate the V

_{PCC}profile given the V

_{initial}value using (3) and plot the P

_{wind}versus V

_{PCC}profile characteristic.

_{wind}-V

_{PCC}characteristic for one of the IG-based scenarios (Scenario 4 in Table 3) and one of the DFIG-based scenarios (Scenario 2 in Table 4), respectively. The V

_{initial}value at the PCC of test systems used for the scenarios considered in Figure 12 and Figure 13 is 1 pu and 0.98 pu, respectively.

_{PCC}profile must be maintained between 95% and 105% of the network nominal voltage to satisfy the steady-state voltage stability requirements defined by the grid codes [3]. Therefore, after plotting the V

_{PCC}-P

_{wind}characteristics for the potential WPP interconnection sites, designers and planners can determine the best PCC site, where the X/R

_{PCC}and SCC values ensure that the grid code requirements are concerned with the magnitude of steady-state V

_{PCC}are met.

_{wind}-dV

_{PCC}characteristic using the proposed model enables to estimate the maximum permissible size of WPP, called P

_{wind}_max, ensuring that the steady-state V

_{PCC}requirements defined by the grid codes would be satisfied. For example, from Figure 12 and Figure 13, the P

_{wind}_max values at the PCC of the test system considered are 3.6 MW and 5.2 MW, respectively. The results presented in Figure 12 and Figure 13 confirm that the predicted P

_{wind}_max gained by the proposed decision tree algorithm literally tracks the reference P

_{wind}_max values obtained by the simulation models.

_{wind}-V

_{PCC}curve characteristic is reduced as the SCR is decreased or the value of the X/R

_{PCC}moves toward 2. In addition, for the DFIG-based WPPs, the accuracy of the mathematical model in predicting P

_{wind}-V

_{PCC}characteristics is low if the PCC site has a small X/R ratio. The proposed decision tree-based model addressed the aforementioned issues by simplifying the WPP sizing and siting through predicting P

_{wind}-V

_{PCC}characteristics with noticeably high accuracy. Similar to the mathematical model developed in [1], the model proposed in this paper requires only two PCC parameters, i.e., X/R

_{PCC}and SCC, to predict the P

_{wind}-V

_{PCC}characteristics. The predicted P

_{wind}-V

_{PCC}characteristic can be used for optimal WPP sizing and siting. Given that the X/R

_{PCC}and SCC are the baseline characteristics of a distribution feeder, their values are generally available or can easily be calculated using fundamental power system analysis methods. More importantly, the verification results shown in Section 3 demonstrated that the proposed decision tree-based model eliminates the issues concerned with the limited accuracy of the mathematical model presented in [1] by providing a negligible prediction error for any SCR and X/R

_{PCC}ratios.

## 5. Conclusions

_{wind}-V

_{PCC}) characteristic at a given potential interconnection point using the distribution system baseline parameters seen at that point, including SCC and X/R

_{PCC}. Taking advantage of the plotted P

_{wind}-V

_{PCC}characteristic, design engineers can carry out an initial predictive assessment on the critical voltage stability criteria, including V

_{PCC}value and P

_{wind}_max, to determine the optimal WPP connection site and its maximum permissible size ensuring the grid code requirements. The proposed model simplifies the siting and sizing of WPPs by removing the need to simulate the whole distribution system and performing computational calculations, which is one of the main advantages of the proposed model over the majority of existing approaches. In addition, the proposed model was benchmarked against one of the latest mathematical methods developed for simplifying WPP sizing and siting to affirm its accuracy in predicting the P

_{wind}-V

_{PCC}characteristic and voltage stability criteria.

_{wind}-dV

_{PCC}curve characteristics is around 2.5% when the X/R

_{PCC}ratio tends to 2, whereas the curves predicted by the proposed decision tree algorithm precisely track the reference characteristics when the X/R

_{PCC}ratio is around 2.

_{PCC}ratio is around 0.5, while the proposed model provided an accuracy of almost 100% over the whole range of the X/R

_{PCC}ratio.

_{PCC}and reducing the uncertainty due to the load deviations by considering the V

_{initial}parameter. In addition, the validation of the presented model using actual systems is important and will be addressed in future studies to further complement this research. The practical verification of the proposed model requires the values of V

_{PCC}, X/

_{RPCC}and SCC obtained from an actual distribution network. However, the authors did not have access to such values. In addition, simulation and modeling the real-world distribution systems require using professional engineering software, such as PSS/e, which is not currently available to the authors. Therefore, as one of the extensions to this research, the authors intend to validate the proposed model using an actual case where a wind power plant is being proposed for further integration.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

IG | Induction generator |

I_{sc} | Short-circuit current |

DFIG | Double-fed induction generator |

dV_{PCC} | Voltage variation concerning the voltage value before wind power plant connection at the point of common coupling |

PE | Prediction error |

PCC | Point of common coupling |

P_{wind} | Power generated by wind power plant |

SCC | Short-circuit capacity |

SCR | Short-circuit ratio |

V_{initial} | Voltage at distribution feeder before the connection of wind power plant |

WPP | Wind power plant |

X/R_{PCC} | Short-circuit impedance angle ratio seen at the point of common coupling |

Z_{sc} | Short-circuit impedance |

## References

- Alizadeh, S.M.; Sadeghipour, S.; Ozansoy, C.; Kalam, A. Developing a Mathematical Model for Wind Power Plant Siting and Sizing in Distribution Networks. Energies
**2020**, 13, 3485. [Google Scholar] [CrossRef] - Ahmed, S.D.; Al-Ismali, F.S.M.; Shafiullah, M.; Al-Sulaiman, F.A.; El-Amin, I.M. Grid Integration Challenges of Wind Energy: A Review. IEEE Access
**2020**, 8, 10857–10878. [Google Scholar] [CrossRef] - Machado, I.; Arias, I. Grid Codes Comparison. Master’s Thesis, Chalmers University of Technology, Göteborg, Sweden, 2006. [Google Scholar]
- Alizadeh, S.M. An Analytical Voltage Stability Model for Wind Power Plant Sizing and Siting in Distribution Networks. Ph.D. Thesis, Victoria University, Footscray, Australia, 2017. [Google Scholar]
- Golieva, A. Low Short-Circuit Ratio Connection of Wind Power Plants. Master’s Thesis, Norwegian University of Science and Technology, Trondheim, Norway, 2015. [Google Scholar]
- Alizadeh, S.M.; Ozansoy, C.; Alpcan, T. In The Impact of X/R Ratio on Voltage Stability in a Distribution Network Penetrated by Wind Farms. In Proceedings of the 2016 Australasian Universities Power Engineering Conference (AUPEC), Brisbane, Australia, 25–28 September 2016; pp. 1–6. [Google Scholar]
- Naik, S.G.; Khatod, D.; Sharma, M. In Sizing and Siting of Distributed Generation in Distribution Networks for Real Power Loss Minimization Using Analytical Approach. In Proceedings of the International Conference on Power, Energy and Control (ICPEC), Sri Rangalatchum Dindigul, India, 6–8 February 2013; pp. 740–745. [Google Scholar]
- Keane, A.; O’Malley, M. Optimal Utilization of Distribution Networks for Energy Harvesting. IEEE Trans. Power Syst.
**2007**, 22, 467–475. [Google Scholar] [CrossRef] - Atwa, Y.M.; El-Saadany, E.F.; Salama, M.M.A.; Seethapathy, R. Optimal Renewable Resources Mix for Distribution System Energy Loss Minimization. IEEE Trans. Power Syst.
**2010**, 25, 360–370. [Google Scholar] [CrossRef] - Khalesi, N.; Rezaei, N.; Haghifam, M.R. DG Allocation with Application of Dynamic Programming for Loss Reduction and Reliability Improvement. Int. J. Electr. Power Energy Syst.
**2011**, 33, 288–295. [Google Scholar] [CrossRef] - Georgilakis, P.S.; Hatziargyriou, N.D. Optimal Distributed Generation Placement in Power Distribution Networks: Models, Methods, and Future Research. IEEE Trans. Power Syst.
**2013**, 28, 3420–3428. [Google Scholar] [CrossRef] - Farhat, I.A. Ant Colony Optimization for Optimal Distributed Generation in Distribution Systems. Int. J. Comput. Inf. Eng.
**2013**, 7, 1094–1098. [Google Scholar] - Ali, A.; Padmanaban, S.; Twala, B.; Marwala, T. Electric Power Grids Distribution Generation System for Optimal Location and Sizing–A Case Study Investigation by Various Optimization Algorithms. Energies
**2017**, 10, 960. [Google Scholar] - Mohammadi, M.; Naseb, M.A. PSO Based Multiobjective Approach for Optimal Sizing and Placement of Distributed Generation. Res. J. Appl. Sci. Eng. Technol.
**2011**, 2, 832–837. [Google Scholar] - Seker, A.A.; Hocaoglu, M.H. In Artificial Bee Colony Algorithm for Optimal Placement and Sizing of Distributed Generation. In Proceedings of the 8th International Conference on Electrical and Electronics Engineering, Bursa, Turkey, 28–30 November 2013; pp. 127–131. [Google Scholar]
- Australian Energy Market Operator. Modelling Requirements. Available online: https://www.aemo.com.au/Electricity/National-Electricity-Market-NEM/Network-connections/Modelling-requirements (accessed on 8 October 2018).
- Chauhan, N.S. Decision Tree Algorithm—Explained. Available online: https://www.kdnuggets.com/2020/01/decision-tree-algorithm-explained.html (accessed on 14 January 2020).
- Poojari, D. Machine Learning Basics: Decision Tree from Scratch. Towards Data Science. Available online: https://towardsdatascience.com/machine-learning-basics-descision-tree-from-scratch-part-ii-dee664d46831 (accessed on 2 August 2019).
- Reginato, R.; Zanchettin, M.G.; Tragueta, M. Analysis of Safe Integration Criteria for Wind Power with Induction Generators Based Wind Turbines. In Proceedings of the 2009 IEEE Power & Energy Society General Meeting, Calgary, Canada, 26–30 July 2009; pp. 1–8. [Google Scholar]
- Bluttman, K. Excel Formulas and Functions for Dummies, 5th ed.; John Wiley & Sons: Hoboken, NJ, USA; pp. 1–400.
- Sayad, D.S. Decision Tree–Regression. Available online: https://www.saedsayad.com/decision_tree_reg.htm (accessed on 1 January 2010).
- Rokach, L.; Maimon, O. Decision Trees. In Data Mining and Knowledge Discovery Handbook; Springer: Boston, MA, USA, 2005; pp. 165–192. [Google Scholar]
- Rocca, J. Ensemble Methods: Bagging, Boosting and Stacking. Towards Data Science. Available online: https://towardsdatascience.com/ensemble-methods-bagging-boosting-and-stacking-c9214a10a205 (accessed on 23 April 2019).
- Glen, S. Prediction Error: Definition. Statistics How To. Available online: https://www.statisticshowto.com/prediction-error-definition (accessed on 2 October 2019).

**Figure 1.**37-bus test distribution system, Reprinted from ref. [1].

**Figure 2.**Nine-bus test distribution system, Reprinted from ref. [1].

**Figure 10.**Comparison of the prediction error of the decision tree algorithm and mathematical model for IG–based WPPs.

**Figure 11.**Comparison of the prediction error of the decision tree algorithm and mathematical model for DFIG–based WPPs.

**Figure 12.**Voltage profile for IG-based WPPs for Scenario 4 in Table 3.

**Figure 13.**Voltage profile for DFIG-based WPPs for Scenario 2 in Table 4.

Case Study | Topology | I_{sc} (kA) | SCC (MVA) | P_{wind} (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 |

Step | Pseudo Code | Description |
---|---|---|

1. | Load IG_data/DFIG_data (extended) | The table that contains extended data (SCR, X/R_{PCC}, dV_{PCC}) is loaded as training data set. |

2. | Feature variable (input) ← SCR,X/R_{PCC} | Assign feature and response variable |

response variable (output) ← dV_{PCC} | ||

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/R_{PCC}, dV_{PCC})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/R_{PCC} | Request input from the user |

6. | P_{wind} ← [SCC/SCR]Input = (SCR, X/R _{PCC}) | Find power points for respective SCR values |

7. | [dV_{PCC}] = predict (Igmodel, Input) | Predict the response variable (dV_{PCC}) from features (SCR, X/R_{PCC}) |

8. | Plot (P_{wind}, dV_{PCC}) | Plot variation in voltage profile with the amount of penetrated power |

Test No. | SCC | X/R_{PCC} |
---|---|---|

1 | 35 | 0.7 |

2 | 70 | 0.6 |

3 | 15 | 0.5 |

4 | 18 | 0.4 |

5 | 33 | 0.75 |

6 | 20 | 1.2 |

7 | 30 | 1.5 |

8 | 17 | 1.9 |

9 | 27 | 2.1 |

Test No. | SCC | X/R_{PCC} |
---|---|---|

1 | 16 | 1 |

2 | 25 | 0.45 |

3 | 45 | 0.75 |

4 | 35 | 0.7 |

5 | 23 | 0.85 |

6 | 45 | 0.6 |

7 | 15 | 1.2 |

8 | 27 | 1.7 |

9 | 34 | 1.9 |

N | P_{wind} | ∆Vp (%) | ∆Vr Related to the Proposed Decision Tree-Based Model (%) | ∆Vr Predicted by the Mathematical Model Proposed [1] (%) |
---|---|---|---|---|

1. | 7 | 2.0312 | 2.0302 | 2.2707 |

2. | 11.67 | 3.158 | 3.1583 | 3.88 |

3. | 17.5 | 3.5325 | 3.5381 | 5.217 |

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## Share and Cite

**MDPI and ACS Style**

Ghimire, S.; Alizadeh, S.M.
Developing a Decision Tree Algorithm for Wind Power Plants Siting and Sizing in Distribution Networks. *Energies* **2021**, *14*, 2293.
https://doi.org/10.3390/en14082293

**AMA Style**

Ghimire S, Alizadeh SM.
Developing a Decision Tree Algorithm for Wind Power Plants Siting and Sizing in Distribution Networks. *Energies*. 2021; 14(8):2293.
https://doi.org/10.3390/en14082293

**Chicago/Turabian Style**

Ghimire, Santosh, and Seyed Morteza Alizadeh.
2021. "Developing a Decision Tree Algorithm for Wind Power Plants Siting and Sizing in Distribution Networks" *Energies* 14, no. 8: 2293.
https://doi.org/10.3390/en14082293