Two accurate hybrid islanding detection schemes for distribution network

Abstract

In this paper, two accurate hybrid islanding detection schemes are proposed based on Wavelet Transform and Stockwell transform (S-transform). The proposed methods use the potential of sequence voltage (negative) retrieved at the target Distributed Generation (DG) location of the distribution network under study. In one of the schemes, Discrete Wavelet transform (DWT) is applied to process the negative sequence voltage signal and for its decomposition, which is further used to extract six statistical features like energy, entropy, mean, kurtosis, standard deviation, and skewness from the reconstructed DWT coefficients. Test and train data sets are generated with the wide variation of loading conditions, and optimal features are chosen from the full feature set by forward feature selection method (FFS) during the training process by an artificial neural network (ANN). After that, the trained system is tested to get the detection result. Another scheme presented in this paper for islanding detection is based on S-transform, which is used to decompose the negative sequence voltage signal. Amplitude, frequency, and phase are the three coefficients acquired from the pre-processing of the raw signal by S-transform. Then the cumulative sums of the energy content of the S-transform coefficients are determined and are compared with a threshold value to get the detection result. The proposed schemes are tested in a distribution network consisting of two 9 MW wind farm driven by six 1.5 MW wind turbine connected to 120 kV main grid through a 25 kV, 30 km feeder. Several cases have been investigated like normal condition, islanding, DG line trip, disconnection of point of common coupling, and sudden change in load to test the performance of the proposed schemes. It can be observed from the results that both the approaches gave high accuracy in the detection of islanding conditions and demarcates properly from the non-islanding state. However, results show that the S-transform based approach provides a better resolution and quick detection of islanding than the wavelet transform approach.

Keywords

Artificial neural network islanding detection wavelet transforms distributed generation S-transform

1 Introduction

Increasing power demand, need for customer reliability, growing popularity for alternative power generation technologies such as fuel cell, wind, water turbine, and solar photovoltaic (PV) systems and customer demands for better power quality, the distributed networks involving Distributed Generations (DGs) are required for most of the power companies. Microgrids are good possible substitute to present conventional centralized power system. Microgrids are limited regional energy suppliers which are very helpful in minimizing energy expenses emissions by taking advantages of distributed energy resources (DERs). This thesis investigates the various optimization techniques which are helpful in design and operation of microgrid. The power system is traditionally consist of centrally controlled power plant which is used to drive various voltage level complex interconnected power system [1]. Distributed generation (DG) is very much significant in the future generation system. It is capable of lowering costs, improving reliability, reducing emission and expanding energy options. A switable penetration of DG regulate the network in the desired way. The size of a distributed generation system has range from few KW to a few MW. DGs has become the driving factor of microgrid operation.

Nowadays whole world is very serious about energy technologies. Due to environmental issues like pollution and global warming the world try to shift from non renewable energy resource like fossil fuels towards renewable energy resource. With the advent of renewable energy sources, the intermittent availability of energy from distributed energy resources add-up to this complexity. Hence, recently the Distributed Generation (DG) has gained popularity and momentum because of awareness and market deregulation for a clean environment [2]. However, some issues limit the uses of DGs, such as islanding detection.

The integration of DG with the grid is a complex process. From protection point of view there should be fast and good communication between DG project developer and grid authorities, this requires complex modeling of protection design of DGs. Therefore, it is essential to note that while using the DG in power distributed system, it is capable of identifying the case of islanding from the non-islanding one. To detect an islanding situation, one has to monitor the parameters of DG output and system, and then decide whether islanding has taken place or not. The islanding detection approaches are classified into two main categories, i.e., local and remote. Remote islanding detection is considered as the grid side detection, and DG side islanding detection is considered as the local detection. Local and remote approaches are further divided into power line signaling schemes, transfer trip schemes and passive, active, hybrid methods, respectively. In this paper, we are investigating the islanding with local hybrid techniques.

The initiatives taken to improve the smartness in the grid must start from the lower stream of the electrical grid, i.e., distribution network. There is traditional evolution of the distribution grid. In recent years, there is huge increment in load demand and due non- linear power electronics and sensitive loads power quality problems arise and this also result in increased distortion in system. Therefore, the future electrical network is required to be flexible, accessible, reliable and cost effective to become smarter grid in all forms of its growth and development. Challenges in power system issues found in the electrical distribution system. Table 1 shows some of the recent references of islanding detection.

Table 1
Recent literature summary

References Summary

[3] An overeview of different islanding detection approaches in terms of their effectiveness, merits, viability, and feasibility has been presented

[4] It presents standard test systems, various issues related to islanding detection and shifting of research trends in different islanding detection approaches.

[5] It proposes a robust hybrid islanding detection method for an early detection of islanding event accurately in distribution systems by using the 2-step genetic algorithm (GA) with DGs.

[6] A hybrid islanding detection approach by combining the remote and passive methods has been proposed in the distribution systems with DGs installed by a 2-step GA approach. Here a hybrid islanding detection approach by combining the remote and passive methods has been proposed.

References	Summary
[3]	An overeview of different islanding detection approaches in terms of their effectiveness, merits, viability, and feasibility has been presented
[4]	It presents standard test systems, various issues related to islanding detection and shifting of research trends in different islanding detection approaches.
[5]	It proposes a robust hybrid islanding detection method for an early detection of islanding event accurately in distribution systems by using the 2-step genetic algorithm (GA) with DGs.
[6]	A hybrid islanding detection approach by combining the remote and passive methods has been proposed in the distribution systems with DGs installed by a 2-step GA approach. Here a hybrid islanding detection approach by combining the remote and passive methods has been proposed.

The voltage signal with negative sequence is used in reference [7] for islanding detection. The energy content reflects various advantages of S-transform over wavelet transforms (WTs) in detecting and localizing the islanding events and wavelet transform signal and S-transform’s standard deviation (SD contour are taken into study. Reference [8] uses wavelet transforms for islanding detection through the analysis of non-stationary signals. An islanding detection approach that provides a reliable detection in two levels is proposed in [9] using entropy, wavelet energy and an active frequency drift method with positive feedback. An islanding detection approach which is applicable for multiple DG units is presented in [10]. An approach for islanding detection of DG by using multi-gene genetic programming is proposed in [11]. An islanding detection approach for an inverter-based DG electrical system is described in [12]. References [13, 14] describes a new islanding detection approach based synchronous DG incorporated in distribution network. Reference [15] presents a passive detection technique for islanding detection approach of microgrid (MG) consisting synchronous and inverter based DGs.

From the literature, it is clear that the islanding operation of DGs is one of the major challenges form the stability point of view. Therefore, there is a pressing need for an accurate and fast islanding detection in a distribution line. The neural network-based methods, in conjunction with signal processing techniques, has the advantages of quick response and increased accuracy. However, the neural network has the demerit of considerable training time, which makes it not so popular in real-time applications. S-transform based schemes are fast, give better clarity by plotting contours, and simple to interpret [16]. The research gap in the area of islanding detection is:

very accurate islanding detection method is not investigated

stability of DGs is not considered

computational time for the detection purpose is not considered

most of the earlier conventional techniques are not so robust and simple which creates difficulty in detection of islanding event.

In this work, the accuracy, fast computational time, robustness are considered to design the proposed hybrid islanding detection scheme. The objective of this work is to develop a fast and accurate islanding detection technique that works efficiently in the power distribution system with the DG interface. To achieve this objective, the following sub-categories are considered.

Pre-processing of negative sequence voltage signal by using DWT or S-transform.

Computational burden to process large feature sets is reduced by using the feature extraction method.

Detection accuracy is enhanced by removing unwanted features by FFS technique.

Total harmonic distortion (THD) is computed for each of events and the results are analyzed graphically on histogram plots.

The proposed method is made robust to parameter variation.

As most of the islanding detection method discussed by earlier researchers have less accuracy, complicated and takes considerable computational time, so this motivated us to propose a technique which will overcome the above-said difficulties and will make the process simple. Also as said above major challenge arises to maintain the stability of DGs when islanding operation takes place and there is always a need of fast and accurate detection method to meet the challenge. So, two-hybrid schemes are presented here, which gives accurate islanding detection, can distinguish the islanding event correctly from other events, is simple, computational time is small and stability of the DGs is maintained. The main contributions of the proposed work are presented next:

Two accurate hybrid islanding detection schemes are proposed.

Six statistical features are introduced for the extraction of information from the collected signal for the first time for analysis purposes in the case of a wavelet-based islanding detection scheme, and it was found from the simulation results that islanding detection becomes easy, simple and accurate by that.

In the wavelet-based scheme, the forward feature selection method is introduced, which enhances the detection accuracy. Also, it was noticed from the simulation results that optimal features give specific information, whereas this information is lost in case of non-optimal features. As a result of which by analyzing with optimal features, higher detection accuracy is obtained.

Another accurate islanding detection approach based on S-transform is proposed here, which uses the cumulative sum of the energy content of the features like amplitude, frequency, and phase for the first time to detect islanding conditions and to distinguish with other events.

The remaining segment of this manuscript is designed as. The detailed methodology of the proposed hybrid computational intelligence (CI) based method for islanding detection in a distribution network is presented in Section 2. Section 3 offers the implementation of the proposed strategies in the distribution network under study. Section 4 describes the simulation results and discussion, and conclusions are presented in Section 5.

2 Proposed hybrid CI based islanding detection technique

The proposed hybrid CI-based islanding detection technique uses the signal processing methods such as DWT in combination with ANN and S-transform approach. DWT is used to reduce the volume of the total data set and converting it into a set of features [17]. Six statistical features, i.e., mean, energy, standard deviation, skewness, entropy and kurtosis are acquired by DWT [18]. The energy of a signal is defined as the squared sum of absolute value of a signal. The standard deviation shows the variation from the signal’s mean value. The mean is the signal’s average value. Kurtosis indicates the distribution system’s outlier prone characteristic. Skewness shows the data’s asymmetric property. Entropy gives the information on the randomness of the signal.

An artificial neural network (ANN) tries to implement the functional characteristics and structure of a biological neural network. It makes a scheme similar to the human brain to get into some decision, followed by a conclusion [19]. ANN consist of a cluster of neurons working together to crack typical problems. The main feature of ANN is the learning process by which it monitors its weight and biases and eliminates the error. Here the proposed ANN is of supervised type with a multilayer feed-forward back propagation training algorithm with input, hidden, and output layers. By subtracting the actual response from the desired one, the error signal is determined, which travels in the backward direction against the synaptic weight direction.

Train and test sets are prepared with the various operational condition to make the scheme robust to parameter variations and scaled-down in the range of [0, 1]. Feature selection is the method to eliminate unnecessary abrupt features, which only makes the learning process complex and reduces accuracy. There are several feature selection methods among which the forward feature selection (FFS) method is adopted in the proposed work. This FFS works by adding appropriate features into a growing subset that can portrait the target correctly.

Here FFS method is used during the training process for selecting the optimal features from the complete feature set. Finally, ANN is used to detect islanding conditions and distinguishing them from non-islanding conditions. Five conditions have been investigated to validate the proposed scheme, i.e., normal, islanding, DG line trip, point of common coupling (PCC) disconnect, and sudden change in load. The first proposed hybrid CI-based islanding detection approach comprises ANN in combination with wavelet transform, and the second one is based on S-transform (ST).

S-transform is a collective properties of short-time fourier transform (STFT) and WT. It gives the multi-resolution technique which consists of absolute phase of every frequency component of the signal. By using WT only, a range of frequency is achieved, but in ST, instantaneous frequency is easily obtained. Also, ST gives a better global view and prone to noise [20]. From the ST, we acquire amplitude, frequency, and phase information of the signal.

In the second proposed detection scheme, negative sequence voltage is first acquired from the DG end, which is then decomposed by ST. After that, feature, like energy, is extracted from the coefficients of S-transform, and its cumulative sum (CUSUM) is determined. A threshold is then set by using the trial and error approach and is compared with the CUMSUM to identify the islanding condition from the non-islanding one. S-transform based Cumulative sum detector is found to be very accurate to determine islanding conditions. The detailed description of WT is presented in references [21, 22], and S-transform is explained in reference [23].

2.1 Performance evaluation using hybrid DWT-ANN method

Negative sequence voltage is retrieved at targeted DG position, and then the signals are decomposed by using DWT [17, 24]. Ten level decomposition is performed to collect the original information, as shown in Fig. 1.

Fig. 1

Ten level DWT decomposition.

In Fig. 1, X[n] is the negative sequence voltage collected from DG-1 end, and g[n] and h[n] are the high and low pass filters whose outputs are approximation (a) and detail (d) coefficients. Statistical features are then obtained from the DWT coefficients. The definitions of the extracted six features are given in [25]. So the feature set consists of 60 features (10 level decomposition×6 features). Train and Test data set are developed with a wide range of operational loading conditions including normal, minimum, and maximum loading. For 48 different operating conditions and 5 cases, train and test data samples are generated. After that, the feature set with the best predictive chances is selected by the FFS method during the training process by ANN. Out of 60 features, ten optimal features are chosen by the FFS method during training, as shown in Table 2.

Table 2

Best Feature Set by FFS Method

Signal	FFS (10 best features)
Voltage	Standard Deviation (D5, D6, D8), Energy (D6, D8), Kurtosis (D8), Skewness (D7), Entropy (D8), Mean (D7, D8).

The performance of FFS approach has been depicted in Fig. 2. It can be observed from Fig. 2 that with the FFS method feature plot, useful information can be collected whereas, without the FFS method feature plot, information is lost. Further, the trained ANN network is tested with the best-selected feature [25]. In the present problem, 240 samples (48 operating conditions×5 cases) are taken, and the size of the training matrix is (168×60) with the test matrix as (72×60), such that the trained data is 70% and the tested information is 30%. Eighteen islanding samples and 54 non-islanding samples are considered for testing. Among 54 non-islanding samples, 12 samples with the normal condition are taken for analysis, and 14 samples each are taken for the other three states, i.e., DG line trip, PCC disconnect, and sudden load change. In ANN, the islanding case is denoted by ’1’ and non-islanding by ’0’. The complete proposed technique by using hybrid DWT-ANN is depicted in Fig. 3.

Fig. 2

Feature plot: a) With the FFS method, b) Without the FFS method.

Fig. 3

Proposed DWT-ANN based technique.

The training process of ANN with feed-forward backpropagation network and Levenberg-Marquardt [26] training function is depicted in Fig. 4.

Fig. 4

Structure of proposed ANN during the training process.

The size of the hidden layer considered is 10. The performance of the network is determined by using the mean square error (MSE) function [27]. The size of the input layer during training depends upon the total data set considered (i.e., 168 in the present problem). The size of the output layer is 1.

2.2 Performance evaluation using S-transform based method

The proposed S-transform based approach uses time-frequency transform for islanding detection in distribution systems incorporated DGs. This method is based on spectral energy content of negative sequence component of voltage signal, and it is used for testing the islanding detection. The negative sequence voltage has been retrieved at the targeted DG location, and decomposition of the signal with S-transform is carried out. After that, the energy of the coefficients of S transform (frequency, amplitude, and phase of the signal) is determined, and the Cumulative sum (CUMSUM) of energy is found. A threshold is selected by trial and error and is compared with CUMSUM energy to detect islanding case. Fig. 5 depicts the islanding detection approach by using S-transform.

Fig. 5

Proposed S-transform based islanding detection technique.

3 Islanding detection in a distribution system

DGs are present in a distribution system along with the main utility grid, which delivers power to various loads. Accurate detection of islanding is very much essential in such a type of system to prevent instability. To show the performance of hybrid technique for an islanding detection approach, a distributed system structure is shown in Fig. 6 [28].

Fig. 6

Structure of Distribution network under study.

The distribution network under study is shown in Fig. 6 consisted of two 9 MW wind farm driven by Doubly fed induction generator (DFIG) [29]. The detailed DFIG model in this distribution network under study is shown in Fig. 7.

Fig. 7

DFIG model under study.

Negative sequence voltage samples are retrieved at (DG-1) end and wind speed is maintained at a speed of 10 m/s [29]. It is found from simulation results that at 200 kHz sampling frequency with a system frequency 50 Hz, the model under study works well, so it is taken for further analysis. Four thousand samples per cycle are collected initially, and two cycles (before and after islanding) are considered for further investigation. The parameters of proposed hybrid model under study are given in Table 3.

Table 3

Parameter Setting of the Model

Equipment	Rating
Generator	Rated MVA = 2500, frequency (f)=50 Hz, rated kV = 120, Base Voltage (Vbase)=120 kV
Distributed generations (DGs)	Two wind farms each of 9 MW with six 1.5 MW DFIG wind turbines connected to a 25 kV distribution network through 30 km, 25 kV feeder
Transformer (T1)	Rated MVA = 47, f = 50 Hz, rated kV = 120/25, Vbase = 25kV
Transformers (T2, T3)	Rated MVA = 1.75*6, Vbase = 0.4 kV, rated kV = 25/0.4.
Distribution Lines	PI-sections, 30 km each, Vbase = 25 kV, rated MVA = 20, rated kV = 25.

4 Results and discussion

In this work, five different cases are investigated, and they are:

Case 1: Normal Condition: All the CBs (as in Fig. 6) are in closed conditions so that the voltage waveform at the DG end is sinusoidal.

Case 2: Islanding Condition: CB-1in Fig. 6 is initially closed and it is opened with a transition time of 0.01 s to 0.02 s. All other CBs are permanently closed. After switching off circuit breaker (CB-1) (in Fig. 6), the entire part of distribution system is isolated from the utility grid.

Case 3: DG Line Trip Condition: CB-1 in Fig.6 is permanently closed. CB-3, as in Fig. 6, is closed initially, and it is then opened with a transition time 0.01 s to 0.02 s.

Case 4: PCC (in Fig. 6) disconnect condition: CB-1 to CB-4 in Fig.6 is initially closed. When the PCC gets detached, then these 4 CBs mentioned above is opened, and the grid gets disconnected from the rest of the system

Case 5: Overloading Condition: Suddenly, the load ‘L2’ in the DG-1 side (as shown in Fig. 6) is increased up to 50%.

All the above cases have been tested for two cycles, one before the event occurrence and other after the event occurrence. Figures 8 12 depict the total harmonic distortion (THD) [29] output for the average case, and other issues, i.e., islanding, DG line trip, PCC disconnect, and overloading condition, respectively in the form of histogram plots with the fundamental frequency taken as 50 Hz.

Fig. 8

THD output for normal condition (Case 1).

Fig. 9

THD output for islanding condition (Case 2).

Fig. 10

THD output for DG line trip condition (Case 3).

Fig. 11

THD for PCC disconnect condition (Case 4).

Fig. 12

THD for overloading condition (Case 5).

From Figs. 8 12, it can be observed that the THD for the normal case comes out to be 5.03%. In contrast, there is an abrupt increase in THD for other cases, i.e., 85.39% for islanding condition, 85.35% for DG line trip condition, 85.29% for PCC disconnect condition, and 5.05% for overloading condition. From these five case studies, it is clear that there is not much variation in THD for overloading conditions compared to the normal case. Therefore, the overloading condition is not considered as an event.

4.1 Simulation results by using hybrid DWT-ANN method

Table 4 presents the change in extracted energy for different cases. This change in energy is calculated by subtracting the energy obtained after islanding from that of the energy obtained from normal conditions.

Table 4
Change in Energy Comparison for Different Cases

Case Change in energy (ΔE)

Normal condition 0.0041

Islanding condition 0.965

DG line trip condition 0.032

PCC disconnect condition 0.025

Overloading condition 0.0076

Case	Change in energy (ΔE)
Normal condition	0.0041
Islanding condition	0.965
DG line trip condition	0.032
PCC disconnect condition	0.025
Overloading condition	0.0076

From Table 4, it can be observed that change in energy is 0.965 for the islanding condition compared to 0.0041, 0.032, 0.025, and 0.0076 for other non-islanding cases. Hence, it can be concluded that in case of an islanding condition, the energy change is much more significant from the normal state, and thus, it can be distinguished from other non-islanding conditions. From the training performance plot depicted in Fig. 13, it can be observed that the neural network achieved the mean square error (MSE) at the end of the training process, and it is converged in 14 iterations.

Fig. 13

Training performance plot of neural network.

From Fig.13, it is inferred that the performance of the neural network (NN) has been trained up to 14 epochs and the best performance is at eight epochs with the best validation performance as 0.10731. Input samples for retrieved energy of negative sequence voltage are taken for both without and with islanding. Assigning the target values as 0 for non-islanding and 1 for islanding, the training, and testing processes are obtained. The test plot with the proposed hybrid DWT-ANN method is depicted in Fig. 14.

Fig. 14

Islanding detection by using proposed hybrid DWT-ANN method.

Figure 14 shows ‘0’ for non-islanding samples and ‘1’ for islanding samples. It can be seen from Fig. 14 that islanding and non-islanding samples are detected with 100% accuracy.

4.2 Simulation results by using S-transform based method

Figure 15 depicts the negative sequence voltage collected from DG-1 end of Fig. 6 having two cycles, one before islanding and one after islanding. As the sampling frequency is taken is 200 kHz, so samples per cycle are 4000.

Fig. 15

Negative sequence voltage plot.

From Fig. 15, it can be observed that one cycle before islanding, the magnitude of the negative sequence voltage is very small. In contrast, after islanding, there is a sudden increase in the magnitude of negative sequence voltage, which indicates the occurrence of islanding condition. Fig. 16 depicts the S-transform plot of the signal shown in Fig. 15.

Fig. 16

Islanding detection using the S-transform plot.

Comparing Fig. 14 and Fig. 16, it can be inferred that the S-transform technique shows better clarity of results as compared to the hybrid DWT-ANN method. From S-transform contour, coefficients like amplitude, frequency, and phase are obtained. After that, energy is extracted from these coefficients, and CUMSUM is determined for each. A threshold is selected by trial and error and is compared with CUMSUM (energy) of S-transform coefficients to detect islanding conditions. To determine the threshold value, the investigation has been carried out with islanding and non-islanding (DG line trip) data, which is shown in Fig. 17.

Fig. 17

cumsum (Energy) Plot.

It can be observed from Fig. 17 that the CUMSUM (energy) plot clearly distinguishes the islanding data from the non-islanding one and decides a threshold which will restrict the two cases, i.e., islanding with non-islanding one. To validate the two proposed methods in this paper, a comparison has been carried out with the results of other researcher’s published work with the same distribution network under study, which is shown in Table 5.

Table 5

Comparison with other Research Works

Scheme	Islanding detection accuracy (%)	Non-islanding detection accuracy (%)
Reference [17]	90	91
Reference [22]	100	92
Proposed hybrid DWT-ANN	100	100
Proposed S-transform based	100	100

It can be observed from Table 5 that both the proposed method in this paper gives 100% accuracy compared to other researcher’s work. Further, the islanding detection time for the two proposed ways is investigated, which is shown in Table 6.

Table 6

Detection Time

Proposed Scheme	Detection time (sec)
Hybrid DWT-ANN	600
S-transform based	90

It can be noticed from Table 6 that S-transform is a faster detection method than the hybrid DWT-ANN method. Though both the proposed ways give 100% accuracy, the S-transform based approach provides more clarity in the visualization of the results and is faster than the other one. So S-transform based method is recommended for islanding detection in a distribution network.

5 Conclusions

This paper focuses on CI based technique in combination with signal processing technique to detect islanding. In this paper, two approaches, i.e., hybrid DWT-ANN and S-transform approaches, are considered. In the wavelet-based scheme, the forward feature selection method is introduced, which enhances the detection accuracy. Also, it was noticed from the simulation results that optimal features give specific information, whereas this information is lost in case of non-optimal features. As a result of which by analyzing with optimal features, higher detection accuracy is obtained. Another accurate islanding detection approach based on S-transform is proposed here, which uses the cumulative sum of the energy content of the features like amplitude, frequency, and phase for the first time to detect islanding conditions and to distinguish with other events. From the obtained results, it is clear that both the approaches gave accurate detection of islanding condition. The S-transform approach of islanding detection passed a better resolution and less simulation time than the hybrid DWT-ANN system. Further the detection results of both the proposed approaches are compared with some other researcher’s work’s impact and are found to give better accuracy. So finally concluded that two robust islanding detection techniques are proposed in this paper, which can be implemented in real-time; however, S-transform based detection method is a better choice due to its clarity in visualization and fast operation. This work can be further extended for detecting the islanding for different DG sources.

Footnotes

Acknowledgments

This research work was supported by “Woosong University’s Academic Research Funding –(2020–2021)”.

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Two accurate hybrid islanding detection schemes for distribution network

Abstract

Keywords

1 Introduction

2.1 Performance evaluation using hybrid DWT-ANN method

Table 4 Change in Energy Comparison for Different Cases Case Change in energy (ΔE) Normal condition 0.0041 Islanding condition 0.965 DG line trip condition 0.032 PCC disconnect condition 0.025 Overloading condition 0.0076

Footnotes

Acknowledgments

References

Table 4
Change in Energy Comparison for Different Cases

Case Change in energy (ΔE)

Normal condition 0.0041

Islanding condition 0.965

DG line trip condition 0.032

PCC disconnect condition 0.025

Overloading condition 0.0076