**3. The Proposed Algorithm for the Protection Scheme**

The algorithm for the recognition of faults in the hybrid power system, incorporated with RE sources, is based on features that are extracted from both the voltage and current signals. The proposed algorithm is implemented in two steps, where in first step faults are detected and in second step, faults are classified. Furthermore, detection of the faults is also performed in two steps, where current-based Wigner distribution index (WD-index) and voltage-based alienation index (ALN-index) are evaluated. The WD-index and ALN-index are multiplied to obtain the proposed fault index (FI), which is found to be effective for the discrimination of faulty events from healthy condition as well as faulty phase from healthy phase. The FI corresponding to the faulty phase will have a higher magnitude compared to the set threshold magnitude (TM) and it has a lower value than TM corresponding to the healthy phase during all conditions. The algorithm was tested on 30 sets of data for each fault type to set a threshold value of 5000. The data set is obtained by changing the parameters including fault impedance, incidence angle of fault, location of faults at various nodes of hybrid grid, presence of noise on both

voltage and current signals etc. Classification of the faults is achieved by estimating the number of faulty phases. However, a ground fault index (GFI) using Wigner distribution function based decomposition of negative sequence current signals is introduced for discriminating double phase fault, with and without the involvement of ground. Deviations in the patterns of current and voltage waveforms during faulty events were used for the identification of faults using proposed algorithm; therefore there is no requirement for parameter normalization. The performance of the algorithm will be affected by the power network configuration and penetration level of the RE. However, the algorithm can be used in the different network configurations and RE penetration levels by changing the threshold magnitude. All steps of algorithm are described with the help of flow chart as illustrated in Figure 3. FI, GFI, current-based WD-index and voltage-based ALN-index are described below. The study is performed in MATLAB/Simulink 2017a software environment on a laptop computer which has a 64 bit operating system, RAM of 4 GB, and Intel (I) Core(TM) i5-3230M CPU@2.60 GHz processor.

**Figure 3.** The algorithm for the recognition of faults on the hybrid power system incorporating renewable energy.

#### *3.1. Current Based Wigner Distribution Index*

Wigner distribution function (WDF) is a phase space distribution function. This is effective in description of signal in a space and frequency at the same time. This can be considered to be a local frequency spectrum of the signal. This can be used for processing of both deterministic and stochastic signals. The WDF is effective in providing local frequency spectrum of the signal. Hence, it is most suitable for analysis of the faulty transients to identify the faulty events. The current signals captured at node 650 are processed using Wigner distribution function over a quarter cycle with a sampling frequency (SF) of 3.84 kHz. Window moving by one sample step is used for the continuous computation of Wigner distribution. Absolute magnitude of the output is evaluated and designated as WD-index. Energy density of current signal is used by the WD-index for estimation of the faults. This is achieved by Bilinear analysis of current signal *I*(*t*) (in time domain ) twice. The WD-index has the advantage of high concentration of energy as well as high resolution of time-frequency [26]. Following relation effectively illustrates the evaluation of WD-index by processing the current signal (*I*(*t*)) [27].

$$
\mathcal{W}\text{Dindex} = \int\_{-\infty}^{\infty} I(t + \frac{\pi}{2})I^\*(t + \frac{\pi}{2})e^{-j\omega\tau}d\tau\tag{5}
$$

here representations of symbols are as follows *t*: time (sliding variable); *ω*: signal angular frequency; *τ*: time domain based signal function.

#### *3.2. Voltage Based Alienation Index*

Alienation index is computed using sample-based alienation coefficients of voltage signals at a SF of 3.84 kHz and designated as ALN-index. This index is evaluated using the correlation coefficient (*r*) between voltage magnitudes at two different time instants as detailed below.

$$ALNindex = 1 - r^2\tag{6}$$

Here, *r* is the correlation coefficient between voltage variables *x* and *y* and can be expressed as detailed below.

$$r = \frac{N\_s \sum xy - (\sum x)(\sum y)}{\sqrt{[N\_s \sum x^2 - (\sum x)^2][N\_s \sum y^2 - (\sum y)^2]}}\tag{7}$$

here *Ns* is the numbers considered in a cycle (in this study *Ns*=64 is considered), *x* is the voltage samples measured at time *t*0, *y* is the voltage samples measured at −*T* + *t*<sup>0</sup> time where T is time period of voltage signal [28,29]. The ALN-index is evaluated with the help of moving window technique for the samples of quarter cycle. Implementation of this index is based on the comparison of data of quarter cycle considered with the data of previous quarter cycle using a moving window (one sample step). This index is effective in reducing the fault detection time because it has the merit of sharp change at the time of fault incidence. This makes the protection scheme fast.

#### *3.3. Fault Index Based on Voltage and Current Features*

A fault index (FI), based on the features of both voltage and current is introduced for recognition of faults in the hybrid power system with RE penetration. This index is computed using element to element multiplication of ALN-index and WD-index as detailed in the following relation.

$$FI = (ALNindex) \times (\mathcal{W}Dindex) \tag{8}$$

The proposed FI effectively identifies the different nature of faults in the hybrid power network with RE penetration by good accuracy and minimum time. This is achieved by comparing the magnitude of FI with pre-set threshold magnitude (TM). Individual application of ALN-index will not detect any type of fault due to its same value for all phases for all the events. However, application of WD-index individually will recognize the faults but time of fault identification will be low, which will reduce the protection speed. Hence, FI combines the merits of both ALN-index and WD-index.
