The Fuzzy Logic allows doing several things, but the most important thing it lets creates and edits fuzzy inference systems. In the matlabsimulink this simulation block diagram can be easily test the fuzzy logic controller. This given system can be done by MATLAB Simulink or by using neuro fuzzy techniques [14] .

In this paper, all the fuzzy set is defined by extending the classical set [15] . If X is the universe of discourse and its elements are denoted by x, then aA be the fuzzy set in the given universe of discourse.Let membership function is given by MF or x in A. The membership value always lies between 0 and 1. Generally in fuzzy interference system there are two types of expert system namely Sugeno type and Mamdani type both are varied by its outputs. The process of mapping all the input to an output is carried out by fuzzy logic controller. Hence based on the mapping all the decision is done as classifying the various line and shunt faults.

The first step in classifying fault is to take the input transmission line currents, and also it finds the angle. Here trapezoidal membership functions used. This model is developed in MATLAB software using fuzzy logic tool box [16] . From the input real and reactive power is calculated by using current and voltage from phase locked loop. The fuzzy rule is formed by applying fuzzy operator. The output of the membership function is shaped on the basis of firing strength of the rules. The product and minimum are most commonly used implication method. Raw data is extracted using Takagi-Sugeno system. It is developed by human expert systems that are purely linguistic rather than numerical data this steps are carried out as shown in Figure 1.

Each rule of the output is added together by the process of aggregation. Implication process is performed by aggregation of truncated output. Defuzzifier is defined as the aggregated output of fuzzy set. In defuzzification

process is the simplest and commonly used is gravity method. The information of all the inputs are combined to a single non fuzzy output which finds the type of fault occurred in transmission line. In this paper the membership functions are taken as a high, normal and low as fault range. It is denoted as follows: μ1, μ2, and μ3.

Positive, negative and zero sequence terminology is used as “Direct, inverse and zero” terminology. The complexity of the differential equations can be reduced by changing variables. Clarke transformation is used for the stationary circuits to the stationary reference frame.

Here α and β are represented as a two phase stationary variables in Clarke’s transformation, β-axis and α-axis are orthogonal. For easy analysis transformation is carried out and by using following equation three phase current value is transformed to two phase. This helps to classify the different line and shunt faults occurred in line. The resulting transformation is:

Here we consider positive sequence current as a direct current, negative sequence current as an inverse current in Figure 2. This current is calculated based on following equation:

Then the real and reactive power is computed separately for direct and inverse components by following equations:

where power is taken as p = 3IcosΦ and reactive power is q = 3IsinΦ. The overall block diagram is given below; it uses instantaneous power theory for computing active and oscillating power after fault. The source voltage is taken as 200 kV at frequency of 50Hz. Let the transmission line length is consider as either 50 km or 100 km. Here 386.4 + j293 mW/km is taken as homopolar sequence impedance (Z_o), 12.73 + j293 mW/km is taken as direct sequence impedance (Z_d). The simpower system toolbox is used to analysis test system for different cases.

The Phase locked loop estimate voltage and phase angle by feedback loop. The reactive and real power is determined by using instantaneous power theory. Here fuzzy block is used separately for direct current computation and inverse current. The above functional block diagram Figure 3. As two sources connected through a transmission lines .Instantaneous current values is taken from three phase transmission line, then current is measured by using current transformer. Three phase current values are converted to two phase reference frame as α and β by Clarke transformation.

In this test system Inverse Clarke transformation is used to get the three phase stationary reference frame from the two axis orthogonal stationary reference frame. Thus PLL is an electronic module which locks the output to the input. Here voltage is taken as input for the P-Q computation after clarke’s transformation and phase angle is used by fuzzy logic controller for power calculations and to separate average and oscillating components. To get three phase current value following formula is used as shown below:

where,

V_a, V_b, V_c are three-phase quantities.

V_α, V_β are stationary orthogonal reference frame quantities.

In this paper, frequency synthesis is done by using phase locked loop. This PLL is mostly used in communication applications. Generally we call phase locked loop as a feedback system its helps to detect the phase error and also it adjust the output phase. It consists of voltage control oscillator which adjusts the phase difference between two phases. Another important component is phase detector, which detects between the input and the output by using this PLL. Akagi [17] proposed a theory with or without neutral wire based on instantaneous values in a power system.

This theory is applicable only for the transient and also for steady state operations this generic current and voltage waveforms is called as Active-Reactive (p-q) theory or Instantaneous Power Theory (IPT). The power calculation of the p-q theory power components that is three phase voltages in the a-b-c coordinates are converted to the α-β-0 coordinates by using Clarke transformation or it is also called as an algebraic transformation in Figure 4. We consider fault transition time is taken from 0.3 sec to 0.35 sec. Similarly for Adaline fault transition time is 0.04sec to 0.24sec.

Where V₁V₂V₃ and i₁ i₂ i₃ are phase voltage and currents.

Where,

p_o is the zero sequence real instantaneous power.

p_ab is the instantaneous value of real power.

q_ab is the instantaneous value of imaginary power.

This all are the above important concepts used in this paper for easy analysis of real and reactive power computation and also by considering harmonics from 1 to 60, which includes both odd and even harmonics has been proposed in this paper.

The different power terms are defined as follows:

Power components of the p-q theory in a-b-c coordinate the currents are obtained. By using instantaneous power theory in a stationary reference frame, the non-linear load currents and also main voltages are determined which is represented in a α-β component. In zero component current is assumed to be null value.

The reactive and real load powers p_l and q_l are given:

During single line to ground fault following equation is obtained. To check the test system efficiency and also the robustness by varying the length of the transmission line as 50 km, 100 km and 200 km, and also by changing the load angle. If any line to line fault occurs in the power system then the time taken fault occurring is more due to the presence harmonics components. This is because of mutual impedance between the phases. Hence the derived equations under the line to line fault condition:

Similarly for line to line ground fault occurs at any point in a test system. Let we consider fault occur between the two phases as b and c, then the following are the equations derived during fault in a transmission line as given. The analysis of this different type of symmetrical components is used for the identification of nature of fault. During normal condition or any symmetrical fault conditions the zero sequence components and negative sequence currents are nearly equal to zero. The above procedure is used to classify the faults, in the three phase to ground fault in the beginning of the fault there will be presence of inverse and homopolar component current and it disappears at the end of the fault. The presence of only negative or inverse components represents the line to line fault has occurred in transmission line has been proposed in [12] . Similarly if negative or inverse component and zero or homopolar components presents in a transmission line be a double line to ground fault.

Table 1 shows the different types of unsymmetrical faults which occurs in the transmission line. Whereas phase fault as the more fault current flow into the system rather than the ground fault. The symbol g represents the ground.

Table 1 shows the fault current magnitude estimated by the fuzzy interference system in an unloaded system. Fault occurs at t = 0.04 s to t = 0.24 s and at the middle of the transmission line length (L = 100 km) with fault resistance of R_f = 20W, the fault magnitude estimated from transmission system is less accurate which is very far away from the source. Thus, a complete fault identification and classification module is done using the fuzzy logic controller [18] . The Adaline is trained separately for the different single line to ground fault, line to line fault and double line to ground fault in Figure 5.

In this paper to identify the faults in transmission line is based on direct, inverse and homopolar currents. Here from 1 to 60 harmonics range is considered. It consists for both odd and even harmonic ranges, the following are the various results obtained during line and shunt faults as shown. In Figure 6 is the phase a to ground faults which shows the presence of both direct and inverse current components.

During line faults such as phase a to phase b the current magnitude will be higher than the ground faults. Since while any fault occurs on the transmission lines the fault current will flow through the ground and also faulted line. Figure 7 shows the double to ground fault as phase a phaseb ground fault. Here we can absorb the magnitude of current is less when compare with the line-line faults. Figure 8 shows the Direct current, inverse current and homopolar current for phase b c fault.

In this system parameters are 200 kV system voltage, source resistance as 0.8929 Ω, source impedance as 16.58 mH. Here the faults as said to be a power quality variation they are classified as either disturbances or steady sate variations. This interferes the normal flow of current is known as fault. In such a condition the fault current will tends to move in either through ground or through affected line. Table 2 shows variation of current during fault condition, it may be either line fault or ground faults. The efficiency of the Adaline and fuzzy techniques in transmission line protection is shown in Table 3.