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High-voltage transmission lines are vital assets to electric utility as these lines transmit electricity generated by power stations to various areas throughout the nation. When exposed to the environments, transmission lines are susceptible to various types of failures such as lightning strikes, flora, and fauna encroachments. Fault on transmission lines can cause total blackout, and hence, fault clearing system is provided to minimize the effect of faults to the power system. The commonly used protection device to curb this problem is the use of protective relays. Failure of protection device may reduce the reliability of power system protection that will affect the total performance of the power system. Hence, the need to carry out analysis on the reliability of protective relays to determine if these relays carry out their function as at when required is envisaged. In this research, 4 years (2013–2016) forced outage data of the relays in Ogorode 330kv transmission network are considered. Several indices are calculated for evaluating the reliability of the relays. Mathematical models were developed through the writing of codes in the MATLAB 2015 environment for different scenarios, and the generated models were used to predict how reliable the performance of the relays will be in the future. The obtained results show that the relays in the network have a debugging failure rate and as such they are mostly affected by random external events.

Adequate power supply is essential for a country’s development,[

The power transmission system is a highly sensitive and safety critical domain. Faults such as switching surges and short circuits cannot only damage the sophisticated and expensive components, like transmission lines or transformers, but could also lead to catastrophic consequences like the 2005 Moscow power blackout.[

Single line diagram of 330kV ogorode transmission station

The method used in this research work is solely dependent on the data obtained from the company log books to calculate the parameters needed for the relay reliability analysis. Operational data for 4 years (2013–2016) comprising forced outage reports on relays, the date, name of the sub-regions/work centers, name of the substation, transmission lines nomenclature, voltage level, relay tripping indication, cause of the outage, time out, outage duration (h), last load recorded (MW), and energy loss (MWhr) per each outage were collated in addition to personal visit to the control room to see how these data are taking and recorded by operators in the events of failure. The indices of reliability have been calculated using equations 1–6[

Where

ROH = relay operating hour

RF = Relay failure

DT = Downtime

NF = Average number of failures in the study period

TNF = The total number of failure in the study period

% ANF = Average number of failure in percentages.

The MATLAB 2015 program was employed in generating the codes subsequently, mathematical models of the relays reliability were developed. The reliability of the relay was modeled as a polynomial function through the use of curve fit tool program in the MATLAB environment based on data collected. The resulting expression under running of the codes is given in equation 8.

Where;

_{1} = −0.02833

_{1} = 0.225

_{1} = −0.5467

_{1} = 1.32.

Similarly, the MATLAB program shown in Appendix B is employed in generating the mathematical model of the failure rate of the relay. The failure rate of the relay is also modeled as a polynomial function of degree three. This also is achieved through the use of curve fitting tool program in MATLAB as contained in Appendix B. This is done to obtain a general expression that models the behavior of the relay failure rate based on the collected data.

The resulting equation on running the codes contained in Appendix B is given in equation 9.

Where

_{2} = −0.022

_{2} = 0.2275

_{2} = −0.7575

_{2} = 0.8740.

The monthly reliability of the relay for the year 2017 is predicted using its mathematical model which is achieved through simulation of its Simulink model with the appropriate input values.

Reliability indices for relay

Predicted monthly reliability of relays for 2017

Plot of predicted reliability with time 2017

The monthly failure rate of the relay for the year of 2017 was also predicted using the obtained mathematical model which is achieved through the writing of codes in the MATLAB environment as shown in Appendix B.

Predicted monthly failure rate for 2017

In many cases, computed data are plagued with errors, and the generated or fitted equation may be taken to be a better representation of the actual relationship between the dependent and independent variables than the collected data. To test the validity and accuracy of a given fitted equation, the following can be carried out to getting an estimate of the error of the fit. The first areas of interest we can use to look at how good the fit is are the residuals. Suppose that we are fitting a function _{i}

Now let the collected data have a mean or average value given by The sum of the squares of the deviation of the collected data from the mean is:

The r-squared value is then computed as follows:

If ^{2} = 1, then the function would be a perfect fit to the collected data. Hence, the closer ^{2} is to 1, the better the fit.

The above model validation computation can be done through the use of MATLAB codes. The MATLAB codes for the computation of ^{2} value for reliability and failure rate of the relay are given in Appendix C and D [

Fitted plot of the reliability with time

The monthly failure rate of the relay for the year of 2017 is predicted using the generated mathematical model. Tables

Comparison of computed and fitted values of the relay reliability

Comparison of computed and fitted values of the relay failure rate

Fitted plot of failure rate with time

According to the property of relay protection system, this research uses the historical forced tripping of the breakers to analyze the MATLAB which was used for the analysis of the relay reliability. The developed model validation and computation are done through the use of MATLAB codes. The mathematical model developed is used to predict the reliability and failure rate of relays in 2017, this is to test its accuracy, and hence, this method provides alternative to other methods used for the same purpose.