Performance Assessment of Solar-Transformer-Consumption System Using Neural Network Approach

: Solar energy is one of the immeasurable renewable energy in power generation for a green, clean and healthier environment. The silicon-layer solar panels absorb sun energy and converts it into electricity by off-grid inverter. Electricity is transferred either from this inverter or from transformer, consumed by consumption unit(s) available for residential or economic purposes. The artificial neural network is the foundation of artificial intelligence and solves many complex problems which are difficult by statistical methods or by humans. In view of this, the purpose of this work is to assess the performance of the Solar Transformer - Consumption (STC) system. The system may be in complete breakdown situation due to failure of both solar power automation subsystem and transformer simultaneously or consumption unit; otherwise it works with fully or lesser efficiency. Statistically independent failures and repairs are considered. Using the elementary probabilities phenomenon incorporated with differential equations is employed to examine the system reliability, for repairable and non-repairable system, and to analyze its cost function. The accuracy and consistency of the system can be improved by feed forward- back propagation neural network (FFBPNN) approach. Its gradient descent learning mechanism can update the neural weights and hence the results up to the desired accuracy in each iteration, and aside the problem of vanishing gradient in other neural networks, that increasing the efficiency of the system in real time. MATLAB code for FFBP algorithm is built to improve the values of reliability and cost function by minimizing the error up to 0.0001 precision. Numerical illustrations are considered with their data tables and graphs, to demonstrate and analyze the results in the form of reliability and cost function, which may be helpful for system analyzers.


Introduction:
In today's scenario, demand of electricity is more than its generation. As known, conventional resources such as fossil fuels, coal, nuclear, natural gases, etc. are decreasing day-by -day due to increase in their consumption in various activities of human beings. To reduce the dependency on conventional / non-renewable energy, it is necessary to promote the use of renewable energy. Water (hydro), Wind, Geothermal, Biomass and Solar energy are considered as renewable energy resources. They can replenish themselves to restore the part, depleted by human activities. The construction of hydro power plant, wind parks, geothermal energy plant, biomass plants are very expensive and establishing far away from human habitat. Thus, construction cost of these plants and electricity transportation from power plant to consumer place are too high.
On the other hand, the solar-powered photovoltaic modules made up of silicon cell layers, metallic frame, glass casing units and wires that absorb solar energy and generate electric current. Solar panels can be installed according to its main three scopes: Residential-scope (on rooftops/ land area of houses and provide electricity to a particular house), Commercial-scope (for business/ economic purpose and non-profitable), Utility-scope (on the central area to provide electricity to a large number of customers). Thus, solar power plant needs large space to assemble only for business purpose, whereas on the other hand it can be easily incorporated on rooftop of houses. Solar energy reduces pollution, global warming, green-house effect etc.. Also, International Energy Agency quotes that 26% of the world's electricity only depends on renewable energy resources and is expected to achieve 30% by 2024. As the tremendous advantages of renewable energy resources viz. lower maintenance cost, health and environmentally friendly, less dependent on import of energy, replenish timely over the nonrenewable energy, the world is evolving to sustainable energy and a sustainable future.
From all this, solar energy is the only renewable energy available from large scale to small scale and approachable for residential area [1][2][3][4] . The authors considered residential solar-powerplant system incorporated with transformer electricity, to generate electricity and that can easily assemble on the roof top of houses. Considered system consists of three main subsystems viz. Solar power automation subsystem comprises Solar panels, off grid inverter, system monitoring unit, Battery bank: electricity from Transformer subsystem to our houses and Consumption unit, as shown in Fig. 1. The prime objective of this work is to study a reliable, economic, and quality rich system.
When the word 'reliable' was inculcated with hardware, software or theory of these, it acknowledged by 'reliability'. During World War II, the word 'reliability' acclaimed for analyzing the missiles. After that reliability leaves an impression on every device to improve the quality of individual component or whole product. As the development continues, complexity of devices increased with the demand of more reliable product [5][6][7] . A remarkable progress has been recognized in the domain of equipment, complex system, industries, and organizations. To estimate the reliability, failure measures of component(s) need to be evaluated. According to theory of reliability, multi-component system can be evolved into mathematical models either in probabilistic or integro-differential equations, by choosing suitable design parameters such as deficiencies, breakdown(s), and recovery of the system [8][9] . One can work out on these equations for analyzing reliability, cost, system availability and the parameters from which system is more effective using well known techniques such as fault tolerant tree, stochastic reward nets, Petri nets, Monte Carlo introducing supplementary variable, copula method, regenerative point method etc. 10 .
All these and many more methods are sufficient to evaluate the different reliability parameters but inefficient to improve the existing result and update the failures and repairs 11 . Many authors discussed the failures and recovery modes of components and hence system performance 12 . System has been analyzed with its reliability and mean time to system failure that may be increased with increasing the number of components in its subsystem [13][14] .
Recent era involves many soft computing techniques such as fuzzy logic theory (inputs depend upon dependency/ interdependency of variables), neural network approach (when the desired output is known and calculated output is improved to desired extent) , evolutionary genetic algorithm etc. to establish the level of results [15][16] . Out of these techniques, neural networks approach, inspired by the biological neurons system of humans, is extensively incorporated with solving and improving the results of problems related to complex engineering structures. Basically, neural network architecture are considered, depends on their components; namely; set of neurons, connected network and learning / training mechanism. Learning mechanisms are mainly derived by Supervised, Unsupervised and Reinforced learning mechanism. In Supervised learning, the system is trained using well defined set of input and output data that is based on previous experience(s).To improve the performance of the system, gap can be evaluated between computed and desired output. In Unsupervised learning, the system is trained using input data along with structured features of self-learning while target output is not present with the network. Different from these, in Reinforced learning, only learning process with reward or penalty is provided to the network that depends on correct or incorrect actions performed. Besides with learning mechanism, structure of interconnected network(s) includes the following architecture:  Single layer feed forward architecture comprises of two layers, input and output, connected by synaptic links that carries the weights. Only output layer computes the result, hence its name is single layer.  Multilayer feed forward architecture incorporate with multiple layers; input, hidden and output; connected by weighted synaptic links. Hidden layer neurons also perform computation before output layer and refine the results. It follows bidirectional propagation i.e. firstly forward and then backward to reduce the error and optimize the results. 867 synaptic links with at least one self-feedback loop, that fed back the output/ variance in output into itself as input. It also performs bidirectional propagation i.e. firstly feed forward followed by recurrent loop. If evaluated result is not up to desired output, the learning mechanism is employed to make changes and move towards the right prediction during back propagation. It stores information as gradient for future amendments. But if initial gradient is small, the upgradation of weights in further layers will be smaller, that arises the problem of vanishing gradients. Due to which, the network fails to train, reducing the error and optimize the results. Keeping all these facts in mind, authors give the priority to neural network multilayered arrangement consists of three main layers: input, hidden and output. These layers are associated with synaptic links that assimilate the weights and learning algorithm to govern the system. A wellconnected set of neurons and learning mechanism describe the process of adjusting/ updating the weights to desired accuracy and minimize the errors in each iteration using feed forward back propagation neural network (FFBPNN) structure and gradient descent algorithm. It was formerly proposed in 1970s for training the system and minimizing the errors appropriate for required precision. Some analysts have applied the evolutionary algorithm on multi-objective optimization problem to evaluate reliability of redundant components. The researchers obtained a novel NN, the variable weights, which determine enormous ability to cope with complicated recognition and classification problems [17][18] .
The stand-alone photovoltaic residential generation system studied the uncertainties of solar radiation due to environmental conditions with component failures 19

. Monte Carlo Simulation
Method is used to evaluate the application of solar panels in a vigorous manner 20 .
Analysts recapitulated the availability, existing status, promotion policies and future possibilities of different forms of solar energy [21][22][23] . Some researchers make it multipurpose and more beneficial for the masses latest inclinations and innovations. To enhance the clean and green energy, they proposed that solar power plants may be installed in such a way that they work in accord with hydro and methods of power generation. The authors discussed the working, and types of solar panels. They highlighted the various applications and methods to endorse the benefits of solar energy, as compared to other forms of conventional energy 24 . This paper is designed to assess the reliability parameters and effective cost of Solar-Transformer-Consumption unit (STC) system and optimize the results up to desired extent using learning mechanism of FFBPNN. System Description: Firstly, French physicist Edmond Becquerel discovered the science of generating electricity with solar panels in 1839. Afterwards, Willoughby Smith (1873), William Grylls Adams and Richard Evans Day (1876), American inventor Charles Fritz (1883) and many more worked on Becquerel selenium solar cell. In 1905, Albert Einstein derived the solar energy potential on broader scale. Daryl Chapin, Calvin Fuller, and Gerald Pearson, firstly, developed silicon photovoltaic cell at Bell laboratory in 1954. By which, solar energy was captured and converted into usable source of electricity. At the beginning, conversion of solar energy into electricity was a slow process as well as the cost was too high. Subsequently, design of solar panels, number of states, federal incentives and policies driven down the cost that is easily available at residential scope as well. For residential scope, the authors examined the Solar-Transformer-Consumption (STC) system, consists of following subsystems: 1. Subsystem S -Solar power automation: It comprised solar panels, off grid inverter, system monitoring unit and Battery bank. The solar panels absorb light from sun and change that energy to DC (Direct Current). The off-grid inverter converts DC to AC and stores it into battery bank. The system monitoring unit administers the power, voltage and current of the system. 2. Subsystem T -Transformer: It connects with electricity power grid, commonly named hydel, and regulates electricity from consumption places to our residence or business.
3. Subsystem C -Consumption unit: Consumption unit or load where the whole electricity is being used for different purposes.
All the units of subsystem S are interconnected and work with reduced efficiency due to failure of off -grid inverter and battery bank if subsystem T works well. At this moment, if subsystem T fails, the system will fail completely. Similarly, if subsystem T may fail first then system reduces its works efficiency and after that, may fails due to failure of off -grid inverter and battery bank. That means, the complete system may fail due to failure of both subsystem S and T simultaneously. of the system state. Failure of subsystem C becomes the cause of complete failure of system from any of the system state. Figure 1 depicts the STC system layout and all its perspectives considered by authors are shown in Fig. 2
Step  Table 1 shows the reliability values for some iterations, which approach to desired output up to 10 -4 error tolerance and graphically depicts in Fig. 7. From equation 39, change in values of cost function, for C 1 =1 unit, C 3 =1 unit and distinct values of repair cost C 2 = 0.1, 0.2, 0.4, 0.6 units, shows in Fig. 8.