Mathematical modelling and optimal multivariable control of chemical processes

This work reports the developnent of a mathenatical model and distributed, multi variable computer-control for a pilot plant double-effect climbing-film evaporator. A distributed-parameter model of the plant has been developed and the time-domain model transformed into the Laplace domain. The model has been further transformed into an integral domain conforming to an algebraic ring of polynomials, to eliminate the transcendental terms which arise in the Laplace domain due to the distributed nature of the plant model. This has made possible the application of linear control theories to a set of linear-partial differential equations. The models obtained have well tracked the experimental results of the plant. A distributed-computer network has been interfaced with the plant to implement digital controllers in a hierarchical structure. A modern rnultivariable Wiener-Hopf controller has been applled to the plant model. The application has revealed a limitation condition that the plant matrix should be positive-definite along the infinite frequency axis. A new multi variable control theory has emerged fram this study, which avoids the above limitation. The controller has the structure of the modern Wiener-Hopf controller, but with a unique feature enabling a designer to specify the closed-loop poles in advance and to shape the sensitivity matrix as required. In this way, the method treats directly the interaction problems found in the chemical processes with good tracking and regulation performances. Though the ability of the analytical design methods to determine once and for all whether a given set of specifications can be met is one of its chief advantages over the conventional trial-and-error design procedures. However, one disadvantage that offsets to some degree the enormous advantages is the relatively complicated algebra that must be employed in working out all but the simplest problem. Mathematical algorithms and computer software have been developed to treat some of the mathematical operations defined over the integral domain, such as matrix fraction description, spectral factorization, the Bezout identity, and the general manipulation of polynomial matrices. Hence, the design problems of Wiener-Hopf type of controllers and other similar algebraic design methods can be easily solved.

Modelling in the evaluation of a manufacturing strategy

This thesis describes research that has developed the principles of a modelling tool for the analytical evaluation of a manufacturing strategy. The appropriate process of manufacturing strategy formulation is based on mental synthesis with formal planning processes supporting this role. Inherent to such processes is a stage where the effects of alternative strategies on the performance of a manufacturing system must be evaluated so that a choice of preferred strategy can be made. Invariably this evaluation is carried out by practitioners applying mechanisms of judgement, bargaining and analysis. Ibis thesis makes a significant and original contribution to the provision of analytical support for practitioners in this role. The research programme commences by defining the requirements of analytical strategy evaluation from the perspective of practitioners. A broad taxonomy of models has been used to identify a set of potentially suitable techniques for the strategy evaluation task. Then, where possible, unsuitable modelling techniques have been identified on the basis of evidence in the literature and discarded from this set. The remaining modelling techniques have been critically appraised by testing representative contemporary modelling tools in an industrially based experimentation programme. The results show that individual modelling techniques exhibit various limitations in the strategy evaluation role, though some combinations do appear to provide the necessary functionality. On the basis of this comprehensive and in-depth knowledge a modelling tool ' has been specifically designed for this task. Further experimental testing has then been conducted to verify the principles of this modelling tool. Ibis research has bridged the fields of manufacturing strategy formulation and manufacturing systems modelling and makes two contributions to knowledge. Firstly, a comprehensive and in-depth platform of knowledge has been established about modelling techniques in manufacturing strategy evaluation. Secondly, the principles of a tool that supports this role have been formed and verified.

Performance modelling and analysis of multiple coexisting IEEE 802.15.4 wireless sensor networks

With the features of low-power and flexible networking capabilities IEEE 802.15.4 has been widely regarded as one strong candidate of communication technologies for wireless sensor networks (WSNs). It is expected that with an increasing number of deployments of 802.15.4 based WSNs, multiple WSNs could coexist with full or partial overlap in residential or enterprise areas. As WSNs are usually deployed without coordination, the communication could meet significant degradation with the 802.15.4 channel access scheme, which has a large impact on system performance. In this thesis we are motivated to investigate the effectiveness of 802.15.4 networks supporting WSN applications with various environments, especially when hidden terminals are presented due to the uncoordinated coexistence problem. Both analytical models and system level simulators are developed to analyse the performance of the random access scheme specified by IEEE 802.15.4 medium access control (MAC) standard for several network scenarios. The first part of the thesis investigates the effectiveness of single 802.15.4 network supporting WSN applications. A Markov chain based analytic model is applied to model the MAC behaviour of IEEE 802.15.4 standard and a discrete event simulator is also developed to analyse the performance and verify the proposed analytical model. It is observed that 802.15.4 networks could sufficiently support most WSN applications with its various functionalities. After the investigation of single network, the uncoordinated coexistence problem of multiple 802.15.4 networks deployed with communication range fully or partially overlapped are investigated in the next part of the thesis. Both nonsleep and sleep modes are investigated with different channel conditions by analytic and simulation methods to obtain the comprehensive performance evaluation. It is found that the uncoordinated coexistence problem can significantly degrade the performance of 802.15.4 networks, which is unlikely to satisfy the QoS requirements for many WSN applications. The proposed analytic model is validated by simulations which could be used to obtain the optimal parameter setting before WSNs deployments to eliminate the interference risks.

Analytical model for active metamaterials with quantum ingredients

We present an analytical model for describing complex dynamics of a hybrid system consisting of resonantly coupled classical resonator and quantum structures. Classical resonators in our model correspond to plasmonic metamaterials of various geometries, as well as other types of nano- and microstructure, the optical responses of which can be described classically. Quantum resonators are represented by atoms or molecules, or their aggregates (for example, quantum dots, carbon nanotubes, dye molecules, polymer or bio-molecules etc), which can be accurately modelled only with the use of the quantum mechanical approach. Our model is based on the set of equations that combines well established density matrix formalism appropriate for quantum systems, coupled with harmonic-oscillator equations ideal for modelling sub-wavelength plasmonic and optical resonators. As a particular example of application of our model, we show that the saturation nonlinearity of carbon nanotubes increases multifold in the resonantly enhanced near field of a metamaterial. In the framework of our model, we discuss the effect of inhomogeneity of the carbon-nanotube layer (bandgap value distribution) on the nonlinearity enhancement. © 2012 IOP Publishing Ltd.

Modelling in the evaluation of a manufacturing strategy

This thesis describes research that has developed the principles of a modelling tool for the analytical evaluation of a manufacturing strategy. The appropriate process of manufacturing strategy formulation is based on mental synthesis with formal planning processes supporting this role. Inherent to such processes is a stage where the effects of alternative strategies on the performance of a manufacturing system must be evaluated so that a choice of preferred strategy can be made. Invariably this evaluation is carried out by practitioners applying mechanisms of judgement, bargaining and analysis. Ibis thesis makes a significant and original contribution to the provision of analytical support for practitioners in this role. The research programme commences by defining the requirements of analytical strategy evaluation from the perspective of practitioners. A broad taxonomy of models has been used to identify a set of potentially suitable techniques for the strategy evaluation task. Then, where possible, unsuitable modelling techniques have been identified on the basis of evidence in the literature and discarded from this set. The remaining modelling techniques have been critically appraised by testing representative contemporary modelling tools in an industrially based experimentation programme. The results show that individual modelling techniques exhibit various limitations in the strategy evaluation role, though some combinations do appear to provide the necessary functionality. On the basis of this comprehensive and in-depth knowledge a modelling tool ' has been specifically designed for this task. Further experimental testing has then been conducted to verify the principles of this modelling tool. Ibis research has bridged the fields of manufacturing strategy formulation and manufacturing systems modelling and makes two contributions to knowledge. Firstly, a comprehensive and in-depth platform of knowledge has been established about modelling techniques in manufacturing strategy evaluation. Secondly, the principles of a tool that supports this role have been formed and verified.

Modelling in the evaluation of a manufacturing strategy

This thesis describes research that has developed the principles of a modelling tool for the analytical evaluation of a manufacturing strategy. The appropriate process of manufacturing strategy formulation is based on mental synthesis with formal planning processes supporting this role. Inherent to such processes is a stage where the effects of alternative strategies on the performance of a manufacturing system must be evaluated so that a choice of preferred strategy can be made. Invariably this evaluation is carried out by practitioners applying mechanisms of judgement, bargaining and analysis. Ibis thesis makes a significant and original contribution to the provision of analytical support for practitioners in this role. The research programme commences by defining the requirements of analytical strategy evaluation from the perspective of practitioners. A broad taxonomy of models has been used to identify a set of potentially suitable techniques for the strategy evaluation task. Then, where possible, unsuitable modelling techniques have been identified on the basis of evidence in the literature and discarded from this set. The remaining modelling techniques have been critically appraised by testing representative contemporary modelling tools in an industrially based experimentation programme. The results show that individual modelling techniques exhibit various limitations in the strategy evaluation role, though some combinations do appear to provide the necessary functionality. On the basis of this comprehensive and in-depth knowledge a modelling tool ' has been specifically designed for this task. Further experimental testing has then been conducted to verify the principles of this modelling tool. Ibis research has bridged the fields of manufacturing strategy formulation and manufacturing systems modelling and makes two contributions to knowledge. Firstly, a comprehensive and in-depth platform of knowledge has been established about modelling techniques in manufacturing strategy evaluation. Secondly, the principles of a tool that supports this role have been formed and verified.

An analytical investigation into shear wall and slab interconnections between reinforced concrete modules for high -rise buildings utilising modular construction under extreme seismic and wind loading

This research investigates a new structural system utilising modular construction. Five-sided boxes are cast on-site and stacked together to form a building. An analytical model was created of a typical building in each of two different analysis programs utilising the finite element method (Robot Millennium and ETABS). The pros and cons of both Robot Millennium and ETABS are listed at several key stages in the development of an analytical model utilising this structural system. Robot Millennium was initially utilised but created an analytical model too large to be successfully run. The computation requirements were too large for conventional computers. Therefore Robot Millennium was abandoned in favour of ETABS, whose more simplistic algorithms and assumptions permitted running this large computation model. Tips are provided as well as pitfalls signalled throughout the process of modelling such complex buildings of this type. ^ The building under high seismic loading required a new horizontal shear mechanism. This dissertation has proposed to create a secondary floor that ties to the modular box through the use of gunwales, and roughened surfaces with epoxy coatings. In addition, vertical connections necessitated a new type of shear wall. These shear walls consisted of waffled external walls tied through both reinforcement and a secondary concrete pour. ^ This structural system has generated a new building which was found to be very rigid compared to a conventional structure. The proposed modular building exhibited a period of 1.27 seconds, which is about one-fifth of a conventional building. The maximum lateral drift occurs under seismic loading with a magnitude of 6.14 inches which is one-quarter of a conventional building's drift. The deflected shape and pattern of the interstorey drifts are consistent with those of a coupled shear wall building. In conclusion, the computer analysis indicate that this new structure exceeds current code requirements for both hurricane winds and high seismic loads, and concomitantly provides a shortened construction time with reduced funding. ^

Modelling the size distribution of cosmic voids

The Standard Cosmological Model is generally accepted by the scientific community, there are still an amount of unresolved issues. From the observable characteristics of the structures in the Universe,it should be possible to impose constraints on the cosmological parameters. Cosmic Voids (CV) are a major component of the LSS and have been shown to possess great potential for constraining DE and testing theories of gravity. But a gap between CV observations and theory still persists. A theoretical model for void statistical distribution as a function of size exists (SvdW) However, the SvdW model has been unsuccesful in reproducing the results obtained from cosmological simulations. This undermines the possibility of using voids as cosmological probes. The goal of our thesis work is to cover the gap between theoretical predictions and measured distributions of cosmic voids. We develop an algorithm to identify voids in simulations,consistently with theory. We inspecting the possibilities offered by a recently proposed refinement of the SvdW (the Vdn model, Jennings et al., 2013). Comparing void catalogues to theory, we validate the Vdn model, finding that it is reliable over a large range of radii, at all the redshifts considered and for all the cosmological models inspected. We have then searched for a size function model for voids identified in a distribution of biased tracers. We find that, naively applying the same procedure used for the unbiased tracers to a halo mock distribution does not provide success- full results, suggesting that the Vdn model requires to be reconsidered when dealing with biased samples. Thus, we test two alternative exten- sions of the model and find that two scaling relations exist: both the Dark Matter void radii and the underlying Dark Matter density contrast scale with the halo-defined void radii. We use these findings to develop a semi-analytical model which gives promising results.

Constraint-force-based approach of modelling compliant mechanisms: principle and application

Numerous works have been conducted on modelling basic compliant elements such as wire beams, and closed-form analytical models of most basic compliant elements have been well developed. However, the modelling of complex compliant mechanisms is still a challenging work. This paper proposes a constraint-force-based (CFB) modelling approach to model compliant mechanisms with a particular emphasis on modelling complex compliant mechanisms. The proposed CFB modelling approach can be regarded as an improved free-body- diagram (FBD) based modelling approach, and can be extended to a development of the screw-theory-based design approach. A compliant mechanism can be decomposed into rigid stages and compliant modules. A compliant module can offer elastic forces due to its deformation. Such elastic forces are regarded as variable constraint forces in the CFB modelling approach. Additionally, the CFB modelling approach defines external forces applied on a compliant mechanism as constant constraint forces. If a compliant mechanism is at static equilibrium, all the rigid stages are also at static equilibrium under the influence of the variable and constant constraint forces. Therefore, the constraint force equilibrium equations for all the rigid stages can be obtained, and the analytical model of the compliant mechanism can be derived based on the constraint force equilibrium equations. The CFB modelling approach can model a compliant mechanism linearly and nonlinearly, can obtain displacements of any points of the rigid stages, and allows external forces to be exerted on any positions of the rigid stages. Compared with the FBD based modelling approach, the CFB modelling approach does not need to identify the possible deformed configuration of a complex compliant mechanism to obtain the geometric compatibility conditions and the force equilibrium equations. Additionally, the mathematical expressions in the CFB approach have an easily understood physical meaning. Using the CFB modelling approach, the variable constraint forces of three compliant modules, a wire beam, a four-beam compliant module and an eight-beam compliant module, have been derived in this paper. Based on these variable constraint forces, the linear and non-linear models of a decoupled XYZ compliant parallel mechanism are derived, and verified by FEA simulations and experimental tests.

Numerical Modelling of Eddy Current Probes for CANDU® Fuel Channel Inspection

Multi-frequency Eddy Current (EC) inspection with a transmit-receive probe (two horizontally offset coils) is used to monitor the Pressure Tube (PT) to Calandria Tube (CT) gap of CANDU® fuel channels. Accurate gap measurements are crucial to ensure fitness of service; however, variations in probe liftoff, PT electrical resistivity, and PT wall thickness can generate systematic measurement errors. Validated mathematical models of the EC probe are very useful for data interpretation, and may improve the gap measurement under inspection conditions where these parameters vary. As a first step, exact solutions for the electromagnetic response of a transmit-receive coil pair situated above two parallel plates separated by an air gap were developed. This model was validated against experimental data with flat-plate samples. Finite element method models revealed that this geometrical approximation could not accurately match experimental data with real tubes, so analytical solutions for the probe in a double-walled pipe (the CANDU® fuel channel geometry) were generated using the Second-Order Vector Potential (SOVP) formalism. All electromagnetic coupling coefficients arising from the probe, and the layered conductors were determined and substituted into Kirchhoff’s circuit equations for the calculation of the pickup coil signal. The flat-plate model was used as a basis for an Inverse Algorithm (IA) to simultaneously extract the relevant experimental parameters from EC data. The IA was validated over a large range of second layer plate resistivities (1.7 to 174 µΩ∙cm), plate wall thickness (~1 to 4.9 mm), probe liftoff (~2 mm to 8 mm), and plate-to plate gap (~0 mm to 13 mm). The IA achieved a relative error of less than 6% for the extracted FP resistivity and an accuracy of ±0.1 mm for the LO measurement. The IA was able to achieve a plate gap measurement with an accuracy of less than ±0.7 mm error over a ~2.4 mm to 7.5 mm probe liftoff and ±0.3 mm at nominal liftoff (2.42±0.05 mm), providing confidence in the general validity of the algorithm. This demonstrates the potential of using an analytical model to extract variable parameters that may affect the gap measurement accuracy.

Towards a Better Modelling and Assessment of Construction Risk: Insights from a Literature Review

This paper reviews the literature of construction risk modelling and assessment. It also reviews the real practice of risk assessment. The review resulted in significant results, summarised as follows. There has been a major shift in risk perception from an estimation variance into a project attribute. Although the Probability–Impact risk model is prevailing, substantial efforts are being put to improving it reflecting the increasing complexity of construction projects. The literature lacks a comprehensive assessment approach capable of capturing risk impact on different project objectives. Obtaining a realistic project risk level demands an effective mechanism for aggregating individual risk assessments. The various assessment tools suffer from low take-up; professionals typically rely on their experience. It is concluded that a simple analytical tool that uses risk cost as a common scale and utilises professional experience could be a viable option to facilitate closing the gap between theory and practice of risk assessment.

Application of meta-analytical probabilistic approach for reliability benefits reflective optimal transmission costing – the case of India

In the deregulated Power markets it is necessary to have a appropriate Transmission Pricing methodology that also takes into account “Congestion and Reliability”, in order to ensure an economically viable, equitable, and congestion free power transfer capability, with high reliability and security. This thesis presents results of research conducted on the development of a Decision Making Framework (DMF) of concepts and data analytic and modelling methods for the Reliability benefits Reflective Optimal “cost evaluation for the calculation of Transmission Cost” for composite power systems, using probabilistic methods. The methodology within the DMF devised and reported in this thesis, utilises a full AC Newton-Raphson load flow and a Monte-Carlo approach to determine, Reliability Indices which are then used for the proposed Meta-Analytical Probabilistic Approach (MAPA) for the evaluation and calculation of the Reliability benefit Reflective Optimal Transmission Cost (ROTC), of a transmission system. This DMF includes methods for transmission line embedded cost allocation among transmission transactions, accounting for line capacity-use as well as congestion costing that can be used for pricing using application of Power Transfer Distribution Factor (PTDF) as well as Bialek’s method to determine a methodology which consists of a series of methods and procedures as explained in detail in the thesis for the proposed MAPA for ROTC. The MAPA utilises the Bus Data, Generator Data, Line Data, Reliability Data and Customer Damage Function (CDF) Data for the evaluation of Congestion, Transmission and Reliability costing studies using proposed application of PTDF and other established/proven methods which are then compared, analysed and selected according to the area/state requirements and then integrated to develop ROTC. Case studies involving standard 7-Bus, IEEE 30-Bus and 146-Bus Indian utility test systems are conducted and reported throughout in the relevant sections of the dissertation. There are close correlation between results obtained through proposed application of PTDF method with the Bialek’s and different MW-Mile methods. The novel contributions of this research work are: firstly the application of PTDF method developed for determination of Transmission and Congestion costing, which are further compared with other proved methods. The viability of developed method is explained in the methodology, discussion and conclusion chapters. Secondly the development of comprehensive DMF which helps the decision makers to analyse and decide the selection of a costing approaches according to their requirements. As in the DMF all the costing approaches have been integrated to achieve ROTC. Thirdly the composite methodology for calculating ROTC has been formed into suits of algorithms and MATLAB programs for each part of the DMF, which are further described in the methodology section. Finally the dissertation concludes with suggestions for Future work.

An iterative analytical design framework for the optimal designing of an off-grid renewable energy based hybrid smart micro-grid

Creative ways of utilising renewable energy sources in electricity generation especially in remote areas and particularly in countries depending on imported energy, while increasing energy security and reducing cost of such isolated off-grid systems, is becoming an urgently needed necessity for the effective strategic planning of Energy Systems. The aim of this research project was to design and implement a new decision support framework for the optimal design of hybrid micro grids considering different types of different technologies, where the design objective is to minimize the total cost of the hybrid micro grid while at the same time satisfying the required electric demand. Results of a comprehensive literature review, of existing analytical, decision support tools and literature on HPS, has identified the gaps and the necessary conceptual parts of an analytical decision support framework. As a result this research proposes and reports an Iterative Analytical Design Framework (IADF) and its implementation for the optimal design of an Off-grid renewable energy based hybrid smart micro-grid (OGREH-SμG) with intra and inter-grid (μG2μG & μG2G) synchronization capabilities and a novel storage technique. The modelling design and simulations were based on simulations conducted using HOMER Energy and MatLab/SIMULINK, Energy Planning and Design software platforms. The design, experimental proof of concept, verification and simulation of a new storage concept incorporating Hydrogen Peroxide (H2O2) fuel cell is also reported. The implementation of the smart components consisting Raspberry Pi that is devised and programmed for the semi-smart energy management framework (a novel control strategy, including synchronization capabilities) of the OGREH-SμG are also detailed and reported. The hybrid μG was designed and implemented as a case study for the Bayir/Jordan area. This research has provided an alternative decision support tool to solve Renewable Energy Integration for the optimal number, type and size of components to configure the hybrid μG. In addition this research has formulated and reported a linear cost function to mathematically verify computer based simulations and fine tune the solutions in the iterative framework and concluded that such solutions converge to a correct optimal approximation when considering the properties of the problem. As a result of this investigation it has been demonstrated that, the implemented and reported OGREH-SμG design incorporates wind and sun powered generation complemented with batteries, two fuel cell units and a diesel generator is a unique approach to Utilizing indigenous renewable energy with a capability of being able to synchronize with other μ-grids is the most effective and optimal way of electrifying developing countries with fewer resources in a sustainable way, with minimum impact on the environment while also achieving reductions in GHG. The dissertation concludes with suggested extensions to this work in the future.

Modelling of an efficient dynamic smart solar photovoltaic power grid system

A smart solar photovoltaic grid system is an advent of innovation coherence of information and communications technology (ICT) with power systems control engineering via the internet [1]. This thesis designs and demonstrates a smart solar photovoltaic grid system that is selfhealing, environmental and consumer friendly, but also with the ability to accommodate other renewable sources of energy generation seamlessly, creating a healthy competitive energy industry and optimising energy assets efficiency. This thesis also presents the modelling of an efficient dynamic smart solar photovoltaic power grid system by exploring the maximum power point tracking efficiency, optimisation of the smart solar photovoltaic array through modelling and simulation to improve the quality of design for the solar photovoltaic module. In contrast, over the past decade quite promising results have been published in literature, most of which have not addressed the basis of the research questions in this thesis. The Levenberg-Marquardt and sparse based algorithms have proven to be very effective tools in helping to improve the quality of design for solar photovoltaic modules, minimising the possible relative errors in this thesis. Guided by theoretical and analytical reviews in literature, this research has carefully chosen the MatLab/Simulink software toolbox for modelling and simulation experiments performed on the static smart solar grid system. The auto-correlation coefficient results obtained from the modelling experiments give an accuracy of 99% with negligible mean square error (MSE), root mean square error (RMSE) and standard deviation. This thesis further explores the design and implementation of a robust real-time online solar photovoltaic monitoring system, establishing a comparative study of two solar photovoltaic tracking systems which provide remote access to the harvested energy data. This research made a landmark innovation in designing and implementing a unique approach for online remote access solar photovoltaic monitoring systems providing updated information of the energy produced by the solar photovoltaic module at the site location. In addressing the challenge of online solar photovoltaic monitoring systems, Darfon online data logger device has been systematically integrated into the design for a comparative study of the two solar photovoltaic tracking systems examined in this thesis. The site location for the comparative study of the solar photovoltaic tracking systems is at the National Kaohsiung University of Applied Sciences, Taiwan, R.O.C. The overall comparative energy output efficiency of the azimuthal-altitude dual-axis over the 450 stationary solar photovoltaic monitoring system as observed at the research location site is about 72% based on the total energy produced, estimated money saved and the amount of CO2 reduction achieved. Similarly, in comparing the total amount of energy produced by the two solar photovoltaic tracking systems, the overall daily generated energy for the month of July shows the effectiveness of the azimuthal-altitude tracking systems over the 450 stationary solar photovoltaic system. It was found that the azimuthal-altitude dual-axis tracking systems were about 68.43% efficient compared to the 450 stationary solar photovoltaic systems. Lastly, the overall comparative hourly energy efficiency of the azimuthal-altitude dual-axis over the 450 stationary solar photovoltaic energy system was found to be 74.2% efficient. Results from this research are quite promising and significant in satisfying the purpose of the research objectives and questions posed in the thesis. The new algorithms introduced in this research and the statistical measures applied to the modelling and simulation of a smart static solar photovoltaic grid system performance outperformed other previous works in reviewed literature. Based on this new implementation design of the online data logging systems for solar photovoltaic monitoring, it is possible for the first time to have online on-site information of the energy produced remotely, fault identification and rectification, maintenance and recovery time deployed as fast as possible. The results presented in this research as Internet of things (IoT) on smart solar grid systems are likely to offer real-life experiences especially both to the existing body of knowledge and the future solar photovoltaic energy industry irrespective of the study site location for the comparative solar photovoltaic tracking systems. While the thesis has contributed to the smart solar photovoltaic grid system, it has also highlighted areas of further research and the need to investigate more on improving the choice and quality design for solar photovoltaic modules. Finally, it has also made recommendations for further research in the minimization of the absolute or relative errors in the quality and design of the smart static solar photovoltaic module.