2. Thesis and Dissertations
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Item A Novel Controller for Switched Reluctance Motor(National Institute of Technology Karnataka, Surathkal, 2013) Shaik, Abdul Ahad; R.Y, UdaykumarElectrical drives are playing an important role in modern industries. In the last two decades an electrical drive named the Switched Reluctance Motor (SRM) drive is receiving considerable attention from industry in adjustable speed drives since it is characterized by robust construction, high operation reliability and efficiency. The successful application of SRM in automobiles depends on the proper motor design and overall cost of the drive which includes converter and controller costs. However, there have been inadequate design experience for SRM’s as compared with more mature BLDC motors and induction motors, and applications are limited so far due to complex design procedure. Therefore, it is necessary to develop a set of design procedures for SRMs. Although the design principles of SRMs are available in different literatures; there is no clear idea in the basic design procedure. These procedures require extensive prior knowledge and experience in designing. The procedure outlined in this thesis requires only basic dimension data for SRM’s. The empirical formulas are used for basic design and since it is difficult to accurately incorporate the saturation effect and the detailed geometrical information in the empirical formulas, the FEM was used for fine-tuning and validating the design. For dynamic behaviour of a SRM and for controller and converter design, the knowledge of the magnetization curves is very essential. Therefore this thesis discusses how the magnetic characteristics of SRMs are obtained by experimental, analytic and FEM. Thereafter a new method of finding the motor winding inductance at different rotor position using 3D FEM is carried out to validate the results as obtained by experimental method. The SRM drive consists of a power converter section that sequentially connects the motor phases independently and a control section that processes rotor position information form a position sensor and generates the phase excitation pulses. A new method to estimate the initial rotor position of the SRM at stand still and during running condition is proposed without the need of magnetisation curves. A pair of position sensors is used to detect the rotor positions and the output signals of the sensors are used as the basic triggering pulses for main switches. The proposed method was implemented by the simple microcontroller based systems. A known sensorless method of finding the rotor position is used to validate the correctness of the proposed method. The proposed method is implemented with the 8/6,1 kW,12000 RPM 8/6 SRM. The experimental results shows that the proposed rotor estimation technique provides good accuracy at different operating conditionsItem Electrical Power Distribution System Management Under Deregulation Regime(National Institute of Technology Karnataka, Surathkal, 2013) Manjunatha Sharman, K.; Panduranga Vittal, K.The distribution system in the electrical power network is the most vital section being nearest to the consumers. The effectiveness of the power delivery to the loads is governed by the design, operation and maintenance of the distribution network. Over the years, the researchers are attempting to achieve improvements in the distribution system performance by adopting newer topologies, strategies for network design and control. In this context, globally the need for distribution system improvement is acknowledged by all countries and since past decade distribution sector reforms are being executed by initiating newer government policies which led to de-regulation regime worldwide. This thesis addresses the issues of DG insertion to distribution system in deregulation regime. The analysis carried out evaluates the feasibility of an Industrial captive power plant to operate as a DG Source, complex issues associated with multiple DG sources insertion to distribution system and impact of DG sources in network reconfiguration. A tool which facilitates decision on power export by an industrial captive power plant to grid has been developed. This tool accounts existing load pattern and generation scenario of the industrial unit. The proposed analytical approach gives with emphasis on choice of improving any specific parameter from either technical or economical perspective. The strategic technique developed proposes a comprehensive index termed as Network Performance Enhancement Index (NPEI). This index is a combination of indices related to loss reduction, voltage profile improvement, voltage regulation, voltage stability. Adapting this index provides enough alternatives to the designer so that he can decide on the most feasible solution. The technique designed for service restoration enumerates the situations of islanding of DGs due to fault in any part of network and guides the operator for supply of local loads in such a situation. This work proposes most feasible schemes for DG insertion to overcome the difficulties in implementation of the conventional fixed solutions schemes. The software tools adopted are SKM Power Tools and MATLAB and all evaluations are done using standard bus structures reported in literature and nearby captive plant data of an industry.Item Adaptive Distance Relay for Statcom Connected Transmission Lines - Development of Dsp Based Relay Hardware, Relaying Schemes and Hil Testing Procedures(National Institute of Technology Karnataka, Surathkal, 2013) M.V., Sham; Panduranga Vittal, K.Flexible AC Transmission System (FACTS) devices are used to enhance the transient stability limit and power transfer capacity of the existing transmission lines. Static Synchronous Compensator (STATCOM) a shunt type FACTS device is used to maintain the voltage at the point of common coupling on the transmission lines. A STATCOM has fast response of about 1-2 fundamental cycles, which matches with the typical response time of the protection subsystem. Hence, its functional characteristics and associated control system introduce dynamic changes during fault conditions in a transmission line. It is important that distance relays perform correctly irrespective of such dynamic changes introduced during faults, as it defeats the purpose of STATCOM installation. The work presented in this thesis is aimed at detailed study on the influence of STATCOM on the performance of distance relay under normal and abnormal operating conditions of the power systems. The work also put forth adaptive distance relaying schemes to mitigate the adverse of impact of STATCOM on distance relay. Its performance is compared with the conventional standalone mho type distance relay, through simulations on a realistic study power system using EMTDC/PSCAD package. A relay hardware to implement, the adaptive relaying scheme has been developed using TMS320F28335 digital signal processor and a simultaneous sampling ADS8556 analog to digital converter. The real time hardware in the loop test bench has been developed, using Doble F6150 power system simulator, to test the performance of the newly developed relaying schemes and relay hardware. The simulation results obtained from EMTDC/PSCAD are used as test signals for this purpose. The evaluation results have clearly demonstrated, the efficacy of the adaptive relaying schemes in mitigating the adverse impact of STATCOM on the distance relay performance.Item Investigations on Non-Invasive Fault Diagnostic Techniques for Three-Phase Induction Motor with Mixed Eccentricity(National Institute of Technology Karnataka, Surathkal, 2013) B L, Rajalakshmi Samaga; Vittal, K.P.Induction motors are extensively used in several industries such as oil, steel, petrochemical to name a few, and their failure may lead to the plant shut down resulting in the heavy financial losses. The motor operation management units are usually supported with protective gear which has the ability to detect the induction motor faults and stall the operation on detection. However, as a routine practice, it is essential to diagnose the defect in the motor by prognostic studies. There are various signature analysis techniques widely practiced in industries to detect nature and causes of failures in induction motor parts. Out of known causes of failures in these motors, 10 to 15% is attributed to the air gap eccentricity faults, thus demanding detection at the earliest. The major objective of this research work is to investigate the robust signatures to characterise the air gap eccentricity in the induction motor. To meet this objective, efficacy of various signatures that mark the presence of eccentricity are explored, and as an outcome it is found that d-q components of stator current can be used as the most suitable detector of machine failure due to mixed air gap eccentricity. Power signatures, Torque signatures and Power factor signatures were used for mixed eccentricity detection in the past by various researchers. These techniques use characteristic harmonics produced at the frequency signifying disturbances produced due to an air gap mixed eccentricity and used as signatures in air gap eccentricity diagnosis. In the present work it is shown that, the extracted d-q components of the stator currents contain characteristic harmonics signifying the presence of eccentricity and proposed as a better technique for performing the signature analysis. This technique is more advantageous and cost effective when compared to torque and power signatures analysis methods, since they are commonly used in controllers which are handling motor control. The scope of research work is modularized into following four phases: Phase 1: At this phase, mathematical expressions are derived for d-q components of stator currents in synchronous reference frame for the induction motor suffering from mixed air gap eccentricity. From the derived expressions, it is shown that they contain eccentricity specific harmonics in them. Phase 2: Here, a dynamic model of squirrel cage induction motor suffering from air gap mixed eccentricity fault is developed. And this model is used in simulatingii various mixed air gap eccentricity conditions and stored as a test data set. By systematic frequency signature analysis performed on the extracted d-q components of stator currents, it is shown that simulation results validate the mathematical expressions derived earlier. Phase3: In this phase, observations made at the phases 1 and 2 are experimentally validated by conducting experiments on 3HP three phase induction motor suffering from mixed eccentricity. In addition a motor mounting frame having special provision for introducing eccentricity is specially fabricated to introduce various degrees of eccentricity. Phase 4: To understand implications of supply voltage imbalances on eccentricity, detection technique is further investigated at this phase. The d-q components of stator currents in synchronous reference frame are often used in controller as control variables, as these are found to be dc signals. But as a part of the research investigation it is also shown that d-q components of stator currents extracted from stator currents of an air gap eccentric machine in synchronous reference frame will contain DC component superimposed with ripple oscillations. This ripple is due to eccentricity and it can be characterized by harmonics frequency even when the machine is fed with 3 phase sinusoidal voltages and running under constant load. As an outcome of all above work finally an integrated air gap eccentric condition monitoring unit and a controller unit for an induction motor has been proposed.Item Voltage Regulation of Power Distribution System with Interconnected Distributed Generators(National Institute of Technology Karnataka, Surathkal, 2013) Shivarudraswamy, R.; Gaonkar, D.N.In the recent years the electrical power utilities are undergoing rapid restructuring process worldwide. Indeed, with deregulation, advancement in technologies and concern about the environmental impacts, competition is particularly fostered in the generation side thus allowing increased interconnection of generating units to the utility networks. These generating sources are called as distributed generators (DG) and defined as the plant which is directly connected to distribution network and is not centrally planned and dispatched. Various new types of distributed generator systems, such as microturbines and fuel cells in addition to the more traditional solar and wind power are creating significant new opportunities for the integration of diverse DG systems to the utility. Inter connection of these generators will offer a number of benefits such as improved reliability, power quality, efficiency, alleviation of system constraints along with the environmental benefits. In order to achieve these benefits with large penetration of DG source in existing utility networks several technical problems are to be fronted such as voltage regulation, islanding of DG, degradation of system reliability, power quality problems, protection and stability of the network. These issues need to be resolved, to pave the way for a sustainable energy future based on a large share of DG and hence a lot of research effort is required. Among the above issues the voltage rise problems have been reported as the foremost concern against the connection of large amounts of distributed generators to mediumvoltage and low-voltage distribution networks. The distribution systems have been planned and designed for unidirectional power flow and operated at constant voltage levels. The connection of the large amount of DG systems to the utility may reverse the power flow resulting in voltage rise above the statutory limits. Present network design practice is to limit the generator capacity to the level at which the upper voltage limit is not exceeded with maximum generation and minimum load. This can lead to a reduction in connectable generation capacity, under utilization of appropriate generation sites. The conventional voltageregulation methods of distribution system are designed with unidirectional power flow in mind and are not going to be effective in presence of a significant number of DG systems. Thus there is a need to redesign these methods to take care of bidirectional power flow or new methods have to be developed to accommodate the large number of DG systems. Thus, development of new voltage control devices/schemes have the potential to revolutionize the control of distribution network. In this thesis steady state voltage rise problem in a distribution networks interconnected with DG is examined. Case studies are presented using simulation results to study the impact of location, magnitude and operating condition of the integrated DG. The impact of other factors such as voltage at the primary substation, distance from the primary substation, demand on the system, type of loads and loading conditions on voltage level of distribution system are also analyzed. A comprehensive study on voltage control in a distribution system by taking in to account a number of DG systems and capacitors under various conditions is also presented in this work. In order to prepare the distribution networks for larger penetration of DG systems, effective voltage regulation methods are required so as to keep the voltage levels within the limits. In this work sensitivity analysis and participation factor based approaches for voltage regulation of typical distribution system are presented. The formulation for determination of voltage sensitivity index for voltage control is also given. The effectiveness of the developed approaches for voltage regulation of typical IEEE 69 bus distribution is analyzed using case studies. The OLTC, switched capacitors and DG systems are considered to regulate the voltage level in the distribution system in this study. Both methods can be used to handle all types of radial distribution system structures regardless of the system size proficiently. Individual control of various voltage regulating device such as OLTC, shunt capacitor including DG in a distribution system may cause unnecessary operations, and consequentlywear, energy consumption as well as voltage disturbances. Thus coordination among these devices for effective voltage regulation can lead increase in number of DG interconnection to utility network. In this work a coordinated regulation method using genetic algorithm is developed. Genetic algorithm is utilized to determine the optimal amount of operation for individual voltage regulating device for given distribution network. The performance of the developed method is analyzed using simulation results through two case studies. The sample load conditions using time varying load profile is considered. The multiple voltage regulating devices such as OLTC, LRT, SC, SVC including DG system is considered in this study. The input load data is very critical for distribution system load flow studies. In most cases time varying load data is required for accurate load flow analysis such as hourly load day for a day or a month. The use of this large data for load flow analysis can complicate the solution approaches. Thus in most of the cases, for validation of voltage regulation methods few samples of data are considered instead of considering the entire load profile. This approach may not accurately represent the load variation of entire profile for load follow analysis. In this work a fuzzy clustering technique for load profile generations is presented. Load profile generation using fuzzy clustering can be more realistic case rather than considering sample load conditions from set of time varying data. Fuzzy clustering is used to find 3 prototypes of hourly load data for a day (24 vectors) instead of considering sample load conditions directly from profile. Load profile generation using fuzzy clustering can be more realistic case as it considers the similarity of variation for entire set of load data. The performance of coordinated voltage control method is analyzed using the load profile generated using fuzzy cluster in this work. Distribution systems are usually unbalanced due to unbalanced loading of the different phases. Besides industrial or domestic customers some distributed generators can also impose an unbalanced operation of electrical networks. Load flow analysis of balanced radial distribution systems will be inefficient to solve the unbalanced cases and the distributionsystems need to be analyzed on a three phase basis. In this thesis load flow solution for a unbalanced system using forward and back sweep method has been presented. The detailed modeling of various components of the distribution system for the unbalanced load flow solution is also given. The performance of the coordinated voltage regulation method using two Case studies using IEEE 13 and 25 bus unbalanced distribution is analyzed through simulation. The simulation results are reported to evaluate the effectiveness of the developed method in voltage regulation of unbalanced distribution system.Item Design and Evaluation of Controllers for Wave Energy Based Electricity Generation System(National Institute of Technology Karnataka, Surathkal, 2013) U., Vinatha; Vittal, K PThe research work presented in this thesis is an effort to recognize the potential issues associated with harnessing wave energy based on oscillating water column principle. A model of oscillating water column based on energy balance concept is proposed. Dynamic model of a wave energy conversion system based on OWC principle consisting of a variable speed Wells turbine driven permanent magnet synchronous generator connected to the grid by means of back to back converters is developed. Results exhibit the randomness in the various quantities like speed of the turbine, torque and powers developed of the turbine and the generators when the input to the system is varying randomly. This demonstrates uncertainty in the wave power due to arbitrariness in the waves and reveals the difficulties in developing an efficient wave harnessing system. Controllers for the generator side and the grid side converters for a grid connected wave energy conversion system are developed. The overall scheme is evaluated under steady state, dynamic and transient operating conditions. Under different operating conditions it is observed that the control scheme provides a good response in terms of power quality and power control. An important constituent for developing the wave energy conversion systems is the Wave Turbine Emulator. It offers a controllable test environment that allows the evaluation and improvement of control schemes for electric generators without construction of costly turbine and help in determining the strength and weakness of energy conversion scheme and the related control technologies. In view of this a wave turbine emulator is designed. For the realization of the wave turbine emulator a three phase permanent magnet synchronous motor is used with VSC controller as a drive. Results presented for different wave pattern as input indicates that the speed dynamics of the wave turbine model is exactly followed by wave turbine emulator developed in laboratory. An attempt is also made to study the behavior of the three phase permanent magnet synchronous generator coupled to the emulator developed.Item Application of Error Correction Codes for Enhancing Data Integrity in Power Line Channel(National Institute of Technology Karnataka, Surathkal, 2013) Itagi, Rajeshwari L; K. P., Vittal; Sripati, U.The use of existing power lines for home/industry/substation automation has drawn the attention of many researchers in the recent years because this infrastructure is easily available everywhere. However, the Power Line channel has been primarily designed for power transfer at low frequencies. Hence, the propagation characteristics of this channel are not well suited to support high speed data transmission and ensuring reliable high speed and error free data transmission on this channel is a very challenging task. Many researchers have been attracted to this challenging field in recent years and a variety of techniques from the domain of Digital Signal Processing and Communication Engineering have been applied to solve some of the challenges posed by this application. The three critical channel parameters namely noise, impedance and attenuation are found to be highly unpredictable and variable with time, frequency and location. Further, the regulatory standards designed to prevent spurious radiation restrict the carrier power that can be used for digital modulation. In this work, we have concentrated on the use of Medium Voltage (MV) Power Line (< 30 kV) for narrow band applications. After a study of relevant literature and an understanding of mathematical models used to describe the variation of channel parameters, a suitable model has been simulated in MATLAB® platform. Simulation results presented by the channel model have been obtained for different channel conditions such as line length, noise variations and variations in transfer function (attenuation) of the channel and for different data size. The frequency band employed in narrowband power line communication is restricted to a value less than 500 kHz. An effort is made in the thesis to devise a powerful error correcting code which can eliminate the errors caused by channel impairments. Power line channel is modeled using multipath model. As noise experienced on power line channels is a mixture of Gaussian and Impulsive varieties, it is modeled by using the Middleton Class-A pdf. Taking into account the channel behavior; two channel coding strategies were deployed. In the first approach a four state Turbo code was combined with a 32-carrier OFDM modulator and the performance of this combination was studied under various channel conditions. In the second approach, a Bose-Choudhari-Hocquenghem (BCH)code was concatenated with the Alamouti Space-Time Block code and the performance of the channel was similarly evaluated. To realize the Turbo coded OFDM scheme, a four state Turbo code using Recursive Systematic Convolutional (RSC) encoder/decoder pair was designed. The output of the encoder was modulated by 32 sub carrier OFDM (designed using IFFT and FFT). The efficacy of this arrangement in ensuring data integrity over the MV power line channel was tested. To realize the second approach, a BCH code with parameters was designed and encoding/decoding processes were implemented. BCH code in concatenation with Alamouti 2x1 space time code (with PSK modulation) was tested. A partial hardware implementation was realized by employing a Digital Signal Processor TMS 320C6713 for encoding/decoding and MATLAB® for simulating the power line channel. Data input present in text form encoded and decoded after transmission through the channel. This process allows the visualization of the power of error correction algorithms. Performance evaluation of the two proposed schemes for channel code and modulation design namely Turbo coded OFDM and BCH coded space time code were carried out. The performance criteria for the evaluation include the bit error rate (BER) at a specific signal to noise ratio (SNR). The reflections at branching points (load locations) vary the attenuation profile of the link. As a result, the effect of different parameters on the channel attenuation was observed based on the number of loads and length of the link. A BER analysis was performed to compare the performance of the channel under impulsive noise conditions under three impulsive scenarios. The first scenario was specified as . The second scenario was specified as and the the third scenario was specified as . A comparison of the relative performance of uncoded and coded schemes reveals the following: Scheme 1 achieves BER of 10-5 at SNR=55 dB for (case 1 impulse noise), with channel attenuation varying between 10 dB to 50 dB. Scheme 2 achieves BER of 10-5 at SNR=50dB for (case 1 impulse noise), with channel attenuation on two paths varying between 18 dB and 6 dB.Both schemes have achieved a BER of 10-5 at SNR=66 dB for case 2 impulse noise), with 10dB to 50 dB channel attenuation for scheme 1 and with 16 dB and 34 dB channel attenuation on two paths for scheme 2. Following remark can be made with reference to the discussion on results: Both schemes 1 and 2 have given equivalent performance under similar channel conditions (attenuation and noise), when the error correcting capacity of channel code used in scheme 2 is . After a thorough study and implementation of both approaches, it was observed that both schemes exhibit equivalent performance under similar channel conditions (attenuation and noise levels). With enhanced error correction capacity with t=11, a BCH coded space time code will require lesser SNR to give the same performance as OFDM under similar channel conditions.Item Rural Electrification in Deep Areas of India and Feasibility Study of Solar Home Systems(National Institute of Technology Karnataka, Surathkal, 2013) Dhruvaraj, Kamalapur Gopalkrishna; Narashimhan, M.C.; Gaonkar, D.N.The majority of the world’s population, primarily living in rural areas, lacks a number of facilities as a result of poverty and insufficient access to energy. The conditions necessary to satisfy basic needs and to promote economic and social development cannot be fulfilled. Most of the people without access to electricity live in thinly populated areas in developing countries and the extension of the grid to these areas are not feasible mainly due to economical reasons. Electricity is a desirable commodity in the majority of the areas, it should be noted that electricity is only one of the options to satisfy the energy needs of the rural population, along with other rural needs. Rural electrification is an integral component of poverty alleviation and rural growth of a nation. The availability of electricity can support advanced development methods such as tele-education and it could provide access to distant information and support for farmers and other entrepreneurs. Hence present study addresses electricity supply for deep rural and remote areas of India. A study of several aspects of rural electrification in India, the role of Government of India and the feasibility of Solar Home Systems is carried out in this thesis.Item Integration of Grid Connected Photovoltaic System with Active Power Filtering Functionality(National Institute of Technology Karnataka, Surathkal, 2014) Jaivant, Naik Anant; R. Y, UdaykumarThe development in the field of power electronics has led to its optimum and efficient use in domestic and industrial arena especially in control and automation processes. In turn this has created a threat in terms of power quality issues. The main issue with such devices and the associated circuits is that they act as non linear loads on the system. Due to this the source/grid current in which they are connected gets polluted. The solution for such problems is the use of power filters. Passive filters have certain drawbacks and hence active filters are predominantly used. To some extent, solution to power quality issues is obtained again using power electronic devices in the form of active power filtering. On the other hand, due to social and environmental issues, there is a rising awareness among masses to use renewable sources of energy. In many places renewable sources like photovoltaic systems are being connected to the grid. Renewable sources such as photovoltaic cells and fuel cells need conversion stage before connecting to the utility grid. Normally a DC-AC inverter is used for this purpose. Hence the performance of such system considerably depends upon the type of inverter used. In order to avail better performance, a multilevel inverter is preferred. But the complexity of control circuitry and the number of devices required are the issues of concern with this type of inverters. Here, an attempt is being made to address these two aspects in a common domain. The features of active filtering can be combined with the PV source connected to the grid so that active and reactive power transfer takes place at the point of common coupling (PCC). In this work a PV source is connected to the grid through a dual inverter which also acts as active power filter. A dual inverter topology is simple three level inverter topology compared to existing multi level topologies. A grid connected photovoltaic system is integrated with active power filtering functionality to address both issues of real power injection and harmonic filtering. The performance of such system is enhanced by using multilevel inverters. A transformer fed from both ends at its primary terminals with two independent voltage source inverters is used to replace a filter inductance of a conventional system.iv In this dissertation firstly a grid connected PV system through a dual inverter topology is modeled and simulated. The system performance is verified under different load and solar cell operating conditions. Secondly, in a power distribution system with nonlinear loads an active power filter is developed with three level (dual inverter) inverter. The source current THD and the source displacement power factor are improved at different loads. Finally, two systems are integrated such that grid connected PV system with active power filter functionality is obtained. This system is tested for different atmospheric as well as load conditions.Item Solar Photo Voltaic Water Pumping System(National Institute of Technology Karnataka, Surathkal, 2014) Kappali, Mrityunjaya; R. Y, UdaykumarWater pumping is an important application of solar photo voltaic (PV) power. However growth in the number of solar pumps is not promising mainly due to higher cost per litre of water pumped and complex technology. These issues can be addressed by harnessing more power per unit installed capacity of solar panel and making the system simple. Present research work has dealt with the aspect of harnessing more power from PV panel using maximum power point tracking (MPPT) for a standalone water pumping system. Literature review indicates the need for MPPT method which is simple, accurate as well as non-interruptive in nature. This thesis has proposed a novel method for accomplishing MPPT wherein only load voltage is to be used as control parameter for MPPT converter (MPPTlv). This method is simpler than the present more commonly employed method of monitoring panel power (MPPTpp) which requires measurement of two parameters (panel voltage & current) and then multiplying them to obtain power. The proposal is substantiated by theoretical explanation and results from simulation & experimental testing. In addition to its simplicity, the new proposal is also found to give higher power output and enhance water yield. An algorithm is developed to show simulation implementation of the proposal made. Another outcome of the present research work is the development of a new strategy “Individual Floor Storage Method (IFSM)” for solar pumping in multi-floored buildings where over head (OH) tanks act as storage elements. Present practice is “Top Floor Storage Method (TFSM)" wherein one single large OH tank is placed on topmost floor. IFSM proposes to employ small tanks at each floor height supplying water to corresponding floor. Water is pumped to the required optimum heights only, avoiding wastage of energy. For a particular power capacity of solar panel, the amount of water lifted will be more. Effective total cost per litre of water lifted is appreciably reduced. In other words, for a particular amount of water to be lifted per day, the PV panel size needs to be less. The two new proposals made in this research work, giving increased water yield from the solar pump for a particular capacity of solar panel, are expected increase the acceptability of solar water pumps and thus contribute to their growth.