Performance evaluation and economic analysis of solar photovoltaic water pumping systems : Case of Abakore borehole water supply system in Kenya

A solar photovoltaic (PV) water pumping system was investigated to determine performance and economic viability. An in-built data logger was used to collect real time data on key performance parameters. Performance indicators were defined and determined, while economic viability was analyzed using life-cycle cost (LCC) method and these costs were compared with a diesel generator pumping system. Solar irradiance varied from 63 W/m 2 to a peak of 857 W/m 2 , corresponding to a maximum power output of 11.75 kW. PV array efficiency of 12.1%, sub-system efficiency of 91.82% and overall efficiency of 5.14% were obtained, which are well comparable to the efficiencies reported elsewhere for similar systems. The LCC analysis showed a 20 year average unit water cost of 0.25 US $/m 3 for solar PV system and 0.6 US $/m 3 for diesel genset system. Solar PV system is found to be more cost effective and suitable for use over conventional sources.


INTRODUCTION
Evidence suggests that developing more water harnessing infrastructures as a solution to the global water scarcity crisis will result in an increased demand for energy, especially for pumping applications since water infrastructure largely relies on energy throughout its value chain (United Nations Education and Science Commission (UNESCO, 2012).It is also expected that groundwater will become increasingly energy intensive as water tables fall in several regions; therefore, making sustainable renewable energy supplies options such as wind and solar key components of water security debate (UNESCO, 2012).This expected shift towards renewable energy sources is further evidenced by the fact that 69% of Africans lack connection to an existing electricity grid *Corresponding author.E-mail: james.origa@gmail.com.
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Study set up
The experimental set-up was a 150 m deep borehole already installed and operational at Abakore village to the south of Wajir County at co-ordinates 0°37'41.98"N,39°42'26.47"E.The directly coupled PV water pumping system comprised of: 1. PV generator Array-96 number 195Wp Yingly JS 195 solar panels arranged in paralel columns of 24 modules connected in 4 series totalying to 18.72 kW 2. Motor-pump assembly-a 3 phase submersible centrifugal pump, LORENTZ PS15k2 C-SJ17-18 pumping with a design total dynamic head of 100 m.
3. Water storage tank-one 50 m 3 masonry constructed tank.The PV characteristics and pump specifications as given by the manufacturer's specifications are in Table 1.

Data acquisition
Data was collected using PS DataModule, an integral data logger and remote monitoring device built-in on the Pump Inveter/Controller.The data was retrieved using an application called PumpScaner.The data logger and PumpScaner have been developed by LORENTZ, a German solar pumps manufacturer, and was purchased together with the pump controller.The PS DataModule uses Bluetooth TM technology to communicate with the LORENTZ PumpScaner Andriod TM APP allowing secure real time data to be viewed and historical data to be collected without physical connections.Using this data logger and retrieval mechanisms, performance of the system was monitored for 30 days.The operating hours of the system were limited to 12 h per day.The following data relevant to operational parameters of solar PV water pumping installations were recorded every 30 min daily during the operating hours (1) Array  4) pump input current (A).The pumping system was designed to operate at a fixed total dynamic head of 100 m.

Economic analysis data
Life-cycle cost (LCC) analysis method which calculates the present worth of all costs, capital, operation and maintenance, and replacement parts over the lifetime of the system was used to perform an economic evaluation of the solar PV water pumping system in comparison with diesel generator water pumping set.Financial data as detailed in Table 2 was provide by Abakore Water Users Association.In the life-cycle cost analysis, the following assumptions and data sources were used: 1.The expected lifetime of the solar system as 20 years and diesel system 10 years.
2. Operation and maintenance costs per year are assumed constant for the systems.
3. The solar pump and diesel pump is replaced every 10 years.4. The storage tank and distribution line costs are not included in the analysis because, it is considered as the same for both cases.
5. The interest rates and inflation rates used were 16.56 and 6.88%, respectively, while the Kenya shillings to US dollar conversion rate was 1 US $ to Kenya shilling 98.6.All values were averages for the preceding year of analysis as extracted from the Central Bank of Kenya.

System performance analysis
The data obtained from Abakore installation have been analysed and treated in order to evaluate the performances and the characteristic parameters of the system.Figure 1 shows the observed solar irradiance in the plane of the PV array (W/m 2 ) and the power output of the PV array (kW).It was observed that the system generated a maximum power output of 11.75 kW from the panels against a solar irradiance input of 778.06 W/m 2 at about mid-day.
Figure 2 shows that the solar pumping system pump discharge started at irradiance level of between 101 and 200 W/m 2 , increasing gradually as solar irradiance increased while the diurnal variation in pump output as shown in Figure 3 indicated on average, production of 16.7m 3 /hr and a total daily production of 156m 3 /day as shown by Figure 4.
Figure 5 shows the scatter plot of the pumping system characteristic curve installed at Abakore generated using measured solar irradiance and pump flow rate data.The Pearson coefficient of correlation was 0.925, and the significant difference by the statistical significant test was meaningful with 1% of levels of significance.
The results indicate an average of discharge of 156 m 3 /day.Figure 6 shows the relationship between nominal power output of the PV Array, the PV array actual power output at field conditions and the hydraulic power generated by the pump.The nominal power is determined as the irradiation received on the array plane multiplied by the standard test conditions efficiency provided by the manufacturer as 14.7%.The nominal power is the ideal power the PV array generator should generate as determined by the manufacturer at standard test conditions.The results showed that the power generated by the PV array is clearly below the ideal power at standard test conditions.Figure 7 shows comparison of the array, sub-system and overal system efficiencies obtained.

Life-cycle cost analysis
Figure 8 compares the life cycle costs for the photovoltaic and diesel powered water pumping systems installed at Abakore.The analysis was caried at an average interest rate of 16.56% and inflation rate of 6.88%.The breakeven point between PV water pumping system and diesel pumping system was found to be in the third year of operation.The results indicate that the life cycle costs of diesel pumping system will increase significantly over the years, while the life cycle costs of solar photovoltaic system is expected to remain fairly constant over the years.While the unit water cost in Ksh/m 3 using photovoltaic pumping system is expected to decrease  over the years, the unit water cost for diesel pumping system will increase significantly.In a similar pattern as the unit water cost, the energy cost in Ksh/m 4 which is the equivalent hydraulic energy for the PV pumping system decreases with years while that of diesel pumping system is expected to increase.The unit cost of water provided by the photovoltaic pump was found to be 104.05Ksh (1.06 $)/m 3 in year one then reduced in the following years to an average of 24.75 Ksh (0.25 $)/m 3 for the 20 year period, while the unit cost using the diesel genset system showed an initial result of 95.58 Ksh (0.96 $)/m 3 in year one and an average of 59.92 Ksh (0.6 $)/m 3 over the 20 year period of analysis.

DISCUSSION
The system obtained a highest PV array conversion efficiency of 12.1%.This is slightly less than the manufacturer provided efficiency of Yingly J195 solar modules of 14.7%.This array efficiency compares well with most literature which cites the achievable efficiency in the conversion of solar radiation to electricity by solar cells in practice to be about 9 to 15.1% under field conditions (Dapkus and Hummel, 1993).This slightly lower efficiency observed at Abakore can be attributed to variations in cell temperature from the standard test conditions.This study did not analyse the effects of temperature variation on PV output but other researchers have shown that the efficiency decreases with increasing temperature (Green, 1982).Other parameters that led to this lower efficiency include changes in the quantity of solar irradiance received on the array plane and incidence angle which varied through the day.Losses in wirings of PV modules into PV arrays and inverter losses are also attributable to the lower PV conversion efficiency.The sub-system efficiency and overall system efficiency exhibited a three-phase changing pattern within a day.Phase 1 occurs between 6 to 9 am, phase 2 from 9 am to 4.30 pm, and phase 3 from 4.30 to 6:30 pm.During phase 1, the sub-system and overall system efficiency starts from zero and increases to a relatively high value, the efficiency remains relatively constant during phase 2 varying from a range of 5.14 to 3.7% for the overall system efficiency.It can be seen that the subsystem efficiency showed the highest value of 81.36% during phase 1 in the early morning and 91.82% at the end of phase 2 in the late hours of the day.This can be attributed to the fact that as the flow rate increases at higher irradiation conditions, the efficiency goes down due to the decrease in the pump efficiency.Even though the efficiencies of inverter and motor normally increase by higher flow rates (higher frequencies), this cannot compensate for the decrease of the pump efficiency.The most important consideration in system design is the match between the motor-pump sub-system and the PV array.The sub-system efficiency is an indicator of the match between the motor-pump sub-system and the PV array.It is obtained as the ration between hydraulic power and the electrical power of the sub-system.The range of 49 to 91% sub-system efficiencies obtained at Abakore shows a good match between the motor-pump and the PV array.The optimum load matching factor for the Abakore PV water pumping system was obtained as an average of 0.66.This value was obtained from the radiation threshold of 200 W/m 2 and from the daily average, hourly solar irradiance curve.This value is comparatively average showing that the system components were averagely well matched and adequately configured.

Conclusions
The key significance of this study was to present the performance results of a system operating under real variable field conditions and not in a controlled laboratory environment.The overall system efficiency obtained for the Abakore installation was 5.14%.This shows good result in comparison with current practice where PV-pumping overall efficiency has considerably improved from 1-3% in 1980s to 3.5-5% in 2016.While the installed capacity was 18.72 kW and the maximum power generated by the PV array was found to be 11.1 kW, the maximum discharged obtained was 25.05 m 3 /h at a power input of 9 kW which is half of the installed capacity.This demonstrates that while improvements in photovoltaic module manufacturing techniques are continuously researched, there still remains a clear need for development towards both improved reliability, efficiency values and components matching of solar pumping sub-systems in order to extract the maximum power capability of the solar generator at all times.The results of the economic analysis demonstrates that the higher initial cost of photovoltaic pumping systems can be justified by the savings in the lower operation and maintenance as well as the increased reliability throughout the useful longer life of the PV system as compared to diesel generator pumping system.

Figure 1 .Figure 2 .
Figure 1.Variation of PV power output and the incident solar irradiance received on PV array plane.

Figure 3 .
Figure 3.Diurnal variation of flow rate of the pumping system.

Figure 4 .
Figure 4. Measured daily volume of water pumped by the system of solar PV pumping at Abakore.

Figure 5 .
Figure 5. Scatter plot of the Abakore system characteristic curve.

Figure 6 .
Figure 6.Relationship between nominal power, PV array output power and the hydraulic power generated by the pump.

Figure 7 .
Figure 7.Comparison of array, sub-system and overall system efficiencies.

Figure 8 .
Figure 8.Comparison of 25 year PV and diesel systems life cycle costs.

Table 1 .
Description of pumping system components.
PV Module: Yingli JS 195, multicrystalline silicon (Standard Test Conditions (STC): 1000W/m 2 , 25°C cell temperature).system(InternationalEnergyAgency, 2015).Solar PV water pumping systems are increasingly being promoted as an attractive alternative to pumping water vis-à-vis conventional diesel generator sets.Kenya is increasingly facing the twin challenge of water scarcity and decreasing energy generation as the capacity of the traditionally used hydro dams are rapidly dwindling due to climate change effects.The water-energy nexus arises from the interconnectedness of the critical role water plays in energy production and the need for energy in the water production chain mainly in abstraction and conveyance.As Kenya seeks to fastrack the realization of a prosperous middle income economy stautus by year 20130 as envisioned in her Kenya Vision 2030 blueprint (Kenya Ministry of

Table 2 .
Costs of the various system components.