Performance estimation of Ntaruka hydropower plant and its comparison with the prediction results obtained by SPSS

Abstract

Hydroelectricity has long been used in Rwanda. The Ntaruka hydropower plant was constructed during the colonial period in the northern part of Rwanda and it is still in operation. This paper evaluates the annual performance of this power plant and highlights several factors, which are vital for future predictions in the energy generation. Literature search and review coupled with energy generation analysis and forecasting were used for the study. Data were collected through site visits and discussions with the staff of the Rwanda Energy Group. Analysis were made by considering some performance factors of the power plant such as net capacity factor, plant use factor, power factor, voltage profile, frequency profile, general energy profile, and annual energy generation profile taking cognizance of hydropower plant installed capacity. Based on the available monthly operation hours of the power plant and its annual energy generation data between 2011 and 2014, predictions were made using the Statistical Package for Social Sciences (SPPS version 20.0) to forecast future energy generation for the power plant. Results show that the annual energy generation of the power plant varies between 1277 and 4524 MWh, with an average of 2912 MWh within the above years, which is much closer to the average real energy generation obtained between 2011 and 2015 and, therefore, the power plant is in good operating condition. Further research is recommended to consider using staffing levels, plant availability factors, and economic efficiency to determine the economic effectiveness and performance indices of the hydropower plant.

Keywords

Hydropower plant performance energy generation forecast SPPS Rwanda

Introduction

Rwanda is located in Central/Eastern Africa with a population of more than 11.5 million and with a land area of 26,338 km². It is likely that only 5.3% of the area is occupied by water whose main sources are Lake Kivu, Lake Muhazi, Lake Ihema, Lake Bulera, Lake Ruhondo, and Lake Mugesera.^1,2 Rwanda is a country with various natural resources for electricity generation, including hydropower, solar, methane gas to power, peat to power, and biomass. A national survey reports that the currently net installed capacity of power plants is totally 216 MW (48% from hydropower and 32% from thermal, 5.7% from solar PV, 14.3% from methane-to-power) (details in Appendix 3) from installed capacity to supply its population. The electricity access rate is currently estimated at 40.5% including 29.5% of on-grid and 11% off-grid). Currently, the Government of Rwanda has set out plans to achieve 512 MW installed power generation capacity by 2023–2024 satisfying 100% universal electricity access (52% on grid and 48% off-grid).^3–5

The national power grid presents high percentage losses (details in Appendix 2), sometimes going beyond 30.0% as shown in Figure 1. (Most of the electric grid infrastructures have been constructed during the colonial period. Current population and electricity users have increased and the result is that electrical grid infrastructure is not as big as its demand.) Fortunately, the Rwanda Energy Group is working tirelessly on reducing these losses in the grid. It is working to upscale the conditions and capacity of power substations by the help of European Union and Belgian Government, installing reactive power compensators to reduce losses and upgrading electric grid infrastructure where needed.^6–17 Hydropower sector in Rwanda has shown good promise, because of the introduction of independent power producers (IPP) to the sector through private sector investment groups. Hydropower plants production record for Rwanda¹⁸ is shown in Appendix 1. Currently, many hydropower plants are operating either as on-grid or off-grid, all to satisfy the electricity demand of the Rwandan population. In addition, other hydropower projects in the country are either commissioned, or under construction and/or development.^18,19 Investment opportunities are available in the hydropower sector in Rwanda. Projects either under construction or under development stages have incentives as in all energy sectors where the government of Rwanda will provide access to transmission and roads for projects related to power generation.²⁰

Table 1.

Power generation (MW) record on November 2016.⁶

No.	Plant type	2010	2011	2012	2013	2014	2015	Nov 2016
1	Hydro	43.25	48.63	48.63	52.43	80.43	80.43	84.43
2	Diesel	37.80	37.80	47.80	47.80	47.80	51.80	51.80
3	Methane gas	3.60	3.60	3.60	3.60	3.60	29.60	29.60
4	Solar	0.25	0.25	0.25	0.25	8.75	8.75	8.75
5	Imports	15.50	15.50	15.50	15.50	15.50	15.50	15.50
	Total	100.40	105.78	115.78	119.58	160.08	186.08	190.08

Table 2.

Power generation (%) record on Nov 2016.⁶

No.	Plant type	2010	2011	2012	2013	2014	2015	Nov 2016
1	Hydro	43.1%	46.0%	42.0%	43.8%	52.7%	44.4%	44.4%
2	Diesel	37.6%	35.7%	41.3%	40.0%	29.9%	27.3%	27.3%
3	Methane gas	3.6%	3.4%	3.1%	3.0%	2.2%	15.6%	15.6%
4	Solar	0.2%	0.2%	0.2%	0.2%	5.5%	4.6%	4.6%
7	Imports	15.4%	14.7%	13.4%	13.0%	9.7%	8.2%	8.2%
	Total	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%

Table 3.

Power generation mix in 2017 (Rwanda) (data gathered on site visit at Rwanda Energy Group).

Technology	Installed capacity (MW)	% share
Renewable energy	113.14	52.4
Nonrenewable energy	102.87	47.6
Total	216.0	100

Electricity from hydropower plants

Energy from flowing water can be used to produce electricity at different levels through hydropower plants. Power from water flows is used as captive energy for hydroelectricity production. Dynamic forces in flowing water are used to turn the turbine connected to a generator for electricity production.²¹ Any hydropower plant comprises three major parts: (a) an electric plant for producing electricity, (b) a dam for controlling water flow, and (c) a reservoir for storing water. Water behind dam flows through the penstock to push against blades of a turbine, which causes it to rotate the shaft connected to the generator to produce electricity. The quantity of electricity generated is proportional to the water head and flow rate. The electricity generated is transported using long-distance electric lines to houses, factories, schools, hospitals, and business hubs.²¹

The power from hydropower plant can be written as follows²²

P = η . ρ . g . Q H

(1)

where P is the power at the generator terminals, expressed in kW, H is the gross head from pipeline intake to the tail water in m, Q is the water flow rate in pipeline, in m³/s, η is the efficiency of plant, g is the gravity that is 9.81 m/s², and ρ is the water density in kg/m³.²² Typically, hydroelectricity is a clean and cheap source of energy, i.e. once dam has been built and all equipment installed, energy from flowing water is free, and it is safe because no fuel is needed except water and helps in low operating cost. Operators control flow of water through turbines depending on quantity of electricity demanded. Hydropower plants constructions need large area, high initial cost, long payback periods, and environmental side-effects like people relocation and internal displacements, coupled with negative effects on wildlife.²³

Case study, data, and research methodology

The hydropower plant under study is an on-grid (run off river) small 11.5 MW hydropower plant located in the northern part of Rwanda, whose water supply is from Burera Lake. It was constructed in late 1950s and was designed to generate 22 GWh electricity annually. It is equipped with three generator units with Francis-type turbines. Net head is 102 m, diameter of penstock is 1.8 m, and diameter of head race is 2.5 m making this hydropower plant worthy of reappraisal, especially because of its construction age in Rwanda, and need to assess its current operational generation effectiveness. Also, aging often leads to more equipment breakdowns, losses, down times, huge maintenance costs, lower efficiency and, probably, inability to run at full rated capacity. Even if case study hydro cannot be operated at full capacity because of age and other constraints, it still serves its purpose of producing hydroelectricity for the Rwanda grid, nonetheless.^24–26

Data collection were conducted using on-site measurements at Ntaruka hydropower plant and in different sections of Rwanda Energy Group Ltd (the organization in charge of Rwanda National Power Grid), such as National Electricity Control Centre, Generation and Transmission sections. Data analysis were carried out on factors like generation performance, power factor, plant use factor, generation voltage profile, generation frequency profile, capacity factor, and annual energy generation capacity per installed capacity (GWh/MW). Based on the annual energy generation (2011–2014) MWh and monthly operation hours, the SPSS software (version 20.0) were used to forecast the energy generation for designated hydropower plant.

Analysis and prediction for case study

Analysis

The available monthly energy generation of designated hydropower plant for 5 years (2011–2015) were collected and analyzed, the results of which are shown in Figure 2. An examination of the results in Figure 2 reveals that a minimum energy generation of 1801 MWh occurred in September 2013 and its maximum value is 4768 MWh that occurred in September 2012. An average value of 2936 MWh has been estimated for the energy generation in each year of the studied time duration (2011–2015).

Based on the annual energy generated (2011–2015) and designed annual energy generation (22 GWh) for the power plant, the minimum generation performance (106.0%) occurred in 2013, while the maximum performance (206.8%) occurred in 2014. Shown in Figures 2, 3, 4, 5, 6, ,8, 10, 11, 12, 13 and Tables 4, 5, 6 are the authors’ calculation based on-site data gathered on visit at Ntaruka hydropower plant while Figures 7 and 9 are the authors’ calculation based on-site data gathered at Rwanda Energy Group – National Electricity Control Center Section.

Power factor is a term used in the efficiency of an electrical circuit and it is defined as the ratio of real power in W to the flow of load named apparent power in VA in a circuit. It is calculated by equation (2) and measured in the range of 0.0–1.0, and sometimes expressed in the percentage value instead of unity. Practically, it should be close to unity and if low, system operation becomes uneconomical. Higher power factor leads to higher efficiency²⁷

P o w e r f a c t o r = \frac{R e a l P o w e r (W)}{A p p a r e n t P o w e r (V A)}

(2)

Some causes of low power factor can be inductive loads, variations in power system loading, and harmonic currents. Some power factor improvement techniques include capacitor banks, synchronous condensers, phase advancers, and automatic generation control.²⁷ Once power factor is improved, advantages include better voltage regulation and power quality, increased available system capacity, avoided low power factor surcharges, reduced power consumption, reduced losses, lower energy costs, cost-effective utilization of utility company generators, and extended utility equipment life.²⁷ Based on the available power factor records during the time studied (2012–2016) as shown in Figure 4, for designated power plant, the lowest power factor (0.883) and highest power factor (0.994) occurred respectively in March and August 2014. The available power net capacitor factor records for the plant, also shown in Figure 5, is expressed in percentage value.

Plant factor or the net capacity factor of a plant is defined as the ratio of actual energy output to potential output, if operated continuously at rated capacity over a period of time, and this factor can be calculated by the following equation²⁸

P l a n t f a c t o r = N e t c a p a c i t y f a c t o r = \frac{E \times 100}{P \times h}

(3)

where E is the energy produced in a certain time period (kWh), P is the installed power capacity (kW), and h is the time period in hours.²⁹

Based on the available plant use factor records during the time studied (2012–2016) as shown in Figure 6, for designated power plant, the highest plant use factor is 63.2% that occurred in 2013 and its lowest value of 56.3% occurred in 2015. In Figure 6, the plant use factor is calculated considering only the operation hours of Ntaruka hydropower plant during 2011–2015 while in Figure 5 the plant net capacity factor is calculated for the power plant in operation for the whole year (year = 365 days = 8760 hours).

The nominal generation voltage level of designated power plant is calculated to be 6.60 kV and the available monthly average voltage levels data (2012–2015) were collected and analyzed. The results are shown in Figure 7. By examination of the results it is revealed that the lowest voltage level is 6.4 kV that occurred in April 2015 and its highest level of 6.85 kV occurred in February 2012. Consequently, lowest and highest voltage level variations were: −3.03% in February 2015 and +3.79% in April 2015. In Rwanda, voltage levels fall within ±3% of the nominal value (6.6 kV), which is the National Standard.³⁰

Consequently, the results for the available monthly average frequency collected data in the period of 2012–2015 are shown in Figure 8, while the nominal generation frequency level of the designated power plant is 50 Hz, same as the National Power Grid Network. Therefore, the lowest frequency level is 49.46 Hz that occurred in August 2015 and its highest frequency level is 50.28 Hz that occurred in June 2012. However, most of these frequency levels fell in the range of 50 Hz + 3% to 50 Hz −5%, which is within the National Standard Level,³⁰ for frequency variations in Rwanda.

Prediction

From the previous sections it follows that various factors affecting the output energy from a runoff river hydropower plant are: installed power capacity, operation hours, net head, flow rate, climatic conditions such as rainfall levels of catchment area, and river water levels.³¹ For Ntaruka hydropower plant, the time records in the period of 2011–2014 of these factors are depicted in Figure 10. The electrical power and the annual energy yield can be calculated from equations (1) and (3), respectively.

E l e c t r i c a l P o w e r = F l o w r a t e \times N e t h e a d \times G r a v i t y \times D e n s i t y \times E f f i c i e n c y

(4)

A n n u a l E n e r g y Y i e l d = C a p a c i t y f a c t o r \times P o w e r \times H o u r s o f u s e i n a y e a r

(5)

where electrical power is expressed in W, flow rate in m³/s, net head in m, density in kg/m³, efficiency in percentage (%), and annual energy yield in kWh.³¹

Based on the available data, average monthly rainfall in Burera Lake does not have much effect on the water level variations in the lake and monthly water levels in the lake keep changing within a small range. Keeping some factors constant for the designated hydropower plant such as net flow rate (12 m³/s), designed head (102 m), and installed capacity (11.5 MW), and referring to the available data of monthly generated energy and operation hours in the period of 2011–2014, a sytnatx in SPSS (Version 20.0) was created to forecast future values of monthly energy generation (MWh) for the coming four years using a simple linear regression. The summary of the model and overall fit statistics are shown in Table 4.

Table 4.

SPSS model summary.

Model summary^b
Model	R	R ²	Adjusted R²	Std. error of estimate	Durbin–Watson
1	0.923^a	0.853	0.850	361.68370	2.006

^aPredictors: (Constant), Monthly operational hours

^bDependent variable: Monthly energy generation (MWh).

The assumptions for simple linear regression were first checked. The adjusted R² of the model is 0.850, with R² equal to 0.853. That means about 85.3% of the variance in the data is in linear regression. The Durbin–Watson d which is equal to 2.006 is between the two critical values of 1.5 < d < 2.5 and this fact confirms that there is no first-order linear auto-correlation effect in the data. The R value (0.923), which is 92.3% measures the correlation between the levels of monthly energy generation and predicated on monthly operation hours. The R² (0.853) is the proportion of variance in monthly energy generation, which is accounted for by monthly operational hours. The adjusted R² measures the success of the model, which shows that the model is 85.0% successful.³²

Furthermore, the Durbin–Watson statistic is used to test for linearity, randomness, independence (noncorrelation), constant variance, and normal distribution in data, with zero mean.³³ Because D-W = 2.006, in our results, there is a very slight negative correlation, which is accentuated by mean $μ = 3.03 \times 10^{- 15}$ , in histogram. We can conveniently say that our model is linear, random, and normally distributed within the limits of acceptable statistical error (since no statistical measure is perfect).

Table 5 shows the F-test, the linear regression, and it shows that for the null hypothesis there is no linear relationship between monthly energy generation and monthly operation hour (R²=0). With F = 266.587 and 47 degrees of freedom, the test is highly significant, which confirms that there is a linear relationship between the variables in the model. Table 5 also shows that the p-value (significance) of the predictor affects the criterion (dependent) variable (monthly energy generation significance criterion (0.000) is less than 0.05, which means that is statistically significant).³²

Table 5.

SPSS F-test.

ANOVA^a
Model		Sum of squares	df	Mean square	F	Sig.
1	Regression	34,873,654.463	1	3,487,354.463	266.587	0.000b
	Residual	6,017,494.604	46	130,815.100
	Total	40,891,149.067	47

^aDependent variable: Monthly energy generation (MWh).

^bPredictors: (Constant), Monthly operation hours.

Table 6 shows the regression coefficients, intercept, and significance of all coefficients and intercept in the model. The gradient (β) is tested for significance because it is different from zero, which means that there is a relationship between the predictor and output energy generation (MWh).

Table 6.

Regression coefficients.

Coefficients
Model		Unstandardized coefficients		Standardized coefficients	t	Sig
Model		B	Std. error	Beta β	t	Sig
1	(Constant)	473.253	158.227		2.991	0.004
1	Monthly operational hours	5.871	0.360	0.923	16.328	0.00

To test the homoscedasticity and normality of residuals, the histogram indicates the residuals approximate a normal distribution as shown in Figure 11. The Q-Q plot of z*pred and z*presid shows that the linear regression analyses have no contribution to the error terms.

The scatter plot in Figure 12 shows that there is zero or no relationship between monthly energy generation and monthly operational hours.³²

The prediction results shows the highest forecast energy generation was 4524 MWh, the lowest forecast was 1277 MWh, and its average forecast was 2912 MWh.

Furthermore, the forecast errors between actual and predicted values were –5.12, +18.14, and –0.82 percentage for highest, lowest, and average energy generation, respectively. It can be seen that only the forecast error (+18.14%) for lowest energy range went beyond the “usual” permissible limits of $\pm 5.0 %$ . This resultant is understandable because it is not a once-off figure but a result of iterations and moderating variables. Nevertheless, because the highest and average forecasts of energy generation were within or close to the 95% confidence interval,³⁴ we suggest the past energy generation data of designated hydropower plant in Rwanda were able to closely predict the future energy generation forecasts using regression analysis.

Conclusion

In this paper, the performance factors of Ntaruka hydropower plant were analyzed and forecasts were made based on the operational hours and energy generation records. Results show that the highest value of energy generation forecast was 4524 MWh, while the lowest value was 1277 MWh, and its average forecast within the studied period 2011–2015 was 2912 MWh, which is much closer to the real energy generation obtained between 2011 and 2015.

The highest hydropower generation of 84.43 MW (44.4% of 190.08 MW) occurred in 2016, while the lowest hydro generation of 43.25 MW (43.1% of 100.0 MW) occurred in 2010. This shows that hydropower has a substantial contribution (45.2% average) to the growth and overall power generation capacity development in Rwanda. The lowest diesel generation of 37.8 MW (36.7% average) was constant for 2010 and 2011. The next higher diesel generation of 47.8 MW (37.1% average) occurred between 2012 and 2014 (inclusive), while the highest diesel generation was 51.8 MW (27.3% average) that occurred in 2015 and 2016, respectively. The diesel power plant contributed 34.2% to the total power generation capacity in Rwanda. The methane gas power plant contributed 3.6 MW each for five years (2010–2014) and increased to 29.60 MW each for 2015 and 2016. The lowest percentage contribution of methane gas power plant was 2.2%, while the highest percentage contribution was 15.6%. Solar power generation was 0.25 MW from 2010 to 2013 (inclusive) and had increased to 8.75 MW each from 2014 to 2016. Its highest percentage contribution to the total generation was 4.6% (out of 190.08 MW), whereas import remained constant at 15 MW from 2010 to 2016, and its percentage contribution has been found to decrease from 15.4% in 2010 to 8.2% in 2016 (Tables 1 and 2).

The analysis results also show that there is no first-order linear auto-correlation effect in the data. The adjusted R² measure shows that the model is 85.0% successful. Furthermore, the model is linear, random, and normally distributed within the limits of the statistical error. The Fisher test also shows that there is no linear relationship between monthly energy generation and monthly operation hours (R² = 0), and it is highly statistically significant.

Above all, the designated hydropower plant is in good operation condition. Further research should be conducted using staffing levels, plant availability factors, and economic efficiency to determine the economic effectiveness and performance indices of the designated hydropower plant.

Footnotes

Author contributions

All listed authors have made substantial, direct, and intellectual contribution to the work and approved its publication.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was funded by the National Natural Science Foundation of China (program no. 51475136), Natural Science Foundation of Hebei Province, China (program no. E2014202230), Universities in Hebei Province, China Science and Technology Research Youth Fund (program no. QN20151002), University Innovation Team Leader Program in Hebei Province (LJRC003).

Samuel Bimenyimana is IEEE student member since 2017. He earned his Bachelor of Science degree in Electrical Engineering from University of Rwanda, School of Engineering, Department of Electrical and Electronics Engineering in 2014. He is currently pursuing Masters-Doctoral program from Hebei University of Technology, Tianjin, China, State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Department of Electrical Engineering. His research interest is all about analysis ( Power system analysis and energy systems analysis).

Godwin Norense Osarumwense Asemota (M’04–SM’13), became a member of IEEE in 2004, and a senior member in 2013. He earned the BS, MS, MBA and PhD degrees in physics, electronic and electrical engineering, finance and banking and electrical engineering, respectively. He teaches electrical power systems engineering and high voltage engineering courses in the Electrical and Electronics Engineering Department, College of Science and Technology, University of Rwanda, Kigali, Rwanda. He is the author of two books and more than 40 journal articles and conference papers. He researches in power systems engineering, high voltage engineering, plantains biology, convex mathematics, number theory, electricity load management, energy efficiency, multivariate analyses, optimisation, statistical inference, finance, banking, investment, stock brokering, bifurcations, critical phenomena, electromagnetics, fibre optics, jump phenomena, cryptography, series solution of differential equations and their applications.

Paula Jeanne Ihirwe received her Bachelor of Science degree in Applied statistics from University of Rwanda, in 2014. She is currently pursuing MBA from Tianjin University in the Department of Economics and Management and her interest is in data analysis.

Cicilia Kemunto Mesa received Bachelor of Science in Energy Engineering from Kenyatta University, Kenya in 2008. She is pursuing master’s degree in Energy and Environmental Engineering at Hebei University of Technology in Tianjin, China. She is also a research scientist in matters energy at the Kenya Industrial Research and Development Institute in Nairobi Kenya.

Lingling Li received her BS degree in Industrial Process Measurement and Control Instrument from Tianjin University, Tianjin, China, in 1989, MS degree in Control Theory and Control Engineering from Hebei University of Technology, Tianjin, China, in 2001, and PhD in Electric Machines and Electric Apparatus from Hebei University of Technology, Tianjin, China, in 2004. Since 2006, she has been a professor with the School of Electrical Engineering, Hebei University of Technology, Tianjin, China. Since 2012, she has been a PhD supervisor with the School of Electrical Engineering, Hebei University of Technology, Tianjin, China. She was an Electrical Engineering postdoctor with Tianjin University, Tianjin, China from 2009 to 2012. She was a visiting scholar with Northeastern University, Shenyang, China from 2014 to 2015. She was a director with Reliability engineering branch of China Mechanical Engineering Society, Beijing, China from 2015 to 2018. She was a visiting professor with National Chin-Yi University of Technology, Taichung City, China from 2016 to 2017. She is the author of more than 100 articles, including more than 10 SCI articles. Her research interests include reliability of electrical apparatus, power system and new energy.

Appendix 1

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