Optimization of Energy Generation Based on Operations and Ecological Integrity Requirements

Slovak Journal Vol. 27, 2019, No. 3, 55 – 62 of Civil Engineering DOI: 10.2478/sjce-2019-0022

OPTIMIZATION OF ENERGY GENERATION BASED ON OPERATIONS AND ECOLOGICAL INTEGRITY REQUIREMENTS

Abdulrasaq A. MOHAMMED1*, Bolaji F. SULE2, Adebayo W. SALAMI2, Adeniyi G. ADEOGUN3

Abstract Address

The management of water resources for different purposes 1 National Centre for Hydropower Research and Development, such as a domestic water supply and municipal, irrigation and University of Ilorin, PMB 1515, Ilorin, Nigeria hydropower generation requires optimization techniques for 2 Department of Water Resources and Environmental efficient reservoir operations. This study focused on the opti- Engineering, University of Ilorin, Ilorin, Nigeria 3 mization of energy generation at Kainji hydropower station in Department of Civil Engineering, Kwara State University Malete, Nigeria Nigeria using operational and ecological integrity constraints. A linear optimization technique was used in optimizing the aver- * Corresponding author: [email protected] age total annual energy generation subject to operational and ecological integrity constraints. The model was solved using LINGO 17.0 software. The results revealed that the optimization Key words approach would increase the total annual energy generation at ● Energy generation, the hydropower station by 1.84%. The outcome of this study can ● ●● Optimization, be adopted by the management of a hydropower station and ●● Kainji reservoir, other decision makers in Nigeria to improve the availability of ●● Ecological integrity onthly discharge. electricity deployed to Nigeria’s national grid without compromising the ecological integrity of a reservoir.

1 INTRODUCTION er production by 6.8 and 6.6% for dissolved oxygen (DO) limits of 5 and 6 mg/l respectively. The optimization of reservoir operations is very important in in- Sule et al. (2018) evaluated the reservoir yield and hydropow- creasing reservoir outputs and has been abundantly investigated in the er potential of Doma Dam, Nasarawa State, Nigeria, using an ANN past (Homa et al., 2005; Chang et al., 2005; Adeyemo, 2011; Usman model in ALYUDA Forecaster XL to extend the available streamflow and Ifabiyi, 2012; Chen et al., 2013). A conventional hydropower res- record at the location. It was observed that at a 50, 75 or 100% usage ervoir operating practice is commonly guided by maximizing energy of the excess stored water with a head of 20 m, the power potential generation without cognizance of the ecological health of the reser- increases. Huang et al. (2013) used a chaotic genetic algorithm to voir. This practice may greatly affect natural conditions, especially optimize hydropower generation with ecological considerations. The water and sediment qualities as well as fish abundance in a reservoir results indicated that the proposed model and algorithm were feasible (Mohammed, 2018). Belayneh and Bhallamudi (2012) used an opti- when dealing with the optimal operation of hydropower generation mization model for management of the quality of water in a tidal river with ecological considerations. at Chennai, India, using upstream releases. It was demonstrated that Niu and Zhang (2002) applied LINGO to optimize the water the volume of the total upstream release could be minimized while supply system in a city in China. The results showed that LINGO maintaining the desired water quality. Shaw et al. (2017) optimized was so precise that the differences between the estimated and actu- a multipurpose hydropower reservoir near Nashville, Tennessee, in al service flow rates were very small. Dutta (2015) determined the the USA using a CE-QUAL-W2 predictive power model integrated reservoir capacity of the Gadana Dam in India using linear program- into a genetic algorithm optimization approach subject to operational ming. The model was analyzed using LINGO software in which the and water quality constraints. The optimization increased hydropow- values of the reservoir were provided and the reservoir capacity was

© 2019 The Author(s). This is an open access article licensed under the creative commons attribution-noncommercial- noderivs license (http://creativecommons.Org/licenses/by-nc-nd/3.0/). 55 Slovak Journal of Civil Engineering Vol. 27, 2019, No. 3, 55 – 62

determined. Ahmed et al. (2013) optimized the yield of the Dokan voir is fed by many tributaries. It lies at an altitude of 108 m above reservoir system in Iraq using LINGO. Two linear programming (LP) sea level, between Yelwa (latitude 10° 53’N: longitude 4°45’E) and models were developed for estimating the maximum safe yield with Kainji (latitude 9° 50’N: longitude 4°35’E). See Fig. 1 for a map of an allowable deficit. The annual reservoir yield was estimated to be Kainji Lake with a Nigeria inset. It is underlain by complex base- 5653.8 Mm3/year. ment rocks such as porphyritic granite, mica and quartzite (Ifabiyi, Salami et al. (2017) evaluated the hydropower potential at the 2011). Doma Dam in Nassarawa State, Nigeria, using optimization tech- The reservoir that resulted from the Kainji dam was built be- niques. The model was solved with LINGO 10.0 software for various tween 1964 and 1968 and commenced operations in 1968 for the mean annual inflow exceedence probabilities. The results revealed purpose of generating electricity (Ifabiyi, 2011). The maximum water that the dam is suitable for hydropower generation between 0.61 and surface elevation is 141.9 m above sea level (masl). Kainji Lake is 0.70 MW. Parsa (2017) optimized the Karun reservoir in Iran using the largest man-made lake in Nigeria with a surface area of 1270 km2. linear programming. The results showed good compliance between The storage capacity is 15 x 109 m3 with a total live storage of 12 x109 the linear programming model with optimal values and the historical m3. The Kainji hydropower reservoir has an installed capacity of 760 observations. MW. The maximum length, width, and mean depths are 136.8 km, The management of a reservoir system is complex due to the 24.1 km, 60 m and 11 m respectively. Kainji reservoir is characterized dimensionalities, nonlinearities, and conflicts between different ob- by a prolonged high temperature, low rainfall and low relative hu- jectives. The optimal operation of a reservoir system typically in- midity; it exhibits evaporation values that are in excess of the rainfall volves optimization and simulation models (Lin and Rutten, 2016). (Abam, 2001). Google imagery of the Kainji reservoir indicating the An optimization model is used to minimize or maximize an objective sampling locations is shown in Fig. 2. function under given constraints, and a simulation model is used to examine how a water system behaves under a set of conditions. In the past, optimization problems have been solved by LP, dynamic pro- 3 METHODOLOGY gramming (DP), quadratic programming (QP), and non-linear programming (NLP) (Lin and Rutten, 2016). Symum and Ahmed (2015) Hydropower operating data from 1970 to 2016 and water and used LP to optimize a water supply and cropping area for irrigation sediment quality data from 2010 to 2015 were collected from the hy- in Bangladesh. An optimization model was formulated to maximize drological and environmental departments of the Kainji hydropower the profits from cultivation while satisfying constraints such as the station respectively. The dam’s seepage and discharges through its cropping area, irrigation water supply, cropping cycle, and market demand. The results provided the optimum value for the cropping area and irrigation water depth that maximized the objective function. Mahsafar et al. (2017) optimized the allocation of agriculture water for the irrigation of multiple crops using nonlinear programming in Iran. The model was solved using the LINGO solver package. The results showed that optimizing the cropping patterns along with the proper allocation of the irrigation water had a substantial potential to increase the net return of the agricultural water. Deeprasertkul (2015) used LP for the optimal reservoir operations of the Chao Phraya river basin in Thailand. The results revealed that the optimal solutions were comparable to the actual volume of the water stored and re- leased from the reservoir. Various optimization methods have been used in reservoir operations, depending on the characteristics of the reservoir system, the specific objectives, the system constraints, and availability of the data (Khare and Gajbhiye, 2013). The existing reservoir operations at the Kainji Dam have been characterized by various problems such as annual flooding and ecological modifications around the dam area, which have negatively impacted the generating capacity of the dam. Therefore, the objective of this study is to optimize the energy generation at the Kainji hydropower station, Ni- geria, based on operations and ecological integrity constraints using LINGO. In this study LINGO optimization software was used due to its availability, effectiveness and accuracy in handling this problem. LINGO is a comprehensive tool designed to make, build and solve various optimization problems. It provides a complete integrated package that includes a powerful language for expressing optimization models (Dutta, 2015). Most water resource allocation problems are addressed using LP (Simonovic, 2009). Optimization models for reservoir operations generally consist of objective functions and constraints (Chen et al., 2013).

2 DESCRIPTION OF THE STUDY AREA

The Kainji dam is located in New Bussa in the Borgu Local Gov- ernment Area of Niger State, Nigeria. The Kainji hydropower reser- Fig. 1 Map of Kainji Lake with inset of Nigeria.

56 OPTIMIZATION OF ENERGY GENERATION BASED ON OPERATIONS AND ECOLOGICAL INTEGRITY...

Fig. 3 Time plot of turbine releases (Mm3) at the station (1970-2016). Slovak Journal of Civil Engineering Vol. 27, 2019, No. 3, 55 – 62

Fig. 2 Google imagery of Kainji reservoir showing the sampling locations

bottom outlets were not considered in this study because they are not Substituting Eq. 2 in Eq. 1 gives Eq. 3: part of the reservoir’s operating parameters. Data on the fish yield from 1995 to 1998 was also collected from the National Institute for (3) Freshwater Fishery Research (NIFFR), New Bussa, Nigeria. The data collected was subjected to monthly variations and statistical analysis. where: 3 The average mean monthly data were used in the formulation of the Rt = turbine release for period t (Mm ) objective function and constraints. The study was carried out at four ɛ = hydropower plant efficiency (%)

sampling locations selected on the upstream and downstream sides of Ht = net head on the turbine (m) = reservoir water level - tail race the Kainji hydropower station. water level The hydropower plant efficiency (ɛ) is constant because the gen- erator and turbine in use at the station remained the same throughout

3.1 Development of the reservoir optimization the observation period. The product of Rt and Ht in Eq. 3 gives the model non-linear function. This is linearized by adopting Taylor’s series ex- ° ° pansion (Salami, 2007). If the average release R t and average head H t A reservoir operation optimization model commonly consists of are available for period (t), then one can write (Loucks et al., 1981) an objective function and constraints (Chen et al., 2013). the linear form as presented in Eq. 4:

(4) 3.1.1 Objective function When substituting Eq. 4 into Eq. 3, this results in Eq. 5: According to the core function of the Kainji reservoir, the annual hydropower energy generation E (MWh) is used as the objective (5) function in the model (Salami, 2007). The function of the optimization process is the maximization of the total annual energy genera- To complete the objective function, the estimated mean monthly values of the releases R and net head H are taken as R° and H° . If the tion. The total annual energy generation is a summation of the twelve t t monthly energy generations (E ), which were estimated using Eq. 1. product of 2.73 and the system efficiency is defined as λ ,the objec- t tive function therefore, becomes Eq. 6. The constants associated with the objective function presented in Eq. 6 were estimated using Eqs. 7 (1)   to10. The mean values Rt and H t are presented in (Tab. 2). where: Z = total annual energy generation (MWh) t = 1 to 12 (6)

Et = monthly energy energy generation generation (MWh) (MWh) i = time step (month) t = 1 to 12 (7)

The energy can be estimated using Eq. 2: t = 1 to 12 (8)

Fig. 1 Map of Kainji Lake with inset of Nigeria. (2) t = 1 to 12 (9)

OPTIMIZATION OF ENERGY GENERATION BASED ON OPERATIONS AND ECOLOGICAL INTEGRITY... 57

Fig. 3 Time plot of turbine releases (Mm3) at the station (1970-2016). Slovak Journal of Civil Engineering Vol. 27, 2019, No. 3, 55 – 62

t = 1 to 12 (10) The limit on the available net head is given as

33 Ht 42 t = 1 to 12 where: where:  3 Rt = mean monthly releases (Mm ) H = minimum net head at time t (m)  t min H t = mean monthly net head (m) Ht max = maximum net head at time t (m)

at == coefficiencoefficients forts the for net the head net in thehead linearized in the objectivelinearized function objective Ht = available net head at time t (m) function bt == coefficiencoefficien ts tsof ofthe the turbine turbine releases releases in in the the linearized linearized objective objec- function1.1.1.4 Turbine release (R) constraints tive function

ct = constantsconstants The available turbine release (Rt) is restrained by the minimum C == summationsummation of of thethe constantsconstants 3 3 and maximum releases Rt min (Mm ) and Rt max (Mm ) respectively as shown in Eq. 14: t = 1 to 12 (14) 3.1.2 Model constraints The limit on the turbine release is given as The objective function is to have energy generation maximized, t = 1 to 12 subject to the operating and ecological integrity constraints. where: 3 1.1.1.1 Reservoir mass balance equation Rt min = minimum net head at time t (Mm ) ) 3 Rt max = maximum net head level at time t (Mm ) 3 The mass balance between the inflow and outflow is given in Eq. 11: Rt = available net head at time t (Mm )

t = 1 to 12 (11) 3.1.2.5 Ecological integrity constraints

where: In order to protect a reservoir’s ecological integrity; dissolved 3 3 St+1 == final final storage storage for for period period t + t1 (Mm+ 1 (Mm) ) oxygen (DO), sediment quality (as a function of heavy metals such 3 2+ 2+ 3+ St = initial storage for period t (Mm ) as copper (Cu ), lead (Pb ) and chromium (Cr ) concentrations), 3 3 - 3- Qt = reservoir= reservoir inflow inflow for for period period t (Mm t (Mm)) algae (as a function of nitrate (NO3 ) and phosphate (PO4 )), and fish 3 3 Rt = turbine= turbine release release for for period period t (Mm t (Mm) ) yields must be adequately preserved as stated by the Tennessee Valley 3 3 Lt = evaporatio= evaporation from n from the the reservoir reservoir for forperiod period t (Mm t (Mm) ) Authority (TVA) in the USA (Sharma and Sharma, 2003). The DO, 3 3 - 3- 2+ 2+ 3+ Gt = release= release over over spillway spillway for for period period t (Mm t (Mm) ) NO3 and PO4 data in water and the Cu , Pb and Cr in sediment t = time (month) at the selected locations were available for a period of six years (2008 to 2013). The data were used in formulating the ecological integrity 1.1.1.2 Reservoir storage constraints constraints.

3 The water stored in the reservoir St (Mm ) should always be 3.1.2.5.1 Concentration of dissolved oxygen indicator 3 above the dead storage St min (Mm ) and within the reservoir’s storage constraint 3 capacity St max (Mm ) as presented in Eq. 12. The concentration of DO at any location i and time t in a reservoir t = 1 to 12 (12) is more than the minimum required as per WHO and the Nigeria Na- tional Environmental Standards and Regulations Agency (NESREA)

The reservoir’s capacity limit is given as: DO standards (DOstd) for freshwater. It is mathematically presented in t = 1 to 12 Eq. 15. The relationship between the mean monthly DO and reservoir where: storage was established using linear regression on the available data 3 St min = minimum reservoir capacity at time t (Mm ) at the power intake and boatyard locations as presented in Eqs. 16 and 3 St max = maximum reservoir capacity at time t (Mm ) 17. The relationships between the mean monthly DO and releases for the turbine operations, which is also the same as the releases at the tailrace location, were also established using linear regression and are 1.1.1.3 Net head constraints presented in Eqs. 18 and 19 respectively. t = 1 to 12 (15) The available net head on the turbine H (m) is restrained by the t t = 1 to 12 (16) minimum and maximum net head, Ht min (m) and Ht max (m) respectively as presented in Eq. 13: t = 1 to 12 (17)

t = 1 to 12 (18) t = 1 to 12 (13) t = 1 to 12 (19)

  Tab. 2 Monthly mean turbine release ( Rt ) and net head ( H t ) for the Kainji Dam (1970-2016).

58 OPTIMIZATION OF ENERGY GENERATION BASED ON OPERATIONS AND ECOLOGICAL INTEGRITY... Slovak Journal of Civil Engineering Vol. 27, 2019, No. 3, 55 – 62

2+ where: Pb std = lead concentration standard =35 mg/kg (Easthouse,

DOi, t DOstd 2009) 3+ DOstd = DO standard = 5.0 mg/l (Mohan et al., 2013; FRN, 2011) Cr i,t = concentration of chronium in sediment allocation i at

DOpi,,t = concentrat ion of DO at power intake at time t (mg/l) time t (mg/kg) 3+ DOy, t = concentrat ion of DO at boatyard at time t (mg/l) Cr std = chronium concentration standard = 95 mg/kg (East-

DOtd, t = concentrat ion of DO at turbine discharge at time t (mg/l) house, 2009) 2+ DOtr, t = concentrat ion of DO at tailrac e at time t (mg/l) Cu pi,t = concentration of copperin sediment at power intake at time t (mg/kg) 2+ 1.1.1.1.2 Sediment quality constraint Cu by,t = concentrat ion of copper in sediment at boatyard at time t (mg/kg) 2+ The concentration of heavy metals (HM) in sediment at any loca- Cu td,t = concentration of copperin sediment atturbine discharge tion i in the reservoir at time t is less than the SQGs proposed by the attime t (mg/kg) 2+ State of Washington’s Department of Ecology (WDOE) for freshwa- Cu tr,t = concentration of copperin sediment at tailrac e at time t ter. It is mathematically written as in Eq. 20. The heavy metals con- (mg/kg) 2+ 2+ 2+ 3+ sidered in this study are: Cu , Pb and Cr . The metals were selected Pb pi,t = concentration of lead in sediment at power intake at time since their availability indicates the presence of other heavy metals in t (mg/kg) 2+ 2+ 2+ sediments (El Badaoui et al., 2013). The WDOE SQG for Cu , Pb , Pb by,t = concentration of lead in sediment at boatyard at time t and Cr3+ are 80, 35 and 95 mg/kg respectively (Easthouse, 2009). The (mgkg) 2+ constraints for the three heavy metals are shown in Eqs. 21 to 23. The Pb td,t = concentration of lead in sediment at turbine discharge relationship between the mean monthly Cu2+, Pb2+, and Cr3+ with the at time t (mg/kg) 2+ reservoir storage and release were established using linear regression Pb tr,t = concentration of lead in sediment at tailrac e at time t as presented in Eqs. 24 to 35. (mg/kg) 3+ Cr pi,t = concentration of chromium in sediment at power intake (20) at time t (mg/kg) 3+ Cr by,t = concentration of chromium in sediment at boatyard at (21) time t (mg/kg) 3+ Cr td,t = concentration of chromium in sediment at turbine dis- (22) charge at time t (mg/kg) 3+ Cr tr,t = concentration of chromium in sediment at tailrace at (23) time t (mg/kg)

(24) 1.1.1.1.3 Algae constraint

- (25) The quantity of algae as a function of nitrate (NO3 ) and phos- 3- phate (PO4 ) at any location i in the reservoir at time t should be more - 3- (26) than the WHO and NESREA standards for NO3 and PO4 in freshwater (Mohan et al., 2013; FRN, 2011). They are mathematically written - (27) as in Eqs. 36 and 37. The relationship between the monthly NO3 and 3- PO4 with reservoir storage and release were established using linear (28) regression for the selected locations as shown in Eqs. 38 to 45.

(29) (36)

(30) (37) (31) (38) (32) (39) (33) (40) (34)

(35) (41) where:

HMi,t = concentration of HM at location i at time t (mg/kg) (42)

HMstd = HM standards Cu2+ = concentration of copperin sediment allocation i at time t i,t (43) (mg/kg) 2+ Cu std = copper concentration standard =80mg/kg (Easthouse, 2009) (44) 2+ Pb i,t = concentration of lead in sediment allocation i at time t (mg/kg) (45)

OPTIMIZATION OF ENERGY GENERATION BASED ON OPERATIONS AND ECOLOGICAL INTEGRITY... 59 Slovak Journal of Civil Engineering Vol. 27, 2019, No. 3, 55 – 62

where: – – NO3 i,t = concentration of NO3 at location i at time t (mg/l) – NO3 std = nitrate standards = 9.1 mg/1 (Mohan et al, 2013; FRN, 2011) 3– 3– PO4 i,t = concentration of PO4 at location i at time t (mg/l) 3– PO4 std = phosphate standards = 0.5 mg/1 (Mohan et al., 2013; FRN, 2011) NO– = concentration of NO– at power intake at time t (mg/l) 3 pi,t 3 3 – – Fig. 3 Time plot of turbine releases (Mm ) at the station (1970-2016). NO3 by,t = concentration of NO3 at boatyard at time t (mg/l) – – NO3 tr,t = concentration of NO3 at tailrace at time t (mg/l) – – NO3 td,t = concentration of NO3 at turbine discharge at time t (mg/l) 3– 3– PO4 pi,t = concentration of PO4 at power intake at time t (mg/l) 3– 3– PO4 by,t = concentration of PO4 at boatyard at time t (mg/l) 3– 3– 3 PO4 tr,t = concentration of PO4 at tailrace at time t (mg/l) Fig. 4 Time plot of reservoir inflow (Mm ) at the station (1970-2016). 3– 3– PO4 td,t = concentration of PO4 at turbine discharge at time t (mg/l)

1.1.1.1.4 Fish yield (FY) constraint

Fish yield can be defined as the portion of fish production re- moved for use by humans over a given period (Hortle, 2007). The Fig. 5 Time plot of reservoir storage (Mm3) at the station (1970-2016). units of a yield are generally kg per capita annually or metric tonnes (Mtonnes) from a given area per year. The fish yield is the best indicator of the size of a fishery, as biological production is impossible to measure in large systems (Hortle, 2007). The mean monthly fish yield (FY) data in the Kainji reservoir at time t in terms of the fish yield was collected from the NIFFR for the period of available re- cords (1994 to 1998) (du Feu and Abiodun 1999). The data was used in the formulation of the fish yield constraints. The fish yield in the Fig. 6 Time plot of energy generation (MWh) at the station (1970-2016). reservoir at time t should be more than the optimum fish yield (FYopt). This is mathematically expressed in Eq. 46. Miranda et al. (2000) studied some characteristics of gill nets and their consequences on 4.2 Optimization of reservoir operation fish yields in a reservoir in Brazil. The results revealed that excessive fishing may limit fish yields and commercial values. It was estimated A total optimum annual energy generation of 2565.892 GWh was that the optimum sustainable fish yield for all species in the reservoir obtained for the mean monthly hydropower reservoir operations at the was 1600 Mtonnes, which was adopted in this study. The relationship Kainji station. The optimum results for the operational head varied between 37.83 to 40.64; the turbine release was constant at 2217.88 between the mean monthly FY data with reservoir storage was estab- 3 3. lished using linear regression as shown in Eq. 47. Mm , while the storage varied between 7391.20 and 10707.22 Mm The optimum results for the ecological integrity indicators varied be- (46) tween 5.7 to 7.2 mg/l, 9.5 to 11.5 mg/l, and 0.5 to 0.99 mg/l for the DO, NO - and PO 3- concentrations respectively in the water. The op- (47) 3 4 timum results for the ecological integrity indicators using the quality where: of the sediment ranged between 27.9 to 68.6 mg/kg, 21.9 to 33.4 mg/ kg, and 40.1 to 95.0 mg/kg for the Cu2+, Pb2+ and Cr3+ concentrations FYt = fish population in the reservoir at timet (Mtonnes) respectively in the sediment. The optimum fish yield varies between FYopt = optimum fish population in a reservoir = 1600 Mtonnes (Miranda et al., 2000) 2583 to 3141 Mtonnes, which were within the range observed for the 3 fish yield measured in the lake. St = reservoir storage at time t (Mm )

3.3 Reservoir operating model solution 4.3 Discussion of the Results

A model was formulated for the hydropower reservoir operating 4.3.1 Reservoir operations system to consider its ecological integrity and determine other associated parameters. LINGO version 17.0 software was used. The monthly variations in the hydropower operational parameters using a time series trend analysis revealed that all the variables varied over time. The trends in the mean monthly turbine releases followed 4 RESULTS AND DISCUSSIONS a similar pattern with the energy generation.

4.1 Monthly variations of operating parameters 4.3.2 Optimization of the reservoir operations The results of the monthly variations in the hydropower reservoir’s operating parameters at the station using time plots are shown The total optimal annual energy generation of 2565.892 GWh in (Figs. 3 to 6). was found to be higher than the actual total annual energy generation

60 OPTIMIZATION OF ENERGY GENERATION BASED ON OPERATIONS AND ECOLOGICAL INTEGRITY... Slovak Journal of Civil Engineering Vol. 27, 2019, No. 3, 55 – 62

of 2519.459 GWh. This implies that the total annual energy genera- as proposed by the WDOE (Easthouse, 2009). This will not impact tion will increase by 1.84%. This will improve the total energy that negatively on the aquatic habitats in the reservoir. could be made available to the national grid from the Kainji hydro- The optimized fish yield (FY) (Mtonnes) in the reservoir revealed power station without compromising the ecological integrity of the that the FY ranges from 2583 to 3141 Mtonnes, which is higher than reservoir. the optimum fish yield (FYopt) of 1600 Mtonnes (Miranda et al., 2000).

The optimum reservoir operation head indicated that Ht var- All the optimum operational and ecological indicator parameters fell ied between 37.39 to 40.64 m, which fell within the limits of 33 to within the observed data except for the release; this contributed to a 3 41 m from the historical data observed. The turbine release Rt (Mm ) 1.84% increase in the annual energy generation without compromis- 3 revealed that there was a Rt constant value of 2217.88 Mm for the ing its operational and ecological integrities. It can be inferred that months that fell within the range of 500 to 3900 Mm3 from the histor- optimizing the reservoir’s operations will increase the total energy ical data observed. Also, the reservoir storage varied between 7391.2 and also ensue the availability of fish present in the reservoir. to 10707.22 Mm3; this implies that the optimized storage is within the limits of 3000 to 12000 Mm3 observed in the actual operations of the Kainji hydropower reservoir. 5 CONCLUSION The optimized DO concentration in the water at the four sampling locations revealed that the DO varied between 5.7 to 7.2 mg/l, This study focused on the optimization of energy generation using which is higher than the minimum DO standard of 5.0 mg/l for fresh- operational and ecological integrity constraints. A linear optimization water fish and other aquatic animals as per the WHO and NESREA technique was adopted in optimizing the average total annual energy standards (Mohan et al., 2013; FRN, 2011). It can be inferred that generation subject to operating and ecological integrity constraints. optimizing the reservoir’s operation will increase the total energy and The model was solved with LINGO 17.0 software. The results re- also improve the DO content in the water. vealed that the optimization approach could increase the total annual - 3- The optimized NO3 and PO4 concentration (as a function of al- energy generation at the Kainji station by 1.84%. This could improve - gae) in the water at the four sampling locations revealed that the NO3 the availability of electricity to consumers in Nigeria. Also, it was ob- 3- and PO4 varied between 9.5 to 11.5 mg/l and 0.5 to 0.99 respectively. served that the ecological integrity indicators were satisfactory when - These are greater than the minimum NO3 standard of 9.1 mg/l and compared to the various standards used in the study. 3- greater than 0.5 mg/l for PO4 in water as specified in the WHO and NESREA standards (Mohan et al., 2013; FRN, 2011). This will fa- vour the growth of algae in the reservoir, which is one of the key Acknowledgement indicators of the ecological health of a reservoir (Sharma and Sharma, 2003). The authors wish to acknowledge the management of the Kain- 2+ 2+ 3+ The optimized Cu , Pb and Cr concentrations in the sediment ji Hydropower Station, Nigeria, for providing the data used in this at the four sampling locations shown in Tables 6 to 8 indicate that the study. The authors appreciate the management of NACHRED for 2+ 2+ 3+ Cu , Pb and Cr varied between 27.9 to 68.6 mg/kg, 21.9 to 35.0 providing environmental and financial assistance in the course of this mg/kg and 39.7 to 95 mg/kg respectively. These fell within the lim- study. The LINDO System, Chicago, USA, is also thanked for pro- 2+ its of 80, 35 and 95 mg/kg SQG standards respectively for the Cu , viding an unlimited version of the LINGO 17.0 software used in this 2+ 3+ Pb and Cr heavy metal concentrations in sediment in freshwater study.

References

Abam, T. K. S. (2001) Modification of Niger Delta Physical Ecol- Chang, F. J. - Chen, L. - Chang, L. C. (2005) Optimizing the Res- ogy: the Role of Dams and Reservoirs. Hydrology and Aquatic ervoir Operating Rule Curves by Genetic Algorithms. Hydrol. Ecology, Proceedings of Workshop organized by IAHS held in Process. Vol. 19, pp. 2277–2289. the UK. pp. 19-29. Deeprasertkul, P. (2015) Linear Programming for Optimal Reser- Adeyemo, J. A. (2011) Reservoir Operation using Multi-Objective voir Operation of Chao Phraya River Basin. International Journal Evolutionary Algorithms-A Review. Asian Journal of Scientific of Innovative Research in Science, Engineering and Technology, Research, pp. 1-12. Vol. 4, No.9, pp. 8054-8063. Ahmed, G. L. - Srivastava, D. K. - Rani, D. (2013) Optimization– du Feu, T. A. - Abiodun J. A. (1999) Fisheries Statistics of Kainj Simulation Models for Yield Assessment of a Single Reservoir Lake, Northern Nigeria Nov. 1994 - Dec. 1998. A Technical Re- System. Journal of Indian Water Resources Society, Vol. 33, No. port Series 13, Prepared by the Nigerian-German Kainji Lake 4, pp. 9-16. Fisheries Promotion Project Submitted to National Institute for Freshwater Fishery Research, New Bussa, Nigeria, pp.1-128. Belayneh, M. Z. - Bhallamudi, S. M. (2012) Optimization Mod- el for Management of Water Quality in a Tidal River using Up- Dutta, S. (2015) Determination of Reservoir Capacity Using Linear stream Releases. Journal of Water Resource and Protection, Vol. Programming. International Journal of Innovative Research in 4, pp. 149-162. Science, Engineering and Technology, Vol. 4, No. 10, pp. 9549- 9556. Chen, Q. - Chen, D. - Li, R. - Ma, J. - Blanckaert, K. (2013) Adapt- ing the Operation of Two Cascaded Reservoirs for Ecological Easthouse, K. B., (2009) Sediment Quality Assessment of Lake Ru- Flow Requirement of a De-Watered River Channel Due to Diver- fus Woods and Chief Joseph Dams. A Technical Report submitted sion-Type Hydropower Stations. Ecological Modelling, ELSEVI- to the U.S. Army Corps of Engineers, Seattle District, Washing- ER, Vol. 252, pp. 266-272. ton State, USA. pp. 1-21.

OPTIMIZATION OF ENERGY GENERATION BASED ON OPERATIONS AND ECOLOGICAL INTEGRITY... 61 Slovak Journal of Civil Engineering Vol. 27, 2019, No. 3, 55 – 62

El Badaoui, H. - Abdallaoui, A. - Manssouri, I. - Lancelot, L. Mohammed, A. A. (2018) Assessment and Modelling of the Impact of (2013) Application of the Artificial Neural Networks of MLP Hydropower Reservoir Operations on the Ecological Integrity of Type for the Prediction of the Levels of Heavy Metals in Moroc- Kainji Lake, Nigeria. An Unpublished Ph.D Thesis Submitted to can Aquatic Sediments. International Journal of Computational Civil Engineering Department, University of Ilorin, Ilorin, Nigeria. Engineering Research, Vol. 3, No. 6, pp.75-81. Niu, Z. G. - Zhang, H. W. (2002) Application of LINGO to the Federal Republic of Nigeria [FRN], (2011) Federal Republic of Solution of the Water Supply Systems Optimal Operation Model. Nigeria Official Gazette, National Environmental Standards and Technical Transactions of Tianjin University, China, Vol. 8, No. Regulation Enforcement Agency Act on Surface and Groundwa- 4, pp. 246-250. ter Regulations. Vol. 98, No. 4(49), pp. 693-727. Parsa, M. S. (2017) Optimal Reservoir Operation of Karun 4 Reser-

Homa, E. S. - - Vogel, R. M. - Smith, M. P. - Apse, C. D.- Huber - voir by Linear Programming. International Academic Institute for Lee, A. Sieber, J. (2005) An Optimization Approach for Balanc- Science and Technology, Vol. 4, No. 1, pp. 110-120. ing Human and Ecological Flow Needs. Proceedings of World Salami, A. W. - Sule, B. F. - Adunkpe, T. L. - Ayanshola, A. M. - Water and Environmental Resources Congress. Bilewu, S. O. (2017) Evaluation of the Hydropower Generation Hortle, K.G. (2007) Consumption and the Yield of Fish and other Potential of a Dam Using Optimization Techniques: Application Aquatic Animals from the Lower Mekong Basin. MRC Technical to Doma Dam, Nassarawa, in North Central Nigeria. Slovak Paper No. 16, Mekong River Commission, Vientiane, Laos. Journal of Civil Engineering, Vol. 25, No. 1, pp. 1-9. Huang, X. - Fang, G. - Gao, Y. - Dong, Q. ( 2013) Chaotic Optimal Sharma, R. K. - Sharma, T. K. (2003) A Textbook of Water Pow- Operation of Hydropower Station with Ecology Consideration. er Engineering. Published by S. Chand and Company Ltd, New Energy and Power Engineering, Vol. 2, pp. 182-189. Delhi, India. Ifabiyi, I. P. (2011) Contributions of Reservoir Elements to Monthly Shaw, A. R. - Sawyer, H. S. - LeBoeuf, E. J. - McDonald, M. P. Electricity Generation in the Jebba Hydropower Reservoir, Nige- - Hadjerioua, B. (2017) Hydropower Optimization using Artifi- ria. Journal of Applied Sciences, Vol. 4, No. 3, pp. 251-264. cial Neural Network Surrogate Models of a High-Fidelity Hydro- dynamics and Water Quality Model. Water Resources Research, Khare, S. S. - Gajbhiye, A. R. (2013) Literature Review on Ap- Vol. 53, pp. 1-18. plication of Artificial Neural Network (ANN) in Operation of Reservoirs. International Journal of Computational Engineering Simonovic, S. P. (2009) Managing Water Resources Methods and Research, Vol. 3, No. 6, pp. 63-68. Tools for a System Approach, UNESCO Publishing, London. Lin, N. M. - Rutten, M. (2016) Optimal Operation of a Network Sule, B. F. - Adunkpe, T. L. - Salami, A.W. (2018) Evaluation of of Multi-Purpose Reservoir: A Review. Science Direct, Vol. 154, the Reservoir Yield and Hydropower Potential of the Doma Dam, pp.1376-1384. Nasarawa State, North Central Nigeria. International Journal of Technology, 9(1): 16-24. Loucks, D. P. - Stedinger, J. R.- Haith, D. A. (1981) Water Re- sources Systems Planning and Analysis. Prentice-Hall, Engle- Symum, H. - Ahmed, M. F. (2015) Linear Programming Model to wood Cliffs, N.J., USA. Optimize Water Supply and Cropping Area for Irrigation: A Case Study for Kalihati. Global Journal of Researches in Engineering, Mahsafar, H. - Najarchi, M. - Najafizadeh, M. M. - Hezaveh, M. Vol. 15, No. 2, pp. 19-24. M. (2017) Optimal Allocation of Agriculture Water for Irrigation of Multiple Crops using Nonlinear Programming. International Usman, A. - Ifabiyi, I. P. (2012) Socio-Economic Analysis of the Water Technology Journal (IWTJ), Vol. 7, No. 1, pp. 20-25. Operational Impacts of Shiroro Hydropower Generation in the Lowland Areas of Middle River Niger. International Journal of Miranda, L. E. - Agostinho, A. A. - Gomes L. C. (2000) Appraisal Academic Research in Business and Social Sciences, Vol. 2, No. of the Selective Properties of Gill Nets and Implications for Yield 4, pp. 57-76. and Value of the Fisheries at the Itaipu Reservoir, Brazil-Para- guay. Fisheries Research, ELSEVIER, Vol. 45, pp. 105-116. Mohan, V. C. - Sharma, K. K. - Sharma, A. (2013) Limnologi- cal Profile of Chenani Hydroelectric Reservoir, Its Connecting Channel and River Tawi in Udhampur District of J&K, India. In- ternational Research Journal of Biological Sciences, Vol. 2, No. 3, pp. 76-79.

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