Multi-reservoir optimization for hydropower production using NLP technique

KSCE Journal of Civil Engineering (2014) 18(1):344-354 Copyright ⓒ2014 Korean Society of Civil Engineers DOI 10.1007/s12205-014-0352-2 − 344 − pISSN 1226-7988, eISSN 1976-3808 www.springer.com/12205 Water Engineering Multi-reservoir Optimization for Hydropower Production using NLP Technique V. Jothiprakash* and R. Arunkumar** Received July 12, 2012/Revised January 2, 2013/Accepted February 27, 2013 ·································································································································································································································· Abstract Deriving the optimal operational rules for a multi-reservoir system serving various purposes like irrigation, multiple hydropower plants and flood control are complex. In the present study, such a multi-reservoir system with multiple hydropower plants are optimized for maximizing the hydropower production and satisfying the irrigation demands using a Non-linear Programming (NLP) technique. The developed NLP model has been applied to Koyna Hydro-Electric Project (KHEP) for maximizing the hydropower production and solved for three different dependable inflow scenarios under various operating policies. The complexity of the problem is such that the power releases and irrigation releases are in opposite direction and are non-commensurate. The total annual power production, monthly power production and the end of the month storage plots are compared for different inflows and operating policies. From the study, it is found that hydropower production can be increased to a minimum of 22% by slightly relaxing the tribunal constraint on releases towards the western side. The optimal releases from Policy 3 are further evaluated using a simulation model. The simulation result shows that the optimal releases have performed satisfactorily over long period of operation. Keywords: multi-reservoir, multi-hydropower plants, optimization, non-linear programming, simulation, reliability ·································································································································································································································· 1. Introduction A systematic study is required for optimizing the operations of a multi-purpose, multi-reservoir system. Optimizing such multi- reservoir system serving various purposes like irrigation, hydropower production and flood control are more complex because of their conflicting objectives. Several optimization techniques like Linear Programming (LP), Non-linear Programming (NLP), Goal Program- ming (GP), Chance Constraint Linear Programming (CCLP), Dynamic Programming (DP) (Loucks et al., 1981) and recently, the evolutionary algorithms were reported in literature for optimizing the reservoir operations. Various studies have been reported on hydropower optimization using different techniques, for example, CCLP (Sreenivasan and Vedula, 1996), Mixed Integer Programming (MIP) (Yi, 1998), Stochastic Dynamic Programming (SDP) (Zahraie and Karamouz, 2004), Bayesian Stochastic Dynamic Programming (BSDP) (Mujumdar and Nirmala, 2007). A review on various techniques used for optimal hydropower production can be found in Momoh et al. (1999a, b). Among these techniques, NLP is widely applied for optimizing hydropower systems (Gagnon et al., 1974; Tejada-Guibert et al., 1990), since it is the most accurate, involves no approximation and uses the physically based non- linear power production function (Barros et al., 2003). A non- linear reliability model was developed by Simonovic and Srinivasan (1993) for optimizing the operations of a multi-purpose reservoir for hydropower generation and flood control. Arnold et al. (1994) compared the two non-linear methods namely, Augmented Price Method (APM) and Sequential Quadratic Programming (SQP) for optimizing a large scale hydropower plant in Zambezi river system, Africa. Sinha et al. (1999) developed a non-linear optimization model for a multi-purpose reservoir operation. It was reported that the developed model successfully integrated the behavior analysis algorithm, automatic differentiation and sequent peak algorithm. Peng and Buras (2000) developed the optimal operation policies for a multi-reservoir hydropower system in Maine, USA using an NLP technique and reported that the model allows decision makers to simulate alternative operation scenarios. A short-term operational model was developed by Teegavarapu and Simonovic (2000) for optimal operation of hydraulically coupled hydropower reservoirs in Manitoba, Canada. Barros et al. (2003) developed a monthly NLP optimization model for the management and operations of the Brazilian hydropower system. Ailing (2004) proposed a decomposition-coordination approach to a multiple hydroelectric reservoir systems of Yellow River, China. Devamane et al. (2006) maximized the irrigation, municipal and industrial releases and hydropower production using a NLP model for a multi-reservoir system in the upper Krishna river basin, India. Liu et al. (2008) decomposed the non-linear hydropower problem using linear approximation for optimal TECHNICAL NOTE *Associate Professor, Dept. of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400-076, India (Corresponding Author, E-mail: [email protected]) **Research Scholar, Dept. of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400-076, India (E-mail: [email protected]) Multi-reservoir Optimization for Hydropower Production using NLP Technique Vol. 18, No. 1 / January 2014 − 345 − short-term hydropower scheduling of a multi-reservoir system. A non-linear multi-objective optimization model was developed by Moosavian et al. (2008) to optimize the annual scheduling of power generation in serial or parallel hydropower plants for dry, medium and wet scenarios. The multiple objectives were reformulated as a single objective using the weighted sum method. It was reported that the wet scenario resulted in increased amount of energy production due to high inflow. Barros et al. (2008, 2009) developed a monthly model to optimize the operation of large hydrothermal system. This study was further extended by Zambon et al. (2011, 2012). Brandão (2010) compared the Equivalent Reservoir Optimization Model (EROM) and the Operational Optimization Model (OPOM) for optimal hydropower production of São Francisco River Hydroelectric System, Brazil. All these studies show that optimizing hydropower reservoirs that serving multiple purposes is challenging. It is also observed that the NLP technique is widely adopted for optimizing hydropower systems. Hydropower production plays a significant role in supplying high valued peak loads. Therefore, planning and operation of hydropower reservoirs is more focused on peak load power generation. However, the problem is much more complex for a multi-purpose reservoir with multiple hydropower plants at different levels and with releases in different directions. The present study deals with optimizing the operations of a multi- reservoir having multiple hydropower plants for maximizing the hydropower generation using an NLP technique. The present study also focuses on the effects of different inflow scenarios for various operating policies in producing peak hydropower. Thus, three different dependable inflow levels namely wet scenario (50% dependable inflow), normal scenario (75% dependable inflow) and dry scenario (90% dependable inflow) are considered to optimize the system. The diversion of large quantity of water for power production has resulted in disputes. Hence, Tribunal constraints are imposed on releases to ensure adequate water for other demands. The effect of this constraint on power production is also modeled and studied in the present study as different policies. Finally, the optimal releases of the best policy are simulated to assess the performance for longer length of observed inflow. 2. Study Area The Koyna Hydro-Electric Project (KHEP) in Maharashtra, India consists of two reservoirs with four hydropower plants, serving multi-purposes like hydropower, irrigation and flood control is considered in this study. The KHEP is the lifeline of Maharashtra, which has four hydropower plants to a total capacity of 1960 MW (KHEP, 2005). The particulars about the two reservoirs in this system, namely, Koyna reservoir and Kolkewadi reservoir and their power plants are given in Table 1 and the location of the power plants are shown in Fig. 1. The Koyna reservoir has three hydropower plants, two on western side (stage 1, 2 and 4) of the reservoir and one at the dam foot on eastern side, namely Koyna Dam Power House (KDPH). The stage 1 and 2 have same head works such as the headrace tunnel, surge well and tailrace tunnel, and hence it is referred to as the single powerhouse (PH I) in the present study. The stage 3 (henceforth referred as PH II) with a capacity of 4 × 80 MW is at Kolkewadi reservoir. The stage 4 (henceforth referred to as the PH III) with a capacity of 4 × 250 MW in KHEP is also in the western side of the Koyna reservoir. The Kolkewadi reservoir is a balancing reservoir, much smaller in catchment area and capacity compared to Koyna reservoir as seen from Table 1. It receives most of its inflow from PH I and PH III tail water and regulates the flow to PH II. Even though the Koyna reservoir is specially constructed for power production, there is also a need to releases for irrigation on the eastern side. Hence, to utilize the head available in the reservoir, the KDPH (henceforth referred as PH IV) was constructed with a capacity of 2 × 20 MW to generate hydropower through irrigation releases. It is worth mentioning that irrigation releases through PH IV flow towards the eastern side of the reservoir, where as the releases to PH I, PH II and PH III are towards the western side of the reservoir. Thus the irrigation releases and power releases are in opposite in direction and are non-commensurate. Diverting large quantity of water to the major hydropower plants on the western side of the reservoir has resulted in serious disputes among the different stakeholders. Hence, the Krishna Water Dispute Tribunal (KWDT, 2010) limited the diversion of water towards western side for power production from Koyna reservoir. In addition, there also exist conflicts among the hydropower plants, since the plants are at different levels and have different generation capacity. Thus, there is a need to optimally utilize the available water for Table 1. Details of Koyna Hydro-Electric Project Hydropower Plants Details Stage 1 & 2 (PH I) Stage 3 (PH II) Stage 4 (PH III) KDPH (PH IV) Reservoir Catchment area (km2) Gross Storage (106 m3) Dead Storage (106 m3) Net Storage (106 m3) Water spread (km2) Koyna 891.78 2797.400 145.00 2652.400 115.35 Kolkewadi 25.40 36.22 25.00 11.22 .1.67 Koyna 0891.780 2797.400 145.00 2652.400 115.35 Koyna 891.78 2797.400 145.00 2652.400 115.35 Power House Generator capacity Head (m) 70 × 4 475 80 × 4 490 80 × 4 109.70 250 × 4 500 20 × 2 59 Fig. 1. Location of Hydropower Plants of Koyna-Hydro Electric Project (Modified after Arunkumar and Jothiprakash, 2012) V. Jothiprakash and R. Arunkumar − 346 − KSCE Journal of Civil Engineering producing maximum hydropower and satisfying the irrigation demands. 3. Model Formulation Among various purposes of a reservoir, hydropower production is very significant for India owing the increasing power demand from various sectors. Loucks et al. (1981) stated that the hydropower production from a reservoir depends on the installed plant capacity, flow through the turbines, average effective storage head and the number of hours operation. Thus, the hydropower production (PHt) in terms of kilowatt-hours (kWh) (Vedula and Mujumdar, 2005) during any time period ‘t’ is given as: (1) where, Rt is the release to power plant during the time period ‘t’, HNt is the net head available during the time period ‘t’, K is the constant to convert the hydropower to kWh and η is the plant efficiency. The average head (Ht) available during a particular time period ‘t’ is expressed as the second order function of the storage and it is given as: (2) Then the net head (HNt) is estimated by deducting the tail water level and the frictional losses from Eq. (2). The objective of the present study is to maximize the power production from all the hydropower plants of the two reservoirs. It is expressed as: Max (3) where, , , and is the power produced from PH I, PH II, PH III, and PH IV respectively during the time period ‘t’ in terms of kWh. The above objective function is subjected to various constraints. The head available in the reservoir should be greater than the minimum drawdown level of the power plant for any time period ‘t’. This is expressed as: t = 1, 2 … 12; n =1, 2, 3, 4 (4) where Hn,t is the average head (m) in the reservoir for the power plant ‘n’ during the time period ‘t’ and MDDLn,t is the minimum drawdown level for the power plant ‘n’ during the time period ‘t’. The power production during any time period ‘t’ should be less than or equal to the maximum generating capacity of the plant. t = 1, 2 … 12; n =1, 2, 3, 4 (5) where PHn,t is the power produced (kWh) from the power plant ‘n’ during the time period ‘t’; Pmaxn,t is the maximum capacity of generation (kWh) for the power plant ‘n’ during the time period ‘t’. Agricultural is a major sector in India in which majority of people depends on it. Hence, in order to satisfy the monthly irrigation demand for all the time period, irrigation demand is set to be greater than or equal to the monthly demand for irrigation during the time period ‘t’. t = 1, 2 … 12 (6) where R4,t is the irrigation release from Koyna Dam on the eastern side during the time period ‘t’ and IDt is the demand for irrigation during the time period ‘t’. This constraint ensures that irrigation demands are completely satisfied before maximizing the power production. Thus, irrigation is given higher priority in this study. As stated earlier, the diversion of huge quantity of water to the western side for power production has resulted in disputes. To ensure adequate water for irrigation on eastern side, Krishna Water Dispute Tribunal (KWDT, 2010) restricted the western side diversion of water. As per this constraint, diversion of large quantity of water to western side for power production was restricted to 1912 × 106 m3. The total annual release for irrigation should be less than or equal to 850 × 106 m3. (7) (8) The storage ‘Sm,t’ in the reservoir ‘m’ during any time period ‘t’ should not be less than the minimum storage (Sm,min) or dead storage and should not be more than maximum storage (Sm,max) or capacity of the reservoir. It is also essential to maintain the reservoir storage at some lower level during the monsoon season to observe the flood and to avoid flooding at the downstream. This is given by (Simonovic and Srinivasan, 1993): t = 1, 2 … 12; m = 1, 2 (9) where θm,t is the required storage to be emptied for flood during the monsoon season for the reservoir ‘m’ during the time period ‘t’. The required flood storages (θm,t) for different time period ‘t’ during monsoon season are fixed as per downstream canal carrying capacity and time required for operating the gates of the reservoirs (KHEP, 2005). The water balance continuity equation for Koyna reservoir is given as: t = 1, 2 … 12; n = 1, 3 & 4 (10) where, S1,(t+1) is the final storage in the Koyna reservoir during the time period ‘t’ (106 m3); S1,t is the initial storage in the Koyna reservoir during the time period ‘t’ (106 m3); I1,t is the inflow into the Koyna reservoir during the time period ‘t’(106 m3); Rn,t is the release to the powerhouse ‘n’ during the time period ‘t’ (106 m3) from the Koyna reservoir; O1,t is the Overflow from the Koyna reservoir during the time period ‘t’(106 m3) and E1,t is the PHt K Rt HNt× η××= Ht C1St C2St 2 C3+ += Z PH It PH IIt PH IIIt PH IVt+ + + t 1= 12 ∑= PH It PH IIt PH IIIt PH IVt Hn t, MDDLn t,≥ PHn t, P maxn t,≤ R4 t, IDt≥ R1 t, R3 t,+( ) 1912 10 6 ×≤ t 1= 12 ∑ R4 t, 850 10 6 ×≤ t=1 12 ∑ Sm min, Sm t, Sm max, θm t,–( )≤ ≤ S1 t 1+( ), S1 t, I1 t, Rn t, O1 t,– E1 t,– n 1= 1 3 4, , ∑–+= Multi-reservoir Optimization for Hydropower Production using NLP Technique Vol. 18, No. 1 / January 2014 − 347 − evaporation losses from the Koyna reservoir during the time period ‘t’, (106 m3). The water balance continuity equation for the Kolkewadi reservoir is given as: t = 1, 2 … 12 (11) where, S2,(t+1) is the final storage in the Kolkewadi reservoir during the time period ‘t’; S2,t is the initial storage during the time period ‘t’ in Kolkewadi reservoir; I2,t is the inflow into the Kolkewadi reservoir from its own catchment area during the time period ‘t’; R2,t is the release to the PH II from the Kolkewadi reservoir during the time period ‘t’; R1,t is the inflow to the Kolkewadi reservoir from PH I during the time period ‘t’; R3,t is the inflow to the Kolkewadi reservoir from PH III during the time period ‘t’; O2,t is the overflow from the Kolkewadi reservoir during the time period ‘t’; and E2,t is the evaporation losses from the Kolkewadi reservoir during the time period ‘t’. The overflow occurs when the final storage exceeds the reservoir capacity. This overflow constraint is given by: t = 1, 2 … 12; m =1, 2 (12) and t = 1, 2 … 12; m = 1, 2 (13) where, Sm,(t+1) is the final storage in the reservoir ‘m’ during time period ‘t’ (106 m3) and this final storage is the initial storage for the next time period ‘t+1’, when there is no overflow. If overflow occurs then Sm,max will be the initial storage for the next time period ‘t+1’ for the reservoir. 4. Results and Discussion The KHEP is optimized for maximizing the hydropower production using the above developed monthly time step NLP model. Earlier, Arunkumar and Jothiprakash (2012) optimized the Koyna reservoir alone, considering it as a single reservoir system. In the present study, both Koyna and Kolkewadi reservoirs are considered together as multi-reservoir system and are optimized using NLP technique. In addition, in the present study, the optimal releases obtained from the NLP model for different dependable inflows are further tested using a simulation model for 49 years of observed inflow. The NLP model is optimized for three different inflows, namely, wet scenario (50% dependable inflow), normal scenario (75% dependable inflow) and dry scenario (90% dependable inflow). The dependable inflows are estimated using Weibull’s method from 49 years of observed inflow. It is observed that the Koyna reservoir receives 95% of the inflow during the monsoon season (Jun - Oct) and the remaining 5% during the non-monsoon period (Nov - May). Thus, the Koyna reservoir completely depends on the monsoon inflow. The major inflow into Kolkewadi reservoir is the power releases from Koyna reservoir through PH I and PH III. Thus, the operation of PH III at Kolkewadi reservoir completely depends of Koyna releases. The average head available in the reservoir is represented as a quadratic function of storage as given in Eq. (2). The constants of the equation, C1, C2 and C3 are estimated by regression analysis from area-capacity-elevation table of the reservoirs. The reservoir evaporation is estimated using the equation developed by Arunkumar and Jothiprakash (2012) and directly incorporated in water balance equation. Based on the tribunal constraints of the above formulated NLP model, four operating policies (Arunkumar and Jothiprakash, 2012) are analyzed for each dependable inflow. These different operating policies will be helpful in assessing the full potential of the reservoir system under different inflow scenarios and release conditions. The policies considered in the present study are: Policy 1 : No binding constraint on eastern and western side releases (all constraints excluding constraint Eqs. (6), (7) and (8)) [To find the full power production potential of the system] Policy 2 : Only annual binding constraint on irrigation (east- ern side) releases (all constraints excluding con- straint Eqs. (6) and (7)) Policy 3 : Both monthly and annual binding constraint on irri- gation (eastern side) releases (all constraints exclud- ing constraint Eq. (7)) Policy 4 : Both western and eastern side binding constraints on releases are considered as per the Tribunal (KWDT 2010) (with all the constraints) The optimal releases of the developed NLP model for these four policies under different dependable inflow scenarios are discussed in the following section. 4.1 Annual Power Production In order to assess the full potential of the project, the formulated NLP model is solved for the above mentioned four policies using three different dependable inflow scenarios. The variation of annual power production for different operating policies resulted from three inflow scenarios is given in Fig. 2. It can be observed from Fig. 2 that the power production decreases among the policy due to restriction on releases as well as with increase in S2 t 1+( ), S2 t, I2 t, R1 t, R3 t, R2 t,– O2 t,– E2 t,–+ + += Om t, Sm t 1+( ), Sm max,–= Om t, 0≥ Fig. 2. Annual Power Produced from Various Policies under Differ- ent Inflow Scenarios V. Jothiprakash and R. Arunkumar − 348 − KSCE Journal of Civil Engineering inflow dependability. However, in case of dry inflow scenario, the annual power production is almost same for Policies 2, 3 & 4. This shows that the power production potential under dry inflow scenario remains the same even if there is no restriction on western side releases. Among all these policies, the Policy 1 has resulted in a maximum power production of 5826.29 × 106 kWh for wet inflow scenario, since there is no restriction on the western and eastern side releases. Even though this Policy 1 has resulted in maximum power production through major power plants on the western side, the releases towards eastern side for irrigation are lower and most of the months are zero for all the inflow scenarios. This shows that the model has reduced the irrigation release on the eastern side to achieve full power production in the western side power plants. Depriving irrigation release is not a viable case in practical, since irrigation is the primary occupation on the eastern side of the reservoir and hence irrigation releases are mandatory. However, Policy 1 shows the full power production potential of the system under unrestricted releases. In order to achieve irrigation releases, the annual irrigation release constraint (Eq. 8) is considered in Policy 2. Under this Policy 2, all the three inflow scenarios have resulted in irrigation releases equal to the annual demand, but not in every month. Considering this constraint (Eq. 8) in the optimization model reduces the power production substantially for all the three inflow scenarios showing that hydropower production and irrigation are conflicting objectives. The reduction in total power production for different inflow scenarios varies between 10-29% compared to Policy 1. The hydropower plants in the western side are having high net head with high generating capacity and hence produce more hydropower for same discharge compared to PH IV at the dam foot on the eastern side. Thus, the power produced from PH IV through irrigation releases is lesser than the power produced at PH I & III for the same discharge. Even though this Policy 2 has satisfied the total annual irrigation demand, the month wise irrigation demands are not met. In order to have irrigation release for all months, both the annual and monthly irrigation demand constraints are considered in Policy 3. This Policy 3 has resulted in irrigation release in all the months as per the monthly demand and the power production is almost similar to that of Policy 2. This Policy 3 is a practically implementable optimal solution, leading to higher power production satisfying all the physical and other demand constraints. In the all these policies, the restriction on releases towards the western side for power production is not considered for all the inflow scenarios and hence the releases are slightly more than the tribunal limit. Hence in Policy 4, all the binding constraints on releases are considered and thus the model has restricted the releases for both power production and irrigation as per the Fig. 3. Monthly Power Production from Hydropower Plants for Wet Inflow Scenario using the NLP Technique: (a) Policy 1, (b) Policy 2, (c) Policy 3, (d) Policy 4 Multi-reservoir Optimization for Hydropower Production using NLP Technique Vol. 18, No. 1 / January 2014 − 349 − tribunal limits. The limitation on releases has reduced the power production significantly for all inflow scenarios. Also, there is not much variation in the power production among the different inflow scenarios in this Policy 4, since the total quantity of release for power production is same. This shows that under restricted releases, the power production is same irrespective of the quantity of inflow received to the reservoir. When compared to Policy 1, the power production decreases by 44% for wet scenario, 38% for normal and 29% for dry scenario in Policy 4. Also, there is a decrease of around 32% and 18% in power production when compared to Policy 3 for wet and normal scenarios, respectively. However, in Policy 4, the dry inflow scenario has produced almost the same hydropower as that of Policy 3. This shows that under dry (less) inflow scenario, the system produces almost the same hydropower irrespective of tribunal release constraints and thus leading to redundancy of this constraint at low inflow scenario. This constraint on the other side increased the storage in the reservoir leading to overflow from the reservoir during normal and wet years. 4.2 Monthly Power Production The monthly power production from different hydropower plants for wet inflow scenario for four operating policies is shown in Fig. 3. From the figure, it can be observed that the Policy 1, 2 and 3 has produced considerable hydropower in all the months. A maximum of 614.74 × 106 kWh was produced in August for both Policy 1 and 2, and minimum of 98.24 × 106 kWh was produced in June for Policy 4 from the system for the wet inflow scenario. Policy 1 has resulted in a maximum firm energy of 417.14 × 106 kWh and decreases among the policies. Among the hydropower plants, PH III has produced maximum of 300 × 106 kWh for all policies because of high head and capacity. The monthly power production for Policy 1 from different hydropower plants is shown in Fig. 3(a). From Fig. 3(a), it can be seen that for most of the months, all hydropower plants have generated maximum possible power, since no restrictions on releases are considered. It also shows that there is a constant power production from PH II for most of the months and depends on the outflow from PH I and PH III. It is also to be observed that PH IV has produced power only in July and August. It can be inferred that there is no irrigation release during most of the months in Policy 1, since no binding constraints on releases are considered. The monthly power produced for Policy 2 from different hydropower plants is shown in Fig. 3(b). In this policy, PH IV has produced only during the monsoon season, Fig. 4. Monthly Power Production from Hydropower Plants for Normal Inflow Scenario using the NLP Technique: (a) Policy 1, (b) Policy 2, (c) Policy 3, (d) Policy 4 V. Jothiprakash and R. Arunkumar − 350 − KSCE Journal of Civil Engineering which shows that releases are only during the monsoon season. However, the total releases are equal to the annual irrigation demand. In Policy 2, not only the total power production but also the monthly minimum power production from the system has decreased considerably compared to Policy 1 since the annual irrigation release constraint is considered. The monthly power produced in Policy 3 from different hydropower plants is shown in Fig. 3(c). It can be seen that there is power production in PH IV in all months. This has lead to the satisfaction of monthly irrigation demand and annual irrigation demand. It is also observed that there is further reduction in firm power production in Policy 3. Both Policy 2 and 3 have produced less power at the end of the season. Fig. 3(d) shows that there is a wide variation in power production among the hydropower plants in Policy 4. All these variations are due to the constraint imposed on western side releases. The monthly power production from different hydropower plants for normal inflow scenario is given in Fig. 4. During normal inflow scenario, only the Policy 1 has resulted in considerable power production in all the months expect PH IV. Both the Policy 2 and 3 has shown a similar trend in power production and also variation is less. A maximum of 477.76 × 106 kWh was produced in October for Policy 2, and minimum of 90.22 × 106 kWh was produced in June for Policy 2 from the system for the normal inflow scenario. The maximum firm energy of 356.33 × 106 kWh is produced from the system for Policy 1. Among the hydropower plants, PH III has produced maximum firm energy in Policy 1 because of high head and capacity. The monthly power production for Policy 1 from different hydropower plants is shown as stacked plot in Fig. 4(a). From Fig. 4(a), it can be seen that for most of the months, PH II has resulted a constant power production. Since there are no irrigation releases, PH IV has not produced any power. The monthly power produced for Policy 2 from different hydropower plants is shown in Fig. 4(b). In this policy, there is a considerable power production from August to March from the system. However, the power production at the start and at the end of the system has reduced. Also, the power production from PH IV is during August to December, indicating that irrigation releases are only during this time period. However, the total releases are equal to the annual irrigation demand. In Policy 2, not only the total power production but also the firm energy has decreased compared to Policy 1 since the annual irrigation release constraint is considered. The monthly power produced for Policy 3 from different hydropower plants are shown in Fig. 4(c). This policy has resulted in power production similar to Policy 2. Also, it can be observed that PH IV has resulted in power production all the months. Fig. 4(d) Fig. 5. Monthly Power Production from Hydropower Plants for Dry Inflow Scenario using the NLP Technique: (a) Policy 1, (b) Policy 2, (c) Policy 3, (d) Policy 4 Multi-reservoir Optimization for Hydropower Production using NLP Technique Vol. 18, No. 1 / January 2014 − 351 − shows the monthly power production from different hydropower plants for normal inflow scenario. From the figure, it is observed that the Policy 4 has produced maximum power during non- monsoon periods and the rest of the period, it maintained a minimum constant production. The monthly power production from different hydropower plants for various policies under dry inflow scenario is shown in Fig. 5. Contrary to other inflow scenarios, the variation in monthly minimum power production from the system is very less among different policies. This shows that under less inflow scenario, the restriction on releases has less impact on power production. However, the total power production is high for Policy 1 and for rest of the policies it is almost the same. The monthly power production for Policy 1 from different hydropower plants is shown in Fig. 5(a). Under dry inflow scenario, all hydropower plants in Policy 1 have considerable power production from June to March expect PH IV. The monthly power produced from different hydropower plants for Policies 2, 3 and 4 are shown in Fig. 5(b), 5(c) and 5(d) respectively. It can be observed that the Policies 2, 3 and 4 have resulted in a similar trend in monthly power production. These three policies have produced power only during the monsoon season, where there will be inflow and during non-monsoon season the power production remains constant. This shows that under dry inflow scenario, the system behaves the same way irrespective of constraints on releases. In general, the wet inflow has resulted in more hydropower production than the normal and dry inflow scenario for all the policies studied. The average power production is also higher for the wet inflow scenario among policies. It is observed that PH III has produced maximum hydropower for all the policies under all the inflow scenarios. It is also observed that the hydropower production in PH III has reduced considerably compared to the other hydropower plants due to constraints on releases. Since the Kolkewadi reservoir receives inflow mainly from PH I and PH III, the power production from PH II varies accordingly. The variation in power production among the wet, normal and dry inflow scenario is less for Policy 4 compared to other policies. Thus, the constraint on eastern side and western side releases reduces the power production from the system. 4.3 End of Month Storage Levels The resulted end of month storage levels for Koyna reservoir for various operating policies is given in Fig. 6. From Fig 6, it can be seen that the storage curve of Koyna reservoir follows a similar trend for all policies. Only the wet inflow scenario has reached the maximum storage in all policies, while the dry Fig. 6. Resulted Storage Curves of Various Policies for Koyna Reservoir for Different Inflow Scenarios: (a) Policy 1, (b) Policy 2, (c) Policy 3, (d) Policy 4 V. Jothiprakash and R. Arunkumar − 352 − KSCE Journal of Civil Engineering Fig. 7. Resulted Storage Curves for Kolkewadi Reservoir Fig. 8. Monthly Average Irrigation Deficit of Policy 3 for Different Scenarios Table 2. Performance Analyses of Policy 3 of NLP Model Scenario MFID AFID AAID (106 m3) PAID (%) Scenario 1 45/588 16/49 74.97 8.83 Scenario 2 10/588 7/49 18.60 2.19 Scenario 3 0/588 0/49 0.00 0.00 inflow scenario reached the maximum storage in Policy 4 due to the restriction in releases. Fig. 6(a) shows the resulting storage levels for Policy 1. It can be observed that the available storage is fully utilized for power production, since there are no binding constraints on releases. Only the wet inflow scenario has reached the maximum capacity of the reservoir in Policy 1 in spite of high power production. The resulting storage levels for Policy 2 and 3 are shown in Fig. 6(b) and 6(c) respectively. Both the policies have similar storage levels. A minor difference is due to the irrigation release during all months in Policy 3. For the Policy 4 shown in Fig. 6(d), the wet and normal inflow have resulted in maximum storage leading to overflow from the reservoir, since the releases are restricted as per the Tribunal limits. The variation in storage levels for dry inflow scenario is the same as that of the other policies, since the power production is also the same. Thus, the releases are same for all the policies irrespective of the tribunal constraint. This shows that even though there are restrictions on releases, due to less inflow, the Policy 4 has only less storage. The resulted Kolkewadi storage curves are shown in Fig. 7 and it is observed that the storage rule curves are same for all the policies and also for three inflow scenarios, since it is just a balancing reservoir. All inflows are completely utilized for power production in Kolkewadi reservoir. 5. Performance Assessment using a Simulation Model The Policy 3 is selected as the best and viable optimal result, since it has satisfied the monthly irrigation demand and also produced considerable power production compared to Policy 4. The performance of the optimal releases of Policy 3 obtained from wet inflow (referred as Scenario 1), normal inflow (referred as Scenario 2) and dry inflow (referred as Scenario 3) are assessed using a simulation model for 49 years of observed monthly inflow. The Monthly Frequency of Irrigation Deficit (MFID), Monthly Average Irrigation Deficit (MAID), Annual Frequency of Irrigation Deficit (AFID), Annual Average Irrigation Deficit (AAID), and Percentage Annual Irrigation Deficit (PAID) (Jothiprakash and Shanthi, 2009) are the performance indices used to assess the optimal results. Table 2 shows the performance of the optimal Policy 3 for longer period. The MFID gives the number of months the deficit occurred to the total simulated months. The table shows the Scenario 1 has resulted in deficit irrigation in 45 months out of total simulated 588 months. The annual average irrigation deficit is also higher for Scenario 1. The Scenario 2 has resulted deficit irrigation release in 10 months. The Scenario 3 has not resulted in any irrigation deficit and has released as per the demand for all the time periods. The volume of monthly average irrigation deficit for all the scenarios is given in Fig. 8. From the figure, it can be seen that the Scenario 1 has resulted in irrigation deficit and the Scenario 2 for few months at the end of the time period. However, the Scenario 3 has not resulted in any irrigation deficit. The optimal releases of Scenario 1 are higher than Scenario 2 and 3 obtained from optimization model. Hence, the simulation results of Scenario 1 encountered higher MFID, MAID, AFID, AAID and PAID than Scenario 2 and 3. However, the deficits mostly occurred at the end of the season for less inflow years. The result shows that irrespective of the inflow in the optimization, the policy performs very well for longer runs with a maximum average irrigation deficit of 8.8% over 49 years. The volume reliability of monthly irrigation release is given in Fig. 9. From the figure, it is observed that all the scenarios have more than 75% reliability. Even though the Scenario 1 has resulted in deficit in few months Multi-reservoir Optimization for Hydropower Production using NLP Technique Vol. 18, No. 1 / January 2014 − 353 − at the end of the season, it has released more than 75% of the demand and similarly the Scenario 2 has released more than 80% of the demand in deficit months. The overall volume reliability is more than 90% for all the scenarios, which shows that the optimal results of Policy 3 are highly reliable. This shows that the resulted optimal releases resulted from Policy 3 for various scenarios may perform better for any kind of inflow. 6. Conclusions In the present study, the KHEP operations are optimized for maximizing the power production through NLP technique. The developed NLP model is solved using Lingo/-Global solver for three different inflow scenarios namely, wet, normal and dry inflows for various operating policies. In general, the wet inflow has resulted in more power production than the normal and dry inflow scenarios for all the policies. The average energy produced is also higher during the wet inflow scenario for all the policies. This study also shows that during the dry inflow scenario, the system produces almost same hydropower for all operating policies irrespective of the release constraints and thus leading to redundancy of this constraint during low inflows. This constraint on the other side increased the storage in the reservoir. It is also observed that PH III has produced maximum power for all the policies for all three inflow scenarios. The effect of constraints on releases has major impacts on PH III causing considerable reduction in power production. On comparing the different policies, it is found that the power production can be increased upon by relaxing the release constraint slightly. Policy 3 shows an increment of 47 and 22% in power production for wet and normal inflow scenario satisfying the monthly irrigation demands compared to Policy 4. The monthly irrigation release has also slightly reduced the power production for Policy 2 and 3. It is also observed that even though the total releases to the hydropower plants are almost same for different policies, the power production varies due to the variation in releases and head. On evaluating the performance of the Policy 3 using a simulation model, the results shows that the optimal releases are highly reliable on longer run. 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