**Operation of Hydropower Systems in **

**O. D. Jimoh**

**Department of Civil Engineering**

**Federal**** University**

**odjimoh@yahoo.com**

**1.0 Abstract **

The combined installed capacity of the three major hydropower stations (Kainji, Jebba and Shiroro) is 1900 MW. The systems have been performing below expectation and could as low as 30%. This has been attributed to maintenance, financial, hydrological and political problems. Hydrological issues such as inter-annual and seasonal variations in inflow to the reservoirs affect the volume of water available for operating the turbines. At some times, the volume of water in the reservoir is low, while at other times, the reservoirs are full without sufficient capacity to receive high inflow during the peak of rainy season in August or September. The later case results in flooding of downstream section of the respective reservoir. This paper presents the result of a study on optimised operation policy based on stochastic dynamic programming. The model was used to assess the operation of Kainji hydropower system in the previous years. The study showed that operation rules adopted between 1996 and 1999 could not handle instantaneous high inflow between August and September because water level in the reservoir was high prior to the arrival of high inflow. It was also observed that volume of water released from the reservoir remained high after the cessation of high inflow. An optimised operation policy performed better in terms of energy generation and flood mitigation. It is recommended that the Managers of reservoirs should adopt operation policy that could handle inter-annual and seasonal variations in flow to the reservoir so as to maximize the benefit of impounding rivers for power generation and minimize the annual flooding of the river plains.

**2.0 Review of hydropower systems in **

Before 1960, the bulk of power
production in

The combined installed capacity of
power stations in

(a) Hydrological factors, such as, (i) seasonal variation in flow to the reservoir, (ii) inter-annual variation in flow to the reservoir, (iii) conflict among competitive uses, and (iv) sediment trapped in the reservoir

(b) Non-hydrological factors, such as (i) maintenance and spare part problems, (ii) inadequate fund, (iii) human resources, and (iv) policy issues.

We shall focus on hydrological
issues as they affect the performance of hydropower systems in

(a) Seasonal variation in flow to reservoirs

Records of monthly inflow from 1970-2005 to Kainji Reservoir, as well
as, those from 1985-2004 to Shiroro Reservoir were collated and analysed (Jimoh, 2008). Figure 1 shows the mean monthly inflow to the reservoirs.

**Figure 1: Seasonal Inflow to Reservoirs**

There are two
distinct peaks at Kainji on River

Flow regime at
Shiroro on River Kaduna exhibits a single peak which occurs in September and
sometimes in August. This phenomenon agrees with the rainfall regime in the
basin. The implication of this is that the reservoir is depleted by evaporation
and release for operating the turbine between November and April.

**Figure 2: The River **

(b) Inter-annual variation in flow

Figure 3 shows the inter-annual variation in the inflow to Kainji Reservoir, as well as Shiroro Reservoir. For Kainji Reservoir, there was a declining trend immediately affect the commissioning of the plant in 1968. The inflow for the post-commissioning stage was as low as 50% of the flow during the planning stage. The effect of this is the inability to fill the reservoir as planned. The flow also exhibits noisy pattern. A similar observation was obtained for the flow into Shiroro Reservoir.

Despite these hydrological challenges, the hydropower systems are expected to: - (i) generate electricity at pre-determined level throughout the year, (ii) control downstream flooding for economic, environmental and social benefits, and (iii) maintain water demand by downstream users. While the first objective requires water level in the reservoir to be as high as possible, the second objective requires the water level to be low prior to the arrival of high inflow. There is a conflict between these two objectives during the pre-flooding season. This requires an optimised operation policy to maximize the benefits of impounding the rivers.

**Figure 3: Inter-annual
variation in flows**

**3.0 Review of reservoir operation models**

Large water projects are failing to produce benefits that provide economic justification for their developments. This situation could be attributed to a number of reasons. Labaide (1993, 2004) enumerated causes of such failure as:

1. Inordinate focus on project design and construction.

2. Inadequate consideration of routine operation and maintenance issues once the project is completed.

3. New unplanned issues which may arise, but were not originally considered.

4. Conflict and competition among competitive uses during drought period.

5. Complex legal agreements, interstate issues and pressure from various special interests.

Thus attention must focus on improving the operational effectiveness and efficiency of existing reservoir system for maximising the benefits of such projects, and minimise adverse effect on the environment. ASCE Task Committee on Sustainability Criteria (1998) described a sustainable water resources system as those designed and managed to fully contribute to the objectives of society, now and in the future, while maintaining their ecological, environmental and hydrological integrity.

Reservoir operation rules could be by simulation or optimization approach. The simulation approach is a search procedure, which involves postulating an operation rule and changing the decisions until the desired objectives are achieved. In optimization approach, the optimal policies are derived without assuming a simplified operation rule. Optimization could be by:-

(i) Linear programming, which is based on linear objective function and a set of linear constraints,

(ii) Network flow optimization, where interconnected reservoir systems are represented as a network of nodes and links (or arcs). The objective function is then approximated by convex, piecewise linear penalty functions characterized through specification of multiple links connecting two nodes, with bounds and unit costs defined by flow limits and slopes of each linear piece (that is, a model based on piecewise linearization of the system),

(iii) Non-linear programming, where objective and constraint functions are differentiable, and

(iv) Dynamic programming, which is applicable to sequential or multistage, decision problems.

The classes (i), (ii) and (iii) models are not effective in handling hydropower system because the system is non-linear and its minimization problem is convex (Quitron, 1981 and Labaide, 2004). Thus, a dynamic programming model is favoured. Dynamic programming model is specific for each subject.

Dynamic programming could be deterministic or stochastic. In deterministic model, the future events are known, whereas, in stochastic model, there is no presumption of perfect foreknowledge of future events. Optimal policies are determined without inferring operating rules. Stochastic dynamic programming (SDP) could be by implicit stochastic optimization (Fig. 4) or explicit stochastic optimization (Fig. 5). The implicit model is based on flow with samples drawn from streamflow synthesis, while the explicit one is designed to operate directly on probabilistic description of random streamflow process (as well as other random variables) rather than deterministic hydrologic sequences (Yeh, 1985 and Stedinger, et al, 1984).

**Figure 4: Schematic sketch of Implicit Stochastic Optimization
Model**

**Figure 5: Schematic sketch of Explicit Stochastic Optimization
Model**

The SDP models attempt to solve the dynamic programming recursive relation adapted to stochastic problems. It is referred to as Markovian decision process. The basic assumption is that the unregulated inflows are temporally uncorrelated but spatial correlation is included. The application of SDP to multireservoir systems is more aggravated by state dimensionality than in deterministic case, particularly when spatial correlation of unregulated inflows must be maintained (Tjeda-Gubert et al., 1995). The present study is considering two reservoirs in series and the main purpose of both reservoirs is generation of electricity. The secondary function of the reservoirs is flood control. The reservoirs are close to each other so that the release from the upper reservoir (Kainji reservoir) is the main inflow to the lower reservoir (Jebba Reservoir). The contribution from catchment between the reservoirs is less than 10% of the release from the upper reservoir. Thus, the system could be considered as a single reservoir with the demand for power generation of the lower reservoir satisfied as downstream requirement. Thus, an SDP model was adopted for this study.

**4.0 Application to Kainji-Jebba system**

For hydro-power reservoir, the system is dynamic and the equations are nonlinear and non-convex. In addition, the unregulated inflows, net evaporation rates, hydrologic parameters, system dynamics and economic gain are treated as random variable. Thus we have large scale, nonlinear stochastic optimization problem. Figure 6 shows a schematic diagram of the Kainji and Jebba Reservoirs system. The objective function of the system is:

f_{t} = B_{t}
+ B_{t-1} + . . . . . B_{T}
+ f_{T+1 } (1)

where B_{t} is the return at stage t due to the release R
given the initial and final storages, f_{T+1} describes the value of
water at the end of stage T, the last stage in the planning period (planning
period is 12 months for this study). The benefit is to maximize power generated
at Kainji and release sufficient water for Jebba reservoir. The analysis starts at time T and moves
backward using the Bellman’s principle which states that: an optimal policy has the property that
whatever the initial state and initial decisions are, the remaining decisions
must constitute an optimal policy with regard to the state resulting from the
first decision.

ORQ

Z (Generator)

**JEBBA**

**RESERVOIR**

**Notation: **I is inflow, Q is release, R is runoff into river
between Kainji and Jebba, S is storage, L denotes losses including evaporation and
seepage, REQ is the discharge through the turbine and ORQ represents other
releases from the reservoir. The subscripts 1 and 2 denote Kainji and Jebba
respectively, and t denotes time.

**Figure 6: Schematic
diagram of Kainji and Jebba Reservoir system**

The reservoir system operation is subject to a number of constraints expressed as:

(i) continuity equation: _{} (2)

where Q_{t} =
REQ_{t} + ORG_{t}, and the loss function is a function of
storage and outflow.

(ii) storage constraint: Smin < St < Smax_{t}
(3)

S_{t+1} ≤ Smax_{t} (4)

Smax_{t} =
RCAP – SFLD_{t} (5)

where Smin is the reservoir dead capacity, Smax_{t}
is the maximum storage at time t and SFLD_{t} is the volume reserved
for flood control in time t. Based on historical record (inflow series to
Kainji Reservoir), the reserved volume at monthly time step is presented in Fig
7.

**Figure 7: Reservoir volume
for flood control**

(iii) Release constraint: Q_{t} ≥ maximum(MQ_{t},
FQ_{t}) (6)

where MQ_{t}
is the obligatory water requirement at time t which is the release from Kainji
Reservoir to meet the minimum demand at Jebba Reservoir. The term FQ_{t}
demotes the firm water delivery at time t which is the release from Kainji
Reservoir to meet the minimum energy demand at Kainji during period of drought.

(iv) energy production, expressed as the energy production capacity (EPC):

EPC_{t} = C * REQ_{t} *
H_{t} * η (7)

where C is the conversion factor for potential to electrical energy, H is the average head over turbine and η is the energy plant efficiency.

The energy that can be produced is restricted by the plant capacity
(PCAP) and number of hours available for energy production (NHP). Thus, the
maximum peak energy produced (MPEP) is: MPEP_{t} = PCAP_{t} * η
* NHP_{t } (8)_{}

The energy produced at any time t is: PKE_{t} = minimum(TEP_{t}, MPEP_{t}) (9)

where PKE is the peak energy produced and TEP is the total energy that can be produced at a particular time

The objective function becomes maximising the energy produced at
Kainji. To solve equations 1 to 9, the characteristics and parameters of Kainji
Reservoir, summarised in Table 1, are needed. A** **monthly reservoir release patterns for the Kainji Reservoir are
obtained where the state variable is the reservoir storage S_{t} at the
beginning of a stage, while the decision variable is the reservoir release R_{t}.
The solution to the recursive equation (1) is obtained by working backwards in
time from the end of the decision horizon. The annual operation model was on
monthly time scale with 20 storage discretization. Figure 8 shows the flow
structure of the computer programme for carrying out the exercise.

**Table 1: Characteristics
of Kainji Reservoir**

Parameter |
Value |

Maximum capacity |
15000 M m |

Minimum capacity |
3500 M m |

Optimum downstream requirement |
1500 m |

Minimum head on turbine |
24 m |

Maximum water surface elevation |
141.9 m.a.s.l |

Annual energy target |
3000 GWh |

Plant capacity |
760 MW |

**Figure 8: Schematic
diagram of the program flow structure**

**5.0 Results and discussion**

Figure 9 shows optimized policy at monthly time step for Kainji
Reservoir. The figure shows the region when the release from Kainji Reservoir
is less than 1500 m^{3}/s (lower left hand portion of each chart).
During this period, the head at the reservoir is optimised but the water
released to Jebba Reservoir is inadequate. The upper right hand portion of each
chart indicates when release to Jebba Reservoir exceeds 1500 m^{3}/s. The figure shows that there are hydrologic
conditions (inflow to reservoir and storage at reservoir) when spillage
(release exceeds 2000 m^{3}/s) occurs in January, February, August,
September and October.

**Figure
9: Optimized release policy for Kainji Reservoir **

**The 1996 - 1999 operation policy**

Flooding of River

There was no significant variation between the monthly inflow
between November and July during the period 1996 to 1999. However, the monthly
inflow in August, September or October varied with year. Significant difference
was observed in September when peak rainfall occurred in the area within

Figure 10(b) shows the release which includes turbine and other
discharges from Kainji Reservoir. The outflow series had a peak value in
October, while inflow series has peak in September. An assessment of the
storage level in Kainji Reservoir (Fig. 11) showed that the reservoir was
within the full zone when high inflow in September arrived resulting in high
spillage in September and October. The situation resulted in flooding
phenomenon of 1998 and 1999. In addition the outflow between December and
February brings the reservoir to a low level in March to May without
commensurate inflow to augment the reservoir water. Available water level in
the reservoir is often below the desired level for energy generation. The
outflow for Kainji Reservoir was higher than 2000 m^{3}/s in September
and October during the period 1996 to 1999. The optimized release from the
reservoir is presented in Fig. 10(c). The figure shows that release could be
maintained below 2000 m^{3}/s throughout the year thereby maximise the
impounded water and reduce flooding of the river plain.

**Figure 10: Operation of Kainji Reservoir between 1996
and 1999 **

Figure 11 shows a comparison of the outflow from Kainji Reservoir in
an optimized policy and as operated in 1998 and 1999. Under an optimized policy
in 1999, the release from the reservoir varied between 658 m^{3}/s in
July and 1750 m^{3}/s in January. Similarly in 1998, the outflow varied
between 149 m^{3}/s in April or May and 1540 m^{3}/s in August
to February. The outflow in 1999 under the Manager’s operation policy varied
between in 679 m^{3}/s in July and 2786 m^{3}/s in October. The
outflow in 1998 varied between 833 m^{3}/s in May, June or July and 3026
m^{3}/s in October. The water released by the Managers in October exceeded
2000 m^{3}/s resulting in flooding. Under the optimized policy, the outflow
from Kainji Reservoir would have maximized the impounded water for energy
generation, met the requirements of Jebba Reservoir and other downstream users,
and reduced the flooding of downstream plain.

**Fig. 11: Outflow in m ^{3}/s
based on optimised ( _O) and manager ( _M) operation policies**

Figure 12 shows the head available for generating electricity under
an optimised operation policy. During the four years (1996 to 1999), it was
possible to achieve the minimum operating head (24 m) was achievable in all
seasons. It was found that the head available for energy generation varied with
season and year. In 1999, the head above turbine exceeded 24 m in all season,
except in July due to high inflow to the reservoir. On the other hand, the head
above turbine was 24 m in five out of 12 months in 1997 and 1998 which was
attributed to the inflow to the reservoir (Fig. 10a). Maintaining the operating
head at minimum level in July in all year enabled the reservoir to satisfy its
flood mitigation requirement. The implication of this phenomenon is that it is
not possible to operate the system at a ‘constant head’ throughout the year.
Thus planners need to seek alternative energy source during the low head period
of the pre-high inflow season.

**Figure 12: Optimised head
of Kainji Reservoir**

**Conclusion**

The main findings of this study are as follows:-

(i)
The rivers in

(ii) The rivers exhibit high inter-annual variation in flow with low and high extremes.

(iii) Operation of existing hydropower systems requires optimal policy due to the identified hydrological variations. The operation policy of Kainji Reservoir at monthly scale has been developed using stochastic dynamic technique.

(iv) The benefit of optimal policy for the hydropower system include:- (a) to obtain optimal head for energy generation during the wet and dry months, (b) have adequate free capacity during the pre-high flow season to store high flow that comes at the peak of rainy season, (c) reduce flooding of downstream plains, and (iv) enables the energy industry to plan for alternative source of energy during the pre-high flow season when there is relatively low head for energy generation.

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**Acknowledgement**

The author expresses his gratitude to Commonwealth Scholarship
Commission in the