On the Short-term Optimisation of a Hydro Basin with Social Constraints

In this paper, an optimisation problem for calculating the best energy bids of a set of hydro power plants in a basin is proposed. The model is applied to a real Spanish basin for the short-term (24-hour) planning of the operation. The algorithm considers the ecological flows and social consumptions required for the actual operation. One of the hydro plants is fluent, without direct-control abilities. The results show that the fluent plant can be adequately controlled by using the storage capacities of the other plants. In the simulations, the costs related to the social consumptions are more significant than those due to the ecological requirements. An estimate of the cost of providing water for social uses is performed in the study.


Introduction
Nowadays, the utilisation of water for electricity production is conditioned by many constraints.In Spain, primarily the Kyoto Agreements and the proposals of the European Commission to 2020 must be considered.The European Commission have specified a goal of 20% of the final energy consumption delivered from renewable sources by 2020 [1].In Spain, 38.6% of the electricity generation comes from renewable resources, mainly from hydro (17.4%) and wind (16.6%) generation [2].Because electricity generation has to compensate for other nonrenewable energy consumptions, electricity production must increase its share of renewable generation.Hydro production is a mature renewable technology that can help reach the ambitious objectives proposed by the European Commission by 2020.
In addition, the exceptionally variable weather conditions of the past few years, most likely due to climate change, complicate the management of water for electricity production.The scarcity and the high variability of water resources have recently reduced the profits in several zones [3][4][5][6].
Many studies have been performed to calculate the optimal operation of a hydro basin.In long-term planning, Soares and Carneiro [7] consider the operation planning of a hydrothermal power system in Brazil.The paper highlights the importance on the control of the head hydro power plants (HPPs) in the basin.Granville et al. [8] consider the stochastic characteristics of the problem, including a representation of the market.The solution algorithm is based on stochastic dual dynamic programming.Cheng [9] applies particle swarm optimisation and dynamic programming for a large scale hydro system in China.Oliveira, Binato and Pereira [10] present two techniques: the extension of a binary disjunctive technique and screening strategies for planning studies in Brazil and Bolivia.Fosso et al. [11] give an overview of the planning tool used in Norway for long, medium and short horizons.Kanudia and Loulou [12] propose a stochastic version of the extended market allocation model for a hydro system in Québec, Canada.
In medium-and short-term planning, Habibollahzadeh and Bubenko [13] compare different mathematical methods: Heuristic, Benders and Lagrange methods for hydroelectric generation scheduling in the Swiss system.Castronuovo and Peças Lopez [14] describe economic profits of the coordination of wind and hydro energies.Zhao and Davison [15] analyse the inclusion of storage facilities in a hydro system, demonstrating the sensitive dependences between some of the parameters of the hydroelectric facility, the expected prices and water inflows.Pousinho, Mendes and Catalão [16] propose a mixedinteger quadratic programming approach for the shortterm hydro scheduling problem, considering discontinuous operating regions and discharge ramping constraints.Simopoulos, Kavatza and Vournas [17] propose a decoupling method, dividing the hydrothermal problem into hydro and thermal sub-problems, which are solved independently.A Greek system is analysed in the study.Di-niz and Piñeiro Maceira [18] use a four-dimensional piecewise linear model for the generation of a hydro plant as a function of storage, turbined and spilled outflows.Shawwash, Thomas and Denis Russell [19] discuss the optimisation model used in the British Columbia hydro system for hydrothermal coordination.
Most of the available reports about the optimal programming of hydro generation have been published in countries with abundant water (Norway [11], Brazil [10], Canada [15], USA [19]).In the algorithms reported by these studies, the restrictions on the social use of water and the ecological minimum flows are either minimally considered or not considered at all, aiming at improving the utilisation of the abundant resource in a strictly economical environment.In Spain, the focus of the present study, ecological flows and social uses of water must be considered for the optimal utilisation of the resource.Pérez-Díaz and Wilhelmi [20] want to assess the economic impact of environmental constraints in the operation of a short-term hydropower plant.For that purpose, a revenue-driven daily optimisation model based on mixedinteger linear programming is applied to calculate the optimal operation of a HPP in the northwest area of Spain.In a more recent paper, Pérez-Díaz et al. [21] propose adding a pumping capability to improve the economic feasibility of an HPP project, always fulfilling the environmental constraints imposed on the operation of the hydropower plant.
This paper presents an optimisation algorithm for calculating the optimal energy bids of a set of HPPs, including the economic objectives for energy generation and the regulations concerning the use of water in the region.The algorithm is applied to the upper Guadalquivir Basin, an area with scarce resources and variable flows, over a 24-hour horizon.Four HPPs are considered in the analysis.Three of them have storage capacity and the other one is run-of-the-river, without directly controllable alternatives.All of the plants are operated jointly with a unique owner or dispatcher (as in current practical operation).Actual data from real power plants and markets are considered in this study, including the travel times of the water (TTW) between the HPPs.The results show that the fluent plant can be controlled to achieve optimal operation by using the upstream HPPs.Moreover, an estimate of the costs of providing water for social uses (as a function of reductions in profits from selling the electricity produced in the market) is made in this study.

Regulations Concerning the Use of Water for Electricity Generation
The Water Framework Directive [22] establishes a Euro-pean Community framework for water protection and management.The objectives of this regulation are the prevention and reduction of pollution, promotion of sustainable water use, environmental protection, improvement in aquatic ecosystems and floods and drought mitigation.This norm was adapted to Spanish regulations by [23].In this directive, the priorities regarding the use of water are fixed.Electricity generation is third in the order of precedence, after the use of water by the population and irrigation requirements.Additionally, this norm specifies the requirement of a Hydrological Plan for each basin or hydrological zone.In [24], the hydro regulations for the Andalucia region (the area considered in this study) are specified.The Guadalquivir Hydrographic Confederation (http://www.chguadalquivir.es) is the organisation designed to control the Guadalquivir basin.This organisation's website features historical data regarding affluences and other hydro information.The minimum levels of flows (ecological flows) are also specified for several points of the river.

The Daily Energy Market
In Spain, the electricity market has been deregulated since 1997 (Electricity Industry Act [25]).Some renewable productions have special incentives for their production (Royal Decree 661/2007 [26]).However, large or pre-existing hydro plants must auction their production in the conventional market without renewable bonuses and, practically, without special market regulation.This is the situation faced by the plants addressed in the present study.
The Spanish energy market is organised into the following sub-markets: futures market, daily market and several intra-daily markets.More than 95% of energy transactions and more than 80% of the economic volume are traded in the daily market [27].There are also other markets that can affect hydroelectric production, such as the reserve and restriction management.For clarity, in this work, only daily market participation will be considered.
In the daily market, producers and consumers make their offers, in terms of energy quantity and prices for each hour of the D + 1 day.The Market Operator oversees the buying and selling of bids using a simple cassation model [28,29].The present paper presents a method to calculate the optimal bids for energy over a 24-hour horizon of the hydro plants in the basin, assuming that the expected prices in these hours are known.The initial conditions of the basin (level of stored water in the reservoirs, current flows, etc.) are known at the beginning of the study.Moreover, the expected flows in the analysed period can be considered known or estimated.The expected flows are depending also of the medium term planning for the operation of the basin.In the present study, an estimation of the prices in the market, for all the hours of the next day operation, is required.This prediction can be obtained from forecasting tools, outside the scope of the present study.With the knowledge of the initial condition, the price forecast and the expected flows, a scenario can be developed.In the present analysis, a determinist approach is used.However, the present method can be easily extended for considering uncertainties in the prices and/or in the expected flows, by solving many probable scenarios.
When the probable scenario is determined, the optimal solution for the operation in the hydro plants in the basin must be calculated.In the present case, ecological and social constraints are also included in the analysis.In the next section, a fully representation of the optimization problem is provided.After the calculation, the optimal flows of waters and the power and energy optimal bids are obtained.For achieving the profits presented in the analysis, it is considered that all the presented bids are accepted in the market, by offering the hydro production at low prices.

Mathematical Representation
The best operation of hydro plants in a basin can be calculated from the solution of an optimisation problem.In this problem, the restrictions to the operation are represented as mathematical constraints.The formulation of the problem is described by Equations ( 1)- (15).

Max.
 , 1 1 , , , 1, , 1, , , 0 9 9 1 , where the variables indicate the following: P i,t , the active power injection to the grid of hydro plant i at hour t; V i,t , the useful volume stored in the reservoir of the hydro plant i in the period t; V i-1,t , the affluence into reservoir i at period t, coming through the river from upstream plant (or plants); , the turbined volume at hour t by plant i; , , the deviated (spilled) volume at hour t by plant i; , the output water consumption for social uses delivered by plant i at hour t; and h i,t , the height of reservoir i at hour t.The following are the parameters in the optimisation formulation: c t , the expected market price of hour t; , the individual affluence into reservoir i at onsidering the flows coming through the not c river from the previous plant; t V , the TTW between the considered HPPs; ,1 and , SP i T V , the specified volumes at the beginning a t the e of the horizon (respectively) by plant i; η i , the average efficiency of the hydro plant i; g, the acceleration of gravity; k 0,i , k 1,i , k 2,i and k 3,i , the coefficients relating volume and height at reservoir i; U i V , the unused volume for electricity generation of resir i; , the minimum daily requirements of water for social uses in hydro plant i; , the minimum and maximum (respectively) hour quirements of water for social uses, in plant i; , the minimum (ecological) volume to be maintained in the river downstream of reservoir i; , the maximum useful reserve and capa f prod (respectively) of hydro plant i; and max i h , the maximum height at plant i.In the equations, the number of hydro plants with reservoirs, nwr is the number of fluent hydro plants (without reservoir), αi is the set of hydro plants upstream from the reservoir i and T is the number of discretisation steps.
The goal of the optim is solved late the optimal production of coordinated hydro plants in a basin in T periods and considering the expected prices in the market (1).Equality constraints (2) and (3) express the energy balances in the hydro plants with and without a reservoir, respectively.When the hydro plant has storage capacity (2), the useful volume in the reservoir can be increased by the individual affluence (rain, tributaries, etc.) and the flows coming from the immediately upstream hydro plants.Additionally, the energy stored in these plants can be reduced by electricity generation and social consumption.When large inflows enter the reservoir, a portion of the water can be deviated by using the spill way to preserve the security of the plant's operation.The amounts of useful energy at the reservoirs at the beginning and end of the programming horizon ( 5), ( 6) are pre-specified quantities.The hydro production efficiency for power production is expressed by using a third-order polynomial Equations ( 7), (8), as a function of the height.In hydro reservoirs with large nonlinear relationships between the height and the stored water (Equation ( 7)), partial approximations by using third order polynomial equations for each level of the reservoir can be adopted.In the present formulation, the social requirements for water are represented as minimum daily consumptions (9) and restrictions on hourly water flows (10).The operation of the hydrological system requires maintaining the minimum ecological levels of water flows into the basin (11).In Equations ( 12)-( 15), the maximum capacities of the equipment of the hydro plants are expressed.
The proposed optimisa water management in the upper basin of the Guadalquivir River, Spain. Figure 2 shows a map of the headwaters of the Guadalquivir River.In the present analysis, typical prices in arket in March 2011 (a month with medium hydro production) in Spain are used to simulate the optimal operation of the hydro system (Figure 4).The acceleration of gravity, g, is 9.81 m/s 2 .
To analyse the effect of the oduction, several cases are considered:  Case A: base case, in which social co ecological flows are not represented.Therefore, the optimisation problem is solved without considering Equations ( 9)-( 11). Case B: ecological f timisation problem is solved without Equation (11).
In this case, the social consumptions are included in the formulation. Case C: social c optimisation problem is solved without Equations ( 9) and (10).In this case, the ecological flows are included in the formulation. Case D: solution of the optim considering both social consumptions and ecological flows.In all of

Base Ca
Ecological Flows igure 5, the optimal plants is shown.The hydro plants at the head of basin (HPPs 1 and 3) put the resources into circulation, if possible, during the high-price periods in the morning.However, the behaviour of these two plants is quite different due to the TTW between the plants in the basin and the type of plants downstream.The production of HPP 1 is limited by the capacity of the run-of-the-river HPP 2 located downstream.In this scheme, all of the water entering HPP 2 is turbined, obtaining the maximum possible profit in the combined operation.HPP3, with a controllable power plant downstream (HPP 4), generates electricity during the early hours of the day at the highest prices and full capacity.The resources coming from HPP 2 and HPP 3 reach HPP 4 in time to be turbined at full power during the hours of maximum daily price.A small quantity of water is turbined by HPP 3 at the hour of the maximum price of the day, hour 21, without reaching HPP 4 during the daily horizon.
As shown in Figure 6, hydro plants HPP 1 and HPP 3 (at the heads of the basin) use the water stored at nning of the day to increase production during the first hours.The inflows in the heads in the evening help recover the specified final values of stored energy at the end of the day.As expected, HPP 2 has no storage capacity.HPP 4 utilises its storage capabilities to wait for higher prices to sell its production in the market.
The reduced storage capacity of HPP 2 distributes the profits throughout the entire programming perio e 7).A higher generation capacity in the plants would centralise the revenue only at the peaks of the price curve.The profit of the joint operation is 165.6 M€.

Optimal Operation Considering onl
In this case, the effect of social consumption is studied al-consumption valu plants.The daily minimum consumption and the hourly limit at each plant are specified in Table 3 of the Appendix, fifth and twelfth columns, respectively.
Figure 8 shows that at the beginning of the day HPP 1 turbines more than the maximum generation PP 2, delivering water for social consumption to HPP 2 and HPP 4. This period has the lowest prices of the day.In the other head plant (HPP 3), social requests are supplied using water with less economic efficiency, eliminating HPP 3 generation at hour 21 (Figure 5). Figure 9 shows the delivery of water for social uses for the four hydro plants.The upstream plants, HPPs 1, 2 and 3, transfer the volumes for social consumption at the beginning of the day, the period with lowest prices.HPP 4, without individual inflows, must yield to this restriction along the following minima of the price curve (hours 16 and 24).HPP 3, with the largest social consumption, also uses the minimum price at hour 24 to fulfil the social requirements.The profile of incremental profits is similar, considering (Figure 10) or without considering (Figure 7) social consumption.However, the final profits are     restrictions (minimum flows in the river) on the profits are analysed.In the prese nt simulations, this restriction can only be imposed at the head plants (HPPs 1 and 3).A ered.With minimum ecological flows in all of 3) generate electricity at all hours of the day.As in Case A, the generation of HPP 1 is restricted by the limited capacity of HPP 2, and HPP 3 mainly generates electricity during the first high-price periods of the day.The ecological restrictions (minimum flow at all hours) make the slope of income almost constant (Figure 12).The profile of the volume turbined becomes flatter, and therefore, there are fewer resources for producing at the hours of maximum price.The optimal profit in this case reaches 163.14 M€ (1.5% less than that without ecological icons on minimum flows in the river do not significantly

5.
constant value of 16 m 3 /s for each plant is consid this value, the the basins can be maintained [32], considering TTW.
Figure 11 shows that the two head plants (HPPs 1 and restrictions).In the present simulations, the restr ti reduce the profit of operation.It must be stressed that these restrictions are not consumptive; they only change the generation times of head HPPs 1 and 3.However, theincrease in the amount of ecological flow can reduce the total profits.

Optimal Operation with Social Consumption and Ecological Constraints
In this case, the effects of the two types of constraints (social consumption and minimum flows) are analysed.
In this case (Figure 13), the optimal profiles of generation are similar to those observed in Case B (Figure 8).However, some differences must be highlighted.First, the ecological minimum flows require generation at HPPs 1 and 3 during all periods.The distribution of social consumption is also dissimilar (Figure 14).In Case B (with social consumption but without considering ecological restrictions, Figure 9), the volumes for social consumption are assigned to hours 2 to 5 in HPPs 1 and 2. The ecological flow requirement shifts the delivery of HPP 1 to hours 2 and 7 and the release of HPP 2 to the end of the day (hours 19 to 24).In HPP 3, delivery for different.When considering social requirements, the total revenue is 137.09M€, 17.20% lower than without human consumption in the basin.

Optimal Operation with only Ecological Constraints
In this case, the individual impacts of the environmental Copyright © 2013 SciRes.CWEEE    social consumption is increased at hour 19 and eliminated at hour 24.HPP 4 continues to provide for social consumption at the end of the day (hour 24) but shifts to small delivery from hour 16 to 15.These changes optimise the utilisation resources, increasing the combined profit of the operation.However, the optimal income this case is 129.90 M€, 21.54% less than that of the base case onstraints).

Comparison of the Analysed Cases
As previously discussed, the economic results of the previous section depend on the type of restrictions added to the base case.Minimum flows in the river can be maintained without a loss of resources, only changing the time of generation.However, the social uses of water are consumptive constraints, extracting resources from the basin.M ction of the amou ree difsent simulations, the ecological requirements of evaluated nstraints depends on the amount of resources injected to the basin.In gical cost (EC) f the affluence is presented.
tively ten times m ers the costs of water delivered for social consumption.in (without social restrictions and ecological c oreover, the economic results are a fun nt of available resources.Therefore, th ferent scenarios are compared here: dry, medium and wet scenarios, for the two types of restrictions.The medium value coincides with the previous affluence (7.94 Hm 3 /day).For comparison purposes, all of the results are obtained by maintaining the data previously used, in particular, the price profile shown in Figure 3.

Results Considering Only Ecological
Constraints In the pre Table 1 (1.6 m 3 /s in HPPs 1 and 3) are maintained.However, the effect of the ecological constraints is in three different situations of affluence.
In Table 1, the first column shows the total inflow in the basin injected in head HPPs 1 and 3.The second and third columns show the optimal incomes obtained without considering or including the ecological constraints (Equations ( 9)-( 11)), respectively.The economic difference between the two previous cases is represented in the fourth column.In the fifth column of the table, the relative cost of the ecological constraints, for each Hm 3 of inflow in the head HPPs, is calculated.Finally, the sixth column shows the relative cost of the ecological constraints, for each Hm 3 of minimum flow requested at the head HPPs of the basin.In this table, it can be seen that the cost of maintaining the ecological co  2 and Figure 15, the cost of maintaining the ecological requirements is far more important in dry scenarios.In fact, maintaining the same ecological flow of 3.42 Hm 3 /day is rela ore expensive than maintaining a flow of 12.47 Hm 3 /day.

Results Considering only Social Consumptions
In the present section, the effect of social consumption (as specified in Table 3, Appendix) in the three previous scenarios of affluence is considered.Accord to the two tabl the costs of er alloated for social uses are larger than those of maintaining ological constraints.In fac nario, the reduction in profit due to the social uses of w r rea e the ec constrain l uses resourc from the basin; the ecological constraint request modi-fication in the pro of generat but the r source re-mains in the river. In

Conclusions
This paper presents an optimisation method to calculate the The algorithm allows for control over the actions of fluent HPPs, modifying the operation of controllable HPPs.The method calculates the maximum profit electricity generation in the daily power market, considering ecological constraints and the social use of water.
The study of different inflow states shows that in this ver, initial evaluations of the costs of provig water for social uses are performed.The proposed algorithm can be easily extended to consider other operational restrictions on the hydro systems.optimal operation of a basin with both controllable and non-controllable hydro power plants.This program considers both social and ecological restrictions, assessing the economic weight of each of them in the management of resources.

Figure 1 .
Figure 1.Flow chart of the proposed algorithm.

Figure 3
shows a sche o power plants (HPPs).Three of them have a reservoir (HPP 1, Doña Aldonza; HPP 3, Guadalmena; and HPP 4, Marmolejo), and the other (HPP 2, Pedro Marín) is runof-the-river.The TTW between the plants is shown in the diagram as T v .Other important data related to the plants are presented in Tables 3, 4 of the Appendix.

3 erage
flow of March 2011) is considered.The same flow (3.972 Hm 3 /day in each HPP) is injected at the heads of the basin and uniformly distributed over 24 hours (0.1655 Hm 3 /hour in each HPP).For simplicity in the analysis, no individual affluences ( ,

Figure 2 .
Figure 2. Geographical position of the Guadalquivir basin and relevant hydro power plants [31].

Figure 3 .Figure 4 .
Figure 3. Spatial distribution of the reservoirs in t pper Guadalquivir basin. he u

Figure 5 .
Figure 5. Production in the four hydro plants, Case A.

Figure 6 .
Figure 6.Energy storage in the hydro plants, Case A.

Figure 7 .
Figure 7. Incremental profits in the basin, Case A.

Figure 8 .
Figure 8. Production in the four hydro plants, Case B.

Figure 10 .
Figure 10.Incremental profits in the basin, Case B.

Figure 9 .
Figure 9. Energy storage in the hydro plants, Case B.

Figure 11 .
Figure 11.Production in the hydro plants, Case C.

Figure 12 .
Figure 12.Incremental profits in the basin, Case C.

Figure 13 .
Figure 13.Production in the hydro plants, Case D.

Figure 15 ,
Figure 15, the curve of variation in the ecolo as a function o As shown in Table 2 and Figure 15, the cost of maintaining the ecological requirements is far more important in dry scenarios.In fact, maintaining the same ecological flow of 3.42 Hm 3 /day is rela ore expensive than maintaining a flow of 12.47 Hm 3 /day.

Figure 16 ,
the relativ cial consum on costs f e three scenarios of affluence are shown.The curve SC, So ., shows the cost of delivering 1 Hm 3 of water from the basin for social uses in the simulated scenarios.The values of this curve can be used to calculate the price of water allocated for human use in the basin as a function of the profits lost in electricity generation.

Table 1 . Costs of ecological re
Table 2 has the same structure as Table 1 but consid-