Short-Term Hydrothermal Dispatch With River-Level and Routing Constraints

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 5, SEPTEMBER 2014 2427

Short-Term Hydrothermal Dispatch With River-Leveland Routing Constraints

Andre Luiz Diniz, Member, IEEE, and Thiago Mota Souza, Member, IEEE

Abstract—Recently, there has been a growing need to considerissues related to multiple uses of water—such as navigation,fishing, or recreation—in the operation planning of electricalpower systems, specially in predominantly hydro systems. Inshort-term models, it is of particular importance to consider max-imum/minimum values and ramp limits for the stream level of ariver. However, in order to properly represent such constraints, itis also necessary to model in detail the river routing, i.e., the waterwave propagation along the channels that connect reservoirs incascade. This paper proposes a linear programming model to rep-resent river stream-level constraints and river-routing effects inthe short-term hydrothermal dispatch problem. Results show thehigh accuracy of the proposed approach to represent maximumhourly and daily river-level variations as well as the impacts oftaking into account a detailed representation of river routing inthe operation of hydrothermal systems.

Index Terms—Hydrothermal dispatch, linear programming,multiple uses of water, river routing.

NOMENCLATURE

Input Data

Expected cost-to-go function at the end ofthe time horizon.

Piecewise linear generation cost function ofthermal plant .

Load in bus at interval .

Demand of area at interval (sum of theloads in the buses belonging to area ).

to Indices of extreme buses (“from”/“to”) ofline .

Set of thermal plants belonging to area .

Set of hydro plants belonging to area .

Natural inflow to hydro plant at interval .

Natural inflow to river point at interval .

Manuscript received September 02, 2013; revised December 16, 2013; ac-cepted January 13, 2014. Date of publication February 03, 2014; date of cur-rent version August 15, 2014. This work was supported in part by CEPEL, theBrazilian Electric Energy Research Center, and Eletrobras. Paper no. TPWRS-01086-2013.A. L. Diniz is with CEPEL, the Brazilian Electric Energy Research Center,

Rio de Janeiro 21941-911, Brazil, and also with the UERJ-State University ofRio de Janeiro, Rio de Janeiro 22220-040, Brazil (e-mail: [email protected]).T. M. Souza is with COPPE-Federal University of Rio de Janeiro, Rio de

Janeiro 21941-972, Brazil (e-mail: [email protected]).Digital Object Identifier 10.1109/TPWRS.2014.2300755

Participation factor of power injection of busin the flow of line .

Set of hydro plants immediately upstreamhydro plant/river point .

Number of areas in which the system isdivided.

Number of buses/lines in the electricalnetwork.

Number of hydro/thermal plants.

Set of areas directly connected to area .

Number of intervals (time steps).

Maximum water delay (in number of timesteps) between reservoirs and , fortime step , when a river routing curve isconsidered.

Water delay time (in hours) between hydroplant (upstream) and hydro plant/riverpoint (downstream).

Upper/lower bound for variablerelated to hydro

plant , thermal plant , energy interchangefrom areas and or line .

Reactance of line .

Control/State Variables

Power flow of line at interval .

Generation of thermal plant at interval .

Generation of hydro plant at interval(negative values for pumping load).

Stream level at river point at interval .

Power interchange from area to area atinterval .

Turbined outflow of hydro plant at interval(negative values for pumping).

Streamflow at river point at interval .

Voltage angle of bus at interval .

Generation of bus at interval (sum ofpowers of hydro and thermal generatorsconnected to bus ).

0885-8950 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

2428 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 29, NO. 5, SEPTEMBER 2014

Outflows of hydro plant that have not yetreached the next downstream reservoir attime step T.

Spillage of hydro plant at interval .

Storage of hydro plant at the end of interval.

I. INTRODUCTION

T HE economic operation of power systems has beenextensively studied for many decades. There are many

different variants for this problem depending on the systemcomponents, constraints, and time discretization that are em-ployed: economic dispatch [1], dynamic economic dispatch [2],hydro/thermal unit commitment, [3], security-constrained unitcommitment [4], and network-constrained hydrothermal sched-uling [5]. In this work, we are interested in a deterministic andcontinuous formulation of the one-week-ahead short-term hy-drothermal dispatch problem (labeled in the sequel as STHTD)in the context of cost minimization in centralized power systemplanning.Obtaining optimal solutions to the STHTD problem is chal-

lenging, due to complex aspects such as: time coupling, sincestorage in the reservoirs depend on the previous operation of thesystem; spatial coupling, because the operation of downstreamplants depends on the discharge of upstream reservoirs; nonlin-earities, mainly in the hydro production function and dc trans-mission losses; very large system sizes, such as in Brazil, withover 140 hydro plants, 95 thermal plants, 5000 buses, and 7000transmission lines; finally, the solution of any STHTD problemshould be performed in coordination to the mid/long term hy-drothermal coordination problems (HTC), either by taking intoaccount storage [5], discharge [6] or generation [7] targets, orby considering water values [3] or more accurate individual [8]or multivariate cost-to-go functions [9], [10] at the end of theshort-term horizon.Instances of the deterministic continuous STHTD problem

can be derived in one or more of the following situations.• In the operation of predominantly hydro systems [5],[9]–[12], provided that hydro inflows can be reasonablyforecast in a 1-week horizon, and the share of uncertainwind generation is small. Moreover, since load variationsin such systems are mainly followed by hydro units,thermal unit commitment (UC) decisions do not havemuch impact in the 1-week system planning and thus canbe left to the day-ahead scheduling problem [13].

• When decomposition procedures such as Benders decom-position [4], [14] and Lagrangian relaxation [7], [13], [15],[16], are applied to solve the more general unit commit-ment problems, leading to STHTD subproblems.

• When robust [17] or stochastic optimization [18] ap-proaches are applied to the stochastic unit commitmentproblem, leading to deterministic STHTD subproblemsassociated to robust counterparts or worst-case scenarios.

A wide range of solution techniques have been employed tosolve the STHTD, depending on the structure of the problemand the characteristics of the constraints that are considered.If the problem is convex, multistage Benders decomposition

[19], [20] and linear programming [12] are suitable. In partic-ular, nonlinear formulations can be handled by nonlinear pro-gramming [21], interior point and network flow algorithms [22],or iterative piecewise linear algorithms [23]. When nonconvexexpressions are taken into account, other decomposition algo-rithms such as Lagrangian relaxation [13], [15] can be employedto split the problem in different subproblems, as well as sto-chastic search algorithms [24].We refer to [25] for an interestingreview on different solving strategies in the case of a determin-istic optimal power flow problem.In this paper, nonlinear characteristics such as thermal gener-

ation costs and hydro production function are approximated bylinear or piecewise linear models, and we consider a dc powerflowmodel of the electrical network in order to apply linear pro-gramming to solve the problem.

A. Multiple Uses of Water

Multiple uses of water have been taken into account for a longtime in the literature of hydro scheduling, as for example withsome minimum/maximum discharge constraints due to irriga-tion, navigation, or environmental purposes [26]–[28]. How-ever, the inclusion of such constraints does not have much im-pact or may even ease the solving procedure in the case of theSTHTD problem, since they only restrict the feasible range fordecision variables related to turbined outflow and/or spillage.By contrast, some seemingly simple constraints such as endstorage targets (e.g., [5], [12], [24]) impose difficulties from theoptimization point of view, since they create an additional in-terdependence among the operation of the hydro plant along alltime steps.Ramp constraints for discharge or storage in order to avoid

sudden variations in downstream river levels [29], [30] are moreinvolving, as well as more sophisticated constraints for the rela-tion between storage of cascaded or adjacent reservoirs and theflow of water in connecting channels [6], [31]–[33].

B. River-Level Constraints and River Routing

Even though some of the constraints mentioned in the pre-vious section may cause difficulties in solving the STHTDproblem, most of them impose a direct relation among oneor more decision variables of the problem, such as storage,turbined outflow and spillage. By contrast, another importanttype of hydro constraints are minimum/maximum values ormaximum hourly/daily variations in the level of the river atsome specific points. Such constraints may be motivated byrequirements related to ship navigation, fishing, environmentalconcerns (related to the flora and fauna of the river) and eco-nomic/recreation activities that may take place in the bordersof the river. From the modeling point of view, these river-levelconstraints involve not only a new entity to be consideredin the problem (referred to in this paper as “river point,” seeSection III) but also include variables that are not representedin the usual formulation of the STHTD problem, such as riverlevels, also known in hydrology as “river stage.”In addition, in order to properly model these types of con-

straints, it is also necessary to represent in detail the riverrouting, i.e., the water wave propagation along the river chan-nels [34], as opposed to more simplified formulations such asusing fixed water delay times between consecutive reservoirs in

DINIZ AND SOUZA: SHORT-TERM HYDROTHERMAL DISPATCH WITH RIVER-LEVEL AND ROUTING CONSTRAINTS 2429

a cascade [3], [5], [11] or even neglecting this water delay. Veryfew applications of river routing together with hydro generationdispatch can be found in the literature [35]–[37], as discussedin our previous conference paper [38]. The constraints relatedto river routing (see Section IV) are important to be consideredin hydro-based systems not only to allow an accurate modelingof the river level constraints mentioned above, but also becauseriver routing may cause a significant impact on the water bal-ance and generation of the hydro plants and, as a consequence,also in the thermal plants dispatch and flows in the electricalnetwork.This paper proposes a linear programming formulation

to model the following aspects in the STHTD problem: 1)river-level constraints in some points along a hydro cascade; 2)hourly and daily river-level variations in such points; 3) riverrouting between consecutive plants and/or river points along thehydro cascades; and 4) a more accurate coordination betweenshort-and mid-term hydrothermal planning, by taking accountend-effects of streamflows along the rivers in the evaluationof final water values. To the best of the authors’ knowledge,such an accurate representation of streamflow-related issueshas not been considered previously in coordination with thedispatch of thermal plants and power flows in the electricalnetwork. Also, from a market perspective, the more accuratecoordination with mid-term planning may have an impacton electricity prices, since they are mostly driven by watervalues. The proposed approach is applied to the operation ofthe large-scale hydrothermal Brazilian, where the accuracy ofour model and the impacts of streamflow constraints on systemoperation are assessed.

II. SHORT-TERM HYDROTHERMAL DISPATCHPROBLEM—TRADITIONAL SETTING

We first present the usual formulation for the 1-week-aheadSTHTD considered in this study, in a cost minimization frame-work, which is typical for centralized power system planning.We assume a multi-area system with areas, thermalplants and hydro plants, and a transmission network with

buses and transmission lines. The number of time pe-riods is . The formulation is given by

(1)

(2)

(3)

(4)

(5)

(6a)

(6b)

(6c)

Fig. 1. Example of three river points , , and along a hydro cascade.

(6d)

(6e)

(6f)

(6g)

for , , ,, and .

The first term in the objective function (1) is the sum ofthermal generation costs during the planning horizon, which arerepresented by piecewise linear functions of power outputin each thermal plant . The second term is the expected costsof thermal generation and energy deficit in the future, whichare evaluated by a multivariate future cost function of thevector of storages in the reser-voirs at the end of the time horizon. Such a function is providedby a mid-term hydrothermal coordination model.Load balance constraints (2) for each system area take into

account only major interchanges between areas and ,whereas line flow limit constraints (3) are considered by a dcload flow with losses as described in [23]. Equation (4) is thewater balance equation for each hydro plant at each time periodin its simpler formulation, with no water delays, which are dis-cussed later in Section IV. The generation of the hydro plant ismodeled as a piecewise linear function (5) of storage , tur-bined outflow , and spillage , as detailed in [39]. Finally,(6a)–(6f) state lower and upper bounds for all variables of theproblem.In Sections III and IV, we describe the modeling of river

level constraints and river routing proposed in this paper for theSTHTD problem.

III. MODELING OF RIVER LEVEL CONSTRAINTS

The hydro configuration is usually represented by cascadedreservoirs and run-of-the river plants spread along one or moreriver basins. In addition to these components, we define a newentity called “river point” (RP), which stands for a given pointalong a river of a hydro cascade where some kind of river levelor flow constraints must be enforced. Each river point is iden-tified by its set of upstream hydro plants and/or river points, aswell as their distance in terms of water delay time. Fig. 1 illus-trates three river points , , and located between twoupstream plants and and a downstream plant .


Fig. 2. Rating curve of a river point, from which (a) bound or (b) rampingconstraints on river levels can be derived.

A. Minimum/Maximum River Levels

The river level in a given point is a nonlinear function of thestreamflow that crosses this point, known as “rating curve,” asshown in Fig. 2. In this sense, it is very simple to formulate aconstraint on minimum/maximum river levels, since it can beturned into a box constraint for streamflows, given as follows:

(7)

where bounds and are obtained by inspection ofminimum maximum levels in the rating curve, since it ismonotonically increasing. The values for streamflow variables

are obtained in the modeling of the river routing, asdescribed in Section IV.

B. Maximum Hourly/Daily Variation on River Levels

At some river points, the level of the stream cannot oscillateabove acceptable values, due to water usage for other activitiessuch as navigation and recreation. This imposes ramping con-straints on the daily/hourly level of the stream as described re-spectively in

(8)

(9)

where and are the maximum allowed hourly anddaily variation on river levels, measured in (m/hour) or (m/day).Constraints (8) and (9) impose some major difficulties, as de-scribed below.• They couple different time steps, especially the secondone, which ranges from all intervals that comprise a subsetof 24 consecutive hours.

• They cannot be directly converted as a single constraint onvariables , since variation of stream level of the riverwith the flow depends on the river level itself, as shown inFig. 2(b).

• The rating curve of a river (Fig. 2) cannot be directly ap-proximated by a piecewise linear function by linear pro-gramming, because it is not overall concave; rather, itsshape is not regular, since in most cases it is obtained asa collection of points measured “in loco.”

• Even if such a curve was concave and a continuous piece-wise linear model was employed, the minimization of theobjective function for the optimization problem would notnaturally lead the solution to be on top of the curve, as in the

Fig. 3. Maximum flow variation as a function of stream flow in order to meetthe maximum-level variation constraint.

case of approximating a concave hydro production func-tion [39].

In this paper, we propose the following approach to representsuch constraints in the STHTD problem.1) Maximum Hourly Variation Constraints: Given a fixed

interval of variation for the river level ( , for example) itis possible to plot a curve that gives the corresponding variation

in the flow as a function of the flow itself, as shown inFig. 3. The maximum flow variation constraint for each timecan be written as shown in

(10)

Through linear regression, we can find the best affine fit tothe points of the curve in Fig. 3, in order to establish a linearrelation between and the value of variation aroundthis point that leads to the maximum level variation . Theresulting constraints are shown in

(11)

2) Maximum Daily Variation Constraints: The same linearregression procedure can be done to obtain an affine function

for the maximum daily variationon the streamflow values. Such constraint has to be applied foreach range of consecutive 24 h, as shown in

(12)

where the set of values for the previoushours before the beginning of the planning horizon are alreadyknown.

C. Remarks

The river point level at the beginning of the study isknown. In our studies the time horizon was discretized in hourlytime steps, so that the number of daily variation constraints is24 per stage. We note that, contrary to usual ramp variation con-straints applied in the literature, not only does the right-handside of constraints (11) and (12) vary with the ramp limit value,but the matrix coefficients also do.Constraints (12) impose a strong link between the decision

variables of several consecutive time steps. As a consequence,solving strategies based on a time decomposition of the problem[20] may suffer from convergence issues, since the number of


Fig. 4. Streamflow routing effect between a hydro plant and a given down-stream element, which can be a river point or another hydro plant.

state variables of each time step is drastically increased, es-pecially if river-level constraints are imposed for many riverpoints.

IV. RIVER ROUTING CONSTRAINTS

In predominantly hydro systems, it is very important to havean accurate representation of the link among several hydroplants and/or river points in cascade. A key issue is the flowof water along the river channel, which introduces some delaybetween the release of water in the upstream reservoir and itsarrival at the downstream point, which can be a river point or ahydro plant. A summary of existing approaches to model suchaspects is given here (for more details, see [38]).• No water delay times: the water released by an upstreamplant arrives immediately at the downstream plant. Sucha model should be avoided, especially for run-of-the-riverplants, and is only acceptable if hydro plants are very closefrom each other along the river and/or the distribution ofhydro generation individually among the plants is not soimportant.

• Constant water delay times: the water released by up-stream reservoir takes hours to arrive at the down-stream plant . Even though this model is more accuratethan the previous one, it does not consider wave or prop-agation effects along the river, which is referred to in thesequel as streamflow/river routing.

• Streamflow routing: the detailed behavior of the floodwave along the channel is represented.

It is very difficult to represent the nonlinear and nonconvexexpressions for the Saint Venant equations necessary for a pre-cise modeling of the streamflow routing (see [40] and referencestherein). A good compromise solution between the two latterapproaches mentioned above is to apply the well-known Musk-ingum method [34]. However, few applications of this methodfor hydro scheduling problem can be found in the literature[35]–[37], [41].In this paper, we consider a so called “streamflow routing”

curve, where different amounts of the water released bythe upstream reservoir reach the downstream reservoir (orriver point ) in different times in the future, with water delaysranging from 0 to (or ). A diagram of this scheme is

presented in Fig. 4.The values of the participation factors can be obtained

directly from empirical streamflow routing curves and may de-pend on the time discretization employed in the problem [38].Hydro balance equations for each hydro plant or river point

in the presence of this river routing modeling are modified asshown, respectively, in

(13)

(14)

In order to keep convexity properties of the STHTD problemconsidered in this paper, we assume that participation factors

do not vary with the value of the discharge of the upstreamplant, which could be a potential limitation for application ofthis procedure. In order to overcome this drawback, differentcurves can be derived for different values of discharge of theupstream plant, and we can use the one that is closer to the dis-charge values that would be expected to occur in the period forwhich the system is being dispatched. Such curves can be asso-ciated with the season of the year and/or the system operatingcondition (low/medium/high inflows) corresponding to the cur-rent week.We note that approximation errors would be larger only if the

discharge of the upstream plant at some time steps differed sig-nificantly from the one to which the streamflow routing curveis related. In this case, we could perform an additional run ofthe model by properly adjusting the participation factors databased on the discharge outputs of the previous run. Maybe wecould even use different streamflow routing curves for low/peakhours, depending on the expected generation profile of the up-stream hydro plant for the next day or week. These procedureswould not cause difficulties for application of the proposed ap-proach from the modeling point of view, since it is just a matterof data.

V. COUPLING WITH MID-TERM MODEL

Near the end of the time horizon, a portion of the amount ofwater released by upstream plants vanishes from the system,since it reaches the downstream plants after time step .This causes two impacts in the optimal short-term schedulingproblem:• a decrease in the generation of upstream plants in the lasttime steps, due to an increase in their incremental genera-tion cost (IGC), which is measured in $/MWh and implicitcompared with thermal incremental costs by the optimiza-tion solver while solving the problem. The IGC of a hydroplant with a downstream plant in the cascade is the ratio(i)/(ii) between: (i) the absolute difference of water values

of plants and (which are the derivatives ofwith respect to ), since water moves from plant

to ; (ii) the efficiency MW/(m s of plant , which isthe derivative of the hydro production function (5) with re-spect to , since the water is used for generation in plant, multiplied by a unit conversion factor. The value of IGCfor plant suddenly increases in time stepbecause the term related to water value of in (i) turns tozero, because the solver does not see this water arriving athydro plant .


• a higher evaluation of system future costs , sincevolumes do not include outflows of upstreamplants which are assured to reach the downstream reser-voir but have not arrived yet, as shown in Fig. 4.

This issue—usually neglected in the literature when dealingwith water delay times—is addressed in the paper by includinga new constraint (15) to take into account the extra amount ofwater which will arrive at plant due to the release of plantfrom time steps to . Variables are also artificiallyincluded in the future cost function , multiplied by thesame coefficient for the water value of hydro plant , as if thewater had already turned into storage in the downstream plant

(15)

(16)

The overall optimization problem (1)–(7), (11)–(16) is adeterministic multistage linear program. Because of some dif-ficulties in the application multistage Benders decomposition(MSBD) due to strong time-coupling of constraints (see resultsin [38]), we solve the overall problem as a big linear program.However, the multiperiod stage definition presented by theauthors in [20] may help solve the problem by MSBD.

VI. NUMERICAL RESULTS

We considered a real test case for the large-scale Braziliansystem comprising 141 hydro plants and 96 thermal plantsspread in four major system areas. The electrical networkhas 5222 buses and 7201 transmission lines. We consideredtwo time horizons: one day and one week, both discretized inhourly time steps.1 The final linear program for the largest casehas 200 782 decision variables and 272,385 constraints, witha matrix containing 1 690 366 non-null elements. We note thatpower flow constraints (3) and (6g) are not directly included inthe linear program, but taken into account through an iterativeprocedure as described in [23]. The problem was solved byusing the Simplex method of IBM OSL solver [42], on an IntelCore2 Quad—2.83-GHz/3.25-GB RAM computer.

A. System Data

1) River-Level Data: Constraints on minimum/maximumvalues for river level as well as maximum hourly and dailyriver-level variations were considered for three major riverpoints for stream level control, as presented in Table I.2) Water Delay and River Routing Data: The problem has

real water delay time data between 91 pairs of upstream/down-stream hydro plants. Table II summarizes the data with infor-mation on the frequency with which value of water delay timeappears in the data. We considered the same streamflow routingcurves of [38], for three pairs of plants (Table III) as well as forthe “Regua-11 gauge” (Table IV), which is located 20 km down-stream the well-known 14 000-MW Itaipu hydro plant, which is

1Since the general data are too large we refer to http://www.ons.org.br fora detailed description of the Brazilian system and present below only the datarelated to the specific constraints proposed in this paper.

TABLE IRIVER POINT AND RIVER-LEVEL CONSTRAINTS DATA

TABLE IIFREQUENCY OF EACH WATER DELAY TIME IN PROBLEM DATA

TABLE IIIRIVER ROUTING CURVES BETWEEN HYDRO PLANTS

TABLE IVRIVER ROUTING CURVE FROM PLANT # 66 TO RIVER POINT #3

the largest plant of the Brazilian system in terms of power ca-pacity. The level of the river in this gauge is subject to strictrules set by the Tripartite agreement among Brazil, Argentina,and Paraguay.

B. CPU Performance

In Table V we show comparative CPU times of solving bothtest cases with or without the features proposed in this paper,


TABLE VIMPACT OF RIVER LEVEL VARIATION CONSTRAINTS AND RIVER ROUTING IN

THE STHTD PROBLEM

TABLE VISATISFACTION OF HOURLY RIVER-LEVEL VARIATIONS FOR RIVER POINT #3 IN

THE 168-H TEST CASE

Fig. 5. Maximum daily variation in level of river point #3.

i.e., modeling of river points, river level variation constraintsand river routing. It can be seen that, even though such Riverrouting results given by the proposed approach strictly obey thecurve defined by the coefficient factors , which are com-puted prior to solving the linear program. As for the river-levelvariation, it is important to verify the accuracy in the satis-faction of original constraints (8) and (9), since they are indi-rectly represented via (11) and (12). Table VI shows the hourlyvariation in the stream level for river points #3 only in thosetime steps where constraints (11) were binding along the timehorizon of the 168-h test case. It can be seen that the error inthe approximation of the exact nonlinear constraint (0.50 m/h)ranges from 0 to 2%. Fig. 5 shows the maximum daily varia-tion in the past 24 h for each time step of the planning horizonfor this same test case. Maximum daily variation was bindingonly during the first day, with a maximum daily variation of1.57 m/day, leading to an error of about 4.4% in the approxi-mation of constraint (12).constraints have a large negative ef-fect for time-decomposition-based solving strategies [38], theimpact for solving the problem as a single linear programmingproblem is mild. We have also tried using the interior point al-gorithm of OSL solver in all cases, but cpu times did not changesignificantly. However, interior point methods could be advan-tageous as compared to the Simplex method if all power flowconstraints (3) and (6g) were included directly in the linear pro-gram, since in this case its size would be much larger.

Fig. 6. Generation of Itaipu power plant with constant water delay times Xwith the streamflow routing proposed in this paper.

Fig. 7. Net energy interchange between the two largest areas with the tradi-tional coupling and the detailed coupling proposed in the paper.

C. Modeling Accuracy

Based on these results, we conclude that the explicit inclusionof river points in the hydro topology (Fig. 1) and representationof constraints (11), (12), and (14) in the problem formulation areable to handle maximum hourly/daily variation requirements onriver levels, with small variations due to modeling precision.

D. Impact on System Operation

Here, we show the impact of taking into account both river-level variation constraints and river routing in the daily opera-tion of a predominantly hydro system. We show in Fig. 6 thegeneration of Itaipu power plant with and without taking intoaccount river routing, where it can be seen that power profilealong the week is smoother in the case with river routing. Theoperation of this plant is particularly interesting because: 1) itis the upstream plant for river point #3 in Table I; 2) it is arun-of-the-river plant whose operation depends on a set of manyplants located upstream in the largest river basin of Brazil; and3) its power generation is very important for the main Braziliansystem area (SE) due to its high power capacity.We note that additional comparative results of the operation

of hydro plants with water delay by taking or not into accountriver routing effects can be seen in our previous paper [38].

E. Coupling With Mid-Term Model

Finally, we verify the importance of a more accurate couplingwith mid-term model when water delay times are considered inthe short term model. Fig. 7 shows the net energy interchange


Fig. 8. Total thermal generation with the traditional coupling and the detailedcoupling proposed in the paper.

and Fig. 8 shows total thermal generation for the two largestsystem areas, with and without taking into account the more de-tailed constraints (13) and (14) proposed in this paper. Anal-ysis of the differences in these two major system operation re-sults between the two cases for the second half of the planninghorizon indicate that the proposed coupling approach has theability to improve the results, by avoiding an unexpected be-havior in the last time steps due to end horizon effects.

VII. CONCLUSION

This paper proposes a linear programming model to representriver-level constraints and river routing effects in the short-termhydrothermal dispatch problem, as well as more accurate cou-pling with mid-term planning when water delay times are con-sidered in the short-term problem. Results show that the pro-posed approach yields a high accuracy to represent maximumhourly and daily river-level variations without a significant in-crease in CPU time. We also illustrate how a detailed repre-sentation of river routing impacts system operation and haveshown the advantages of the more accurate coupling proposedin the paper between short- and mid-term planning. This ap-proach is actually implemented in the short-term hydrothermaldispatch model that has been validated by the Brazilian Inde-pendent System Operation to be used as a guideline for actualsystem operation in the future.

ACKNOWLEDGMENT

The authors would like to thank the Brazilian IndependentSystem Operator (ONS) for providing the system operationdata, especially those related to the detailed representation ofthe electrical network and the operation characteristics of thehydro plants.

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Andre Luiz Diniz (M’06) received the B.Sc. degreein civil engineering, M.Sc. degree in operationsresearch, and D.Sc. degree in optimization fromthe Federal University of Rio de Janeiro (UFRJ),Rio de Janeiro, Brazil, in 1996, 2000, and 2007,respectively, .Since 1998, he has been a Researcher with the

Brazilian Electric Energy Research Center (CEPEL),Rio de Janeiro, Brazil, working in short-. mid-, andlong-term optimization models for hydrothermalcoordination. He is also an Assistant Professor

with the Statistics Department, State University of Rio de Janeiro (UERJ),Rio de Janeiro.

ThiagoMota Souza (M’13) received the B.Sc. degree in civil engineering fromthe Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil, in 2011.He was with CEPEL, the Brazilian Electric Energy Research Center, where

he worked in the short-term hydrothermal scheduling models, particularly withthe mathematical modeling of the operation of hydro plants. He is now withCOPPE-Federal University of Rio de Janeiro, Rio de Janeiro, Brazil.

Documents

Short-Term Hydrothermal Dispatch With River-Level and Routing Constraints