IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 16, NO. 2, MAY 2001 301

A Practical Hydro, Dynamic Unit Commitment andLoading Model

Thomas K. Siu, Senior Member, IEEE, Garth A. Nash, and Ziad K. Shawwash

Abstract—We describe the Dynamic Unit Commitment andLoading (DUCL) Model that has been developed for use inreal-time system operations at BC Hydro (BCH) to determine theoptimal hydroelectric unit generation schedules for plants withmultiple units and complex hydraulic configurations. The problemis formulated and solved with a novel procedure that incorporatesthree algorithms. First, an expert system is used to eliminateinfeasible and undesirable solutions. Second, dynamic program-ming is used to solve the optimal static unit commitment problemfor a given plant loading, feasible unit combinations, and currenthydraulic conditions. Third, the DUCL problem is formulatedand solved as a large-scale network problem with side constraints.Output from the model includes DUCL schedules, spinning andoperating reserve, and trades curves such as that between waterusage and the number of unit switches. The innovative use of theprocedure allows the model to effectively schedule hydro units forthe energy and capacity markets in real-time. Application of themethod is demonstrated by determining the 24-time-step DUCLschedule for a 2700 MW plant with ten units of four different unittypes.

Index Terms—Dynamic programming, expert systems, hydro-electric power generation scheduling, hydro unit commitment,network programming.

I. INTRODUCTION

T HE BRITISH Columbia Hydro Power Authority (BCH) inCanada operates 30 hydroelectric facilities and 31 reser-

voirs in 6 major basins and 27 watersheds. Over 90% of theinstalled generating capacity of about 11 000 MW is hydroelec-tric, while energy purchases and thermal generation contributeless than 5% of total domestic energy use. About three-quartersof the electricity is produced at major installations on the Peaceand Columbia River systems, while other main energy sourcesinclude smaller hydroelectric facilities on the B.C. Coast andVancouver Island and a natural-gas-fired generating stationin the Vancouver area. The BCH customer base consists of1.53 million residential, light and large industrial and tradecustomers [1].

As the electric power industry continues to change rapidly,the traditional monopolistic environment will inevitably makeway for increased competition. To take advantage of the compet-itive environment, BCH has realized that they must operate theirsystem to maximize the value of their resources at the various

Manuscript received September 8, 2000.T. K. Siu and G. A. Nash are with the Resource Management, BCH, 6911

Southpoint Drive, Burnaby V3N 4X8 Canada.Z. K. Shawwash is with the Department of Civil Engineering, University of

British Columbia, Vancouver, BC V6T 1Z4 Canada.Publisher Item Identifier S 0885-8950(01)03796-8.

levels of planning for power supply operations. As a step toachieve this objective BCH conducts optimization studies ex-tending from the long-term at the strategic level [2] to short-termoperations, including real-time [3]. A hierarchical approach foroptimal operation of the hydroelectric generating system can bedivided into several computationally manageable levels. Theseare:1

1) Strategic long-term operation planning covering 1 to4 years with a monthly time-step;

2) Medium-term optimization over a daily or weekly timestep for up to a year; and

3) Short-term optimization with an hourly or sub-hourlytime step with two components: a) the Short Term Op-timization Model (STOM), which produces an optimalplant schedule for up to a week [3]; and b) The DynamicUnit Commitment and Loading model (DUCL), whichtakes STOMs optimal plant generation schedule andproduces an optimal DUCL schedule covering everytime step.

The unit commitment (UC) problem is to determine an op-timal schedule of all available units over a planning horizon so asto meet all system, plant and unit constraints, as well as meet theload and ancillary service demands. It has been widely recog-nized that a proper commitment of all available units is a crucialstep in achieving the overall goals of economic and reliable op-eration of the power system. The UC problem has been studiedso extensively that a quick search with IEEExplore providesmore than a hundred papers addressing the topic. Various mathe-matical programming and heuristic-based approaches have beenproposed. These include, priority listing [4], [5], dynamic pro-gramming (DP) and its modification [6], [7], the Langrangianrelaxation [8]–[10], network flow [11], branch and bound [12],artificial intelligence [13], expert systems [14], simulated an-nealing [15], evolutionary programming [16], [17] and the in-tegrated algorithm [18]. However, the few papers that deal withthe hydro UC problem either consider only the plant loadingproblem [11], or do not model complex hydraulic configurationsin detail [16], and therefore only partially solve the completehydro DUCL problem. This paper describes the DUCL Modelthat has been developed for use in real-time system operationsat BCH to determine the optimal hydroelectric unit generationschedules for plants with multiple units and complex hydraulicconfigurations. In what follows, the main features of the math-ematical models are outlined briefly, and the implementationprocess and results are briefly discussed.

1The real time dispatch is handled by a separate transmission entity.

0885–8950/01$10.00 © 2001 IEEE

302 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 16, NO. 2, MAY 2001

II. THE HYDRO, DYNAMIC UNIT COMMITMENT AND LOADING

MODEL (DUCL)

A. Objectives

It is well recognized that hydro plants with significantstorage and generating capacity provides a relatively highlevel of operating flexibility, and they enable BCH to competefavorably in both the energy and capacity markets. From thisperspective, both STOM [3] and DUCL were developed toassist the scheduling engineers in managing BCH resources andto make good operational and trading decisions while meetingthe constraints. The optimal plant static unit commitment(SPUC) solution that only minimizes the use of water withoutconsidering start-up costs of the units is not acceptable, becausethese costs are a key component of operating costs for hydrounits [19]. Switching units on and off increase the maintenanceexpenditures due to wear and tear on wiring and on mechanicalequipment, and could potentially cause forced outages due tomalfunctions in the control equipment during start-up. As thecompetitive market for ancillary services continues to expand,a realistic objective function for DUCL should include thetrade-offs amongst the cost of water usage, start-up costs,and the value of ancillary services for the operating periodconsidered.

B. Functional Requirements

The generation operations office is responsible for directingthe short-term operation of the hydroelectric and thermal gener-ating facilities. The office works very closely with POWEREXs(the BCH electricity trade subsidiary) real-time energy traderswho sell and purchase electricity and ancillary services in thespot power markets in the US and Alberta. The office alsoprepares the daily, hourly and sub-hourly generation sched-ules using the Load Resource Balance (LRB) system. Theseschedules are updated and sent regularly to the grid controlcentre for real-time dispatch. For the DUCL model to be usedeffectively and reliably by the scheduling engineers in theirdaily operations, the following set of functional requirementswere set out by the users:

• It should rely on a reliable and accurate data base;• It should be easy to use and able to be run by any autho-

rized user in the BCH computer network;• It should be fully integrated with the LRB system;• It should incorporate the set of rules, guidelines, and

heuristics used by the scheduling engineers; and• It should complete a 24 time-steps study for any plant in

the shortest time possible.

C. Main Components and Structure of the Model

DUCL consists of four main components: the Graphical Userinterface (GUI), the Expert System, the DP component, andthe network solver. The GUI is coded in Visual Basic and islaunched from the LRB system, which provides DUCL withthe operational input data. The GUI allows the user to: selectthe plants to be included in the study; set the study starting timestep and the number of time steps in the study; and verify theplant loading and reservoir level schedules prepared by STOM.

It also allows users to review the plant and unit constraints,reserve and switching requirements, and provide a platform toinput the set of rules, guidelines and heuristics used. The expertsystem contains the set of rules, guidelines, heuristics and con-straints that the system operator takes into consideration anduses them to eliminate infeasible and undesirable solutions. TheDP algorithm derives the optimal static unit commitment so-lutions for a given plant loading, unit combination, and cur-rent hydraulic conditions. The network model uses two softwarepackages: AMPL [20], which is used to formulate the optimiza-tion problem as a large-scale network problem with side con-straints; and CPLEX [21] is employed to solve it. The resultspresented include DUCL schedules, spinning reserve for eachtime step, and trades curves such as that between water usageand the number of unit switches.

D. The DUCL Mathematical Model Formulation

To meet the above objectives and functional requirements,the DUCL model integrates three algorithms, as detailed inbelow. A generalized mathematical formulation of the problemis presented first.

For a given generation , in time step , in plant , forebaylevel, , downstream water level , spill release

, and unit availability, , the DUCL problem is to findthe optimal unit commitment combinations schedule ,which minimizes the following objective function:

Min:

(1)

Here the first term represents the water cost of turbinerelease,, , in m /s and is the time-step in

seconds, where is the cost of water in $/m. The secondterm represents the value of spinning reserve and is thevalue of spinning reserve in $/MWHr and is the spinningreserve in MWHr. The third term represents the start-up cost,

, in $. Several constraints are included in the model toreflect the set of physical and operational requirements that mustbe satisfied and these include the following.

Generation of unit at is constrained by the minimumand the maximum physical and operational

limits,

(2)

represents the set of minimum loads in the unit’s operatingzone ranges. The maximum generation capability of a unit isa function of the gross head on the unit , the maximumturbine limit, or the maximum rated generator limit, ,

(3)

Similarly the maximum and minimum turbine discharges, limit the unit’s turbine discharge as follows,

(4)

SIU et al.: A PRACTICAL HYDRO, DYNAMIC UNIT COMMITMENT AND LOADING MODEL 303

For plants with multiple powerhouse facilities, the turbine re-lease, , of unit in powerhouse , , is a functionof the power generation of the unit, , and the unit’s grosshead,

(5)

This formulation covers configurations where there are multiplepowerhouses in a plant, and each powerhouse has separate pen-stock and tailwater configurations. If net head is used then theabove relationship should include tunnel, penstock and unit pen-stock head losses. The gross head of a unit is a function of theplant’s forebay and its tailwater levels ,

(6)

and the tailwater level depends on the plant’s total discharge anddownstream water level , (e.g., downstream reservoir,river, ocean, etc.),

(7)

The total plant turbine release, needed to generate ,also depends on the committed unit combination , where

, and are the set of all possible unit combina-tions for a given set of unit availabilities .

Finally, units in plants are usually operated to provide forancillary services, such as spinning reserve,

(8)

and operating reserve requirement, ,

(9)

As and are neither easily determined norreadily available in most utilities, scheduling engineers areusually more comfortable removing them from the objectivefunction and replacing them with a set of additional rulesand constraints on the maximum number of unit switches,minimum number of units on-line, etc.

The hydro DUCL problem is a large-scale and complexoptimization problem, the solution of which is not only difficultto solve but also requires huge computer time. The proposedsolution algorithm was found to yield accurate and practicalresults and save significant computer time and hence, can beused in preparing unit generation schedules in real-time systemoperation.

E. Solution Algorithm

The solution algorithm relies on the hierarchical approachdescribed in Section I above and detailed below. STOM islaunched from the LRB system to perform a planning study andto produce generation, total discharge and forebay schedulesfor a number ofplants in the BCH system. These schedules

meet the firm load demand, prescheduled and spot importsand exports trading schedules, and satisfy the physical andoperational constraints. STOM makes the optimal trade-offbetween present benefits, expressed as revenues from spotenergy transactions, and the potential expected long-termvalue of resources, expressed as the marginal value of waterstored in reservoirs. The DUCL system uses these and/or otherschedules contained in the LRB system, displays them to thescheduling engineer and implement the following proceduresand algorithms to derive the dynamicunit generation schedules.

1) Expert System Procedure:The expert system componentin DUCL achieves two objectives. First, it ensures that the op-timal unit loading schedules implicitly incorporate the set ofrules and guidelines that must be followed by the schedulingengineers. Second, it ensures that only feasible and desirableunit commitment and loading schedules are included in the op-timization process, and therefore, it considerably reduces thesize and the complexity of the optimization problem. The expertsystem runs in two instances. In the first instance, it screensto eliminate infeasible unit combinations based on the followingrequirements:

• plant loading, ;• unit availability, ;• current hydraulic conditions (to calculate );• ancillary services requirements;• fixed unit loading requirements, to comply with unusual

unit operating conditions; and• minimum number of units on line requirement.

The results of the first screening instance is the set of fea-sible and desirable unit commitment and loading combinations

, which is then fed to the DP component, as detailed inSection II-E-2.

In the second instance, the expert system is employed toprocess the results of the DP algorithm and eliminate unitcombinations with an efficiency loss with respect to the mostefficient UCL, that is deemed undesirable by the schedulingengineer. For the example considered in Section IV, forlow to medium plant loading levels, committing all unitsavailable in a plant could yield a loss in efficiency in excessof 15%, or an equivalent energy loss of about 80 MWHr.The general practice is to limit the loss in generation effi-ciency to less than 2%. The results of the second screeninginstance consists of the set of feasible and desirable UCcombinations , which is then fed to the network program,as detailed in Section II-E-3.

Many other rules can be added to reflect other heuristics andguidelines that the scheduling engineers use in their daily opera-tions. These rules can be that first unit on line is the last offline;preference order for loading and unloading units, energy andcapacity market depths, ramp-up/down, minimum on/off times,etc.

2) Dynamic Programming Procedure:The objective of theDP component in DUCL is to calculate the optimal static plantUC and loading schedule for all feasible unit combinations

. DP results includes the plant and individual unitturbine discharges ( , ), and the plant and unit gener-ation efficiency, for each unit combination in for eachwhere . The DP incorporates detailed hydraulic

304 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 16, NO. 2, MAY 2001

Fig. 1. The DUCL network programming problem.

modeling in the search algorithm [22]. The objective functionis simply, to minimize the total plant discharge for each,

Min:

for all

subject to (2)–(7),

(10)

3) Network Program:The remaining problem is to select aUC combinations schedule, , that minimizes the amount ofwater used and the number of switches for the entire operationperiod. It is a binary problem and is best modeled as a networkprogramming problem:

Min:

(11)

where , , are the arcs that connecteach node to all nodes, as illustrated in Fig. 1.

The optimization is subject to:

(12)

where , is the number of switches forunit of plant when changing from unit commitment combi-nation to (e.g., as indicated in Fig. 1, going fromcombination 1110 atto 1001 at requires switching unit 1on and unit 2 and 3 off); and is the maximum numberof allowable unit switches for plant during the study period;and

(13)

where is the maximum number of allowable unitswitches for unit during the study period; and

(14)

Fig. 2. Schematic of the DUCL implementation process.

for . Equation (14) ensures the selection of onlyone unit commitment for each time-step. Continuity in the se-lection of the unit commitment at each node is enforced by:

(15)and the initial condition is given by,

(16)

Solving (11)–(16) yields a potential unit commitment andloading schedule that uses the least amount of water whilemeeting all the constraints. However, for reasons not capturedby the objective function or the constraints, another scheduleusing the same quantity of water may be preferable. Additionalschedules can be found through the use of secondary objectivefunctions. For example, if (12) is not a binding constraint,while constraint (13) is, it may be possible to find a schedulethat uses the same quantity of water, over the model horizon,with fewer unit switches. Such a schedule can be found by firstadding a constraint that fixes the quantity of water used at thevalue found for the solution of (11)–(15), and then replacing(11) with the objective of minimizing the total number ofswitches. Other secondary objectives can be used to distributea fixed number of unit switches amongst the individual unitsgiven a fixed quantity of water.

III. I MPLEMENTATION PROCESS

The implementation process of the solution algorithm isshown in Fig. 2. Input data for DUCL is automatically gener-ated by the LRB/STOM system, and the client communicationprotocol calls the server and transfers data and launches theexpert system module. The expert system calls a module tocalculate the maximum plant generating capability, and screensfor feasible combinations. It then calls SPUC to generate theoptimal unit loading schedules. DP calls the AMPL/CPLEXsystem, where a further screening for feasible combinations forthe efficiency margin requirement is carried out. The networkproblem is then formulated by AMPL, and CPLEX is calledto solve the problem. Once the optimization is complete,control returns to AMPL to write results out and the clientcommunication protocol calls the results display software inthe LRB system and the session ends.

SIU et al.: A PRACTICAL HYDRO, DYNAMIC UNIT COMMITMENT AND LOADING MODEL 305

Fig. 3. Unit generation, plant efficiency and operating and spinning reserveschedules.

TABLE IDUCL UNITS SWITCHING SCHEDULE

IV. RESULTS

To illustrate the results from DUCL, a sample 24 hourschedule for the G. M. Gordon Shrum (GMS), the largest plantin the BCH system, is used. GMS is a 2700 MW plant with tenunits of four different unit types. Unit efficiencies are rankedas follow: units 9 and 10 are the most efficient, then 1–5, and6–8 are the least efficient. Units 1 and 2 could be operated insynchronous condense. The plant is usually operated to followthe system load, and sometimes it is operated in AutomaticGeneration Control (AGC) mode. Fig. 3 and Table I illustratesthe results of running DUCL for GMS. It can be seen thatDUCL scheduled the units to maximize the efficiency (byswitching off inefficient units) and to minimize the number ofunit switches (by uniformly switching on/off the same units).

Fig. 4 indicates that as the number of switches increases,the marginal value of each additional switch decreases. The re-sults strongly suggest that in determining an operation scheduletradeoffs should be made between the number of switches thatare allowed and the quantity of water used for power generation.

Fig. 5 illustrates the performance of the expert system inscreening and eliminating infeasible and undesirable unit com-minations for the set of rules employed in this study.

Fig. 4. Water used vs. number of switches.

Fig. 5. Performance of the expert system in eliminating infeasiblecombinations.

Finally, the entire run for the study took about 150 seconds tocomplete.

V. CONCLUSION

We have presented a fast efficient decision support systemto plan the real-time unit generation scheduling at BCH. Thesystem is suitable for use on real-time scheduling of generationunits for the energy and capacity markets. The major contribu-tion of the work is the innovative use of the best features andcapabilities of each of the three algorithms to reduce computa-tional time and produce high quality results. The use of the ex-pert system alone would not produce the same quality of results.The exclusive use of DP or a network solution would requireenormous computational time and would not be acceptable forreal-time operation. The use of a GUI reduces the preparationtime and data errors making the software package useful for thescheduling engineer.

ACKNOWLEDGMENT

The authors would like to thank R. Gosselin for adaptingSPUC to this work, and to A. Cheng and N. Dai for work on theexpert system component. Thanks to C. Fingler, D. Robinsonand the rest of the scheduling engineers for providing expertknowledge and for testing the DUCL system.

306 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 16, NO. 2, MAY 2001

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Thomas K. Siu (S’72–M’78–SM’88) received the B.Sc. degree from LoyolaUniversity of Los Angeles in 1973, the M.Sc. and Ph.D. degrees in system en-gineering from University of California at Los Angeles in 1975 and October1976, respectively. He joined University of Calgary in 1977 as a Lecturer andPost-Doctoral Fellow. Since 1978, he has been with British Columbia Hydro(BCH) and currently is a Specialist Engineer. He is a Canadian member of theColumbia River Treaty Operating Committee. He serves on the editorial boardof Electric machines and Power Systems.

Garth A. Nash received the B.A.Sc. and M.A.Sc. degrees in civil engineeringfrom the University of Toronto in 1993 and 1995, respectively. Currently, he iscompleting requirements for the Ph.D. degree in the Department of Civil Engi-neering at the University of British Columbia (UBC). His post-graduate studieshave been supported by NSERC Post-graduate awards and a University Grad-uate Fellowship. He has been with BCH since 1999.

Ziad K. Shawwashreceived the B.Sc. degree in civil engineering in 1982 fromNew England College, New Hampshire, USA. He studied at UBC, Vancouver,Canada, and completed his M.A.Sc and Ph.D. degrees in water resources in 1995and 2000, respectively. He is now an Adjunct Professor and Research Associateat UBC.