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Operational planning for pumped storage power station using heuristic techniques
Operational planning for pumped storage power station using heuristic techniques D Lidgate Department of Electrical Engineering and Electronics, University of Manchester Institute of Science and Technology, PQ Box 88, Manchester M60 1QD, UK M Ramirez, J Villaroel and J A Balbas Formerly at University of Manchester Institute of Science and Technology J Hill System Operations Branch, Central Electricity Generating Board, North West Region, Europa House, Cheadle Heath, Stockport, Cheshire, U K
A computer algorithm is described that coordinates, economically, the operation o f a large pumped storage scheme with an existing thermal generation system. It uses heuristic techniques to establish a system model for operation, based largely on the manual merit order method, and it incorporates several operating constraints, including generator maximum and minimum generation levels, minimum shutdown times and loading and unloading rates. Designed specifically as an operational planning tool, the algorithm produces a unit commitment and load schedule for every half-hour interval o f any load curve sypplied. By costing this schedule with and without the pumped storage scheme, a pumping cost is obtained that can then be compared with other methods or frequency control. Finally, by extending the schedule to include hydrogeneration, the economic benefit o f using the scheme in this mode may also be evaluated. Keywords: hydroelectric power stations, algorithms, load
flow
I. Introduction The traditional method of controlling frequency in the UK Central Electricity Generating Board (CEGB) system is by means of free governor action on the generating sets as primary control and by manual dispatch to prevent excessive cumulative time error as secondary control. This is then supported by sets in a hot standby condition to cover for plant loss.
Received: 13 January 1981
Vol 4 No 2 April 1982
This method of control has become increasingly uneconomical as the smaller, more flexible plant is retired, as the proportion of nuclear plant is increased (which, on economic grounds alone, is undesirable for use in frequency control) and the performance of mechanical governors tends to reduce the overall efficiency of a generating station. Two of the most promising alternatives to this form of frequency control are gas-turbine-powered generators and conventional hydroelectric plant. In both cases, the generators may be started and synchronized to the system rapidly, either manually or automatically by low frequency relays, and then shut down rapidly. However, the design of modern turbo alternators has resulted in minimum operating costs being obtained by running the generating sets at full load continuously. Clearly, this is not possible for all sets, particularly during the overnight trough when load may be much reduced, as can be seen in Figure 1. Consequently, some generators may be kept running with considerable spare capacity. The facility of a pumped storage power station to shape the overnight load curve and hence utilize this spare capacity, together with the inherent lack of conventional hydroelectric stations on the CEGB system and the ever increasing cost of fuel oil, suggests that pumped storage stations need to be studied further. The purpose of this study was to consider the economic coordination of the Dinorwic ~ pumped storage scheme, now under construction in North Wales, with the existing CEGB system. The main objective was to investigate the operation of this scheme, the main parameters of which are shown in Table 1, as a frequency control device, by obtaining a cost for the pumped water and hence a comparison with other forms of frequency control for which costs are more readily available. This could then be extended to study the effects
0142-0615/82/020111-09 $03.00 © 1982 Butterworth & Co (Publishers) Ltd
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Figure 1. Input load data; upper trace: winter, lower trace: summer
on conventional plant of pumping during the overnight trough and the financial benefit that could be expected by using this scheme in a purely economic mode during the midday peak. The present paper describes a computer algorithm based on a heuristic approach to system operation =. That is, a system model has been developed, using logic and commonsense derived by observation and inspection, to replace mathematical models which are too complex to implement. It is based on the present manual merit order method a of operation but is modified to take account of other operating constraints and the addition of the large pumped storage scheme. It is a purely economic algorithm and does not take account of system security or transmission losses. Since the algorithm is intended as an operational planning tool, and would normally be used weeks or months ahead of the actual operation, it is felt that greater accuracy is not required. The generating network and especially the size of the pumped storage plant are, however, assumed to be fixed and, hence, their development 4 need not be considered.
II.
Development of
computer algorithms
I1.1 Data requirements Before one can begin any economic study of the operation of pumped storage schemes, or indeed of conventional hydroelectric schemes, it is necessary to establish a model for operation with only fossil or nuclear powered generators. As for any system, two separate items of information must be available in order to commit and then load these 'thermal' generators. The first of these is the load curve as shown in Figure 1, which would normally be the load expected to be supplied in the next operating period plus some spare capacity to allow for errors in the prediction and for plant failure. In this study, the load curves used to test the algorithms represent actual loads supplied in the past and do not, therefore, incorporate any spare capacity. (The justification for using these curves will be discussed in Section III.) To further reduce the complexity of the algorithms, the time period studied was divided into 30-minute intervals, the load being considered constant for each interval, as shown in Figure 1.
1 12
The remaining data required is the cost of generation and the operating constraints of each generator. Since the generators used by the CEGB are of the single steam throttle valve type, with an essentially linear input-output characteristic, the costs required are the average full load generation cost and the incremental cost, both expressed in £/MWh. The operating constraints are maximum and minimum generating levels, minimum shutdown time and maximum loading and unloading rates. This data is supplied in the form of a merit order, as shown in Table 2, and a table of increasing incremental costs, as shown in Table 3. To reduce the time required to check each schedule obtained, Tables 2 and 3 represent a 'reduced merit order' of some 80 generators. This was obtained by, initially, considering all the generators in one power station to be one large generator. Power stations could then be grouped together by type and operating cost. This enabled the 132 power stations, made up of over 600 generators, operated by the CEGB in 1979/80 to be reduced to manageable proportions, although no modifications to the algorithms are required to enable each generator to be considered individually. The data shown in Tables 2 and 3 is representative of the data actually used, although the costs have been normalized. The derivation of the offline costs shown in Table 2 will be given in Section II.4. 11.2 Unit commitment As stated earlier, the operation of the 'thermal' generating sets has been based on the merit-order method of operation, that is, commitment in order of average full load generation costs and loading of committed sets to full load in order of increasing incremental costs. Thus, the unit commitment procedure is started for the first time interval by comparing the load value for that interval with the cumulative capacity column in Table 2. Sufficient generators are then committed so that their cumulative capacity just exceeds the system load. This is then repeated for all intervals of the load curve. The schedule obtained, however, may not be feasible because of the operating constraints. Initially, the loading and unloading constraint is neglected, so that only the minimum shutdown time can affect this schedule.
Table 1. Parameters of Dinorwic pumped-storage scheme Number of machines Type Speed Electrical output per machine Total output Total water storage Head Pump load per machine Total pump load Cyclic efficiency (for output > 60% full load) Total pumping energy Time to fill reservoir at total pump load Time to empty reservoir at total output
6 reversible pump-turbines 500 rpm 279 MW (maximum) 1674 MW 8400 MWh generation 540 m 290 MW (essentially constant) 1740 MW 78% 10 728 MWh 6.16h 5.02 h
Electrical Power & Energy Systems
Table 2. Order of merit schedule Offline costs Maximum capacity, MW
lative capacity, MW
Minimum capacity, MW
Production cost
Minimum shutdown, h
844 680 1 240 1 875 1 426 1 400
844 1 524 2 764 4 639 6 065 7 465
200 410 390 984 883 840
1.00 1.33 6.14 6.57 6.61 6.68
10 6 7 8 8 6
Cumu-
Position t 2 3 4 5 6
Name LID 1LL-3 110311-1 WW05WW-1 AA07AA-5 KK08KK-1 XX09XX-6 etc.
No load cost (,4)
D
C
D
C
100 168 1 322 2 018 1 732 1 811
YYY YYY YYY YYY YYY YYY
YYY YYY YYY YYY YYY YYY
1 000 810 1 458 1 759 1 674 1 644
3 2 4 5 5 4
Cold
Hot
000 430 374 277 022 932
Production cost = average full load generation cost Y Y Y - o n l y available f o r l o w merit generators
Table 3. Order of increasing incremental cost
Position
Name
1 2 3 4 5 6
LID 1LL-3 110311-1 WW05WW-1 KK08KK-1 XX09XX-6 AA07AA-5 etc.
Maximum capacity, MW
Minimum capacity, MW
Incremental Minimum cost shutdown, (B) h
No load cost
Load rate cold, MW/min
Load rate hot, MW/min
Shutdown rate, MW/min
840 680 1 240 1 426 1 400 1 875
200 410 390 883 840 984
1.00 1.26 5.89 6.30 6.32 6.35
100 168 1 322 1 732 1 811 2 018
XXX XXX XXX XXX XXX XXX
XXX XXX XXX XXX XXX XXX
XXX XXX XXX XXX XXX XXX
10 6 7 8 6 8
X X X -- actual data not available
This is taken into account by the algorithm by identifying, for each generator, all offline periods and comparing disconnection times with subsequent reconnection times. If elapsed time is less than the minimum shutdown time, the schedule is altered so that the generator is not switched off for those intervals. However, for the first and last intervals, generator states are not available, and incorrect schedules may be obtained. This is overcome by supplying extra load data, both lead and lag. In practice, it was found that the load curve should contain three peaks with a total duration of approximately 48 h s.
it will be unloaded by Table 2. Only if generators are prevented from shutting down by their operating constraints is loading performed by Table 3. The algorithm can now complete the load scheduling and, for every 30 min interval, identify each committed
I
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The resulting final commitment schedule with no violation of the minimum shutdown times can then be given in diagrammatic form, as in Figure 2. 11.3
Load scheduling
Once a satisfactory unit commitment schedule has been obtained, the load to be supplied by each generator must be determined. This would normally be done by loading to full load in order of increasing incremental costs. However, if the generator ordering shown in Tables 2 and 3 is not the same, then generators with higher incremental costs could have their outputs varied continuously as generators of lower merit but lower incremental costs are subsequently committed. To prevent this rather unsatisfactory situation, the basic approach is modified so that if the load curve is increasing, generators are loaded by Table 2. If the load is decreasing and a generator will subsequently be shut down,
Vol 4 No 2 April 1982
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generator and quantify its power output. This can be printed either generator by generator for all intervals or, as shown in Table 4, for all generators in one time interval. 11.4 Costing To obtain an operational cost of the schedule just derived, two factors must be taken into consideration. Clearly, any generator synchronized to the supply system and supplying power must have an online cost given by: F(£/h) = A + B- P
j Ccold
~-"
In addition to these costs, however, every generator not running for the full costing period must incur offtine costs, every time it is disconnected and then subsequently reconnected. Several methods of representing offline costs have been proposed previously 6, but a very simple model has been adopted for this study. It has been assumed that, once a unit is disconnected, the cost of bringing it back into service is, basically, an exponential function which increases with time offline, as shown in Figure 3. The model itself involves unnecessary computation, so two linear approximations to the curve have been used, as shown in Figure 3. The two approximations, referred to as hot start and cold start, have no direct link with physical conditions but correspond roughly to generators shut down only for the overnight trough (or two-shifted) and those used infrequently for peak lopping. In both starting conditions, the offline cost of each generator may be determined from: a(£) = c + D- t
(2)
where C is in £, D is in £/h and t is the number of hours offline. The constants take on different values, depending on the starting condition, as shown in Figure 3, and also
D~Ld
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y.
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where A is the no-load cost, B the incremental cost and P the electrical output in watts. Thus, for each 30-minute interval, the online cost of each generator may be found from equation (1). Since the load is, in reality, continuously variable, an average online cost for each interval is obtained by taking a simple average of that and the next interval's costs. Total online costs for any desired period may then be found by summing the average costs of the required number of intervals.
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vary with the maximum output of the generator. Since offline costs were only available for a few generators, the costs shown in Table 3 have been derived proportionally from these by a small subroutine incorporated in the generator input data file. The criterion for identifying the state of a generator as either hot or cold start (which is the main reason for supplying a load curve with three peaks) assumes that if a generator is not required at any time in this period, its offline cost is zero. If a generator is required for only one peak, and not previously or subsequently, then it is in a cold-start condition. All other generators must be in a hotstart condition. As can be seen from Figure 2, a generator offline period may be only partly within a costing period. In such cases, it is assumed that the part of the total offline costs of that generator to be allocated to the costing period is directly proportional to the time offline within the costing period. The overall system cost for any period can then be obtained by a simple summation of on- and offline costs for the required number of intervals. The algorithm has been designed so that, provided the full load curve is supplied, the system may be costed for any period longer than 1 h. In practice, it being likely that Dinorwic will be operated on a 24 h cycle, this has been used as the standard costing cycle, although the starting point can be varied at will.
Table 4. Sample loading schedule Time: 2.30 h
Thermal generation: 31 211 MW
Load value: 29 471 MW
Pump load: 1 740 MW
Cost: 165 962 units
Station
Loading, MW
Station
Loading, MW
Station
Loading, MW
LL01LL-3 AA07AA-5 GG10GG-6 JJ 13J J-3 HH16HH-4 BB19BB-1 UU22UU-2 BB25BB-3 112811-4
844 1 875 1 370 328 2 015 1 033 2 120 3 340 358
110311-1 KK08KK-1 EEllEE-4 LL14LL-4 SS17SS-8 MM20MM-3 XX23XX-7 VV26VV-8 CC29CC-1
680 1 426 1 810 920 920 303 567 1 084 304
WW05WW-1 XX09XX-6 KK12KK-2 RR15RR-3 NN18NN-4 002100-1 VV24VV-6 NN27NN-2 ZZ30ZZ-4
1 240 1 400 2 240 340 1 896 116 749 1 815 118
1 14
max max max max max max max max
max max max max max max max max max
max max max max max max max max min
Electrical Power & Energy Systems
In all cases, the system cost can be expressed as:
Total cost = E
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III. Coordination of pumped storage scheme
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II1.1 Derivation o f pumping cost It is n o r m a l l y a c k n o w l e d g e d t h a t there are three d i s t i n c t m o d e s o f o p e r a t i o n f o r a p u m p e d storage scheme, assuming that the upper reservoir has been filled in a previous
pump cycle. The generators can be used in the spin-generatein-air mode, in which the turbine runners are filled with compressed air and the generators motor at a much reduced load. In this condition, they are able to meet sudden load changes in the system caused by plant failure and also to perform frequency control by balancing small mismatches between load and generation. The third mode of operation is the economic mode, which was probably the first intended use of pumped storage schemes, in which the pumped water is used to replace less efficient thermal plant during the load curve peak. As a result of the first two modes, however, it is not necessary to incorporate spare capacity in the schedules, since the output of the pumped storage scheme provides spare capacity during the day, and switching off pumps provides spare capacity during the overnight trough. (It is, however, very easy to incorporate spinning reserve in this approach, if required, as will be shown later.) The main restriction imposed at this stage on the Dinorwic scheme was that the upper reservoir should be full at some prespecified, but variable, time each day. It was then 40000 i
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V o l 4 N o 2 A p r i l 1982
[ 16
[ 18
I 20
I 22
Time, h
Figure 5. H y d r o g e n e r a t i o n schedule; - tion,--hydrogeneration
t h e r m a l genera-
assumed that the cost of this water could only be determined by costing the entire system twice, once with the scheme and once without. Finally, since the full number of hydrogenerators would not be required for frequency control at all times, spare capacity (and water) could be used in the economic mode and a cost benefit could be obtained. To calculate the pumping cost, therefore, the algorithm calls the pumping subroutine immediately after the costing of the system using thermal plant only. Since, clearly, the cheapest pumping costs will be obtained when the system load demand is least, the subroutine identifies that interval with the lowest load (interval 1 in Figure 4). The spare capacity available for pumping in this interval is obtained by comparing the system load with the total committed generation obtained from the original thermal schedule. The number of pumps that may be used in this interval can then be obtained from: integer (n) =
total committed generation-- load
< 6 (4)
29O since the average pumping load per machine is 290 MW. For this interval, the amount of water pumped, W, expressed in terms of equivalent megawatt-hours of generation, can be found from: W=nx 290x½x0.78
30o00
I 14
"l
(s)
where 0.78 is the overall cyclic efficiency of the pump generate cycle. This quantity must then be added to the initial reservoir level and compared with the required level. If less, the interval with the next lowest load (see Figure 4) is selected, and the process is repeated. It is repeated until the water pumped in an interval just exceeds the required level. At this point, the calculation is reversed and the amount of pumping actually required in this interval is used to calculate the reduced pumping load. (In practice, pumps would always be used at full load for a reduced time, but the structure of the algorithm does not allow this.) At this stage, it has been established how the upper reservoir should reach its desired level, and the additional load imposed in each pumping interval has been determined. By adding this load to the original system load, a new curve
115
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I0000
0
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I 6
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Figure 6. Final load curves; - - final load curve
24
h
original load curve,
-
is obtained, as shown in Figure 6. The unit-commitment and load-scheduling algorithm described in Section II can now be repeated with the new curve, and a system cost, including pumping, can be obtained. The difference between this cost and the original total cost gives the cost of pumping which, when divided by the amount of water pumped (in megawatt-hours) gives a production cost suitable for incorporation in a merit order. There are two problems that arise during the derivation of a pumping schedule in this manner. First, it is possible that committed spare capacity will be insufficient to fill the upper reservoir in the overnight trough. (To prevent the subroutine attempting to use low-merit generators for pumping, the pumping period is confined to the interval between the beginning of the costing period and the prespecified 'fill' time.) To complete the pump cycle, therefore, extra power is required from the thermal plant. The last, or highest merit, generator to be shut down is identified, and its output is added to the existing committed generation where appropriate. The pumping subroutine is then repeated with the new committed-capacity schedule. If sufficient capacity is still not available, more and more generators are committed until the upper reservoir reaches the required level. The second problem is that simply using the upper reservoir capacity as the required level leads to an average cost for the full 8 400 MWh of generation. This is clearly incorrect as there are, in fact, several distinct levels of pumping costs. These may be obtained either by specifying different upper reservoir levels to be reached and obtaining a pumping cost for each, or, since this will also give average values, obtaining a cost (and water level) using spare spinning capacity only and then similar figures as each extra generator is committed. 111.2 Pump storage plant in generating mode As stated in Section l, the prime objective of this study 7 was to obtain a pumping cost that would enable one to compare the cost of frequency control by the pumped storage scheme with alternative methods. As such, that comparison is outside the scope of this paper. However, even when used in the frequency control mode, it is unlikely that all six of the Dinorwic machines will be required simul-
116
taneously. Therefore, some machines (and water) will be available for use in the economic mode, the actual number varying with the time of day, and these may be used to directly offset the cost of pumping. The hydrogeneration subroutine has been developed to quantify this saving. To prevent unnecessary or incorrect computation, this subroutine may be used only for time intervals between the last interval in which pumping took place and the last interval of the costing period. For each of these intervals, the number of machines and quantity of water available for generation may be prespecified, subject, of course, to not exceeding the maximum output (1 674 MW) or upper reservoir capacity (8 400 MWh). The only other restriction of any importance is that the efficiency of the turbines falls with reducing output. Thus, if output falls below 168 MW (60% of full load), a parabolic efficiency curve has been assumed to reflect the increased water usage. In many respects, the hydrosubroutine is the reverse of the pumping subroutine. It would be expected that the least efficient thermal generator would be supplying the peak of the load curve. Thus, the first step is to identify the load value of tile peak of the load curve (within, of course, the permitted intervals). The program then subtracts 279 MW (the maximum output of one machine) from this and draws a horizontal line on the load curve, as shown in Figure 5. For each interval whose load exceeds this value, the amount of water required to totally replace the thermal generators above the line is calculated. In each case, the hydrogeneration required is compared with the maximum output and maximum water usage permitted in that interval. If either limit is exceeded, the power output and water used is set at the maximum permissible before proceeding to the next interval. When all intervals have been considered, the amount of water used is summed and compared with the initial level of the upper reservoir. If less, that is more water is available, a further horizontal line is drawn 168 MW below the first, and the whole process is repeated. If greater, a rough estimate is made of the excess power being replaced, and a line is drawn this value above the first. before the process is repeated. This iterative procedure is continued until the total amount of water used is within 1 MWh of the total available. The only restriction made is that no thermal plant may be replaced whose average full load generation cost is less than the pumping cost derived earlier. Thus, as for the pumping subroutine, for each interval in which hydrogeneration is permitted, the output of the pumped storage station is known. In this case, subtraction of this value from the corresponding load value gives a new load curve incorporating both pumping and hydrogeneration, as shown in Figure 6. The unit-commitment and load-scheduling program can now be run for a third time with this new load curve, and the resultant thermal system can be costed. The overall saving by using the pumped storage scheme can now be obtained by subtracting this cost from the original total system cost without using the pumped storage scheme. It is, of course, possible that the upper reservoir cannot be emptied economically during one cost period. In this case, the reservoir level and pumping cost would become part of the input data of the next costing period. The new pumping cost for this period could then be the average of the carried
Electrical P o w e r & Energy Systems
Reod J generotor doto-I
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1
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No Yes
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igure 8
It must be admitted that the economic benefit of using gas turbines in this way is small, being very much less than 1% of the total cost a. However, the reduced maintenance cost of thermal plant is not quantified in this way, and, of course, purely economic operation of gas turbines is not their prime function.
Figure 8 l
[Coil costing J ~ C o I I
chosen to be of two time intervals, or 1 h duration, can readily be replaced by gas turbines. The gas turbine data necessary to run the computer program is supplied as for all the other generators and incorporated in the merit order (Table 2) thus allowing normal economic operation if required. However, for peaks of 1 h duration or less, the gas-turbine subroutine replaces the thermal generators concerned by a number of gas turbines whose combined capacity just exceeds the capacity of the thermal generators replaced. Since gas turbines are normally run at full load, this load is effectively subtracted from the load for each interval, and the unit-commitment and load-scheduling program is rerun, as for the other subroutines, to cost the resultant generator system.
pump I I
subroutine
V. Incorporation of loading and unloading rates drogenerot~on Ye~l~ C~' hydro ] I suorouTmel
No
I Print results J Figure 7. Flowchart of computer algorithms
forward pumping cost and the pumping carried out in the new period. The computer algorithms described in Sections II and III are shown in Figure 7.
IV. Incorporation of gas turbines One of the alternatives to using a pumped storage plant for peak lopping duties is to use gas turbine powered alternators. These are relatively low powered generators (~< 70 MW) but with the capability of synchronizing and reaching full output very quickly. Consequently, their main application is for standby and frequency control duties. From an economic point of view, they can be regarded as having zero offline cost but a comparatively high running cost. The attractions of also using gas turbines for peak lopping, and this includes all maxima on the load curve, are that the online cost is to a certain extent offset by the zero offline cost, and, more importantly, that some thermal units may be replaced entirely, thus further reducing offline costs and making some thermal unit duties less arduous. It is also possible that online costs can be reduced by {greventing some generators operating at reduced load in troughs. To incorporate the use of gas turbines in this computer algorithm, consider the final schedule of generators as shown in Figure 2 in which some generators are required for very short periods of time. Peaks of this type, arbitrarily
Vol 4 No2 April 1982
In the development of the computer algorithms so far described, it has been assumed that all generators may change their outputs from minimum load (or synchronizing load) to full load in less than one time interval. Although this is true for some generators, it is not true for all, especially after a cold start or when the set is returning to service after maintenance. To modify the existing algorithms to take account of this, a separate loading and unloading rate subroutine has been developed. If required for a particular study, it is entered immediately after the final unitcommitment schedule has been obtained by the main program. The full load-scheduling routine of the main program is not then used, although the load on each generator in the very first time interval must be determined by the normal merit-order technique. Any errors incurred in this load schedule can be neglected, since the first interval is normally well in advance of the costing period. The philosophy used by this subroutine is, for each generator committed in time interval 1, to determine the maximum or minimum load that the generator can supply in time interval 2 by adding or subtracting the maximum load change permitted in one interval to the load supplied in time interval 1. If the values obtained would exceed the maximum or minimum output of the generator, they are set at the appropriate limit. The maximum permitted load supplied by the generators is then summed for all committed generators including the permitted output of any generator committed in time interval 2. This cumulative total is then compared with the required load. If it is greater, each generator is loaded in order of merit (Table 2) using the techniques described in Section II but with maximum and minimum outputs being replaced by maximum and minimum permitted outputs, respectively. If, however, the total is less, then the next generator in the merit order (Table 2) must also be committed in time interval 2 to meet the demand, all generators then being loaded as before. It should be noted that this eventuality should only occur for an increasing load curve when already committed generators cannot increase their output sufficiently rapidly. For a decreasing load curve, the unit-commitment schedule should have ensured that sufficient output is available and,
117
for the number of generators normally committed on a system such as this, it should always be possible to schedule load so as not to violate any minimum permitted outputs. The net effect of this will be to increase the number of generators not running at maximum output in any given interval.
Figire 7 [Read unit commitment I
1
ISchedule load fOr interval/I ISeleet next time intervofl
i
[,Calculate maximum and minimum permd-ted outputs I
Using the generator outputs obtained in this way for time interval 2, the permitted maximum or minimum loads supplied in time interval 3 can now be determined and the process repeated. The procedure is then repeated until all time intervals have been considered.
[Sum maximumOutputsI .
~ The problem remaining is that, although no violations of loading or unloading rate now exist, the unit-commitment schedule may have been altered and there may be violations of other operating constraints, particularly minimum shutdown time. A check for this must now be made and the unit-commitment schedule altered accordingly. This in turn will affect the load schedule, so that this part of the subroutine must also be repeated. This iterative procedure is continued until no violations are present.
=
]
[Commitnextgenerator(s} I
t
J
[Schedule load I
Yes
A flow diagram of the loading and unloading rate subroutine is shown in Figure 8.
[Returnto moinprogram] VI. Conclusions A computer program has been described, that, by the use of heuristic techniques, has enabled the operation of a large pumped storage power station to be studied in relation to an existing generation network. Based largely on the manual merit-order scheduling technique, it incorporates many generating-plant constraints and allows overall system costs, including both on- and offline costs, to be studied. When the program, written in ANSI FORTRAN, was used on a CDC 7600 computer system, compilation time, regardless of which subroutines were in use, remained fairly constant at 2.53 s. Execution time depended, of course, on the number of generators required. The winter load curve required a maximum of 53 generators and had an execution time of 1.41 s, while the summer load curve required 17 generators and 0.71 s. In both cases, these results refer to 48 h load curves, of which the central 24 h were costed. Although the technique is not a true optimization method, the results produced compare very favourably with more sophisticated procedures 9, particularly with respect to shorter computation times, and are being used as an 'upper bound' for the comparison of results. Being an operational planning tool, the programs are not expected to produce exceptionally accurate results. Consequently, it was not felt necessary to incorporate transmission losses or distribution of generation, although this is not a particular problem on the CEGB system. The overall cyclic efficiency of the Dinorwic plant, quoted as 78%, is the manufacturers' specification at the station busbars. It might be expected that transmission losses should be incorporated in this figure, since Dinorwic is some distance from any industrial load centre. In practice, these losses may also be neglected since pumping power would be expected to be obtained from an adjacent nuclear power station and the system load in the immediate vicinity of the pumped storage station is 700 MW.
. .n
Figure 7 Figure 8. Flowchart of loading and unloading rate subroutine Current development of the algorithms is incorporating further operational constraints and, especially, the use of different pumping cycles. This is particularly important for the study of 7 day cycles, which are commonly used in pumped storage power stations 4' ~o. The use of past load data without spinning reserve can be said to penalize this pumped storage scheme. To obtain a more accurate assessment of its economic benefits, the schedule using thermal generators only should include conventional plant partly loaded to provide spare capacity. This can be achieved quite simply in this model by committing generators to the load curve plus spinning reserve but loading to the load curve only. Again, the accuracy achieved in this way is adequate for the purposes of this study. One of the advantages of using heuristic techniques is that the information produced by the algorithm is in a form more suited to the present manual control system. However, as with more sophisticated techniques performing both unit commitment and load scheduling n, the schedules produced must be subjected to, for example, load-flow and system-security studies before being implemented. As part of a project to investigate the operation of online control systems, particularly automatic generator control, the results of this study are being used as base data for a generation-allocation algorithm.
Vl I. Acknowledgements The authors wish to thank the University of Manchester Institute of Science and Technology, and the Central Electricity Generating Board, North West Region, for the use of their facilities and for permission to present this paper. In particular, they wish to thank A Brameller
I:lP_c_tric~l Power & Enerav Systems
(UMIST), and P W Aitchison, of the Department of Applied Mathematics, University of Manitoba, Canada, for their advice and assistance. M Ramirez, J Villaroel and J A Balbas also wish to thank the Gran Mariscal de Ayacucho (Venezuela) for their financial support during the course of this project.
6 7
8 V l l l . References 1 Hernen, B 'The world's most advanced pumped storage scheme' Electr. Rev. Vol 200 (1977) pp 29-32 2 Starr, M K Operations management Prentice-Hill, USA (1978) 3 Cooper, A R 'Load dispatching and the reasons for it, with special reference to the British grid system' J. Inst. Electr. Eng. Vol 95 II No 12 (1948) pp 713-732 4 Cochran, A M, Isles, D E and Pope, I T 'Development of pumped storage in a power system' Proc. Inst. Electr. Eng. Vol 126 No 5 (1979) pp 433-438 5 Ramirez, M F Heuristic approach to the unit commitment of thermal power stations MSc Dissertation,
Vol 4 No 2 April 1982
9
10
11
University of Manchester Institute of Science and Technology, UK (1978) Kerr, R H e t al. 'Unit commitment' IEEE Trans. Power Appar. & Syst. Vol PAS~5 No 5 (1966) pp 417-421 Villaroel, J Control of a pumped storage station MSc Dissertation, University of Manchester Institute of Science and Technology, UK (1978) Balbas, J A Economic coordination of a pumped storage power station MSc Thesis, University of Manchester Institute of Science and Technology, UK (1980) Aitchison, P W and Brameller, A 'Optimizing unit commitment' Proc. 2nd Int. Conf. on Large Engineering Systems University of Waterloo, Ontario, Canada (1978) 'Bibliography on pumped storage to 1975' IEEE Trans. PowerAppar. & Syst. Vol PAS-95 No 3 (1976) pp 839850 Dillon, T Set al. 'Integer programming approach to the problem of optimal unit commitment with probabilistic reserve determination' IEEE Trans. Power Appar. & Syst. Vol PAS-97 No 6 (1978) pp 2154-2166
119
A computer algorithm is described that coordinates, economically, the operation o f a large pumped storage scheme with an existing thermal generation system. It uses heuristic techniques to establish a system model for operation, based largely on the manual merit order method, and it incorporates several operating constraints, including generator maximum and minimum generation levels, minimum shutdown times and loading and unloading rates. Designed specifically as an operational planning tool, the algorithm produces a unit commitment and load schedule for every half-hour interval o f any load curve sypplied. By costing this schedule with and without the pumped storage scheme, a pumping cost is obtained that can then be compared with other methods or frequency control. Finally, by extending the schedule to include hydrogeneration, the economic benefit o f using the scheme in this mode may also be evaluated. Keywords: hydroelectric power stations, algorithms, load
flow
I. Introduction The traditional method of controlling frequency in the UK Central Electricity Generating Board (CEGB) system is by means of free governor action on the generating sets as primary control and by manual dispatch to prevent excessive cumulative time error as secondary control. This is then supported by sets in a hot standby condition to cover for plant loss.
Received: 13 January 1981
Vol 4 No 2 April 1982
This method of control has become increasingly uneconomical as the smaller, more flexible plant is retired, as the proportion of nuclear plant is increased (which, on economic grounds alone, is undesirable for use in frequency control) and the performance of mechanical governors tends to reduce the overall efficiency of a generating station. Two of the most promising alternatives to this form of frequency control are gas-turbine-powered generators and conventional hydroelectric plant. In both cases, the generators may be started and synchronized to the system rapidly, either manually or automatically by low frequency relays, and then shut down rapidly. However, the design of modern turbo alternators has resulted in minimum operating costs being obtained by running the generating sets at full load continuously. Clearly, this is not possible for all sets, particularly during the overnight trough when load may be much reduced, as can be seen in Figure 1. Consequently, some generators may be kept running with considerable spare capacity. The facility of a pumped storage power station to shape the overnight load curve and hence utilize this spare capacity, together with the inherent lack of conventional hydroelectric stations on the CEGB system and the ever increasing cost of fuel oil, suggests that pumped storage stations need to be studied further. The purpose of this study was to consider the economic coordination of the Dinorwic ~ pumped storage scheme, now under construction in North Wales, with the existing CEGB system. The main objective was to investigate the operation of this scheme, the main parameters of which are shown in Table 1, as a frequency control device, by obtaining a cost for the pumped water and hence a comparison with other forms of frequency control for which costs are more readily available. This could then be extended to study the effects
0142-0615/82/020111-09 $03.00 © 1982 Butterworth & Co (Publishers) Ltd
111
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Figure 1. Input load data; upper trace: winter, lower trace: summer
on conventional plant of pumping during the overnight trough and the financial benefit that could be expected by using this scheme in a purely economic mode during the midday peak. The present paper describes a computer algorithm based on a heuristic approach to system operation =. That is, a system model has been developed, using logic and commonsense derived by observation and inspection, to replace mathematical models which are too complex to implement. It is based on the present manual merit order method a of operation but is modified to take account of other operating constraints and the addition of the large pumped storage scheme. It is a purely economic algorithm and does not take account of system security or transmission losses. Since the algorithm is intended as an operational planning tool, and would normally be used weeks or months ahead of the actual operation, it is felt that greater accuracy is not required. The generating network and especially the size of the pumped storage plant are, however, assumed to be fixed and, hence, their development 4 need not be considered.
II.
Development of
computer algorithms
I1.1 Data requirements Before one can begin any economic study of the operation of pumped storage schemes, or indeed of conventional hydroelectric schemes, it is necessary to establish a model for operation with only fossil or nuclear powered generators. As for any system, two separate items of information must be available in order to commit and then load these 'thermal' generators. The first of these is the load curve as shown in Figure 1, which would normally be the load expected to be supplied in the next operating period plus some spare capacity to allow for errors in the prediction and for plant failure. In this study, the load curves used to test the algorithms represent actual loads supplied in the past and do not, therefore, incorporate any spare capacity. (The justification for using these curves will be discussed in Section III.) To further reduce the complexity of the algorithms, the time period studied was divided into 30-minute intervals, the load being considered constant for each interval, as shown in Figure 1.
1 12
The remaining data required is the cost of generation and the operating constraints of each generator. Since the generators used by the CEGB are of the single steam throttle valve type, with an essentially linear input-output characteristic, the costs required are the average full load generation cost and the incremental cost, both expressed in £/MWh. The operating constraints are maximum and minimum generating levels, minimum shutdown time and maximum loading and unloading rates. This data is supplied in the form of a merit order, as shown in Table 2, and a table of increasing incremental costs, as shown in Table 3. To reduce the time required to check each schedule obtained, Tables 2 and 3 represent a 'reduced merit order' of some 80 generators. This was obtained by, initially, considering all the generators in one power station to be one large generator. Power stations could then be grouped together by type and operating cost. This enabled the 132 power stations, made up of over 600 generators, operated by the CEGB in 1979/80 to be reduced to manageable proportions, although no modifications to the algorithms are required to enable each generator to be considered individually. The data shown in Tables 2 and 3 is representative of the data actually used, although the costs have been normalized. The derivation of the offline costs shown in Table 2 will be given in Section II.4. 11.2 Unit commitment As stated earlier, the operation of the 'thermal' generating sets has been based on the merit-order method of operation, that is, commitment in order of average full load generation costs and loading of committed sets to full load in order of increasing incremental costs. Thus, the unit commitment procedure is started for the first time interval by comparing the load value for that interval with the cumulative capacity column in Table 2. Sufficient generators are then committed so that their cumulative capacity just exceeds the system load. This is then repeated for all intervals of the load curve. The schedule obtained, however, may not be feasible because of the operating constraints. Initially, the loading and unloading constraint is neglected, so that only the minimum shutdown time can affect this schedule.
Table 1. Parameters of Dinorwic pumped-storage scheme Number of machines Type Speed Electrical output per machine Total output Total water storage Head Pump load per machine Total pump load Cyclic efficiency (for output > 60% full load) Total pumping energy Time to fill reservoir at total pump load Time to empty reservoir at total output
6 reversible pump-turbines 500 rpm 279 MW (maximum) 1674 MW 8400 MWh generation 540 m 290 MW (essentially constant) 1740 MW 78% 10 728 MWh 6.16h 5.02 h
Electrical Power & Energy Systems
Table 2. Order of merit schedule Offline costs Maximum capacity, MW
lative capacity, MW
Minimum capacity, MW
Production cost
Minimum shutdown, h
844 680 1 240 1 875 1 426 1 400
844 1 524 2 764 4 639 6 065 7 465
200 410 390 984 883 840
1.00 1.33 6.14 6.57 6.61 6.68
10 6 7 8 8 6
Cumu-
Position t 2 3 4 5 6
Name LID 1LL-3 110311-1 WW05WW-1 AA07AA-5 KK08KK-1 XX09XX-6 etc.
No load cost (,4)
D
C
D
C
100 168 1 322 2 018 1 732 1 811
YYY YYY YYY YYY YYY YYY
YYY YYY YYY YYY YYY YYY
1 000 810 1 458 1 759 1 674 1 644
3 2 4 5 5 4
Cold
Hot
000 430 374 277 022 932
Production cost = average full load generation cost Y Y Y - o n l y available f o r l o w merit generators
Table 3. Order of increasing incremental cost
Position
Name
1 2 3 4 5 6
LID 1LL-3 110311-1 WW05WW-1 KK08KK-1 XX09XX-6 AA07AA-5 etc.
Maximum capacity, MW
Minimum capacity, MW
Incremental Minimum cost shutdown, (B) h
No load cost
Load rate cold, MW/min
Load rate hot, MW/min
Shutdown rate, MW/min
840 680 1 240 1 426 1 400 1 875
200 410 390 883 840 984
1.00 1.26 5.89 6.30 6.32 6.35
100 168 1 322 1 732 1 811 2 018
XXX XXX XXX XXX XXX XXX
XXX XXX XXX XXX XXX XXX
XXX XXX XXX XXX XXX XXX
10 6 7 8 6 8
X X X -- actual data not available
This is taken into account by the algorithm by identifying, for each generator, all offline periods and comparing disconnection times with subsequent reconnection times. If elapsed time is less than the minimum shutdown time, the schedule is altered so that the generator is not switched off for those intervals. However, for the first and last intervals, generator states are not available, and incorrect schedules may be obtained. This is overcome by supplying extra load data, both lead and lag. In practice, it was found that the load curve should contain three peaks with a total duration of approximately 48 h s.
it will be unloaded by Table 2. Only if generators are prevented from shutting down by their operating constraints is loading performed by Table 3. The algorithm can now complete the load scheduling and, for every 30 min interval, identify each committed
I
st pea k
5O
2 nd peo k
l
ii
The resulting final commitment schedule with no violation of the minimum shutdown times can then be given in diagrammatic form, as in Figure 2. 11.3
Load scheduling
Once a satisfactory unit commitment schedule has been obtained, the load to be supplied by each generator must be determined. This would normally be done by loading to full load in order of increasing incremental costs. However, if the generator ordering shown in Tables 2 and 3 is not the same, then generators with higher incremental costs could have their outputs varied continuously as generators of lower merit but lower incremental costs are subsequently committed. To prevent this rather unsatisfactory situation, the basic approach is modified so that if the load curve is increasing, generators are loaded by Table 2. If the load is decreasing and a generator will subsequently be shut down,
Vol 4 No 2 April 1982
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113
generator and quantify its power output. This can be printed either generator by generator for all intervals or, as shown in Table 4, for all generators in one time interval. 11.4 Costing To obtain an operational cost of the schedule just derived, two factors must be taken into consideration. Clearly, any generator synchronized to the supply system and supplying power must have an online cost given by: F(£/h) = A + B- P
j Ccold
~-"
In addition to these costs, however, every generator not running for the full costing period must incur offtine costs, every time it is disconnected and then subsequently reconnected. Several methods of representing offline costs have been proposed previously 6, but a very simple model has been adopted for this study. It has been assumed that, once a unit is disconnected, the cost of bringing it back into service is, basically, an exponential function which increases with time offline, as shown in Figure 3. The model itself involves unnecessary computation, so two linear approximations to the curve have been used, as shown in Figure 3. The two approximations, referred to as hot start and cold start, have no direct link with physical conditions but correspond roughly to generators shut down only for the overnight trough (or two-shifted) and those used infrequently for peak lopping. In both starting conditions, the offline cost of each generator may be determined from: a(£) = c + D- t
(2)
where C is in £, D is in £/h and t is the number of hours offline. The constants take on different values, depending on the starting condition, as shown in Figure 3, and also
D~Ld
§
y.
(1)
where A is the no-load cost, B the incremental cost and P the electrical output in watts. Thus, for each 30-minute interval, the online cost of each generator may be found from equation (1). Since the load is, in reality, continuously variable, an average online cost for each interval is obtained by taking a simple average of that and the next interval's costs. Total online costs for any desired period may then be found by summing the average costs of the required number of intervals.
dG .
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l
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I 12
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24
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stort I 60
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Figure 3. Offline costs
vary with the maximum output of the generator. Since offline costs were only available for a few generators, the costs shown in Table 3 have been derived proportionally from these by a small subroutine incorporated in the generator input data file. The criterion for identifying the state of a generator as either hot or cold start (which is the main reason for supplying a load curve with three peaks) assumes that if a generator is not required at any time in this period, its offline cost is zero. If a generator is required for only one peak, and not previously or subsequently, then it is in a cold-start condition. All other generators must be in a hotstart condition. As can be seen from Figure 2, a generator offline period may be only partly within a costing period. In such cases, it is assumed that the part of the total offline costs of that generator to be allocated to the costing period is directly proportional to the time offline within the costing period. The overall system cost for any period can then be obtained by a simple summation of on- and offline costs for the required number of intervals. The algorithm has been designed so that, provided the full load curve is supplied, the system may be costed for any period longer than 1 h. In practice, it being likely that Dinorwic will be operated on a 24 h cycle, this has been used as the standard costing cycle, although the starting point can be varied at will.
Table 4. Sample loading schedule Time: 2.30 h
Thermal generation: 31 211 MW
Load value: 29 471 MW
Pump load: 1 740 MW
Cost: 165 962 units
Station
Loading, MW
Station
Loading, MW
Station
Loading, MW
LL01LL-3 AA07AA-5 GG10GG-6 JJ 13J J-3 HH16HH-4 BB19BB-1 UU22UU-2 BB25BB-3 112811-4
844 1 875 1 370 328 2 015 1 033 2 120 3 340 358
110311-1 KK08KK-1 EEllEE-4 LL14LL-4 SS17SS-8 MM20MM-3 XX23XX-7 VV26VV-8 CC29CC-1
680 1 426 1 810 920 920 303 567 1 084 304
WW05WW-1 XX09XX-6 KK12KK-2 RR15RR-3 NN18NN-4 002100-1 VV24VV-6 NN27NN-2 ZZ30ZZ-4
1 240 1 400 2 240 340 1 896 116 749 1 815 118
1 14
max max max max max max max max
max max max max max max max max max
max max max max max max max max min
Electrical Power & Energy Systems
In all cases, the system cost can be expressed as:
Total cost = E
m=]
'
2
×-
40000
+Ec°
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(3) where Fro, n is the cost per hour of generator n in interval m , j and k are the initial and final intervals, respectively, of the costing period and G n is the offline cost of generator n within the costing period.
III. Coordination of pumped storage scheme
o,
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II1.1 Derivation o f pumping cost It is n o r m a l l y a c k n o w l e d g e d t h a t there are three d i s t i n c t m o d e s o f o p e r a t i o n f o r a p u m p e d storage scheme, assuming that the upper reservoir has been filled in a previous
pump cycle. The generators can be used in the spin-generatein-air mode, in which the turbine runners are filled with compressed air and the generators motor at a much reduced load. In this condition, they are able to meet sudden load changes in the system caused by plant failure and also to perform frequency control by balancing small mismatches between load and generation. The third mode of operation is the economic mode, which was probably the first intended use of pumped storage schemes, in which the pumped water is used to replace less efficient thermal plant during the load curve peak. As a result of the first two modes, however, it is not necessary to incorporate spare capacity in the schedules, since the output of the pumped storage scheme provides spare capacity during the day, and switching off pumps provides spare capacity during the overnight trough. (It is, however, very easy to incorporate spinning reserve in this approach, if required, as will be shown later.) The main restriction imposed at this stage on the Dinorwic scheme was that the upper reservoir should be full at some prespecified, but variable, time each day. It was then 40000 i
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V o l 4 N o 2 A p r i l 1982
[ 16
[ 18
I 20
I 22
Time, h
Figure 5. H y d r o g e n e r a t i o n schedule; - tion,--hydrogeneration
t h e r m a l genera-
assumed that the cost of this water could only be determined by costing the entire system twice, once with the scheme and once without. Finally, since the full number of hydrogenerators would not be required for frequency control at all times, spare capacity (and water) could be used in the economic mode and a cost benefit could be obtained. To calculate the pumping cost, therefore, the algorithm calls the pumping subroutine immediately after the costing of the system using thermal plant only. Since, clearly, the cheapest pumping costs will be obtained when the system load demand is least, the subroutine identifies that interval with the lowest load (interval 1 in Figure 4). The spare capacity available for pumping in this interval is obtained by comparing the system load with the total committed generation obtained from the original thermal schedule. The number of pumps that may be used in this interval can then be obtained from: integer (n) =
total committed generation-- load
< 6 (4)
29O since the average pumping load per machine is 290 MW. For this interval, the amount of water pumped, W, expressed in terms of equivalent megawatt-hours of generation, can be found from: W=nx 290x½x0.78
30o00
I 14
"l
(s)
where 0.78 is the overall cyclic efficiency of the pump generate cycle. This quantity must then be added to the initial reservoir level and compared with the required level. If less, the interval with the next lowest load (see Figure 4) is selected, and the process is repeated. It is repeated until the water pumped in an interval just exceeds the required level. At this point, the calculation is reversed and the amount of pumping actually required in this interval is used to calculate the reduced pumping load. (In practice, pumps would always be used at full load for a reduced time, but the structure of the algorithm does not allow this.) At this stage, it has been established how the upper reservoir should reach its desired level, and the additional load imposed in each pumping interval has been determined. By adding this load to the original system load, a new curve
115
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oooo r
_~20000
I0000
0
0
I 6
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-
Figure 6. Final load curves; - - final load curve
24
h
original load curve,
-
is obtained, as shown in Figure 6. The unit-commitment and load-scheduling algorithm described in Section II can now be repeated with the new curve, and a system cost, including pumping, can be obtained. The difference between this cost and the original total cost gives the cost of pumping which, when divided by the amount of water pumped (in megawatt-hours) gives a production cost suitable for incorporation in a merit order. There are two problems that arise during the derivation of a pumping schedule in this manner. First, it is possible that committed spare capacity will be insufficient to fill the upper reservoir in the overnight trough. (To prevent the subroutine attempting to use low-merit generators for pumping, the pumping period is confined to the interval between the beginning of the costing period and the prespecified 'fill' time.) To complete the pump cycle, therefore, extra power is required from the thermal plant. The last, or highest merit, generator to be shut down is identified, and its output is added to the existing committed generation where appropriate. The pumping subroutine is then repeated with the new committed-capacity schedule. If sufficient capacity is still not available, more and more generators are committed until the upper reservoir reaches the required level. The second problem is that simply using the upper reservoir capacity as the required level leads to an average cost for the full 8 400 MWh of generation. This is clearly incorrect as there are, in fact, several distinct levels of pumping costs. These may be obtained either by specifying different upper reservoir levels to be reached and obtaining a pumping cost for each, or, since this will also give average values, obtaining a cost (and water level) using spare spinning capacity only and then similar figures as each extra generator is committed. 111.2 Pump storage plant in generating mode As stated in Section l, the prime objective of this study 7 was to obtain a pumping cost that would enable one to compare the cost of frequency control by the pumped storage scheme with alternative methods. As such, that comparison is outside the scope of this paper. However, even when used in the frequency control mode, it is unlikely that all six of the Dinorwic machines will be required simul-
116
taneously. Therefore, some machines (and water) will be available for use in the economic mode, the actual number varying with the time of day, and these may be used to directly offset the cost of pumping. The hydrogeneration subroutine has been developed to quantify this saving. To prevent unnecessary or incorrect computation, this subroutine may be used only for time intervals between the last interval in which pumping took place and the last interval of the costing period. For each of these intervals, the number of machines and quantity of water available for generation may be prespecified, subject, of course, to not exceeding the maximum output (1 674 MW) or upper reservoir capacity (8 400 MWh). The only other restriction of any importance is that the efficiency of the turbines falls with reducing output. Thus, if output falls below 168 MW (60% of full load), a parabolic efficiency curve has been assumed to reflect the increased water usage. In many respects, the hydrosubroutine is the reverse of the pumping subroutine. It would be expected that the least efficient thermal generator would be supplying the peak of the load curve. Thus, the first step is to identify the load value of tile peak of the load curve (within, of course, the permitted intervals). The program then subtracts 279 MW (the maximum output of one machine) from this and draws a horizontal line on the load curve, as shown in Figure 5. For each interval whose load exceeds this value, the amount of water required to totally replace the thermal generators above the line is calculated. In each case, the hydrogeneration required is compared with the maximum output and maximum water usage permitted in that interval. If either limit is exceeded, the power output and water used is set at the maximum permissible before proceeding to the next interval. When all intervals have been considered, the amount of water used is summed and compared with the initial level of the upper reservoir. If less, that is more water is available, a further horizontal line is drawn 168 MW below the first, and the whole process is repeated. If greater, a rough estimate is made of the excess power being replaced, and a line is drawn this value above the first. before the process is repeated. This iterative procedure is continued until the total amount of water used is within 1 MWh of the total available. The only restriction made is that no thermal plant may be replaced whose average full load generation cost is less than the pumping cost derived earlier. Thus, as for the pumping subroutine, for each interval in which hydrogeneration is permitted, the output of the pumped storage station is known. In this case, subtraction of this value from the corresponding load value gives a new load curve incorporating both pumping and hydrogeneration, as shown in Figure 6. The unit-commitment and load-scheduling program can now be run for a third time with this new load curve, and the resultant thermal system can be costed. The overall saving by using the pumped storage scheme can now be obtained by subtracting this cost from the original total system cost without using the pumped storage scheme. It is, of course, possible that the upper reservoir cannot be emptied economically during one cost period. In this case, the reservoir level and pumping cost would become part of the input data of the next costing period. The new pumping cost for this period could then be the average of the carried
Electrical P o w e r & Energy Systems
Reod J generotor doto-I
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1
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No Yes
---
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igure 8
It must be admitted that the economic benefit of using gas turbines in this way is small, being very much less than 1% of the total cost a. However, the reduced maintenance cost of thermal plant is not quantified in this way, and, of course, purely economic operation of gas turbines is not their prime function.
Figure 8 l
[Coil costing J ~ C o I I
chosen to be of two time intervals, or 1 h duration, can readily be replaced by gas turbines. The gas turbine data necessary to run the computer program is supplied as for all the other generators and incorporated in the merit order (Table 2) thus allowing normal economic operation if required. However, for peaks of 1 h duration or less, the gas-turbine subroutine replaces the thermal generators concerned by a number of gas turbines whose combined capacity just exceeds the capacity of the thermal generators replaced. Since gas turbines are normally run at full load, this load is effectively subtracted from the load for each interval, and the unit-commitment and load-scheduling program is rerun, as for the other subroutines, to cost the resultant generator system.
pump I I
subroutine
V. Incorporation of loading and unloading rates drogenerot~on Ye~l~ C~' hydro ] I suorouTmel
No
I Print results J Figure 7. Flowchart of computer algorithms
forward pumping cost and the pumping carried out in the new period. The computer algorithms described in Sections II and III are shown in Figure 7.
IV. Incorporation of gas turbines One of the alternatives to using a pumped storage plant for peak lopping duties is to use gas turbine powered alternators. These are relatively low powered generators (~< 70 MW) but with the capability of synchronizing and reaching full output very quickly. Consequently, their main application is for standby and frequency control duties. From an economic point of view, they can be regarded as having zero offline cost but a comparatively high running cost. The attractions of also using gas turbines for peak lopping, and this includes all maxima on the load curve, are that the online cost is to a certain extent offset by the zero offline cost, and, more importantly, that some thermal units may be replaced entirely, thus further reducing offline costs and making some thermal unit duties less arduous. It is also possible that online costs can be reduced by {greventing some generators operating at reduced load in troughs. To incorporate the use of gas turbines in this computer algorithm, consider the final schedule of generators as shown in Figure 2 in which some generators are required for very short periods of time. Peaks of this type, arbitrarily
Vol 4 No2 April 1982
In the development of the computer algorithms so far described, it has been assumed that all generators may change their outputs from minimum load (or synchronizing load) to full load in less than one time interval. Although this is true for some generators, it is not true for all, especially after a cold start or when the set is returning to service after maintenance. To modify the existing algorithms to take account of this, a separate loading and unloading rate subroutine has been developed. If required for a particular study, it is entered immediately after the final unitcommitment schedule has been obtained by the main program. The full load-scheduling routine of the main program is not then used, although the load on each generator in the very first time interval must be determined by the normal merit-order technique. Any errors incurred in this load schedule can be neglected, since the first interval is normally well in advance of the costing period. The philosophy used by this subroutine is, for each generator committed in time interval 1, to determine the maximum or minimum load that the generator can supply in time interval 2 by adding or subtracting the maximum load change permitted in one interval to the load supplied in time interval 1. If the values obtained would exceed the maximum or minimum output of the generator, they are set at the appropriate limit. The maximum permitted load supplied by the generators is then summed for all committed generators including the permitted output of any generator committed in time interval 2. This cumulative total is then compared with the required load. If it is greater, each generator is loaded in order of merit (Table 2) using the techniques described in Section II but with maximum and minimum outputs being replaced by maximum and minimum permitted outputs, respectively. If, however, the total is less, then the next generator in the merit order (Table 2) must also be committed in time interval 2 to meet the demand, all generators then being loaded as before. It should be noted that this eventuality should only occur for an increasing load curve when already committed generators cannot increase their output sufficiently rapidly. For a decreasing load curve, the unit-commitment schedule should have ensured that sufficient output is available and,
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for the number of generators normally committed on a system such as this, it should always be possible to schedule load so as not to violate any minimum permitted outputs. The net effect of this will be to increase the number of generators not running at maximum output in any given interval.
Figire 7 [Read unit commitment I
1
ISchedule load fOr interval/I ISeleet next time intervofl
i
[,Calculate maximum and minimum permd-ted outputs I
Using the generator outputs obtained in this way for time interval 2, the permitted maximum or minimum loads supplied in time interval 3 can now be determined and the process repeated. The procedure is then repeated until all time intervals have been considered.
[Sum maximumOutputsI .
~ The problem remaining is that, although no violations of loading or unloading rate now exist, the unit-commitment schedule may have been altered and there may be violations of other operating constraints, particularly minimum shutdown time. A check for this must now be made and the unit-commitment schedule altered accordingly. This in turn will affect the load schedule, so that this part of the subroutine must also be repeated. This iterative procedure is continued until no violations are present.
=
]
[Commitnextgenerator(s} I
t
J
[Schedule load I
Yes
A flow diagram of the loading and unloading rate subroutine is shown in Figure 8.
[Returnto moinprogram] VI. Conclusions A computer program has been described, that, by the use of heuristic techniques, has enabled the operation of a large pumped storage power station to be studied in relation to an existing generation network. Based largely on the manual merit-order scheduling technique, it incorporates many generating-plant constraints and allows overall system costs, including both on- and offline costs, to be studied. When the program, written in ANSI FORTRAN, was used on a CDC 7600 computer system, compilation time, regardless of which subroutines were in use, remained fairly constant at 2.53 s. Execution time depended, of course, on the number of generators required. The winter load curve required a maximum of 53 generators and had an execution time of 1.41 s, while the summer load curve required 17 generators and 0.71 s. In both cases, these results refer to 48 h load curves, of which the central 24 h were costed. Although the technique is not a true optimization method, the results produced compare very favourably with more sophisticated procedures 9, particularly with respect to shorter computation times, and are being used as an 'upper bound' for the comparison of results. Being an operational planning tool, the programs are not expected to produce exceptionally accurate results. Consequently, it was not felt necessary to incorporate transmission losses or distribution of generation, although this is not a particular problem on the CEGB system. The overall cyclic efficiency of the Dinorwic plant, quoted as 78%, is the manufacturers' specification at the station busbars. It might be expected that transmission losses should be incorporated in this figure, since Dinorwic is some distance from any industrial load centre. In practice, these losses may also be neglected since pumping power would be expected to be obtained from an adjacent nuclear power station and the system load in the immediate vicinity of the pumped storage station is 700 MW.
. .n
Figure 7 Figure 8. Flowchart of loading and unloading rate subroutine Current development of the algorithms is incorporating further operational constraints and, especially, the use of different pumping cycles. This is particularly important for the study of 7 day cycles, which are commonly used in pumped storage power stations 4' ~o. The use of past load data without spinning reserve can be said to penalize this pumped storage scheme. To obtain a more accurate assessment of its economic benefits, the schedule using thermal generators only should include conventional plant partly loaded to provide spare capacity. This can be achieved quite simply in this model by committing generators to the load curve plus spinning reserve but loading to the load curve only. Again, the accuracy achieved in this way is adequate for the purposes of this study. One of the advantages of using heuristic techniques is that the information produced by the algorithm is in a form more suited to the present manual control system. However, as with more sophisticated techniques performing both unit commitment and load scheduling n, the schedules produced must be subjected to, for example, load-flow and system-security studies before being implemented. As part of a project to investigate the operation of online control systems, particularly automatic generator control, the results of this study are being used as base data for a generation-allocation algorithm.
Vl I. Acknowledgements The authors wish to thank the University of Manchester Institute of Science and Technology, and the Central Electricity Generating Board, North West Region, for the use of their facilities and for permission to present this paper. In particular, they wish to thank A Brameller
I:lP_c_tric~l Power & Enerav Systems
(UMIST), and P W Aitchison, of the Department of Applied Mathematics, University of Manitoba, Canada, for their advice and assistance. M Ramirez, J Villaroel and J A Balbas also wish to thank the Gran Mariscal de Ayacucho (Venezuela) for their financial support during the course of this project.
6 7
8 V l l l . References 1 Hernen, B 'The world's most advanced pumped storage scheme' Electr. Rev. Vol 200 (1977) pp 29-32 2 Starr, M K Operations management Prentice-Hill, USA (1978) 3 Cooper, A R 'Load dispatching and the reasons for it, with special reference to the British grid system' J. Inst. Electr. Eng. Vol 95 II No 12 (1948) pp 713-732 4 Cochran, A M, Isles, D E and Pope, I T 'Development of pumped storage in a power system' Proc. Inst. Electr. Eng. Vol 126 No 5 (1979) pp 433-438 5 Ramirez, M F Heuristic approach to the unit commitment of thermal power stations MSc Dissertation,
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10
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University of Manchester Institute of Science and Technology, UK (1978) Kerr, R H e t al. 'Unit commitment' IEEE Trans. Power Appar. & Syst. Vol PAS~5 No 5 (1966) pp 417-421 Villaroel, J Control of a pumped storage station MSc Dissertation, University of Manchester Institute of Science and Technology, UK (1978) Balbas, J A Economic coordination of a pumped storage power station MSc Thesis, University of Manchester Institute of Science and Technology, UK (1980) Aitchison, P W and Brameller, A 'Optimizing unit commitment' Proc. 2nd Int. Conf. on Large Engineering Systems University of Waterloo, Ontario, Canada (1978) 'Bibliography on pumped storage to 1975' IEEE Trans. PowerAppar. & Syst. Vol PAS-95 No 3 (1976) pp 839850 Dillon, T Set al. 'Integer programming approach to the problem of optimal unit commitment with probabilistic reserve determination' IEEE Trans. Power Appar. & Syst. Vol PAS-97 No 6 (1978) pp 2154-2166
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