CONTROLLED EMISSION DISPATCH

Jerome K. Delson

University of the Negev,

Beer-Sheva, Israel FIRST PAGI

AbWtAact mental objectives at minimum operating cost has been

-I made available.

A method is described for commiting generators

and scheduling their output so as to comply with en- A complete and practical method for solving this

vironmental objectives such as limitations on emis- 1 problem, is presented here. It is based on a simple

sion of oxides of sulfur, oxides of nitrogen or dis- " technique used by economists. The key is the use of

charge of heat into watercourses. The limitations may k conversion factors that permit the pertinent items (in

apply to emissions or to resulting ambient concentra- this case the environmental objectives) to be treated

tions and may apply simultaneously to more than one in monetary units rather than in the original physical

type of residual. The method depends on the use of units by which these items are described. The convermonetary conversion factors. For each set of environ- '-sion from physical to monetary units is achieved by

mental objectives and each system load level, minimum extending the concept of "price". For detrimental reoperating costs are achieved. The examples presented siduals, la market does not exist, and appropriate

are based on the characteristics of the generators in prices must be invented for the sake of analysis.

the Israeli power system. Once a price has been invented, the production of detrimental residuals at each station enters costwise

INTRODUCTION /. into the analysis in exactly the same way that the

price of fuel or the variable component of labor enter

The object is to generalize the load dispatch and\ into the programs for commitment of generating units

unit commitment procedures in order to take into and for their economic dispatch. It is worthwhile to

account protection of the natural environment. More note that standard algorithms can be used, and thus

specifically, the goal is to schedule the power output the technique allows inclusion of such regular feaof each generator to meet given environmental object- A tures as transmission losses and energy transactions

ives at minimum operating cost. The schedule that among interconnected power systems.

achieves this objective will be called controlled

emission dispatch. The manner of inventing and applying the appropriate prices for the detrimental residuals and the

It is assumed that the environmental objective interpretation of the results is presented through the

are stated either as limits on the emission of detri- following example.

mental residuals or as limits on the resulting ambien 4

concentrations of these residuals. The residuals in- C

clude combustion products such as sulfur dioxide and

nitrogen oxide and also waste heat, which is the ther-X

mal residual that is usually discharged into a watercourse or a cooling tower. The limits are stated, for /

example, as the number of tons of sulfur dioxide (SO2) Xlg NOx/hour

or oxides of nitrogen (NOx) emitted to the atmosphere 2

or as the maximum permissible concentration of these

substances at ground level. Similarly, the environmental objective for thermal energy may be given in

terms of a limit on the quantity of heat released to a 300

watercourse or as a limit on the resulting rise of

temperature in the watercourse. In all of these cases,

a mathematical relationship must be available that/

describes the output or dispersion of residuals from - each generator as a function of generator power out- s

put, An example of an emission-type function is given 200-

in [1] and of an ambient type function is given in

[2].

The problem still remains, however, of choosing

'the best (least cost) generating schedule from among is 0

the alternative schedules that would satisfy the environmental objectives. In the articles that have k

dealt with this subject,l'2'3 this problem has not

been solved and no procedure that achieves environ-

% 0 s0 100 5 200

< ~~~~OUTPUT - MW

Paper T 74 156-6, recommended and approved by the IEEE Power System Fig. 1. NOx Emissions from the 50-MW and 225-MW

Engineering Committee of the IEEE Power Engineering Society for presentation at Uni t

the IEEE PES Winter Meeting, New York, N.Y., January 27-February 1, 1974.

Manuscript submitted September 5, 1973; made available for printing November

16, 1973. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

1359
CONTROL OF NOx Tel Aviv area at minimum cost to the power system.

This example assumes that, for the Israeli power The NOx emissions from the Tel Aviv generators

system, temporary limits are imposed on NOx emissions are given in Fig. 1. The data is hypothetical, but an

in the main metropolitan area (Tol Aviv), but emission example of this type of data based on measured emislimits are not placed on the other stations, which are sions is given in [1]. For the generators committed

located in Ashdod and Haifa. The generators to be op- to operate, labor and expenses other than fuel are

erated consist to two 50 MW and two 225 MW units in considered invariant, and only the fuel expenses of

Tel Aviv and a total of two 30 MW, three 50 MW, four the power system are included in the analysis. The,

75 MW and two 125 MW units at the Ashdod and Haifa fuel is oil and costs $20 per metric ton. The fuel

stations -- a system total of 1310 MW. The practice rates on both an average and incremental basis are

assumed is that each committed unit will be operated shown for the various types of units in Fig. 2. The

at no less than 40% of its rated full-load output. average and marginal operating costs are obtalned from

The object is to prepare dispatch schedules for the same data by referring to the right-hand scale of

various levels of system load so that the generators Fig. 2.

in each case meet the specified emission limits in the

GRAM/kWhM MILL/kWh

° 1- , , , ,~~~ , I' I 'iI

300 50 mw 0061 50200

l-~~~~~~~

30MW MW

30x 0 M150M 605M 60 6 0 6 0 8 3 4 4 5 5

2 125MW2M25M 2 25 L5

Lii

SUBOTA 46L0 6 u44U 7 U 4 5 6 6

I100 - AVERAGE FUEL RATE2

MARGINAL (INCREMENTAL) FUEL RATE

Te0vv(oeisinlmt

0 50 100 150 200

OUTPUT - MW

Figs. 2. GENERATOR FUEL RATES

Table 1. Minimum-cost Generator Schedules --No Limit on NOx Emissions

Marginal Cost [mills/kWh] 4.0 4.1 4.2 4.4 4.6 4.8 5.2 5.6 8.0 10.0 15.0 20.0

Ashdod and Haifa (CAPACITY) (OUTPUT --MEGAWATTS)

2 x 30OMW 60 24 24 24 24 24 24 24 24 56 58 60 60

3xSTMOTMW 150 60 60 60 60 60 60 88 138 144 147 1350 150

4 x 75 MW 300 120 120 120 120 120 250 284 290 299 300 300 300

2 x 125 MW 250 100 160 210 -230O 235 237 239 241 246 250 250 250

Tel Aviv (noemission limit)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1 e n A'
If there were no NOx emission limits, minimum op- h erating cost would be obtained by scheduling the gen- $/hoir

erators so that their marginal operating costs are

equal. This is the standard "economic dispatch" procedure. It is implemented by picking values for the

marginal cost and then noting the output for each generator. As shown in Fig. 2, marginal costs increase

with generator output, so that as the generator output

ranges from its minimum to- its maximum output, its | 1 Reniaty $/kg NOx 3/

marginal cost covers a corresponding range. If the

marginal cost for the system is below the minimal mar- /

ginal cost of a generator, the generator is scheduled

at its minimum output; conversely, if the selected

marginal cost is above the maximum marginal cost of a

generator-, the generator is scheduled at its maximum

output. The procedure is illustrated in Table 1. For 0

marginal costs ranging from 4 to 15 mills/kWh, system

output covers it full range from 524 to 1310 MW.

To schedule the generators with a limitation on

NOx emissions from the Tel Aviv units, the procedure 500

is as follows. The emissions are converted into monetary units by inventing or assuming a price. The

total cost of operating the Tel Aviv units is then

taken as the cost of fuel plus the implied cost of the

NOx emissions. For example, if the output of one of

the 225-MW units is 200 MW, its fuel consumption rate 0 _ ,

is 215 gram/kWh (Fig. 2, solid curve). Its fuel cost I

is then: 0 50 100 150 200

(215g/kWh)($20/1 06g) (200xlO3kW) = $860/hour OUTPUT - MW

From Fig. 1, at 200 MW the NOx emission rate is 290 kg

per hour. Thus, fiI-. 3; Operatimg Co"sts for thexe 50-5MW asd 225-MW

Penalty Rate --- Operating Cost, $/hour -- Un4ts irncluding NOx penarlty. $/kg NOx Fuel Penalty Total

0 860 0 860

l 860 290 1150

2 860 580 1440 method in which small increments are used to approximate the differentials.

In this manner, the curves of total cost that are Graphical calculation of the new marginal cost shown in Fig. 3 can be constructed. The marginal cost

curves cain be obtaiined by tak ing the slope of the curves for the 50-MW unit in Tel Avivr is shown in

total cost curves. The new marginal cost curves for Table 2. The first four columns calculate the deri- thtel Avivcunts Thernw marginal cost .u.v.s.f. vative of the NOx emissions with respect to output.

curves from Fig. 1 for the other generating units can This derivative is multplisadded to the marginal cost be used to obtain new generator schedules similar to Nxeisosadrsl saddt h agnlcs

those-in Table 1. of fuel as shown in the last four columntof Table 2.

Thus the marginal cost for zero penalty in column 5 is

The new marginal cost curves for the Tel Aviv t d f

units, however, can be obtained directly from the NOx times the fourth column is added to the zero-penalty

emission curves in Fig. 1 and the marginal cost curves marginal cost to obtain the figure in the sixth column,

in Fig. 2. It is not necessary to construct the etc.

curves shown ih Fig. 3, as the marginal cost can be The resulting marginal cost curves as well as the obtained by differentiating each part of the function. a

T nus * ~~~~~~~~~~average cost curves are shown in Fig. 4. The.marginal

C(M) = F(M) + pE(M) cost curve lies below the average cost when the averor C = F + pE age cost is decreasing, above it when the average cost

and C' F' + pE'

and c = f + pe Table 2. Marginal Operating Cost for 50-MW Unit

The combined cost C, the fuel cost F and the NOx Including Penalty for NOx Emissions

emission E are all functions of the power output M, (1) (2) (3) (4) (5) (6) (7) (8)

written explicitly in the first equation or implicitly M E AE AE

in the second. The conversion factor or price penalty AM

"p" for the NOx emission is not a function of power p=O p=l p=2 p=3

output. The derivatives With respect to M of C, F, 20 10.3 3 6 0.90 5.04 5.94 6.84 7.74

and are written E C', F' and E' in the third equation. 24l 3.9 *3 0.95 5.10 6.05 7.00 7.95

The average values of C, F, and E are denoted in the 28 17.7 408 1009 5.16 6.16 7.16 8.16

fourth equation as c, f, and e. They are derived by 32 21.7 446° -1.15 5.22 6.367 7.52 8.67

dividing the first equation by the power output M. 36 26.3 5'2 1.30 5.28 6.58 .8 91

The algebra can be carried out quite readily if the 40 31.5 60 1.5 5.3 6.8 87.36 9.186

fuel cost curve F and the emission curve E are expres- 44 37. 635 1.5705 5.464 67.19 8.94 10.69

sed as analytical functions. (This is usually done 46 41.0 4 .0 57 .0 97 17

using binomial or exponential terms). The computation 48 45.0 54 2.°5°0 10.0 1O2.50 195.00° 17.50°

can also be carried out stepwise by the graphical 50 50.0* * * *

1361
20 l

_ ItLS/kWh

AVERAGE COST

1.

_ --~~~MARGINAL COST-I _I

$03i Penalty $1/kg Penalty $2/kg Penalty W3kg Penalty

O~~~~~~~~~~~~~ 10/ 

O 50 0 5c 0 50 -L so

OUTPU1 MW -

Fig. 4. Marginal and Average Operating Casts for the 50-MW Unit Including NOx Penalty

is increasing, and ihtersects the average cost curve creased, this is entirely due to a decrease in the

at its minimal point. output of the 225-MW units. The 50-MW units actually pick up load. Thus the decrease in NOx emissions from Generating schedules obtained at various levels the Tel Aviv Station is due to two factors: a de- of marginal cost -- using the composite marginal cost crease in station output and a shift in the loading

curves for the Tel Aviv units -- are shown in Table 3 from the larger units to the smaller units. and the corresponding NOx emissions are listed in

Table 4. By iterative calculation using small incre- INTERPRETATION OF RESULTS

ments in the value of the composite marginal cost, the

minimum-cost generator schedule is obtained for each The above case indicates how a reduction in local specified level of system output and each specified NOx emissions could be achieved by a change in genera- limit on NOx emission. tor dispatch schedules. As is generally true in such situations, each step in the reduction of emissions Assume, for example, that the scheduled system becomes increasingly expensive. In the first step output is 1200 MW. Emission of NOx from the Tel Aviv shown in Table 5 (from p = 0 to p = $1/kg NOx), the Station would be 707 kg/hour under regular economic emission rate is reduced by 103 kg NOx/hour. Fuel load dispatch with no NOx restriction. Emission de- cost is increased by $60/hour, which is equivalent to

creases, however, if a price is applied as follows: $0.58 per kg reduction in NOx emissions. In the rep EMISSION-- --- OUTPUT -------- maining three steps shown in Table 5, the correspond- s/kg NOx kg NOx/hour $/kg-NxkgNxhou Tel Aviv Avv Ashdod-Haifa A d -H a ing costs are, respectively, $1.01, $1.46 and $4.14, per kilogram reduction in NOx emissions. The complete 0 707 523 677 shift from the emission level with no NOx restrictions 1 604 489 711 to the minimal emissions that are shown in the last 2 533 460 740 column of Table 5, gives a 30% reduction in NOx emis- 3 496 443 757 sion from the Tel Aviv Station at a 4% increase in the

Thus, as the conversion or penalty factor increases total fuel expenditure for the power system. These

output is shifted from Tel Aviv to the Ashdod and results are similar to an example given in [1] for the Haifa Stations. When p reaches a value of $3/kg NOx, power system serving Los Angeles, California. There, AshdoAaffa and are practcaLi their full capa- '11'a switchover from economic load dispatch to a schedule andpuHafaromte paTclAvvSatthirn fullo capae for mninimum NOx emission leads to a 12.6% reduction in dcity outpurtheifro the tetlAvivstatio cannot beroe emission from the power stations at an increase of ductaiedmuhautheif0thM oalsseWotu.i 1.8% in total fuel costs. The degree of the reduction

is less in this example as it was achieved by shifts

Details on this shift in generator loading and on among generators according to their relative NOx emis- the esulingchane in NOxemisionsfro theTel sion rates, without the aid (as in the Tel Aviv examAvv Station are shown in Table 5. Although the total pl)oim rtn pwefom usdeheaa output of the Tel AYVi Station decreases as p is in-i

1362
Table 3. Minimum-cost Generator Schedules -- Regulated NOx Emissions

Composite Marginal Cost [mills/kWh] 4.0 4.6 5.2 5.6 8.0 10.0 15.0 20.0

(CAPACITY) (OUTPUT -- MEGAWATTS)

Ashdod and Haifa Units 760 304 439 635 693 745 755 760 760

Tel Aviv Units

CASE 1: p = $1/kg NOx

2 x 50 MW 100 40 40 40 40 95 96 100 100

2 x 225 MW 450 180 180 180 240 438 442 450 450

Tel Aviv Subtotal 550 220 220 220 280 533 538 550 550

SYSTEM TOTAL 1310 524 659 855 973 1278 1293 1310 1310

CASE 2: p = $2/kg NOx

2 x 50 MW 100 40 40 40 40 82 94 98 100

2 x 225 MW 450 180 180 180 180 320 420 445 450

Tel Aviv Subtotal 550 220 mY 22 m0 3TUT '513 To

SYSTEM TOTAL 1310 524 659 855 913 1147 1269 1303 1310

CASE 3: p = $3/kg NOx

2 x 50 MW 100 40 40 40 40 54 85 96 100

2 x 225 MW 450 180 180 180 180 200 316 438 448

Tel Aviv Subtotal 550 m 220 220 254 401 534 5

SYSTEM TOTAL 1310 524 659 855 913 999 1156 1294 1308

Table 4. NOx Emissions from Tel Aviv Station and Total System Output

versus Composite Marginal Cost

Composite Marginal Cost [mills/kWh] 4.0 4.2 4.6 5.2 5.6 8.0 10.0 15.0 20.0

BASE CASE (no NOx restrictions) (EMISSIONS -- kg NOx/hour)

2 x 50 MW 21 21 21 46 82 90 94 100 100

2 x 225 MW 122 500 628 636 638 642 676 676 676

1 43 521 649 682 m 732 770 776 776

Total System Output-- Megawatts 524 844 916 1139 1224 1281 1303 1310 1310

CASE 1: p = $1/kg NOx

2 x 50 MW 21 21 21 21 21 88 90 100 100

2 x 225 MW 122 122 122 122 206 636 646 676 676

143 143 143 143 227 724 736 776 776

Total System Output -- Megawatts 524 634 659 855 973 1278 1293 1310 1310

CASE 2: p = $2/kg NOx

2 x 50SMW 21 21 21 21 21 64 86 94 100

2 x 225 MW 122 122 122 122 122 352 578 660 676

1 43 143 14 14 143 -416 664 754 776

Total System Output -- Megawatts 524 634 659 855 913 1147 1269 1303 1310

CASE 3: p = $3/kg NOx

2 x 50 MW 21 21 21 21 21 30 68 90 100

2 x 225 MW 122 122 122 122 122 148 344 636 666

143 143 143 143 143 178 412 726 766

Total System Output -- Megawatts 524 634 659 855 913 999 1156 1294 1308

As was stated earlier, the generator schedules its upper or lower limits. For such generators, the

that are derived using a monetary conversion factor p composite marginal cost for the generator equals the X

are the schedules that achieve the minimum fuel cost for the system. If a generator is scheduled at its

for a given emission level. This can be seen because upper limit, its composite marginal cost will fall bethe method minimizes the composite cost, i.e., the sum low (or at most equal) the value of X. The differof the cost of the fuel and the NOx "penalty". To ence between the composite marginal cost and X equals

prove this, consider alternative schedules that lead the multiplier associated with the operating limit.

to the same emission but have different fuel costs. Like X, the multiplier has an economic interpretation.

Since the emission is the same, the penalty is the Whereas X is the increase in cost (mills/kWh) if the

same, and therefore the schedule that minimizes the system load is increased by one unit, the multiplier

composite operating cost also minimizes the fuel com- represents the decrease in operating cost if the capaponent of the operating cost. city of the generator could be increased by one unit.

The technique of minimizing the composite operat- INTERSYSTEM TRANSFERS

ing cost can be carried out in more formal notation by

applying the Kuhn-Tucker conditions.2'4'5 This is a In the transfer of power from one system to angeneralization of the Lagrange-multiplier method. The other, consider the utilities that purchase power. In

composite marginal cost is designated by A, the Lag- terms of the Israeli system, assume that Tel Aviv is a

range multiplier. The constraints, expressed as mne- separate corporate entity and that the Ashdod-Haifa

qualities, are the upper and lower operating limits of Corporation is willing to sell power to it. The Tel

the individual generators. Each of these operating Aviv load is 500 MW, and the sales price of the first

limits also has a "multiplier" associated with it, 2 MW block of power from the Ashdod-Haifa generators

which is zero in the cases where the constraint is not is 5.18 mills/kWh. The price of the second 2 MW block

binding, i .e., where the generator is not operating at is 5.28 mil1ls/kWh, with the pri ce i ncreasing 0.1 mill1s

1363
Table 5. Minimum-cost Generator Schedules for 1200-MW System Output

NOx Emissions at Tel Aviv Station, kg/hours

Two 50-MW Units 70 72 72 75 82

Two 225-MW Units 637 532 461 421 407

707 604 533 496 489

Generator Output, MW

Ashdod and Haifa

2 x 30 MW 24 27 48 59 60

3 x 50 MW 127 143 145 148 150

4 x 75 MW 287 295 299 300 300

2 x 125 MW 239 246 248 250 250

SUBTOTAL 677 711 740 757 760

Tel Aviv

2 x 50 MW 85 86 86 88 92

2 x 225 MW 438 403 374 355 348

TEL AVIV SUBTOTAL 523 489 460 443 44

SYSTEM TOTAL 1200 1200 1200 1200 1200

Composite Marginal Cost, mills/kWh 5.34 6.95 8.55 11.60 X

Conversion or Penalty Factor, $/kg NOx 0 1 2 3 X

System Operating Costs, $/hour

Fuel 5644 5704 5776 5830 5859

NOx penalty 0 532 1066 1488 X_

5644 6236 6842 7318 0

per kWh for each additional 2 MW. requirements of 500 MW and receives a request for

power from Ashdod-Haifa. The Tel Aviv generators are

If Tel Aviv operated without environmental re- producing 2 x 31 MW and 2 x 219 MW with a marginal

strictions, the output of the four generators would be fuel cost of 5.18 mills/kWh. At what price could the

2 x 31 MW and 2 x 219 MW; their marginal fuel cost power be sold?

would also be 5.18 mills/kWh, and there would be no

purchases from Ashdod-Haifa. The NOx emission would If Tel Aviv station was not subject to an NOx be 675 kg/hour. emission constraint, a sales price of 5.18 mills/kWh

for the first block of power would recover costs. If,

Assume that the environmental objective is to however, the Tel Aviv station were not permitted to

limit NOx emission from the Tel Aviv Station to 625 increase its output, it would be forced to shift power

kg/hour. This could be done by rescheduling the Tel from the 225-MW units to the 50-MW units as the aggreAviv units, i.e., by loading fully the 50-MW units and gate power output increased. The increment in cost

dropping back the output of the 225-MW units. Should would not be F' (which equals 5.18 mills/kWh), but

this be done, or should power be purchased from rather F' + pE', where p is chosen to satisfy the

Ashdod-Haifa? emission constraint. Inclusion of the factor pE'

would tend to inhibit transfer of power from Tel Aviv Minimal cost for the 500-MW load and the 625 kg to the Ashdod-Haifa system, i.e., it automatically NOx/hour emission occurs when the generator outputs distributes power production in the way that most

are 2 x 33 MW and 2 x 210 MW with 14 MW purchased from economically satisfies environmental objectives. Ashdod-Haifa. The composite marginal cost is 5.78

mills/kWh, i.e., CONCLUS IONS

F' + pE' = C' In the notation used in this paper, the rules for

50-MW units 5.20 + 0.58 = 5.78 optimal load dispatch for a system with n generators

225-MW units 4.23 + 1.55 = 5.78 are:

The value of p, the monetary conversion factor, is 1. For minimum cost, no emission constraint: $0.52/kg NOx. The solution was obtained by iterating Fi = Fl =

on C' and-p until the load and emission constraints

were satisfied. i.e., marginal fuel costs are equated.

This is the minimum-cost generating schedule that 2. For minimum emission, but not minimum cost:

meets the environmental objectives, and yet is should

be noted that the marginal fuel cost F' of 50-MW units E1 E2 = *.. nat does not equal that of the 225-MW units; furthermore, i.e., marginal emission rates are equated.

power is purchased from Ashdod-Haifa even though the 3. For minimum cost with emission constraint:

marginal fuel cost for the Tel Aviv generators is less

than the cost of the purchase -- and the Tel Aviv gen- Ci = C2 == C=

erators are not operating at their capacity limits

In other words, if the environmental objective is to i.e., composite marginal costs are equated. In

be achieved, the regular procedure for economic load this case,

dispatch based on equating marginal fuel costs cannot F' + pE' = F' + pE =

be applied.1 1 2 2 where the conversion factor p is selected so that

Next, consider uti1i ties that sel 1 power. For the emission constrai nt i s satisfied.

example, assume that Tel Aviv supplies its own power 4. For minimum cost with constraints on two types of

1364
emissions: Discussion

Fi + pEi + qGi = F2 + pEk + qG2 = ... H. H. Happ (General Electric Company, Schenectady, New York): The

where p is the conversion factor chosen to satisfy author has presented a good procedure for recognizing emissions in the

constraints on type E emissions and q is the con- dispatch of generators. The paper is clear and concise.

version factor to satisfy constraints on type G He may wise to expand upon his comments on the applicability of the method to Unit Commitment mentioned in the Abstract, since a emissions. number of factors besides dispatch enter into that function6. Any

actual power system experience with the method the author can relate,

Statement No. 4 can be readily generalized to or of the near term implementation being planned, would also be of

more than two types of emissions, but as the number of interest.

constraints in increased, the number of feasible alternatives decreases and the analysis becomes super- 6H.H. Happ, R.C. Johnson, W. J. Wright, "Large Scale Hydro-Thermal

fluous. Unit Commitment - Method and Results," IEEE Trans. on PAS, Vol. 90,No.3, 1971,pp. 1373-1384.

Statement No. 1 is a special case of No. 3 with Manuscript received February 4, 1974.

p = 0; statement No. 2 is a special case of No. 3 with

p = 00 In statement No. 3, p has the same value for

all generators if the environmental objective applies T. A. Green (Rockwell International, Anaheim, Ca.): The author has

only to their aggregate residual output. If, however, presented a very timely and practical technique for an extension of

from the environmental standpoint, it is more import- standard incremental loading practices to include "costs" of emissions

ant to control emissions from some generators than along with fuel cost in the scheduling and dispatching of electric power

from others, then p takes on separate values for the units.

individual generators. (In the first example, p was In the past, minimum emission dispatching has been labelled as a individu Alhogener Hatorsu.otfr eAi) means of avoiding the real problem of cleaning up the units themselves.

zero for Ashdod and Hai fa, but not for Tel Aviv) . While this is certainly desirable, the fuel crisis has forced utilities to

return to use of dirtier fuels. This situation has enhanced this author's

*As in regular economic load dispatch, the above contribution. The ability to blend the emissions costs with the normal

rules are subject to additional conditions. The sum fuel costs is quite innovative and sensible. This avoids the use of two

of the generator outputs must at least equal the spec- classes of dispatching and the need to switch between them. The ability

ified total system output, and in the process of equa- to single out individual or groups of units to constrain is also significant.

ting marginal costs, some generators may reach and re- It would also appear that in the case where taxes are assessed on

main at either their upper or lower limit of power effluents, that these taxes could be used to calculate the conversion

output. The difference between the marginal cost of factor or price penalty "p." Did the author consider if this could be

such generators such genrators adnd the mrginal margi nal cstost ofof geeratorsThe generators readily performed? invention of the price penalty conversion factor is the key to not at their output limits is a measure of the value the success of this approach. Has the author anticipated how he would

to the system of the generators capacity, i.e., it is iterate this quantity based on actual operating results in order to

the marginal amount by which system costs could be re- effectively constrain the real emissions? Would not this factor be

duced if the generator's output could be extended. "invented" differently if ground level buildup is used in place of stack

The conversion of environmental constraints. into emissions? Hopefully the approach would not be victimized by a highly

costs applies to each step in planning and operating a sensitive selection of yet another "turning factor" more dependent on

power system. It is readily applied to systems that "art"thenengineering.

contain ctransmissinhroele hydroelectricmuntst c units adndtontoysirems systemsTe mthodich in which dispatching, The fueloneshortage based has on minimizing stirred up concerns for yet another form of fuel or BTU use. Has the author transmi ssi on losses mus t be cons idered. The method is~ considered how this cost function would be combined with the need to

a useful concept in intersystem power transactions: control emissions?

for a company that intends to achieve stated environ- While the concern over emissions is well placed, this discussor

mental objectives, the correct figure to quote in such would not want to see the standing needs to provide adequate regulating

transactions is the composite marginal cost which in- margin6 and system regulation7 overlooked in extending established

cludes the factor pE' that converts environmental ob- techniques for control.

jectives into monetary terms.

[6] W.O. Stadlin, "Econimic Allocation of Regulating Margin", IEEE

Transaction Paper No. 7 1TP99-PWR, 1971.

REFERENCES [7] C. W. Ross, T. A. Green, "Dynamic Performance Evaluation of Computer-Controlled Electric Power System," IEEE Transaction

1. Gent, M.R., and Lamont, J.W., "Minimum-emission PaperNo.71TP593-PWR, 1971.

Dispatch", IEEE Transactions on Power Apparatus and ManuscriptreceivedFebruary 19, 1974.

Systems, November/December, 1971, PAS-90 (6): 2650-60.

2. Sullivan, R. L., "Mini mum Pollution Dispatching", R. L. Sullivan (University of Florida, Gainesville, Fla.): Professor Delson

Paper C 72 468-7 read at the 1972 IEEE Summer Power is to be commended for making a substantial thrust into a problem area

Meeting, 9-14 July, 1972, at San Francisco. that is certainly relevant in view of the concern by all segments of society for living the good life without creating a hostile environment.

3. Sul livan, R. L., and Hackett, D. F., "Air Quali ty The paper has clearly shown how through a simple monetary conversion

Control Using a Minimum Pollution Dispatching Algor- the problem of dispatching to satisfy NOx emission constraints can be .Cotr.l Using a Mngiriiu P

nd Idsptci ng lgor- formulated as a rather simple extension of economic dispatching. ri th", (mimeo) Engineering and Industrial Experiment The paper has addressed not only the single area problem but it

Station, University of Florida, 1973. has also shown that the controlled emission dispatching technique can

be used to assess the true cost to company A of selling power to

4. Kuhn, H.W., and Tucker, A.W., "Nonlinear Program- company B in light of NOx constraints. As Professor Delson points

ming", Proceedings of the Second Berkeley Symposium out, the technique could easily be extended to include any species of

on Mathematical Statistics and Probability, J. Neyman pollutant assuming emission rate curves of the form depicted in Fig. 1

(editor), Berkeley: University of California Press adequately describe the emission rate of the pollutant in question.

1951, pp. 481-92. In reviewing the paper only two questions appeared to reoccur,

and they are (1) how does one choose the penalty factor p to insure

5 . Tei chroew, D., "An Introducti on to Management Sci- that a certain NOx level will not be exceeded, and (2) would it not be

ence:Deterinistc Modls", ew Yok, Jon Wily and more important, in some cases, to dispatch units based on the ambient ence Deeriisi Moes"9e6Yr,JonWle4n air quality rather than emissions from power plants which are located Sos, In. 1964 some distance from the load centers? If Professor Delson would com-

- ~~~~~menton these two points it would be appreciated.

Manuscript received February 19, 1974.

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J. K. Delson. Briefly, the discussers raised the following questions: Incorporation of environmental controls into peratingprocedures

1) How to evaluate the monetary conversion factor "p". such as regulation of margin and unit commitment involves no change

2) How to iterate p to meet environmental restrictions. in the algorithms. All that is required is a generalization of the produc3) The effect of an actual tax in place of a monetary conversion tion cost to include the invented cost component associated with

factor. production of the detrimental residuals. The "art", if there is any, is not

4) How to incorporate- environmental objectives in operating pro- in the hands of the load dispatcher but rather in the hands of the public

cedures such as regulation of margin and commitment of units. and its authorities who must make the economic/environmental

5) The effect of controlled emission dispatch on fuel consumption. decisions.

6) Control of ambient (ground-level) concentrations. The rate of fuel consumption may either increase or decrease as a

7) Field experience. result of controlled emission dispatch. Control of oxides of sulfur

In standard economic dispatch routines, generator outputs are a increases cost but tends to reduce fuel consumption. On the other

function of the marginal cost X, and if this parameter is varied over a hand, control of NOx-by shifting load from new to older units-tends

broad enough range, the schedules will cover the range of possible to increase fuel consumption. If there is an acute fuel shortage, the

system outputs. An example is given in Table 1. When the marginal price of fuel would be expected to rise; in comparison, p would become

cost Xis varied in fine steps, many intermediate load levels are obtained. less significant and the remaining terms in the dispatch algorithm

This is the enumerative method. Another method to obtain a specified would minimize fuel consumption. Simply stated, to minimize fuel

aggregate output is to use an iterative method on a digital computer; a consumption, set p = 0.

third method is to use a feedback loop on an analog computer. Load shedding, as a means of meeting environmental objectives,

Enumeration, iteration, and feedback are applicable to controlled also fits into the framework of controlled emission dispatch. Just as in

emission dispatch, although there are at least two variables, X and p, intersystem transfers, a price must be used. For load shedding, this

because the objective is to satisfy at the lowest possible cost both load would be the cost assigned to the loss of each increment of load.

requirements and environmental restrictions. The enumerative approach Environmental control based on ground-level concentrations is

is illustrated in Tables 3 and 4. The results of an enumerative- complicated by the possibility that the measured values may result from

iterative approach are shown in Table 5. Here, values for the conversion a variety of sources. Effective control makes it necessary to identify the

factor p were enumerated, but iteration was used to obtain the specific contribution of the individual sources. A method for doing this is

value of 2X for an output of 1200 MW. In this example, calculated NOx outlined in references 2, 3.

emissions at the Tel Aviv Station decreased from 707 to 489 kg/hour. Some field experience on dispatch used for control of emissions

To obtain a speciflc emission between these two values, iterations could was brought up in the oral discussion'that took place when the paper

have been performed by adjusting the value of p, or an analog computer was presented at the PES Winter Meeting in New York. An East Coast

could have been utilized with two feedback loops. utility was ordered to restrict its SO2 emissions and complied by shutControlled emission dispatch does not become more complex if ting down units in order of their age (or, presemably, heat rates). This

environmental restrictions differ among generating units, even if a meant that average instead of incremental emission rates were the basis residual such as NOX is controlled in one district and another such as for dispatch-reminiscent of the early methods used for load dispatch. SO2 is controlled elsewhere. For control of two or more residuals at the Controlled emission dispatch would probably result in lower operating

same generating station, the theory remains straight-forward, but the cost. Nonlinear programming could also have been used, but such implementation becomes more complicated. A recent paper considers methods do not yield a value for the marginal cost and tend to become

the effect of a tax, similar to conversion factory, placed simultaneously cumbersome when extended to general operating problems.8

on emissions of NOx, SOx, and particulates. The result obtained is Please note a typographical error: the right-hand side of the first

that emissions of NOx decrease, but SOx and particulate emissions equation in "Control of NOx" should read $860/hour in place of

increase! Tax rates were assumed to be the same for each type of $890/hour. Also note that the University of the Negev has been residual; this is not a realistic assumption, but never mind. The welfare renamed the Ben Gurion University of the Negev.

of the community might best be served by trade-offs such as this - less

of one residual but more of another. This administrative decision would

be possible if the public authorities determine the conversion factors or REFERENCES

tax rates for each type of residual.

There are at least two differences an actual tax would have in [6] Lamont, J. W., and Gent, M. R., "Environmentally-Oriented

comparison to regulations that place physical limits on residuals. First, Dispatching Techniques", presented at the Eighth IEEE Power

the load dispatcher would receive values for the monetary conversion Industry Computer Application Conference, Minneapolis, Minn.,

factors from the public authorities, so that he would have only one June 4-6, 1973.

parameter (X) to vary, just as in standard economic dispatch. If the [71 Kneese, A. V., and Bower, B. T., Managing Water Quality:

resulting control of residuals were not satisfactory, the public Economics, Technology, Institutions, Baltimore: The Johns Hopauthorities-not the load dispatcher-would adjust the price. Secondly, kins Press, 1968.

the added tax burden would give the utility another incentive to [81 Finnigan, 0. E., and Fouad, A. A., "Economic Dispatch with

develop quickly the technology for control of residuals. Such taxes or Pollution Constraints". Paper C 74 155-8 presented at the IEEE

"effluent charges" have proved to be effective incentives for cleaning up Power Engineering Society Winter Meeting, New York, January rivers.7 27-February 1, 1974.

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