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 re

### operating 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 

### appro

### priate 

## 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) X lg 

### 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 en

### vironmental 

### 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 andapprovedby the IEEE Power System Fig. 1. NOx Emissions from the 50-MW and 225-MW Engineering Committee ofthe IEEEPowerEngineeringSocietyforpresentationat Uni t the IEEE PES Winter Meeting, New York, N.Y., January 27-February 1, 1974. Manuscript submitted September 5, 1973; made available for printingNovember
16, 1973.

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

1359CONTROL 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

G

### RAM/

### kWhM 

### MILL/kWh



# ° 1- , , , 

# ,~~~ , 

# I' I 

# 'iI 300 

### 50 mw 

## 0061 50200

l-~~~~~~~ 30MW MW



### 30x0 

### M150M 605M

### 60 6 

### 0 6 0 8 

### 3 4 4 5 5 

### 2 125MW 

### 2M25M 

### 2 25 L5

Lii

SUBOTA 

### 46 L0 6 u44 U 7 U 4 5 6 6I100

- 

### AVERAGE FUEL 

### RATE2

MARGINAL 

### (INCREMENTAL) FUEL RATE

Te 

# 0vv(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 (no

emission limit)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1 A e n '

### 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)($20/106g) (200xlO

### 3kW) = 

### $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 taking the slope o

### f 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 Aviv 

# cunts Ther

nw 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 E are written C', F' and E' in the third equation. 24 l 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 W 

### 3kg 

### 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 Aviv 

### Ashdod-Haifa ing costs are, respectively, 

### $1.01, $1.46 and $4.14,



## $/kg-Nx kgNxhou Tel Avv A d -H a 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, Ashdo and Aaffa are practcaLi their full capa- '11'a 

## switchover from economic 

### load dispatch to a 

### schedule 

## andpu 

# Hafaromte paTcl



# AvvSatthirn fullo capae for 

# mninimum NOx 

### emission leads to a 

### 12.6% 

### reduction in 

# dcity 

# outpurthe ifro the

# tetl 

# Avivstatio cannot be

# roe emission from the power 

### stations at an 

### increase of 

## ductaied muhauthe 

## if0 thM 

# 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 exam

### Avv 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 1362Table 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 0 

### m 

### 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 

### 143 521 649 682 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 50 SMW 21 21 21 21 21 64 86 94 100 2 x 225 MW 122 122 122 122 122 352 578 660 676 143 

### 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 be

### the 

### method minimizes the 

### composite cost, 

### i.e., the sum low 

### (or at most 

### equal) the value of X. The differ

### of 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 price increasing 0.1 

### mill1s 1363Table 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., CONCLUSIONS



### 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 2 E * = .. 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 

### uti1ities that sel1 power. For the emission constraint is satisfied

. example, assume that Tel Aviv supplies its own power 4. For minimum cost with constraints on two types of
1364emissions: Discussion



## Fi + 

## pEi +

## qGi = F2 + 

### pEk + qG2 = ... H. H. Happ (General ElectricCompany, Schenectady, NewYork): The where p is the conversion factor chosen to 

### satisfy authorhas presented agoodprocedureforrecognizingemissionsinthe constraints on type E 

### emissions and q is the con- 

### dispatchof

### generators. Thepaperisclearandconcise. version factor to 

### satisfy constraints on 

### type G He maywisetoexpanduponhis comments ontheapplicabilityof the method to Unit Commitment mentioned in theAbstract, since a emissions. number of factors besides dispatch enter into that function6. Any actual power system experiencewiththemethodtheauthorcanrelate, Statement No. 4 can be readily 

### generalized to or of the near term implementation being planned, wouldalsobe of more than two types of 

### emissions, but as the number of interest. 

### constraints in 

### increased, the number of feasible al

### ternatives decreases and the 

### analysis becomes super- 6H.H. Happ, R.C. Johnson, W. J. Wright, "LargeScaleHydro-Thermal fluous. Unit Commitment

- MethodandResults," IEEETrans. onPAS, Vol. 

### 90,No.3, 

### 1971,pp. 1373-1384. Statement No. 

### 1 is a special case of No. 3 with ManuscriptreceivedFebruary4, 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 authorhas 

### 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 loadingpractices to include "costs" ofemissions ant to 

### control emissions from some generators 

### than alongwith fuel costinthe schedulinganddispatchingofelectricpower from 

### others, then p 

### takes on separate 

### values for 

### the units. 

### individual 

### generators. 

### (In the first 

### example, p was Inthe past, minimum emissiondispatchinghasbeen labelled asa individu

# Alho gener

# Hatorsu.otfr eAi) means of

### avoidingthereal

### problemof

### cleaninguptheunitsthemselves. zero for Ashdod and 

### Haifa, but not for Tel Aviv)

. While this is certainly 

### desirable, the fuel crisis has forced utilities to return to use ofdirtier fuels. This situation has enhancedthisauthor's 

### *As in regular economic load 

### dispatch, the above contribution. The abilitytoblend the emissions costswiththenormal rules are 

### subject to 

### additional conditions. The sum fuel costs is quite innovative and sensible. This avoids theuse oftwo of the generator 

### outputs must at 

### least 

### equal the spec- classes of

### dispatchingandtheneedtoswitchbetweenthem. Theability 

### ified total system output, 

### and in the process of equa- tosingleoutindividualorgroupsofunitsto constrainisalsosignificant. 

### 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 considerifthis couldbe such generators nd the marginal ost of generators readilyperformed?



### such

### genrators ad 

## mrginal cst of 

## geeratorsThe invention of the

### pricepenalty conversionfactoristhe

### keyto not at 

### their output 

### limits is a measure of 

### the value the 

### success of this 

### approach. Has theauthoranticipatedhowhewould 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

### groundlevelbuildup isused inplaceofstack The conversion 

### of 

### environmental 

### constraints. into emissions? 

### Hopefullythe

### approachwouldnotbevictimized

### bya

### highly costs 

### applies to 

### each step in 

### planning and 

### operating a sensitive selectionofyet another 

### "turning factor" more dependenton power system. It is readily applied to systems that "art"thenengineering. 

### contain hydroelectric units 

### nd to systems in 

### which The fuel shortage has stirredup 

### concerns foryetanotherformof 

### ctransmissin hroele c 

## muntst ad 

## ton ysirems Te 

## mthodich dispatching, onebased onminimizing fuel orBTUuse. Hastheauthor transmission losses must be considered. The method 

# is~ considered how this cost functionwouldbe combinedwiththeneedto 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 wouldnotwanttosee the standingneedstoprovideadequateregulating 

### 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, "EconimicAllocation ofRegulatingMargin", IEEE TransactionPaperNo. 71TP99-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., "Minimum 

### Pollution 

### Dispatching", R. L. Sullivan

### (UniversityofFlorida,

### Gainesville,Fla.): ProfessorDelson Paper C 72 468-7 

### read at 

### the 1972 IEEE Summer Power istobecommendedformakingasubstantialthrustinto aproblemarea 

### 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 ahostileenvironment. 3. 

### Sul

### livan, R.

### L., and 

### Hackett, D.

### F., "Air 

### Quality Thepaperhasclearlyshownhowthroughasimplemonetary conversion 

### Control 

### Using a 

### Minimum Pollution 

### Dispatching Algor- the

### problem of

### dispatching to

### satisfyNOx emissionconstraints canbe 

# .Cotr.l Using a

# Mngiriiu P 

### nd

# Idsptci ng l

# gor- formulated as a rather simple extension of economic dispatching. ri

### th", (mimeo) Engineering and Industrial Experiment The paper has addressed not onlythe single areaproblembut 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

### easilybe extended to include anyspecies of on 

### Mathematical Statistics 

### and 

### Probability, J. 

### Neyman pollutant 

### assuming emission ratecurvesofthe form

### depictedin

### 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 appearedtoreoccur, and they are (1) how does one choose the penalty factorp to insure 5

. Teichroew, D., "An Introduction to Management 

### Sci- that a certainNOx level will not be exceeded, and (2) woulditnotbe ence:Deterinistc Modls", ew Yok, Jon Wily and more

## important, insomecases,todispatchunitsbasedontheambient 

# ence Deeriisi 

# Moes"9e6Yr,JonWle4n air

# quality rather than emissions frompowerplants which are located 

### Sos, In. 1964 some distance from the load centers? IfProfessor Delson would com-

- 

### ~~~~~mentonthese twopointsitwouldbe appreciated. Manuscript receivedFebruary 19, 1974.
1365J. K. Delson. Briefly, the discussers raised the following questions: Incorporationofenvironmentalcontrolsinto peratingprocedures

1) Howtoevaluatethemonetaryconversionfactor

### "p". such as regulation ofmargin and unit commitment involves nochange 2) Howtoiteratep tomeet environmental restrictions. in the algorithms. All that is requiredisageneralizationoftheproduc3) The effect of an actual tax in place of a monetary conversion tion cost to include the invented cost component associated with factor. productionofthedetrimentalresiduals. The

### "art",ifthereisany, isnot 4) How to incorporate- environmental objectives in operating pro- inthehandsoftheload

### dispatcherbutratherinthehandsofthe

### 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) Controlofambient (ground-level) concentrations. The rate offuel consumption may eitherincreaseordecreaseasa 7) Fieldexperience. result of controlled emission dispatch. Control of oxides of sulfur In standard economic dispatch routines, generatoroutputs are a increases cost but tends to reduce fuel consumption. On the other function of themarginal cost X, and ifthis parameter isvaried over a hand, control of

### NOx-by shifting load fromnewtoolderunits-tends broad enough range, the schedules will cover the range ofpossible to increase fuel consumption. If there is an acute fuel shortage, the system outputs. An example is given in Table 1. When the 

### marginal priceoffuelwouldbeexpectedtorise; incomparison, pwouldbecome costXisvariedinfine steps,manyintermediate loadlevels areobtained. less significant and the remaining terms in the dispatch algorithm This is the enumerative method. Anothermethodtoobtain a

### specified would minimize fuel consumption. Simply stated, to minimize fuel aggregate output is to use an iterative method onadigital computer; a consumption, setp = 0. third method is to use a feedback loop on an 

### analog computer. Load shedding, as a means ofmeeting environmental objectives, Enumeration, iteration, and feedback are applicable to controlled also fits into the framework of controlled emissiondispatch. Justasin emission dispatch, although there are at least two

### variables, X andp, intersystem transfers, a price must be used. For load shedding, this because the objective is to 

### satisfy at thelowest

### possible costbothload would be the cost assigned to the loss of each increment of load. requirementsandenvironmentalrestrictions.The enumerative approach Environmental control based on ground-level concentrations is is illustrated in Tables 3 and 4. The results of an enumerative- complicatedbythepossibilitythatthemeasuredvaluesmayresult from iterative approachare showninTable 5.Here, values fortheconversion avarietyofsources. Effectivecontrolmakesitnecessarytoidentifythe factorp were enumerated, butiterationwasusedtoobtainthe

### specific contribution of the individual sources. A method for doing this is value of2X for an output of 1200MW. Inthisexample, calculatedNOx outlinedinreferences2, 3. emissions at the TelAviv Station decreased from 707 to 489

### kg/hour. Some field experience on dispatchused for control ofemissions Toobtainaspeciflcemissionbetweenthese twovalues, iterationscould was brought up in the oral discussion'that tookplace when the paper havebeenperformedby

### adjustingthevalueofp, oran

### analogcomputer was presented at the PES WinterMeeting inNewYork. AnEastCoast couldhavebeenutilizedwithtwofeedback

### loops. utilitywas ordered to restrict its 

### SO2 emissionsand compliedbyshutControlled emission dispatch does not become more complex if ting down units in orderoftheirage (or, presemably, heatrates). This environmental restrictions differ among generating 

### units, even if a meant that average instead ofincremental emissionrateswerethebasis residual such as

### NOX is controlled in one district and another such as fordispatch-reminiscent ofthe earlymethods used for loaddispatch. 

### SO2 iscontrolledelsewhere. Forcontroloftwo ormoreresidualsatthe Controlled emission dispatchwould probably result inloweroperating 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 avalue forthemarginalcostandtendtobecome theeffectofatax, similarto conversion

### factory, placed

### simultaneously cumbersomewhenextendedtogeneraloperating

### problems.8 on emissions of

### NOx, SOx, and particulates. The result obtained is Please note a typographical error: the right-hand side ofthe 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 arealistic assumption, but nevermind. Thewelfare renamedtheBenGurionUniversityoftheNegev. of the communitymightbestbeserved

### bytrade-offssuchasthis

- less ofoneresidualbutmoreofanother. Thisadministrativedecisionwould be possible ifthepublicauthoritiesdeterminethe conversionfactorsor REFERENCES taxratesforeachtypeofresidual. 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 onresiduals. 

### First, Dispatching Techniques", presented at the Eighth IEEE Power the load dispatcher would receive values for the monetary conversion Industry ComputerApplication Conference, Minneapolis, Minn., factors from the public authorities, so that he would have 

### only one June4-6, 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, kinsPress, 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 ofresiduals. Such taxes or Pollution Constraints". Paper C 74 155-8 presented at the IEEE "effluent

### charges"haveprovedtobeeffectiveincentivesfor

### cleaningup Power Engineering Society WinterMeeting, New York, January 

### rivers.7 27-February 1, 1974.

1366