### MINIMUM-EMISSION DISPATCH

M. R. Gent Dept. of Water and Power City 

### of Los 

### Angeles 

### John 

### Wm. Lamont 

### Univ. of So. 

### California Los 

### Angeles, Calif.

Abstract-A program has been developed for on-line steam unit dispatch that results in the minimizing of Nitrogen Oxide emissions. A unique mathematical representation of the steam generating units coupled with a Newton-Raphson 

### convergence technique for 

### dispatch produces base points and participation factors for any load level and any unit configuration. Emission reductions and corresponding cost increasesare compared to standardeconomic dispatch.

INTRODUCTION Economy dispatch is defined as supplementary regulation applied to the speed governors of the generators 

### operating within a controlled system for the purpose of allocating generation changes on an optimum economy basis.1 Minimum emission dispatch is a similar type of supplementary regulation used to minimize the total 

### stack emission of nitrous oxides for the entire power system. Although this supplementary regulation may be controlled either manually or automatically, this paper presents the logic used in an actual program to control unit loading automatically and compares results 

### obtained by minimum emission dispatch (MED) andeconomic dispatch (ED). Since the beginning of the free enterprise system, manhasalways tried to maximize his profits while reducing his 

### expenses. Prior to 1940, most utilities tried to minimize cost by 

### supplying light 

### loads from the most efficient plant or plants.2 Power to meet increasing system load was supplied by the most 

### efficient plant until that 

### plant reached its point of maximum efficiency. Further 

### increases in 

### system load were suppliedbythenextmost efficient plant ina similarmanner; each plant was added in terms of its efficiency. When 

### it was 

### finally accepted that this method failed tominimize cost, theuse ofthe incremental fuel cost method was 

### developed and put 

### into use. This 

### second method also 

### had its 

### shortcomings for most 

### power systems, since transmission losses were 

### neglected.3 4 In 1943, E. E. George produced a paper which presented a transmission-loss formula including transmission losses as 

### function of the powers of the 

### individual sources. Since then, many distinguished personnel from the 

### power industry have written numerous papers pertaining to 

### economic dispatch and 

### penalty 

### factors.5'6'7'8 In the past few 

### years the 

### power 

### industry has been 

### shocked by 

### that element of society 

### referred to as 

### "ecologists". At first, 

### there was 

### emphasis on 

### beautification, both 

### underground, and overhead, followedby the

### multitude of

### arguments against nuclearplant sites. All of these objections to 

### power system facilities have been 

### well founded; however, no public outcry has ever been as loud or as justified as the plea 

### for clean 

### air. For 

### example, a

### numberof

### utilities have been 

### temporarily thwarted in their

### attemptstobuild

### muchneeded thermal fossil fuel generating stations. Minimum 

### cost can 

### no longer be the goal of 

### operation if 

### society is to continue to exist. Many 

### organizati-ons, including the utilities, realize the necessity of cleaning up our environment as evidenced by the planned 

### phase-out of coal as a steam plant fuel and the regulatory agencies' insistence on the burning of low-sulfur fuel oil. Minimum emission dispatching is one method which all powerutilities havewithin theirgrasp to

### help fight the battle 

### against air

### pollution.
Paper 71 C 26-PWR-I-A, recommended and approved by the Power System Engineering Committee of the IEEE Power Group for presentation at the 1971 PICA Conference, Boston, Mass., May 24-26, 1971. Manuscript submitted January 13, 1971; made available forprintingJune 9, 1971. 

### ECONOMICDISPATCH Based on 

### the results of 

### studies,. the 

### Los Angeles Department. of Water and 

### Power (DWP) 

### concluded that 

### for an 

### interim 

### period transmission losses could be neglected without 

### introducing significant error into its dispatch calculations. Hence, 

### economic dispatching (ED) is done 

### based on the 

### solution of the 

### familiar equation: 2,3 

# dFn = dPn 

# SN (1) where Fn= 

### input to

### plant nindollarsperhour 

### Pn=

### output from

### plantn

### inmegawatts X = 

### incremental cost of received power in dollars per

### megawatthour 

### subject tothe

### followingconstraint: 

### k 

### p

- 0 

### (2) £ n - 

## PR °(2 n=1 

### where 

## PR = total power received by the 

### loads connected to the 

### trans- mission 

### system. 

### Thus, economic 

### dispatch is achieved 

### by solving a set of non

### linear 

### equations in such a manner that the total cost is minimized 

### for a 

### particular system load. The 

### representation of the individual 

### generatorsis

### discussedin alatersection.

MINIMUMEMISSION Minimum emission 

### dispatching (MED) may be 

### required by governmental 

### and 

### regulatory agencies in 

### the near future to control and 

### reduce air 

### pollution. 

### Many factors determine how power 

### plants contribute to air 

### pollution. The 

### following factors should be included:9
1. 

### Type and

### grade of fossil fuel

### employed. 2. 

### Proximityof

### plant sitesto

### heavily

### populated areas. 3. 

### General

### topographyand

### geographyof area. 

### 4. 

### Prevailingclimate and

### meteorological conditions. 5. 

### Proximity and 

### number 

### ofotherindustries inrelation topower 

### plant sites. 6. Concentration 

### of power 

### plants in any 

### given urban area or 

### city district.
For some or all of the above 

### factors, regulatory agencies, including the Air Pollution Control District of Los 

### Angles County (APCD), 

### might decide to limit 

### power 

### plant stack emissions in certain areas whichhave

### high concentrations 

### of contaminants. 

### MED may be 

### accomplished by substituting a different set of 

### generator 

### representations into the economic 

## dispatch program. The 

### MED 

### generator 

### equations for each unit are functions ofnitrous oxides 

### (NOX) versus 

### megawatt

### output, instead of 

### input (cost of

### Btu's) versus 

### megawatt 

### output for ED. The 

### normal minimum emission program minimizes the total 

### system 

### output of

### NOX for a

### given system load. As one 

### mightsuspect, however, while the sum 

### of 

### 'the 

### parts is 

### minimized, each 

### part is not 

### necessarily minimized. 

### Using the normal condition 

### (ED) as 

### base, it is 2650quite natural that, while thetotalnumberoftonsofNOXemittedinto

the atmosphere is less while on MED, the individual 

### plant's participation in 

### the total 

### pollution may have 

### increased. Forvarious reasons, it may 

### be 

### desirable to limit a

### particularplant or

### plants to a

### maximum percent increase over

### ED. 

### A second program 

### (MEDPC) has been 

### developed which limits the total stack emission from any plant to a given precent- increase, overthe

### normal EDemissionlevel. 

### TheMEDPCprogramoperates inthe followingmanner: 1. Foragiven systemloadtheEDprogramissolved. 2. TheNOXemissionforeachplantiscalculated. 

### 3. For any plant whose NOX emission is to be limited during MED, the megawatt output which wouldproducethemaximumallowable 

### NOX emission is calculated. The new unit maximum load is the smaller value 

### of the number just calculated forallowableNOXandthe maximumunitrating. 

### 4. The 

### MED program is then solved for the same 

### given system 

### load using the new unit maximum calculated in the previous step. 

### GENERATOR REPRESENTATION All 

### of the 

### Department's steam-fired units have been tested at 

### 25%, 50%, 75%, and 

### 100% of rated load to determine the Btu input 

### and NOX emission at these levels of load. The results 

### from one of 

### theNOXemissiontestsis showninFigure 1 in the Appendix. 

### Mathematically, these curves 

### of NOX output in 

### Tons/Hour as a 

### function of Net Output in megawatts have been represented by 

### the equation 

### Y = 

## Al + 

### A2X + 

### A3e 

### A4X +A5eA6X, (3) which is a combination of a straight line and two exponentials. Because of the limited number of data points, equation 3 has been re

### duced to 

### Y = 

## A1 + 

### A2X + 

## A3Ae (4)
The 

### functional 

### relationship thus described between NOX output 

### and net power output for each generator unit is substituted in the 

### dispatching program to achieve MED; whereas the customary Btu input-megawatt output function of the same form is usedby the 

### dispatchingprogramtoachieveED. The 

### development ofthe

### coefficients

### A1, A2, A3 andA4 

### foreither 

### minimum emission 

### dispatch or economic 

### dispatch isa

### relativelysimple procedure. A flow chart 

### (Figure 2) andbrief 

### explanation of the solution

### procedurehavebeenincludedasanAppendix. It is 

### the opinion 

### of the 

### authors that this 

### function (Eq. 

### 4), when usedtorepresent 

### eachunit, has

### several advantages, including: 1. 

### The

### functionis

### monotonicallyincreasing. 

### 2. It 

### eliminates the 

### inaccuracies and 

### cumbersome 

### calculations 

### required of 

### straight-line segments. 3. 

### Unlike a 

### polynomial, all 

### derivatives exist. 

### 4. Most 

### importantly, it appears to 

### be the truest 

### and most accurate

### representation.



### THECOMPUTER

### SYSTEM The 

### ED-MED program is 

### presently being utilized in a quasi online state 

### by 

### the DWP Load Dispatch Headquarters. DWP ispresently 

### converting 

### from the 

### Leeds and 

### Northrup Load Frequency Control 

### Equipment, described in Reference 5, to an all-digital system which 

### includes two on-line IBM 1800 process control computers 

### interconnected with an IBM 

### 360/65. Automatic execution of the program 

### will occur when a change is made in unit configuration, unit 

### minimumormaximumlimits, fueltypeorfuelprice. Presently, a combination of the two systems is in use. Two 

### CRT's (IBM 

### 2250's) are located in the immediate proximity of the dispatcher through which he initiates the execution of the program. The primary 

### IBM 1800 accepts 

### the data supplied through the 

### CRT (such as a 

### unit 

### change) by the 

### dispatcher. Changes are 

### made by the use 

### of a 

### light pen on the 

### input 

### display shown in 

### Figure 4 of the Appendix. The 

### input data 

### is then 

### transmitted to the IBM 

### 360 over a 

### 5000 foot underground communication line. An immediate interrupt occurs 

### within the IBM 

### 360, resulting in the execution of the 

### ED-MED program, 

### Upon 

### completion, the 

### results are 

### returned to 

### the initiating 

### IBM 

### 1800 and 

### displayed on 

### the CRT for the 

### dispatcher. Figures 5 and 6 are 

### actual copies 

### ofthe

### displays

### containingthe

### results. Until such time as the 

### IBM 

### 1800's assume 

### the 

### complete role, it is necessary 

### for the 

### dispatcher to 

### transfer the results to 

### the 

### L&N Analog equipment. In order to prevent error 

### and for 

### convenience, a 

### "copy" feature has been 

### included that 

### provides a 

### "hard 

### copy" on a 

### temporarily 

### installed printer. This 

### function is 

### activated 

### by lightpenning 

### "COPY" as 

### shown on the 

### displays 

### (Figures 5 

### and 

### 6).
THE 

### PROGRAM The basic computer program can be 

### coded in 

### 60-100 statements in either 

### PL/l or Fortran. 

### As with most 

### operational programs, the core 

### requirement is 

### largely a function of the 

### Input/Output. The flow chart is 

### shown as Figure 3. In most 

### applications a 

### comparison of

### ED versus 

### MED isdesirable as output. 

### For

### dispatching purposes it is 

### also necessary to

### have

### output for an 

### Economy 

### Energy quote. 

### Such an

### output 

### featuring incremental and 

### decremental costs for 100 

### MW increments is 

### shown as a

### display in

### Figure 7. The mechanics 

### of the program are such 

### that an 

### input 

### key is examined to determine whether 

### ED, MED or

### both are 

### desired. The ED output is 

### always 

### generated first, if both are 

### required, and then the generator 

### coefficients and necessary 

### variables are 

### loaded to 

### perform the MED 

### dispatch. MEDPC, as 

### previously indicated, requires prior execution

### ofED. Execution time 

### of the 

### Load 

### Dispatcher's version

### varies with 

### the 

### availability of the 

### IBM 

### 360/65 but averages to 

### about 

### 30 seconds from CRT 

### input to 

### CRT output. 

### Actual 360 CPU time is 

### 3.5 seconds de

### pending on the 

### particular unit 

### configuration and

### possible unit 

### loading limitations. 

### PRODUCTION 

### PLANNING Presently, steam units are 

### committed to service 

### based upon the 

### daily spinning reserve 

### requirements and 

## economics.10 Eventually, it is 

### anticipated that 

### agencies 

### will require units to be 

### deployed on a minimum emission basis 

### (either MED or

### MEDPC) as 

### opposed to 

### the present 

### economic 

### basis. Preliminary 

### investigations from a 

### computer program

### being

### developed indicate

### little, ifany

### changes, willbe

### required in

### commitment

### priortyscheduleofunits. 

### Nearly all of the programs 

### using 

### dispatch techniques have been modified to handle 

### MED. 

### All production 

### planning and 

### fuel-use studies 

### require comparisons of the two 

### methods of 

### dispatch and the 

### results to 

### indicate 

### effective reductions and 

### increased costs 

### of operation.


### COMPARISON OF 

### DISPATCHING METHODS
To 

### show how emissions of 

### NOX are reduced and costs are in

### creased, four examples were 

### preparedincorporatingaparticularconfiguration 

### of DWP steam units. For the example, only steam load is 

### required and no 

### particular attention is given to hydrothermal coord

### ination. 

### Daily steam 

### load patterns 

### consisting of 

### twenty-four values were studied 

### forthe following four cases: 1. 

### Typical summer

### peakload

### day. 2651TABLE I. COMPARISON OF MINIMUM EMISSION DISPATCH AND ECONOMIC DISPATCH

MWHRS 

### PLANT ED 

### MEDPC* NED HARBOR 

### 588 991 

### 887 VALIEY 

### 6,704 7,816 11,834 

### SCALTERGOOD 

### 5,383 6,540 5,680 HAYNES 35,951 33,279 30,225 TOTAL 

### 48,626 48,626 48,626 NET 

### DIFFERENCE PER CENT DIFF. TYPICAL SUMER PEAK LOAD DAY TONS OF NOX MEGABTUS ED MEDPC* NED ED NEDPC* 

### ED 0.86 1.57 1.34 7,257 11,160 10,121 

### 6.56 7.88 12.72 

### 67,260 77,594 

### 117,718 5.30 

### 7.84 5.92 

### 50,210 

### 60,984 52,948 

### 47.57 39.20 32.71 

### 313,173 290,629 265,012 

### 60.29 56.49 52.69 437,900 

### 440,367 445,799 -3.80 -7.60 +2,467 +7,899 

### -6.30 -12.61 + 

### 0.56 + 

### 1.80 COST IN DOLLARS ED MEDPC* NED 

### 2,413.65 3,711.73 

### 3,366.23 22,370.12 25,807.20 

### 39,151.66 16,699.07 20,282.44 17,609.68 

### 104,157.40 96,659.55 88,140.09 

### 145,640.24 146,460.92 148,267.66



### +820.68 +2,627.42

+ 

### 0.56 + 

### 1.80

PLANT ED 

### HARBOR-- 513 

### VALLEY 

## 4,948 SCATTERGOOD 

### 4,026 HAYNES 

### 32,644 

### TOTAL 

### 42,131 NET 

### DIFFERENCE PER CENT 

### DIFF.



### PLANT ED 

### HARBOR 

### 488 

### VALLEY 4,288 SCATTERGOOD 

### 3,416 HAYNES 

### 27,361 TOTAL 

### 35,553 NET 

### DIFFERENCE PER CENT 

### DIFF.

PLANT ED 

### HARBOR 

### 480 

### VALLEY 

### 3,36o SCATTERGOOD 1,920 

### HAYNES 

### 17,567 TOTAL 

### 23,327 NET 

### DIFETRENCE PER CENT 

### DIFF. MWHRS

MEDPC* MED 

### 877 755 

## 5906 

## 10,862 5,592 

### 4,680 29,756 25,834 42,131 42,131

MWHRS 

### NEDPC* NED 

## 749 

## 656 5,030 

### 8,880 

### 4,530 3,846 

### 25,244 22,171 

### 35,553 

### 35,553

MWRS NEDPC* MED 527 

### 499 

### 3,680 4,742 2,794 2,622 

### 16,326 

### 15,464 23,327 23,327 ED



### 0.77 

## 4.7 3.28 40.33 

### 49.12

ED 

### 0.75 

### 4.08 2.46 32.02 39.31 TYPICAL SUMNER MIIMUM LOAD DAY TONS OF NOX 

### MEGABTUS MEDPC* NED ED NEDPC* NED 

### 1.32 1.10 

### 6,546 10,023 

### 8,830 5.70 

### 11.16 51,436 

### 6o,054 108,088 3 5.74 

### 4.02 38,200 52,126 43,868 

### 331.84 24.84 

### 284,006 261,011 

### 228,257 ?44.6o 

### 41.12 380,188 

### 383,214 

## 389,,043 -4.52 -8.00 +3,026 

### +8,855 -9.20 

### -16.29 + 

### 0.80 + 2.33

TYPICAL WINTER PEAK LOAD DAY 

### TONS OF NOX 

### NEGABTUS 

### MEDPC* NMED ED 

### NEDPC* 1.11 

### 0.95 6,342 8,795 

## 4.78 

## 8.94 45,594 52,200 4.o8 2.88 

### 32,864 42,664 

### 25.09 19.93 

### 239,896 223,676 a 

### L35.o6 32.70 

### 324,696 327,335 

### -4.25 -6.61 +2,639 -lo.81 -16.82 + 

### 0.81 MED 

### 7,892 

### 89,356 36,566 198,094 

### 331,908 +7,212

+ 

### 2.22

TYPICAL 

### WINTER MNIMM LOAD DAY 

### TONS OF 

### NOX MEGABTUS ED 

### MEDPC* 

### NED ED 

### MEDPC* NED 

### 0.74 0.79 

### 0.76 6,272 6,696 

### 6,44o 3.26 

### 3.54 

### 4.52 37,516 

### 4o,346 50,050 

### 1.02 

### 1.68 

### i.48 20,024 

### 27,472 25,988 

### 17.33 

### 13.62 12.29 

### 158,962 

### 149,944 142,786 22.35 19.63 

### 19.05 

### 222,774 224,458 225,264 -2. 72 

### -3.30 +1,684 

### +2,490 

### -12.17 -14.77 + 

### 0.76 + 1.12 COST IN DOLLA ED NEDPC* 2,183.21 3,333.62 17,107.42 

### 19,972.76 

### 12,704.76 17,336.60 

### 94,456.27 86,809.05 126,451.66 127,452.03



### +1,000.37

+ 0.79

ED 

### 2,109. 

### 15,164.( 10,930. 

### 79,786.: 107,989.'

ED 

### 2,085.E 12,477.C 

### 6,659.( 52,869.: 74,091. LS



### 3'1 71 12C

+r

COST IN DOILARS 

### NEDPC* 25 

### 2,925.08 02 

### 17,361.58 2c 

### 34 14,189.68 1i 

### 17 

### 74,391.95 6r 

### 78 108,868.29 llC

+ 

### 878.51 +'

+ 

### 0.81 +



### COST IN 

### DOLLARS NEDPC* 

### 38 

### 2,226.88 2 20 

### 13,418.22 1( 

### 62 9,136.84 E 11 

### 49,869.60 

### 47 31 

### 74,651.54 71

+ 

### 559.73 4

+ 

### 0.76 4 NED

2

### ,936.89 5,948.82 

### 4,589.82 5,915.42 

## 9,390.95 2,939.29 2.32



### NED 

### 2,624. 

### 71 

### 9,718, 70 

### 2,161.16 

### 5,883.26 

### 0,387.83 2,398.05 

### 2.22

NED 2 

### 8141.o 6,645.90 

### 8,643.60 7,488.59 

## 4,919.89

+ 

### 828.08

+ 

### 1.12

*NOTE: VALLEY PLANT is limited to a 

## 20% increase in 

### NOX Emission under Minimum Emission 

### Dispatching (MEDPC). 26522. 

### Typical summerminimum

### loadday.

3. 

### Typicalwinterpeak

### loadday. 

### 4. Typicalwinterminimum

### loadday. Table 

### 1 isa

### briefsynopsis

### oftheresultsof

### theexamples. It is 

### interesting to 

### note that a 

### comparison 

### of the two 

### methods ED 

### and MED, 

### applied to a 

### "Typical Summer 

### Peak Load 

### Day", indicates that an increase in 

### fuel 

### consumption and cost on 

### the order of 1.8 percent 

### results in a 

### sizable 

### NOX decrease 

### of 7.6 tonsper 

### day or 

### 12.6 percent. 

### Each utilitymust consider a 

### reduction of thisnature inits

### proper perspective. From 

### Reference 11, power 

### plants are 

### responsible for 57 percent 

### of the 

### daily NOX emissions 

### from 

### stationary sources in 

### Los 

### Angeles 

### County. After consideration is

### given to 

### transportation, power 

### plant contribution to 

### NOX emissions reduces to 

### 14 percent of 

### the total tons per 

### day. Hence if

### all power

### utilities in 

### Los

### Angeles County were to 

### employ MED with similar 

### results, the 

### NOX emissions 

### could be reduced by 1.8 percent. 

### Therefore, 

### considering no action other than conversion to 

### MED by electric utilities 

### in Los

### Angeles County, the percent cost

- percent benefit ratio 

### appears to be 1. That 

### is, for 

### every one percent 

### increase in 

### fuel cost 

### resulting from 

### MED, a benefit 

### of one percent 

### decrease incontaminationofthe

### atmosphere fromNOXis

### enjoyed.

INCREMENTAL COST 5. Research is 

### also needed in 

### determining the 

### feasibility of emission 

### dispatching based on 

### multiple emission 

### reduction such as 

### NOX and 

### S02. Future 

### plans call for continued work in emission 

### dispatching including an 

### attempt to find a suitable method for incremental cost 

### using emission 

### dispatching and 

### investigation into 

### S02 emission dis

### patching. 

### Although methods 

### expressed in this 

### paper are not 

### new, the 

### applications are. 

### Using the methods outlined 

### in this 

### paper, the 

### power 

### industryhas another tool in its

### hands to aid 

### in

### curbing air

### pollution.
APPENDIX Derivation of 

### generator 

### representation 

### equation coefficients.
Source of Data
An 

### elaborate test 

### program is 

### presently underway to 

### insure that 

### unit 

### representation is 

### always as correct as 

### possible. It is 

### hoped that continuous 

### stack-gas monitoring 

### equipment will be 

### purchasedandthat amobile 

### laboratorywill soonbe

### ready. The 

### results ofa 

### typical NOX emission test are 

### shownin

### Figure 1.



### HAYNES 3 

### 8 4 Most power

### utilities, either through pooling agreements or 

### inter

### change agreements, have economy energy provisions for transactions 

### with 

### neighboring systems. 

### These transactions 

### generally involve 

### incremental and

### decremental costs. In 

### fact, nearly all 

### recent contracts call for 

### energy costs to be based 

### on incremental costs where 

### energy types range 

### from emergency to

### economy. 

### Figure 8 

### shows the 

### futility of the 

### incremental and decremental principles when 

### applied to a system of fossil fuel units 

### operating on 

### MED. The 

### smooth contiguous curve is, of 

### course, the incremental 

### fuel cost 

### for any system 

### load level 

### using ED. The 

### seemingly random 

### points 

### falling

### both above and below the ED curvearewhat theauthors 

### feel is the 

### incremental cost of one 

### megawatt dispatched by the 

### MED program 

### for all load levels attainable with the particular set ofunits usedin

### thisexample. It is hoped that further investigation and perhaps closer tolerances will 

### uncover a 

### method of 

### computing incremental costs 

### that willbe

### meaningful.



### CONCLUSIONS
In

### general, the

### followingconclusionshavebeen

### reached: 1. Reduced NOX emission is 

### possible 

### through systematic sched

### uling.2. 

### MED-MEDPC 

### scheduling results in 

### higher operating costs. 3. Better public relations may be obtained 

### by a 

### utility whose actions showconcern

### forthe

### plightofthe environment. 

### 4. Utilities need to 

### inform the 

### general public of their contribution to 

### pollution and what 

### they are 

### doing to reduce and eliminate thevarious 

### formsof

### pollution. With 

### regard to 

### the further 

### development and use of the MED

### MEDPC scheduling, these 

### further conclusions should be stated: 

### 1. 

### MED or 

### MEDPC is an 

### extremely 

### simple program to 

### implement regardless ofwhetherplant orunit dispatchisemployed. 

### 2. The two to 

### threepercent 

### loss in

### efficiencymaybe an

### excellent investment incleanairand

### publicrelations. 3. 

### Definite improvement is needed in the methods of 

### obtaining and the accuracy of the 

### emission output data. 

### 4. Further research is needed in 

### implementing transmission losses andNOXemission

### dispatching. 

# .301

_

### _X


# D 

# <XX-t~~~~~~-/

I 

# -- I

# 0-v-r---~ _-

_ 

# HK .1 

## -i-KY 

# 0 

# 11

100 200 

### 300 NET 

### MEGAW^ATTS E3 

### DWP TEST DATA 

## 9) APCD DATA Fig. 1. Typical NOX 

### Emission Test Data
Problem:
It is 

### necessary to fit a given number of data 

### points by 

### afunction ofthe form:
Y = A + Bx + 

### CeDX. 

### Using the least square 

### criteria as a 

### standard for 

### goodness of fit, itbecomesnecessaryto 

### findaminimumvalue of

### S, where



### n 

### S =E 

### (Y

i Y

## i) *(A2) S is a 

### function of the variables 

### A, B, C, and D. S is

### minimized 

### by taking the 

### partial derivatives of S with respect to

### A, B, C, and D 

### and 

### setting them 

### equal to zero. 2653 

### (Al)

### Complications are

### introduced, however, due

### tothe

### presenceof

### the

exponential term. 

### This prohibits the 

### partial derivatives from 

### becoming linear equations. This obstacle can be overcome by assuming a

### value of D 

### and solving the set of linear 

### equations obtained by taking 

### the partial of 

### S with respect to A, B, and C and setting them equal 

### to zero.The

### resultingsetof

### equationsin

### matrix form

### is: An 

### iterative process is 

### employed wherebyrepeatedvalues of

### Dn+1 are 

### 'used in 

### the solution of equations A3 throughA5 

### until the 

### change in D is 

### less than apredetermined tolerance. 

### Equation Al can now 

### be 

### solved with any value of MW 

### (X), using 

### the coefficients obtained through the describedmethod of 

### solution, 

### for the corresponding NOX emission. Similar results for ED are

### obtained

### byusing

### Btu'sinstead

### ofNOXemission.


### N 

# ~EXi
Dxi e Xi 

# rEeDxi

Xi x e 

## Z

# xeDxi xi e

# 2Dxi

YiI


## ! 

# xiyi Dxi 

## {ie 0 _ -_



### A



### B

C

where Dhasbeen

### initiallyassumed. 

### There exists a value 

### of D 

### which satisfies necessary condition that 

### aS = 0. Since



### aD 

### equation A3 and 

### the



### as 2 

### Dxi Dx aD = 

### 2 

# Z~Cxie (A+Bxi+Cel 

# .-Lyi)

# =0° (A4)

D cannot be obtained 

### directly. The 

### suggested 

### approach is the use 

### of the 

### Newton-Raphson 

### technique for the next 

### approximation of D as 

### shown in 

### A5. 

## f(Dn)

f

### '(Dn)' 

### where f(D) =

## a-. (A5) \ 

### Input: Generator 

### coefficients, minimums, maximums, 

### commitment, and 

### fuel costs 

## LCalculate unit 

### incremental rates at unit max 

### and mins
1. 

### I Set all unit 

### outputs to 

### minimum I 

### Input: Load 

### requirement
Calculate unit 

### first 

### derivatives 

### (incr. rate) and 

### 2nd derivatives
Calculate 

### average 

### incr. rate
Do 

### all 

### unit incr. rates 

### NO compare 

### within tolerance YES 

### of the 

### average?/ Output: Unit 

### Mws/

Calculate new 

### unit 

### outputs 

### using Newton's Method for 

### distributing residual 

### power

.. - 

# ~~~~~~~~~~~I Fig. 3. EDor

### MED

### Program

- Basic

### FlowChart

Fig. 2. GeneratorCoefficient Program Basic Flow Chart 

### REFERENCES [1] N. Cohn, Control of Generation and Power Flow on 

### Interconnected 

### Systems, New York: Wiley, 1961. 

### [2] W. D. 

### Stevenson, Elements 

### of Power System Analysis, New 

### York: McGraw Hill, 

### 1962. [3] L. K. 

### Kirchmayer, Economic Operation of Power 

### Systems, New York: 

### Wiley, 1958. 

### [4] E. E. 

### George, 

### "Intrasystem Transmission 

### Losses," AIEE 

### Trans

### actions, vol. 

### 69, Part 

### I, 1950, pp. 626-631. 

### [5] P. G. 

### Lubisich, "Use of Computers in Generation 

### Scheduling," AIEE CP-60-1397. 

### [6] P. G. 

### Lubisich, 

### "Penalty Factors from Power-System 

### Equations," AIEE

### Transactions, August 1958, pp. 

### 494-501. 

### [7] J. B. 

### Ward, 

### "Economy Loading 

### Simplified", AIEE 

### Transactions, December 1953, pp. 

### 1306-1312. 

### [8] A. F. 

### Glimn, L. K. 

### Kirchmayer, V. R. 

### Peterson, G. W. 

### Stagg, 

### "Accuracy Considerations in Economic 

### Dispatching 

### of 

### Power 

### Systems

- 

### I,"AIEE

### Transactions, December 

### 1956, pp. 

### 1125-1137. 

### [9] G. D. 

### Friedlander, "Power Pollution and the 

### Imperiled Environment

-

### II", IEEE

### Spectum, December 

### 1971, pp. 

### 65-75. 

### [10] P. 

### G. 

### Lowery, 

### "Generating Unit 

### Commitment by 

### Dynamic Pro

### gramming", IEEE Trans. 

### Power Apparatus and 

### Systems, vol. 

### 85, May 

### 1966, pp. 

### 422. 

### [11] 

### Profile of Air 

### Pollution Control in Los 

### Angeles 

### County Los 

### Angeles: Air 

### Pollution Control 

### District, January 1969. 2654 

### I

# GENERATION DISPATCH INPUT DATA

HARBOR UNIT 

### i UNIT 2 

### UNIT 3 

### UNIT 4 UNIT S 

### VALLEY 

### UNIT I 

### UNIT 2 

### UNIT 3 

### UNlT 4 

## SCATTERGOOD UNIT i 

### UNIT 2 

### HAYNES 

### UNIT i 

### UNIT 2 

### UNIT 3 

### UNIT 4 

### UNIT 

### 5 UNIT 4 IN/OUT MAX NET 

### LIMIT MW

0 0
0 0

I I I I

I I

I I I I I I 018

Oil 

## 0t4

i3 i'3

115 11i



### 233 

### 234 232 

### 234 344 MIN NET LIMIT MW 

### 020 020 020 

### 020 020

030 

### 030

O-qo



### 040 0'0 

## 150 150



### GAS PRICE

. 

### ECON SCHED 

### ENERGY QUOTE 

### EMIS SCHED 

### OIL PRICE 

### .34810



### CIL *GAS 

### EXECUTE CONFIRM



### RESET

Fig. 4. GenerationDispatchInput DataDisplay

2655 

### SAVE MASTER 

### + 

# Oj. t 2 3 

## 4

- 

## 5 4 1 

## 8 

## I*

### MO DA T I

### ME 11 02 

### 0ol0 

# ECONOMIC DISPATCH 

# SCHEDULE
DWP 

## HARBC STEAM BASE P 

## 2414 2 00 

# -2o0 2400 

## 2300 2200 

## 2100 2000 

## too0 1800 

## 1100 

## I'40 150oo 1400 1300 1

## 200 

## 1100 1000 

## ENERGY MASTER tt 

## '3 41 

## 32 

## 21 24 23 

## 22 

## 21 21 21 

## 21 21 21 21 21 21 

## 21 OUOTE JR VAL 

### )ART BASE 540 

### 48 508 

### 22 44' 

### 312 5 33' 3 

### 210 1 

### 2 244

218 

## 244

184 

### 0

144 0

144 

### 144 

### 0 144 0 144 0 .144 0 144 0 144

GAS 

## GEN INPUT 

## .LEY 

## SCATTERGOOD

PART BASE PART 

# 3'4 42 10 

## 35' *2 14 

## 340 54 14 

## 324 54 .13 

### 313 

# 41 301 

## 24 1 

## 214 22 8 

## 284 2# 8 

## 218 34 ¶ 

## 241 40 10 

## 251 0 

## 21 238 

## 13 225 0 

### 0 

## 225 0 

### 0 

# 225 0 0 

## 225 0 0 

### 225 0 

### 0 

## 225 PRICE .3iX15 ECON SCHED E HAYNES 

## 1-4

BASE PART 

### *s5 

# oS 

# 04 ¶ 5 0 

### * 5 0 

# "45 13 

# 152 

# 5' 5' 840 52 188 

# q48 140 40 

## 100 4 

# '3' 48 

## 548 

## 14 

## 4¶2 12 

# 420 12 348 58 

## 210 2 288 

## OIL PRICE EMIS SCHED HAYNES 

### 5-&

BASE PART 

## 108 

# 108 108 485 

# '5' 

# '33 *21 

## 408 5S15 584 

## 514 

# 5"1 542 518 

## 410 

## 442 420 

# 322 .34810 COPY 0 0 

### 23 

### 24 

### 24 

# 12 13 t3 13 10 

### 15 

## 1I 24 28 28 42 

## l8

Fig. 5. 

### EconomicDispatchScheduleDisplay



### 2656DA 

# T8 IME 1 02 

### 0l00 

# MINIMUM EMISSION SCHEDULE -HARBOR 

## BASE PART
52 4 48 4 44 2 

### 1 3 

## 3, 

## 3 

# 33 , 3' 

# 2 3 3 1 

## 32 2 

## 2 

# 2 2s , 25 

## 2 2 2 23 

## 2 22 I 

# 21 0 

## 21 0 

### 21 

## tUOTE VALLEY

BASE PART 

### 540 

### 540 540 

### 534 524 

### 514

50 

### 484 414 

### 442 448 

### 41i 

### 314 330 212 208 144 144 

### GAS 

### GEN INPUT 0
0



## .to
14

t2 10 

## 12 14

32 

### 40

58 

### 4 

### 4 0
PRICE 

### ECON

### SCATTERGOOD HAYNES 1-4 

### BASE 

### PART 

### BASE 

### PART

~~~0 15 

### 34¶ 

### X5 18 

### 333 ¶41 12 34 

### 321 ¶13 34 

### 310 81¶ 

### 32 

## 211 841 33 

### 288 814 

### 40 

### 232 154 5' 

## 214 #8 58 

### 210 

### 440

1 53 

### 2X3 581

5 

### 54 258 533 

### 5 41 

### 253 48 1

4 31 

## 241 44¶ 

### 3 

### 32 24 4 11

4 32 

### 242 385

11 83 

### 225 302 

### .3ti15 OIL PRICE 

### SCHED EllIS SCHED HAYNES 

### 5-4 BASE PART
108 

### 41t 5¶8 

## 542 

## 50o 458 418 

## 381 358 

### 334
314 

### 308 308 308 308 308 308

3108 

## .34810 COPY 

### 38 81 5' 42 42 40 31 23 24 20

0

0 

### 0 0 0

Fig. 6. MinimumEmission ScheduleDisplay

2657 

## DWP STEAM

2400 

## 2400 2300 

## 2200 

## 210O 2000 ¶ 

## 00 

## 180o 1100 1 

### 00 

## 15o0 1400 1

## 300 

## 1200 1100 1000 

## ENERGY MASTER t

### MO DA 

### TIME I 1 02 0,00 

# ECONOMY ENERGY QUOTES

MILS 

### PER KWH


### MW 

# 2400 2500 

# 2400 2300 

# 2200 

# 21O0 2000 100


## 1100 

# 1'400

1

### 400 

### 1

## 300 1200 

# 1100o -100MW 

# 3.4144 

# 3.2115 3. 

### 1114 

# 3.0151 

# 3.013k 2.1182 

# 2.142k 2.1101 2.8834 2.8505 

# 2.8120 

# 2.1411 

# 2.111k 2.4143 2.4352 2.5820 0 MW

3. 

### 4148 

# 3.3111 3.

# 2210 3. 1

# 135 3.0344 

# 2.11 1 

# 2.1515 

# 2.1253 2.8158 2 .81 10 

# 2.8301 2.1140 2.1418 2. 

# 114 2.4552 2. 152 +

# 1OMW 

# 3.1508 3.4144 

# 3.2115 

# 3.1114 

# 3.0151 3.0

# 151 2.

# ¶182 

# 2.142k 2.1101 2.8834 

# 2.8505 2

# .8120 

# 2.1 11 2.

# *11k 2.

# 143 

# 2.3352

ENERGY QUOTE 

### GAS 

### MASTER GEN INPUT 

### PRICE 

## .31415 ECON 

### SCHED 

# OIL PRICE

EMIS SCHED

Fig. 7. EconomyEnergyQuotesDisplay

2658 

### .3C810 COPY..+.++ I* I+ * **t .+ :+ :* .+ .* .++. .& +. .Sb .* .fi .* .+ .X***+*v*§ .*6-§**+-§-*--^4v++4ltz

. W~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ' , , ,_X:
.. . ... . . . . . . . .

.. . . . .. ., ; ;

e. i. 

## .1- cC



### 3. I') C)

C:

c, . 3.0 

### Ct
CP C:

C) C:

I 103 

### 2.80) VC

2, . 

# Jo)

.60

2l 

### 1090() 110(J 1 ) 

### J 1300 14 

### )() ) 

### J6(o) 1700" 1800 

### 'Fotal Net Generation In MW 

### 190 2000 2100 21t ?

Fig. 8. Incremental Fuel Cost Curves for ED (Solid Line) and MED (Points) Of

. r I

.. .... .... . .... ..

.. ...

.... .t -Itt I I t ttt ilft t? t+tt tttt ++t f-ft -1 

### "T.-Ahil. 1-31.1+

.... .... .... 1+1.,.1 It .1

. ......... +-+ 

### 4it

### ti-ttI tt tt tt tt
... .... .... .... .... .... .... ... .... .... T i 44 4

.... .... ..... ++ +t tt ;"I + 

### .4-ilo 

# *1 I I -++ tt.. 4 ! Ittt 'tIt i ftt . . .

..... 

### li,
t 1i

.... .... 4"I -t

+I 14114 i 11 VHT', ill": ItItI I.Fltt
.

t+- + ++441 

### ;+ t, +T +I + ++ + ++.

... ii tti

.... .... .. 111+jUj4 tit

.- 

# fllr4

# T'! ttt 

# VW+4+31
-+++ ... I I . 

## Tt tt

rTT 'TT -T-.- f,;+

t i1Jff.1tjj!tj1

... .... .... +++ + + ti .tlV i4" 1:1+ :... - :::+ ttt ft+t
...... t t. .t

:;-. --o-*+- -tw 4- .6;6 I1+i i -.!!1,+1 tt fl-I ++f 41+-, + + . . + t. ioi I -ii.- +; + + +

+++- 4

.... ....

::4 :: 11. ++ +-+ .
+

.... .... .... ... .... .... ..... ... jlp 1: I1+t .4

.... . ..

.... .... .. ... .... .... ... ... ... ... tfft I... f+

.... ... t 47. 

## it

... .... .... .. .... tt ........... to.; A

... r

.... ... .. io;
I a

.... .... .... 11 .1 t + ++ Lt. t

. . . . . . + fof. 4i4i

... ... +1

.... ... .01! ".tt LI ii. i" ln.

.... ... .... ... .... .... .. ...... 444#itt

. . . .... .... AK-+.

.... ...

. . . .

. . . . . . . .

. . . . . . . 14: le i

... .. ... .... +Wo, 3 .... .... .... .... . . . . .:11:: :V

. .+.+.;r: :

. . . . . . . . . . . . 44 #t it#: o. i op. i i-

. ... 1! I

### t' t t I+

......... .... LImtnt +t ttt It V -1. 11% I.: +#

### IM1140,111111 3110M., I +I

.... ... .... .... .... .... 44. -i

.. .... .. ii;; ;Ti ii *.- .4, 4- *441 T! i!!! tt:!

... .... .... .... .. .... .... .... .... ..... .... ... a ;I;; ii +4, :.44 4ions. "-it

.... .... .... .... .... ... .1- a +1

.. ....... ..... . . ............ ?- i4" 4. +; .... .... .... 3 14 ttl- --f+ 41 41 -+ :-+

. +.+. . .. ... .- t+ t .t++1:-t- 1-t 1+t.. Itt
-3, t+tt tt

+ t-t i4 4'. t + -tt'-

+ t,t 4

- T.-.T

+ +

+f-t -T-



# 1.1'.+14, t: T. J,

....... 

### . AT hs(),

### Discussion

Norton Savage (Federal Power Commission, 

### Washington, D.C,): The paper describes an 

### ingenious 

### application of the 

### incremental 

### loading technique to minimization 

### of a 

### factor other than cost: emission 

### of nitrogen oxides by a 

### fossil steam 

### boiler. Efforts such as

### tlhis, to 

### apply existingmethods fornewpurposes, are tobe

### encouraged. The 

### authors' remarks

### regarding further investigation with respect to minimum emission of sulfur oxides, are of interest. Have they made any analysis of the relationship between emission ofNOX and sulfur oxides and/or particulates? A useful study would be an examination of total volume of pollutant emission as affectedby the programs described. Since the 

### system-wide reduction 

### of NOX emission is achieved at the expense of an increase in fuel consumption, itwould appear that the quantity of other pollutants may be increased. Ifsuch increase does take place, it would be in order to evaluate the 

### relative undesirability of the nitrogenous compounds and the other emissions. Several questions come to mind 

### regarding the function used 

### by the authors to represent the relationship between NOX output and generator net power output. First, a 

### least squares 

### polynomial fit could be obtained by standard procedures 

### without the 

### necessity 

### of an iterative program. Did the authors find the exponential a better fit to the test data for all the plants? Second, for a 

### common-header system, will the constants 

### of the equations 

### change 

### significantly for the various possible combinations of boilers in 

### service? Third, ifboilers (common-header or unit type) are equipped to burn more than one kind of fuel individually or in combination, will the constants change significantly as the mix of fuels changes? It would seem that even if a single fuel such as coal is used, the constants of the NOXoutput formula would be strictly valid if very tight quality controlwere tobe exercisedonthe coal supplysource. One further remark is in order regarding Figure 8 of the paper. The figure seems to indicate that system loads less than 1550 MW (approximately) always result in minimum-estimate 

### incremental costs that are greater than economic dispatch cost, but loads greater than 1550 MW will in many instances result in minimum-emission incremental costs beingless thaneconomic dispatch costs. Would the authors careto comment onthis seeminganomaly? The views expressed herein are those of the author and do not represent an official statement of the Federal Power Commission. Manuscript received June 1, 1971.

L. S. VanSlyck (American Electric Power Service 

### Corporation, New 

### York, N. Y. 10004): In the opinion of this discusser, the authors have taken a "have solution, will find problem" approach in their philosophy of air pollution control. They have sought to minimize a cost function subject to certain constraints when the philosophy should have been to eliminate the problems at their sourcerather than to "live with them" as it were. What they propose should have been recommended only as a temporary amelioration of pollutant emission for existing 

### facilities until plant equipment modification or fuel conversion, or more effectual solutions could be found and implemented. The true solution to noxions gas emission by power plants is one of elimination rather than control, or as the authors propose 

### "optimization". The authors are referred to a recent 

### authoritiative andmost significant paperinthisarea 

### (1).
REFERENCE 

### [I] Sporn, Philip, "Our Environment-Options on the way into the Future". IEEE Spectrum, May 1971, pp. 49-58. Manuscript receivedJune 10, 1971. M. R. Gent and John 

### Wm. Lamont: The authors wish to thankMr. Savage for his excellent comments. The 

### Department of Water and Power does not burn coal in its Los Angeles area power 

### plants, the primary fuel being natural gas, 

### supplemented by 

### low-sulfur, low ash fuel 

### oil during 

### curtailment. Natural gas firingresults in

### approximately one thousand times the amount 

### of oxides of 

### nitrogen as oxides of sulfur. Since, as in our summer peak day 

### example, the amount of natural gas used is increased only 1.8 percent while the oxides 

### of nitrogen are reduced 12.6%whileonMED, thetotal amount of

### pollution is reduced. As far as we can determine, sulfur oxides are 

### directly proportional to the number of btu's burned and could best be controlled by btu dispatch if they are determined to be the 

### pollutant of chiefconcern. The exponential curve fit was chosen as a generator representation for severalreasons. Theyinclude: a. Abetterrepresentation thanwitha

### polynomial. b. All derivates are continuous and the 

### functions are 

### always monotonically increasing. c. Same number of coefficients are always necessary. Although an iterative approach is 

### required to evaluate the 

### coefficients for an exponential curve fit, it is necessary to calculate these constants only once. The initial value assigned to the 

### "D" coefficient seems to have little effect onthe CPUsolution time. The Department of Water and Power does not have any commonheader plants and such systems were not 

### considered. The constants would probably change 

### significantly for the various 

### combinations in a 

### common-header system. It should be 

### possible, 

### however, to 

### modify the program to accept 

### common-header plants 

### by either 

### generating coefficients at the time of program execution or 

### storing several sets of coefficients. With regard to 

### multi-fuel firing, the 

### Department uses 

### natural gas, switching to oil only when sufficient natural gas is not available. It is not our normal practice to burn in the mixed 

### fuel mode 

### for extended periods. We have not seriously 

### examined the condition 

### of mixed firing in individual units or on the system. Onthe DWP 

### System, fuel oil logistics determine where and how much oil isburned. 

### Testing would be required to adequately represent generators under mixed firing as well as the 

### common-header conditions mentioned 

### by Mr. Savage. We perhaps took too much liberty in 

### defining incremental cost as the cost of the next megawatt. The curve and points 

### of 

### Figure 8 would seem to indicate the incremental cost at 2000 mw is less while on MED than ED. Comparing the cost of each megawatt 

### before the 

### 2001st shows an average of 3.048 

### $/mwh for MED 

### and 

### $2.989/mwh for ED. Since cost plays no part in MED, the next incrementofpower could very easily cost less while 

### maintaining equal incremental emission 

### rates. In reply to Mr. Van Slyck, electric utilities, 

### including American Electric Power, have many problems; one of the largest and most costly problems being air pollution. If this discusser had taken the time to 

### thoroughly read this paper, he would have seen the material proposed by the authors was 

### presented only as an interim solution. 

### Moreover, an inquiry on Mr. Van Slyck's part would have 

### enlightened him to the fact that minimum emission dispatching 

### has been 

### required bythe

### governmental control agencies

### pf

### California. Fuel conversion has become outmoded as a 

### solution. All steam plants in Los Angeles County have burned only 

### natural gas when available, 

### supplemented by low-sulfur fuel oil (less than 

### 0.5% sulfur byweight) sinceJanuary 1964. Fewutilities, includingMr. 

### Van 

### Slyck's, have operatedwith these stringent 

### limitations. The authors believe the elimination of 

### oxides of nitrogen to be impossible as long as fossil fuels are burned at high temperatures; however, interim solutions should be considered until 

### such processes as 

### off-stoichiometric burning are fully explored. Other 

### utilities may soon be faced with regulations limiting the amount and types 

### of fuel used as well as the amount of pollution generated. 

### Hopefully, the ideas presented will aid in an interim solution until elimination of air pollution is reasonably feasible. Manuscript received July 6, 1971.

2660