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Real-Time Urban Power Dispatch with Ambient Air Quality Constraints
REAL-TIME URBAN POWER DISPATCH WITH AMBIENT AIR QUALITY CONSTRAINTS Kai-ching Chu, Mohammad Jamshidi* and Richard E. Levitan IBM Thomas]. Watson Research Center, Yorktown Heights, New York 10598 U.S.A.
When there is the possibility of too much pollution due to circumstances such as poor weather conditions, extreme demand for power generation, or automobile driving, there is the need for the authorities to issue an "alert" or "emergency" notice, enforcing emission cutdowns from their sources. The strategy of such emission reductions can be one of the following. I
Abstract: A power dispatch methodology for urban utility company facing ambient air quality constraints is developed. This approach consists of I) a real-time air dispersion model for the urban area and its surrounding region, 2) a fuel minimization procedure which will generate a schedule to satisfy the demand and the constraints on pollution concentration. Forecast meteorological data and ambient air quality information are assumed ami/able for the procedure.
One is the prorated reduction policy in which all the sources would reduce their emissions by the percentage proportional to their share of polluting the environment. Such prorated reduction can be determined through the statistical data given by day-to-day surveillance of the pollutant concentrations. This approach may be difficult to implement because it would depend on the availability of accurate and fair assessment on the part of the environmental protection authorities.
1. THE PROBLEMS OF URBAN AIR POLLUTION ABATEMENT The industrialization and environment are at opposite ends of development plans. On one hand, industrial development is necessary for economic growth. On the other hand, should such plans be carried out without constraints, it would be at the expense of environment deterioration. For industrial establishments such as power utilities, oil refineries, steel mills, etc., the concern for economy and clean environment are usually conflicting, and careful design and planning are needed particularly to deal with this dilemma.
Another policy is based on successive reduction policy through which the largest controllable emitter will be asked to cut down in the case of an emerging pollution alert. Then the next largest controllable source will have to abate its emissions, and so on, until satisfactory air quality can be achieved. Usually, for urban areas this means that the first such sources to undertake the abatement are the power utility companies.
The quality of the ambient air has been of great concern in many regions in recent years, with the air pollution problem generally most severe around large metropolitan areas. The pollution sources which emit chemicals unfavorable to human health can usually be classified as stationary or mobile. The stationary sources are the various industrial plants, and residential areas and commercial districts. A common example is the power plants, particularly coal-fired ones, which emit ash, sulfur dioxide, particulate, etc. Mobile sources, like automobiles, which emit carbon monoxide and other chemicals, also have had devastating effects on the urban air quality. From the viewpoint of pollution control, the first important problem is identifying all the sources and assessing their relative impacts on the environment and human health.
An alternative in weighing and ranking different emission sources in abatement strategies is by their cost effectiveness instead of the total amount of emissions. Such an approach should reflect the costs and probable disruption of the area 's normal life and economy. In this paper, the main concern is the maintenance of air quality within an urban area through proper dispatching operation of the power plants. The power utility companies are the major sources of air pollution, judging from both their emissions and cost-effectiveness in pollution abatement. 2. POWER PLANTS EMISSION ABATEMENT
A great number of power plants throughout the world generate electricity by the use of coal. The dominance of coal in the electric power industry has existed for a long time. With the recent great price increases in oil and the fast depletion of its reserve, an even greater need for coal has been realized. Unfortunately, with the current technology, the use of coal has unfavorable environmental impacts. As an example, the annual S02 emission from power plants in the U.S. was 20 million tons in 19702 which accounted for 55 % of all the S02 emission. From this 55 %, 46.5% was from coaland 8.5% from oil-fired plants. I The situation in the url)an areas is even worse . The annual S02 concentration in several urban areas of the U.S. already exceeds the 0.03 to 0.04 ppm level .3 Many power plants near the metropolitan
The responsibility assessment of emission abatement within an urban area can be achieved through continuous monitoring of the air quality under various meteorological conditions around major sources. The surveillance of the ambient air quality can, in the long run, provide statistical records and give an indication of the types and extents of pollutants and their sources. This pollution surveillance should also include its correlation with the time, location and weather conditions.
·Presently on leave from Department of Electrical Engineer ing, Pahlavi University, Shiraz, Iran.
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urban areas are thus required to be oil- or gas-fired to maintain a lower S02 emisssion. There are a number of alternative emission abatement policies to incorporate with the "economic dispatch" of power within the utility companies. In extreme cases. it can be the complete shutdown of certain units within the company and importation of power from others. Under normal conditions. the utility company may have such options as fuel switching and load shifting among its plants. The load shifting is a less severe real-time approach which would not greatly disturb the power plant operation. The loads on the more polluting units (especially during peak hours) can be shifted to other plants with low-sulfur fuels. superior pollutant removal or dispersion capabilities (scrubbers and taller stacks). or to those at more favorable locations (better weather conditions. downwind. away from cities). The real-time power dispatch. considering the generation costs and the air quality. are the primary concern of this paper. The previous approaches suggested for this problem involve the imposition of one of these operation limits : (I) total maximum emission. 4 . 7 or (2) maximum pollutant concentration using a Gaussian plume dispersion modeI 8. 12 . For the first approach. the dispersion effects of favorable meteorological conditions are ignored. The second. while taking pollution dispersion into account. has only a steadystate model which cannot properly deal with varying power demand and weather conditions.
In this paper it is assumed that a study of urban background emissions similar to those considered in [14] or [17] has been conducted and the forecast CbaCkgrounit' ;xj,yj) is available at certain urban monitoring points (xj,y). j= 1.2 .... for time t I . Such forecasts are then used for the power dispatching. 3.2 Power Plant Emission The dispersion model for power plant emission with high background pollution must work on real-time. be adaptable to the changing conditions. and be reasonably accurate for the regions involved. The integrated Gaussian puff model used in this paper satisfies these requirements. This model is based on the statistical theory of turbulent diffusion and empirical data supporting it have been found by Sutton.1S Frenkiel. 19 Ogura,2° and others. Such a model would provide proper concentration levels for a wide wind speed range . including the stagnation situations. Time variations in the meteorological conditions. such as wind speed. atmospheric stability classes. and inversion layer height. will be accommodated. 14 ,ls Assuming there are N individual point sources and that Qj(t). the emission from source i at t. is constant over time intervals Ilk' the pollutant concentration at t' and ground location (x,y.O) can be expressed as
(1)
+ CbaCkgrOund(t ' ;x,y) Proposed by Chu et aJ.13, a new approach handles the dispatching problem for isolated plants with a model which emphasizes the dynamic property of pollutant dispersion and its forecast. In [13]. the integrated Gaussian puff diffusion modeP4·'s was introduced to handle specifically the changing weather and load conditions. In this paper. the approach considered in [13] will be proposed for the real-time power dispatch under air quality constraints around urban areas where other background sources are present. 3. MODELLING OF AIR POLLUTION DISPERSION The general background sources in urban areas. such as those of transportation and residential and commercial combustion. are difficult to curtail. and the control task is beyond the scope of this paper. We will simply describe briefly the efforts for modelling such sources. 3.1 Background Area Sources The modelling of urban background sources has been based either on the integration of concentration equation or on the approximation by equivalent point sources and consideration of their dispersion. Shieh et al. 14 have developed a numerical method for integrating the Gaussian puff dispersion equation of S02 to represent concentration from area sources. The authors have made a number of simplifying assumptions in order to include constant emission. wind speed. atmospheric stability' and turbulent intensity. Shir and Shieh '7 have also devised a numerical integration scheme for the partial differential equation representing the pollutant mass conservation over the area. Another method requires a great deal more data on emission, various meteorological parameters. surface roughness and chemical reaction rates. Still a third approach for urban air pollution modelling. considered by Roberts et al. ls represents the area sources by equivalent point sources computed upwind using estimated dispersion coefficients and propagation time. Then the area concentration is approximated by the use of the Gaussian puff dispersion model.
where t and t' are measured in the multiples of Ilk' and G(.) is the transfer coefficient representing the impact of a unit puff at t from the stack to the concentration at location (x.y) and time t ' . In the case of S02' no chemical reactions are assumed to take place in the atmosphere; therefore superpositions of the puffs would be applied. Function G(.) disperses'in time in a form of Gaussian distribution: G(t.t' ;x,y) ex p
=
[(2,,)3 / 20 .(t.t' )Oy(t,t' )o.(t.t I )]-1.
{_~ r(x-Xc(t,t' »)2 +(Y-Yc(t,t' »)2 + (Zc(t,t') 2]} 2l\ o.(t,t ' )
o,(t,t' )
0z(t,t' )
(2)
where [xc(t,t '),yc(t,t ' ),zc(t,t I )] are the center coordinates of the dispersed puff ellipsoid at t', emitted at t and o.(t,t' ), o,(t,t I ) and 0z(t,t ' ) are its standard deviations in space distribution in the x,y,z directions. 16 Coordinates (xc,yc,zc) can be updated by extrapolation with the average wind velocity vector during time intervals Ilk' When the atmospheric stability remains steady between t and t', approximately linear relations between o's and (t '-t) in logarithmic scales can be assumed. Reflections at ground level and the inversion layer can be handled by assuming proper additional sources and taking all of them, real and imaginary, into account. IS 4. AIR QUALITY CONSTRAINTS Our primary concern of air pollutions are their concentration and exposure durations instead of their total emission volume. Since it is the level of concentration that will affect human health, vegetation and materials. To this end, a certain moving average will be defined for pollutant concentrations. If the concentration of a certain pollutant at time t I is C(t I ;x,y) , its average over time duration w beginning at T is
'For its classification in terms of intensity of turbulence and thermal stratification of the atmosphere, see Turner.16
Real-time urban power C
( . _ 1 T+w I. wmean T.x.y) - w- ~" _T+1C(t .X.y).
311
(3)
where w is the window in which the average is taken (e.g .• 3 hr.. 24 hr.. etc.) and such window moves along the time horizon. Table I is part of the air pollution standards. set by the 1970 U. S. Clean Air Act. which also reflect this viewpoint of moving average constraints.21 The moving average standards require that (3) for each type of pollution be lower than a certain maximum level C wmax for all locations (x.y) and all time T.
(7)
is a required constraint. For practical systems with small losses. L(P,) can be approximated around the nominal load conditions by the quadratic form 22
(8) where constants Bmn (m.n= I •.. .•N) form a posItive semidefinite matrix. Upper and lower limits on the range of power generation for each plant are given by for all t.
Let s; be the pollutant content of a unit of fuel fired at plant i and F;(p;,) be the fuel consumption rate at the i-th plant when its output power is p;,. Substituting Q;(t) = s;F;(p;,) and (I) into (3) . we obtain T+w
~1'~T+l~;' s;FJp;)GJt.t I ;x . y)~Cwmax- CwbaCkgmund(T;x,y) (4)
for all T and (x,y). Ideally. we would like to monitor the relation (4) for all locations in the area covered. and implement (4) as inequality constraints in the dispatching problem. This is. of course. computation ally un feasible and not actually necessary. Only certain locations in an area are likely to have unsatisfactory air quality. particularly those in the city and in the downwind directions from the plants. This consideration naturally leads to the simpler requirement that (4) be satisfied for a set of selected locations (xj,yj).j= 1•.. .•M. The approach we are using is to select these (xj,y/s as the expected average local maxima of pollution concentration. precomputed on the basis ofthe forecast weather conditions and power generation schedules D Now denoting (xj>Yj) simply by j. the set of constraints (4) becomes T+w
W;-:~T+7;,s;F;(p;,)GJt . t I ;j) ~ C wmax - C w backgmund(T;j). (5)
for all T and j= I ... .. M. This expression is part of the optimization problem to be described in the following section. For illustrative purposes . only one type of pollutant (say. S02) and one time averaging window width ware indicated in (5). For several types of pollutants or time average durations. one simply employs as many such inequalities as would be necessary. 5. FORMULATION OF THE DISPATCH OPTIMIZATION PROBLEM
The environmental dispatch problem is essentially that of ordinary economic dispatch incorporated with air quality constraints (5). The requirement is to determine a feasible generation schedule for all power plant units with the minimum fuel cost while meeting the total demand and having the pollution concentration levels lower than specific standards for all times T and for all locations j in the area. Consider the N generating plants. and let the cost of a unit of fuel at plant i be c;. Such c; are generally different among the plants. The total cost of fuel consumed per hour is
(6)
~;c;F;(p;t) '
and the total power produced is
~;P ; t .
If P Dt is the total desired level of power generation to meet demand at time t. and L(P t) is the transmission losses at t to be readily defined below. then
(9)
Assuming P Dt as a specified quantity at t. the ordinary economic dispatch problem is to choose P;t' i= I .....N. to minimize (6). subject to the constraints (7) and (9). Other considerations. such as fuel availability and power interchange with other companies. could be added as constraints. Examining the requirement of (5) versus the other constraints. it is important to note the difference in their time scales. While the ordinary economic dispatch problem usually needs to be solved every 2-15 minutes to insure meeting the fast-varying demand P Dt • weather conditions and the associated G;(t.t ';j) will change at a much slower pace. It would be an unnecessary and even impossible job to track and update requirement (5) every 2-15 minutes. Our approach of solving the optimization problem. then. is to consider it in both long-term (around I hour) and short-term (2-15 minutes. or as frequently as necessary) modes. In the long-term mode. the explicit inequality (5) will be considered with forecast weather conditions. and the forecast power output levels P;t. The latter refer to the long-term averages (say. hourly) of the power outputs. The impact of pollution constraints on the generation cost will be assessed as an impost within each long-term period. Such assessment will be used to modify the cost function for short-term dispatching. in which the constraint (5) will no longer be considered explicitly. The long-term optimization problem is to Minimize
~t~;c;F;(p;t)'
(10)
subject to constraints (7). (9). and (5) and any other operation constraints. The index t runs as I .. ..•T max' where time is discretized in long-term intervals (say. I hour) and T max is the end value of the time horizon (say. 24 hours) . Here. all the PH's are the average values within each interval. Their solution will also satisfy a set of Kuhn-Tucker conditions: c;(dF/ dp;th\( I-OL(Pt) / oP;t)-~;t+r;t T+w + [~j~tl'jtw-'s;~t' ~T+1G;(t.t I ;j)](dF/dp;t)=O. i=I.2 •...• N;
(11)
t= 1.2 •...• T max'
where the A·s. the fs and rs, and the I"s are the Lagrange multipliers corresponding to (7), (9). and (5), respectively. Now the expression T+w TI;t = ~jt~" _T+ll'j,W- 1s;G;(t.t I ;j)
(12)
can be given an interesting interpretation. It represents a marginal shadow impost or "environmental tax" given a specific weather condition and background level to be added to the fuel cost at plant i and period t when the generation level is P;t. As has been shown in [131. we can replace the original dynamic decision problem coupled with constraint (5) by a set of uncoupled economic dispatch problems and execute them on a short term basis. These short term computations are based on a modified cost c; + TI;t' where the imposted tax TI;t are obtained by the long term optimization.
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6. AN ILLUSTRA TIYE EXAMPLE In this section the proposed real-time urban power dispatch program will be examined for a system of three power plants, one coal-fired and two oil-fired. One of the oil-fired plants is near a city where the forecast background S02 concentration level for a particular day, from three monitoring points, are given by Table 2. Figure 1 shows the assumed geographical location of the plants relative to the city. The numerical data for this power system are presented in Table 3, where F i (.) are linear throughout the operation range of our concern. We are considering a day for which the forecast wind speed, and direction and atmospheric stability class are given. These forecast data are nonuniform over the area. Generally the wind in the west of the region is strong while that by the city is near stagnation. The meteorological conditions and the background level are set deliberately to the extreme so that appreciable pollution effects can be seen . Power Plant I is located primarily in the upwind direction of the city. The computed positions of the three additional monitoring points determined by the proposed algorithm in the prevailing downwind direction and the original three city monitoring points are also shown in Fig. 1. Table 4 shows the total system power demand along with the would-be S02 concentrations (3 hour averages) without any air quality control imposed on the dispatch. Considering C lmax = 0.5 ppm and C 24m a. = 0.1 ppm for S02 (Table 1), it clearly shows that both standards have been violated to various extents at the first , fourth , and sixth monitoring points. The worst violation occurs between hours 12 and 17.
plants. Unlike the fixed ad hoc monetary emission penalties assumed by some previous researchers, our flexible environmental taxes are linked directly to the changing weather and load conditions. This would in effect project less stringent emission requirements over the entire generation schedule. The proposed methodology not only is more efficient but also suggests a more rational tax structure (i.e., weather and load dependent) for the governmental regulatory agencies to impose environmental taxes. This observation is further justified by Chapman's study2l which presented a critical examination of the "sulfur emission tax" imposed by the U.S. government. His general conclusions are that (i) the tax would cause significant reductions in emissions and damages, (ii) it has little effect on electricity demand growth, and (iii) it results in greater social benefits than costs, in particular if the U.S. Clean Air Act is not implemented 2 l The two-mode (short- and long-term) power dispatch considered here is also very promising from the implementation point of view. In fact in an environmental/economic power dispatch algorithm, the Gaussian plume and a socalled "transient models" are used by the Tennessee Valley Authority24 for long- and short-term dispatching, repectiveIy. One of the logical extensions to the present work is the inclusion of an online, preferably hourly or daily , updating of the background S02 concentrations. This would require a great deal of additional data on the various other sources: emissions, traffic flows, mixing heights. solar radiations and so on.
For the long-term problem with environmental con straints, we need to impose the constraint (5) with C lmax = 0.5 ppm , and C24max = 0. 1 ppm. The new schedule is given in Table Sa. Daily averages of the pollution concentrations for monitoring point I and point 6 turn out to be the binding constraints.
8. REFERENCES 1.
U. S. Environmental Protection Agency, Guide for air pollution episode avoidance, Office of the Air Programs, Publication No. AP-76 , Research Triangle Park, N.C.. June,I971.
The environmental fuel impost nit for the three plants is presented in Table 5 b. It can be seen that Plants I and 3 are penalized by the impost. The values of such impost are high at hours 1-2 and 9-19. The former is due to poor weather conditions, the latter to heavy background and great power demands. The fuel imposts nit' i= 1 ,2, .. ,N and t= 1,2, ... can be incorporated with the fuel cost c i for optimizing the short term dispatching in which the air quality constraints are not explicitly considered. The S02 daily average level in the area before irr,posimg, constraints (5) is shown in Fig. 2. That after the imposing, in Fig. 3.
2.
S. H . Schurr, Energy research needs, National Technical Information Service. PB-207 516 , U.S. Department of Commerce , Springfield, Va., October, 1971.
3.
U. S. National Air Pollution Control Administration, "Air Quality Criteria for Sui fur Oxides," NAPCA Pub. AP-50, Government Printing Office. Washington D. c., January, 1969.
4.
M. R. Gent and J. W. Lamont, "Minimum emission dispatch," IEEE Trans. Power App. Syst .• PAS-90, November-December, 1971, pp. 2650-2660.
5.
J. K. Delson, "Controlled emissions dispatch," IEEE PES Winter Meeting. paper T74-156-6. New York, N. Y., January, 1974
6.
0. E . Finnigan and A. A. Fouad. "Economic dispatch with pollution constraints," IEEE PES Winter Meeting, paper C-74-155-8, New York, N. Y., January, I974.
7.
J. W. Lamont, K. F. Sim, and E.P. Hamilton Ill, A multi-area environmental dispatching algorithm, Proc. 9th IEEE PICA , New Orleans. La. , June , 1975 , pp. 242-246.
8.
R. L. Sullivan, "Minimum pollution dispatching ," IEEE PES Summer Meeting, paper C72-468-7, San Francisco, Calif. , July, 1972.
9.
R. L. Sullivan and D. F. Hackett, "Air quality control using a minimum pollution dispatching algorithm ," Environm . Science and Tech. 1. , 8, 1974, pp. 679-680.
10.
P. G. Friedman, Power dispatch strategies for emission and environmental control, lnstr. in the Power
The redistribution of power plant generation levels reveals the fact that most of the pollutants created by the oil-fired Plant 1 and the coal-fired Plant 3 during the peak hours were eliminated by shifting their loads to the second plant which burns a less polluting fuel . i.e. oil, remote from the city, and has a more favorable weather condition. For the example considered, the dispatching algorithm with air quality constraints has reduced the peak S02 level by 67 % compared with the conventional dispatching program . 7. CONCLUSIONS An online power dispatch with background urban emission and air quality constraints is presented. The emphasis is placed on the dynamic dispersion of power plant emmision in surrounding regions which include urban areas. The binding air quality constraints as applied to the long-term dispatch provide a set of "environmental imposts" or "taxes" which may be used as an additional cost for the generation of power. This self-imposed tax, in our opinion. is a very practical scheme for curtailing the air pollution surrounding the power
Real-time urban power Primary Standards
Indust ., 16, 1973, pp. 59-64.
S. R. Carpenter, T. L. Montgomery, J. M. Leavitt, W. C. Colbauch and F . W. Thomas, "Principal plume dispersion models: TVA power plants, J . Air Pol. Cont. Assoc., 21, August, 1971.
11.
M. F. Ruane, J. Gruhl, F. C. Schweppe, B. A. Egan, D. H. Fyock, and A. A. Slowik, "Supplementary control systems-a demonstration," IEEE PES Summer Meet ing, paper F7 5-474-7, San Francisco, California, July, 1975 .
12.
13.
K. C. Chu, M. Jamshidi and R. E. Levitan, "An approach to online power dispatch with ambient air pollution constraints, IEEE Trans. on Automatic Control, AC-22 , June,) 977 .
14.
L. J. Shieh, B. Davidson, and 1. P. Friend, "A model of diffusion in urban atmospheres : S02 in Greater New York ," Proc . Symp. on Multi-source Urban Diff. Models , EPA, 1970, pp. 10.1-10.39.
15.
16.
D. B. Turner, "A diffusion model for an urban area," J. Appl. Meteorol. , 3, February, 1964, pp. 83-91.
17.
C. C. Shir and L. J. Shieh, "A generalized urban air
0. G. Sutton, "Theory of eddy diffusion in the atmosphere," Proc. Roy. Soc., SeT. A (London) 135, Augun, 1968 , pp. 575-582 .
19.
F. N. Frenkiel, "Application of statistical theory of turbulent diffusion to micrometeorology," J . Meteorol., 9, August, 1952, pp. 252-259.
20.
Y. Ogura, "Theoretical distribution functions of matters emitted from a fix point," Meteorol. Society Japan J., 32 (Series 11), January, 1954, pp. 22-26.
21 .
U. S. Federal Register, 36, no. 84 (Part 11), April 30, 1971 , p. 8187.
22.
L. K. Kirchmayer, Economic Operation of Power Systems. New York: John Wiley, 1958, Chapter 4.
23.
D. Chapman, "A sulfur emission tax and the electric utility industry," Energy Systems and Policy, I, 1974, pp.I-30.
24.
J. M. Leavitt, L. A. George and R. E. Clark, "Sulfur dioxide emission limitation (SDEL) program at TV A power plants," J. of Air Pollution Control, 26, December, 1976, pp.II33-1140.
Fuel Cost oil $15 / bl.
2 3
oil $15 / bl. coal
0 . 8~ / kg.
Sulfur Content
8.323 kg. S02 / bl.
Max. Freq.
ppm
Max. Freq.
0.03
annual avg.
0.02
annual avg.
0.14
24hr. avg. once/ yr.
0.10
24hr. avg. once/yr.
0.50
3hr. avg. once/yr.
Hour
Station I
Station 2
Station 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0 .032 0.027 0.029 0.046 0 .065 0.051 0.060 0.096 0.109 0.113 0.111 0.105 0.072 0.060 0.058 0.056 0 .054 0.052 0 .054 0.056 0 .060 0.071 0.101 0.111
0.000 0.000 0.000 0.002 0.004 0 .008 0.030 0.045 0.050 0.055 0.058 0.029 0.015 0.015 0.015 0.018 0.020 0.025 0.023 0.020 0.018 0.018 0.019 0.020
0.025 0.029 0.026 0.025 0.025 0.050 0.101 0 .126 0.139 0.126 0.101 0 .076 0.078 0.080 0.083 0.084 0.082 0 .083 0.083 0.086 0.091 0.083 0.063 0.050
Table 2.
Fuel Consumption Rate Fi(Pit) (per hr.)
8.323 kg. SO/ bl.
ppm
Average Levels of Background S02 in the Urban Area (ppm)
pollution model and its application to the study of S02 distributions in the St. Louis metropolitan area," J. Appl. Meteorol., 13, no. 2, March, 1974, pp. 185-204. 18.
Average Hourly Background S02 Levels (ppm)
Transmission Loss Coefficient Matrix B (Mw)-I
29.2+.813Plt+ ·00148PIt2 20.29+ 1.28IP2t+ .Oo'I86P2t2
57.00 gm. S02/ kg. 3200+298P3t + .32P3t2
Secondary Standards
Table I. Air Quality Standards for Sulfur Dioxide
J. J. Roberts, E. S. Croke and A. S. Kennedy, "An urban atmospheric dispersion model," Proc. Symp. on Multi-Source Urban Diff. Models, EPA, 1970, pp. 6.1-6.71.
Power plant i
313
[ 8650 10-5 • -2.112 -1.215
Table 3. System Operation Data for the Example
-2.112
Power Output Range Pimin:5Pi:5Pimax (Mw) 400 :5 Pit :5 1200
10.500
-121'] -.531
100 :5 P2t :5 1500
- .531
5.813
80 :5 P3t :5 900
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-
N
W+E
140 120 IJ)
~
COAL-FIRED POWER PLANT OIL - FIRED POWER PLANT ,.'-,, AIR QUALITY MONITORY POINT '., URBAN AREA TRANSMISSION LINE
[:=J
~. -
S
100
'E I
~
80
a:: 0
z
60 40 20 00
6
20
40
60
80
100
120
140
160
180
200 220
EAST (miles) Figure 1 Locations of power plants and the city in the illustrative example
Power and S02 Moving Average Schedule: Cost = $ 851,154 Hour
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Power Power Output (MW) Demand At Plant (MW) 2 3 1281 1162 1030 1112 1039 1089 1628 1834 1996 2321 2484 2508 2353 2275 2157 2027 2071 2318 2100 2055 1747 1639 1418 1297
400 400 400 400 400 400 498 615 706 907 990 1026 913 881 812 720 745 907 769 733 558 501 400 400
100 100 100 100 100 100 287 387 468 621 722 713 651 598 537 488 510 619 518 506 352 296 169 100
824 696 555 642 564 618 900 900 900 900 900 900 900 900 900 900 900 900 900 900 900 900 900 843
Line Loss (MW) 44 34 25 30 26 29 58 68 79 109 128 131 112 105 93 82 85 109 88 84 63 58 51 45
Three Hour S02 Moving Average Concentration (ppm) at Station 4 2 3 5 6 .029 .036 .060 .071 .077 .076 .092 .107 .112 .113 .106 .101 .105 .119 .140 .158 .175 .188 .204 .233 .265 .275 . 185 .086
Day
.000 .001 .002 .005 .014 .028 .042 .051 .056 .049 .036 .022 .018 .021 .028 .039 .049 .057 .062 .070 .078 .086 .060 .031
.027 .027 .026 .034 .061 .103 .145 .158 .149 .126 .115 .110 .113 .111 .109 .107 .105 .101 .099 .096 .086 .071 .041 .018
.001 .001 .001 .001 .000 .000 .015 .052 .092 .160 .271 .368 .495 .531 .556 .544 .585 .444 .247 .024 .005 .005 .004 .002
.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .025 .038 .052 .043 .040 .027 .011 .000 .000 .000 .000 .000 .000 .000
.003 .007 .006 .005 .000 .000 .006 .029 .031 .101 .418 .619 .886 .850 .979 .888 .679 .350 .103 .009 .007 .003 .001 .001
Twenty-Four Hour S02 Average Concentration (ppm) at Station 2 4 5 3 6 .131 Table 4.
.038
.090
Dispatching Schedule without Environmental Constraints
.183
.010
.249
Real-time urban power
315
Power and S02 MoYing Average Schedule: Cost = $ 1,220,800 Hour
1 2 3 4 5 6 7 8 9 10 Il 12 13 14 15 16 17 18 19 20 21 22 23 24
Power Power Output (MW) At Plant Demand (MW) 2 3 1281 1162 1030 1112 1039 1089 1628 1834 1996 2321 2484 2508 2353 2275 2157 2027 2071 2318 2100 2055 1747 1639 1418 1297
400 400 400 400 400 400 438 478 485 585 677 659 880 486 551 400 400 400 494 654 558 501 400 400
100 100 100 100 100 100 346 526 696 964 1056 1387 1470 1254 1500 1500 1500 1500 807 585 352 296 169 100
824 696 555 642 564 618 900 900 900 900 900 668 237 705 330 350 395 650 900 900 900 900 900 843
Three Hour S02 Moving Average Concentration (ppm) at Station 2 4 5 6 3
Line Loss (MW) 44 34 25 30 26 29 57 70 87 128 149 206 234 171 224 223 224 233 101 84 63 58 51 45
.029 .036 .060 .071 .077 .076 .092 .107 .1l2 .1l2 .102 .092 .087 .092 .106 .116 .123 .124 .128 .137 .153 .166 .116 .058
.000 .001 .002 .005 .014 .028 .042 .051 .056 .049 .036 .022 .018 .019 .024 .032 .038 .042 .043 .047 .051 .055 .038 .020
.027 .027 .026 .034 .061 .103 .145 .158 .149 .125 .112 .104 .104 .101 .099 .097 .095 .093 .093 .091 .083 .068 .039 .017
.001 .001 .001 .001 .000 .000 .011 .033 .054 .088 .144 .232 .297 .316 .277 .243 .215 .152 .077 .009 .004 .004 .004 .002
.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .074 .122 .164 .173 .186 .144 .061 .000 .000 .000 .000 .000 .000 .000
.003 .007 .006 .005 .000 .000 .006 .029 .031 .089 .197 .249 .327 .278 .325 .300 .278 .179 .068 .009 .007 .003 .001 .001
Twenty-Four Hour S02 Average Concentration (ppm) at Station 2 4 5 6 3
Day
.100 Table 5a.
.087
.030
.090
Dispatching Schedule Subject to Environmental Constraints
Hour
Plant 1
Plant 2
Plant 3
1 2 3 4 5 6 7 8 9 10 Il 12 13 14 15 16 17 18 19 20 21 22 23 24
40.660 13.610 0.250 0.002 0.033 0.282 2.968 7.773 13.838 18.699 17 .605 27.929 22.125 39.791 50.305 61.371 67.164 61.097 16.065 4.004 0.151 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00132 0.00190 0.00802 0.00001 0.00000 0.00000 0.00002 0.00564 0.01899 0.00285 0.03864 0.16046 0.31251 0.13495 0.29189 0.27555 0.29362 0. 18684 0.00221 0.00444 0.00159 0.00013 0.00086 0.00000
Table 5b.
Environmental Fuel Imposts, ($ / fuel unit)
nil
.039
.100
K. -C. Chu, M. Jams hidi and R. E. Levitan
316 150
100 :I:
~ z
o
.002
:I: I~
o
(J)
o .002 -50 -130
-100
o
100
200
WEST - - - - - - - - EAST
Figure 2 CONTOURS OF TWENTY -FOUR HOUR SULFUR DIOXIDE AVERAGE ON DAY WITHOUT ENVIRONMENTAL CONTROLS (ppm)
150
100 :I:
~
o z
.002
:I: I-
~
o(J)
o
-50 -130
-100
o
100 WEST - - - - - - - - EAST
Figure 3 CONTOURS OF TWENTY-FOUR HOUR SULFUR DIOXIDE AVERAGE ON DAY SUBJECT TO ENVIRONMENTAL CONTROLS (ppm)
200
When there is the possibility of too much pollution due to circumstances such as poor weather conditions, extreme demand for power generation, or automobile driving, there is the need for the authorities to issue an "alert" or "emergency" notice, enforcing emission cutdowns from their sources. The strategy of such emission reductions can be one of the following. I
Abstract: A power dispatch methodology for urban utility company facing ambient air quality constraints is developed. This approach consists of I) a real-time air dispersion model for the urban area and its surrounding region, 2) a fuel minimization procedure which will generate a schedule to satisfy the demand and the constraints on pollution concentration. Forecast meteorological data and ambient air quality information are assumed ami/able for the procedure.
One is the prorated reduction policy in which all the sources would reduce their emissions by the percentage proportional to their share of polluting the environment. Such prorated reduction can be determined through the statistical data given by day-to-day surveillance of the pollutant concentrations. This approach may be difficult to implement because it would depend on the availability of accurate and fair assessment on the part of the environmental protection authorities.
1. THE PROBLEMS OF URBAN AIR POLLUTION ABATEMENT The industrialization and environment are at opposite ends of development plans. On one hand, industrial development is necessary for economic growth. On the other hand, should such plans be carried out without constraints, it would be at the expense of environment deterioration. For industrial establishments such as power utilities, oil refineries, steel mills, etc., the concern for economy and clean environment are usually conflicting, and careful design and planning are needed particularly to deal with this dilemma.
Another policy is based on successive reduction policy through which the largest controllable emitter will be asked to cut down in the case of an emerging pollution alert. Then the next largest controllable source will have to abate its emissions, and so on, until satisfactory air quality can be achieved. Usually, for urban areas this means that the first such sources to undertake the abatement are the power utility companies.
The quality of the ambient air has been of great concern in many regions in recent years, with the air pollution problem generally most severe around large metropolitan areas. The pollution sources which emit chemicals unfavorable to human health can usually be classified as stationary or mobile. The stationary sources are the various industrial plants, and residential areas and commercial districts. A common example is the power plants, particularly coal-fired ones, which emit ash, sulfur dioxide, particulate, etc. Mobile sources, like automobiles, which emit carbon monoxide and other chemicals, also have had devastating effects on the urban air quality. From the viewpoint of pollution control, the first important problem is identifying all the sources and assessing their relative impacts on the environment and human health.
An alternative in weighing and ranking different emission sources in abatement strategies is by their cost effectiveness instead of the total amount of emissions. Such an approach should reflect the costs and probable disruption of the area 's normal life and economy. In this paper, the main concern is the maintenance of air quality within an urban area through proper dispatching operation of the power plants. The power utility companies are the major sources of air pollution, judging from both their emissions and cost-effectiveness in pollution abatement. 2. POWER PLANTS EMISSION ABATEMENT
A great number of power plants throughout the world generate electricity by the use of coal. The dominance of coal in the electric power industry has existed for a long time. With the recent great price increases in oil and the fast depletion of its reserve, an even greater need for coal has been realized. Unfortunately, with the current technology, the use of coal has unfavorable environmental impacts. As an example, the annual S02 emission from power plants in the U.S. was 20 million tons in 19702 which accounted for 55 % of all the S02 emission. From this 55 %, 46.5% was from coaland 8.5% from oil-fired plants. I The situation in the url)an areas is even worse . The annual S02 concentration in several urban areas of the U.S. already exceeds the 0.03 to 0.04 ppm level .3 Many power plants near the metropolitan
The responsibility assessment of emission abatement within an urban area can be achieved through continuous monitoring of the air quality under various meteorological conditions around major sources. The surveillance of the ambient air quality can, in the long run, provide statistical records and give an indication of the types and extents of pollutants and their sources. This pollution surveillance should also include its correlation with the time, location and weather conditions.
·Presently on leave from Department of Electrical Engineer ing, Pahlavi University, Shiraz, Iran.
309
310
K.
-c.
Chu, M. Jamshidi and R. E. Levitan
urban areas are thus required to be oil- or gas-fired to maintain a lower S02 emisssion. There are a number of alternative emission abatement policies to incorporate with the "economic dispatch" of power within the utility companies. In extreme cases. it can be the complete shutdown of certain units within the company and importation of power from others. Under normal conditions. the utility company may have such options as fuel switching and load shifting among its plants. The load shifting is a less severe real-time approach which would not greatly disturb the power plant operation. The loads on the more polluting units (especially during peak hours) can be shifted to other plants with low-sulfur fuels. superior pollutant removal or dispersion capabilities (scrubbers and taller stacks). or to those at more favorable locations (better weather conditions. downwind. away from cities). The real-time power dispatch. considering the generation costs and the air quality. are the primary concern of this paper. The previous approaches suggested for this problem involve the imposition of one of these operation limits : (I) total maximum emission. 4 . 7 or (2) maximum pollutant concentration using a Gaussian plume dispersion modeI 8. 12 . For the first approach. the dispersion effects of favorable meteorological conditions are ignored. The second. while taking pollution dispersion into account. has only a steadystate model which cannot properly deal with varying power demand and weather conditions.
In this paper it is assumed that a study of urban background emissions similar to those considered in [14] or [17] has been conducted and the forecast CbaCkgrounit' ;xj,yj) is available at certain urban monitoring points (xj,y). j= 1.2 .... for time t I . Such forecasts are then used for the power dispatching. 3.2 Power Plant Emission The dispersion model for power plant emission with high background pollution must work on real-time. be adaptable to the changing conditions. and be reasonably accurate for the regions involved. The integrated Gaussian puff model used in this paper satisfies these requirements. This model is based on the statistical theory of turbulent diffusion and empirical data supporting it have been found by Sutton.1S Frenkiel. 19 Ogura,2° and others. Such a model would provide proper concentration levels for a wide wind speed range . including the stagnation situations. Time variations in the meteorological conditions. such as wind speed. atmospheric stability classes. and inversion layer height. will be accommodated. 14 ,ls Assuming there are N individual point sources and that Qj(t). the emission from source i at t. is constant over time intervals Ilk' the pollutant concentration at t' and ground location (x,y.O) can be expressed as
(1)
+ CbaCkgrOund(t ' ;x,y) Proposed by Chu et aJ.13, a new approach handles the dispatching problem for isolated plants with a model which emphasizes the dynamic property of pollutant dispersion and its forecast. In [13]. the integrated Gaussian puff diffusion modeP4·'s was introduced to handle specifically the changing weather and load conditions. In this paper. the approach considered in [13] will be proposed for the real-time power dispatch under air quality constraints around urban areas where other background sources are present. 3. MODELLING OF AIR POLLUTION DISPERSION The general background sources in urban areas. such as those of transportation and residential and commercial combustion. are difficult to curtail. and the control task is beyond the scope of this paper. We will simply describe briefly the efforts for modelling such sources. 3.1 Background Area Sources The modelling of urban background sources has been based either on the integration of concentration equation or on the approximation by equivalent point sources and consideration of their dispersion. Shieh et al. 14 have developed a numerical method for integrating the Gaussian puff dispersion equation of S02 to represent concentration from area sources. The authors have made a number of simplifying assumptions in order to include constant emission. wind speed. atmospheric stability' and turbulent intensity. Shir and Shieh '7 have also devised a numerical integration scheme for the partial differential equation representing the pollutant mass conservation over the area. Another method requires a great deal more data on emission, various meteorological parameters. surface roughness and chemical reaction rates. Still a third approach for urban air pollution modelling. considered by Roberts et al. ls represents the area sources by equivalent point sources computed upwind using estimated dispersion coefficients and propagation time. Then the area concentration is approximated by the use of the Gaussian puff dispersion model.
where t and t' are measured in the multiples of Ilk' and G(.) is the transfer coefficient representing the impact of a unit puff at t from the stack to the concentration at location (x.y) and time t ' . In the case of S02' no chemical reactions are assumed to take place in the atmosphere; therefore superpositions of the puffs would be applied. Function G(.) disperses'in time in a form of Gaussian distribution: G(t.t' ;x,y) ex p
=
[(2,,)3 / 20 .(t.t' )Oy(t,t' )o.(t.t I )]-1.
{_~ r(x-Xc(t,t' »)2 +(Y-Yc(t,t' »)2 + (Zc(t,t') 2]} 2l\ o.(t,t ' )
o,(t,t' )
0z(t,t' )
(2)
where [xc(t,t '),yc(t,t ' ),zc(t,t I )] are the center coordinates of the dispersed puff ellipsoid at t', emitted at t and o.(t,t' ), o,(t,t I ) and 0z(t,t ' ) are its standard deviations in space distribution in the x,y,z directions. 16 Coordinates (xc,yc,zc) can be updated by extrapolation with the average wind velocity vector during time intervals Ilk' When the atmospheric stability remains steady between t and t', approximately linear relations between o's and (t '-t) in logarithmic scales can be assumed. Reflections at ground level and the inversion layer can be handled by assuming proper additional sources and taking all of them, real and imaginary, into account. IS 4. AIR QUALITY CONSTRAINTS Our primary concern of air pollutions are their concentration and exposure durations instead of their total emission volume. Since it is the level of concentration that will affect human health, vegetation and materials. To this end, a certain moving average will be defined for pollutant concentrations. If the concentration of a certain pollutant at time t I is C(t I ;x,y) , its average over time duration w beginning at T is
'For its classification in terms of intensity of turbulence and thermal stratification of the atmosphere, see Turner.16
Real-time urban power C
( . _ 1 T+w I. wmean T.x.y) - w- ~" _T+1C(t .X.y).
311
(3)
where w is the window in which the average is taken (e.g .• 3 hr.. 24 hr.. etc.) and such window moves along the time horizon. Table I is part of the air pollution standards. set by the 1970 U. S. Clean Air Act. which also reflect this viewpoint of moving average constraints.21 The moving average standards require that (3) for each type of pollution be lower than a certain maximum level C wmax for all locations (x.y) and all time T.
(7)
is a required constraint. For practical systems with small losses. L(P,) can be approximated around the nominal load conditions by the quadratic form 22
(8) where constants Bmn (m.n= I •.. .•N) form a posItive semidefinite matrix. Upper and lower limits on the range of power generation for each plant are given by for all t.
Let s; be the pollutant content of a unit of fuel fired at plant i and F;(p;,) be the fuel consumption rate at the i-th plant when its output power is p;,. Substituting Q;(t) = s;F;(p;,) and (I) into (3) . we obtain T+w
~1'~T+l~;' s;FJp;)GJt.t I ;x . y)~Cwmax- CwbaCkgmund(T;x,y) (4)
for all T and (x,y). Ideally. we would like to monitor the relation (4) for all locations in the area covered. and implement (4) as inequality constraints in the dispatching problem. This is. of course. computation ally un feasible and not actually necessary. Only certain locations in an area are likely to have unsatisfactory air quality. particularly those in the city and in the downwind directions from the plants. This consideration naturally leads to the simpler requirement that (4) be satisfied for a set of selected locations (xj,yj).j= 1•.. .•M. The approach we are using is to select these (xj,y/s as the expected average local maxima of pollution concentration. precomputed on the basis ofthe forecast weather conditions and power generation schedules D Now denoting (xj>Yj) simply by j. the set of constraints (4) becomes T+w
W;-:~T+7;,s;F;(p;,)GJt . t I ;j) ~ C wmax - C w backgmund(T;j). (5)
for all T and j= I ... .. M. This expression is part of the optimization problem to be described in the following section. For illustrative purposes . only one type of pollutant (say. S02) and one time averaging window width ware indicated in (5). For several types of pollutants or time average durations. one simply employs as many such inequalities as would be necessary. 5. FORMULATION OF THE DISPATCH OPTIMIZATION PROBLEM
The environmental dispatch problem is essentially that of ordinary economic dispatch incorporated with air quality constraints (5). The requirement is to determine a feasible generation schedule for all power plant units with the minimum fuel cost while meeting the total demand and having the pollution concentration levels lower than specific standards for all times T and for all locations j in the area. Consider the N generating plants. and let the cost of a unit of fuel at plant i be c;. Such c; are generally different among the plants. The total cost of fuel consumed per hour is
(6)
~;c;F;(p;t) '
and the total power produced is
~;P ; t .
If P Dt is the total desired level of power generation to meet demand at time t. and L(P t) is the transmission losses at t to be readily defined below. then
(9)
Assuming P Dt as a specified quantity at t. the ordinary economic dispatch problem is to choose P;t' i= I .....N. to minimize (6). subject to the constraints (7) and (9). Other considerations. such as fuel availability and power interchange with other companies. could be added as constraints. Examining the requirement of (5) versus the other constraints. it is important to note the difference in their time scales. While the ordinary economic dispatch problem usually needs to be solved every 2-15 minutes to insure meeting the fast-varying demand P Dt • weather conditions and the associated G;(t.t ';j) will change at a much slower pace. It would be an unnecessary and even impossible job to track and update requirement (5) every 2-15 minutes. Our approach of solving the optimization problem. then. is to consider it in both long-term (around I hour) and short-term (2-15 minutes. or as frequently as necessary) modes. In the long-term mode. the explicit inequality (5) will be considered with forecast weather conditions. and the forecast power output levels P;t. The latter refer to the long-term averages (say. hourly) of the power outputs. The impact of pollution constraints on the generation cost will be assessed as an impost within each long-term period. Such assessment will be used to modify the cost function for short-term dispatching. in which the constraint (5) will no longer be considered explicitly. The long-term optimization problem is to Minimize
~t~;c;F;(p;t)'
(10)
subject to constraints (7). (9). and (5) and any other operation constraints. The index t runs as I .. ..•T max' where time is discretized in long-term intervals (say. I hour) and T max is the end value of the time horizon (say. 24 hours) . Here. all the PH's are the average values within each interval. Their solution will also satisfy a set of Kuhn-Tucker conditions: c;(dF/ dp;th\( I-OL(Pt) / oP;t)-~;t+r;t T+w + [~j~tl'jtw-'s;~t' ~T+1G;(t.t I ;j)](dF/dp;t)=O. i=I.2 •...• N;
(11)
t= 1.2 •...• T max'
where the A·s. the fs and rs, and the I"s are the Lagrange multipliers corresponding to (7), (9). and (5), respectively. Now the expression T+w TI;t = ~jt~" _T+ll'j,W- 1s;G;(t.t I ;j)
(12)
can be given an interesting interpretation. It represents a marginal shadow impost or "environmental tax" given a specific weather condition and background level to be added to the fuel cost at plant i and period t when the generation level is P;t. As has been shown in [131. we can replace the original dynamic decision problem coupled with constraint (5) by a set of uncoupled economic dispatch problems and execute them on a short term basis. These short term computations are based on a modified cost c; + TI;t' where the imposted tax TI;t are obtained by the long term optimization.
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Chu, M. Jamshidi and R. E. Levitan
6. AN ILLUSTRA TIYE EXAMPLE In this section the proposed real-time urban power dispatch program will be examined for a system of three power plants, one coal-fired and two oil-fired. One of the oil-fired plants is near a city where the forecast background S02 concentration level for a particular day, from three monitoring points, are given by Table 2. Figure 1 shows the assumed geographical location of the plants relative to the city. The numerical data for this power system are presented in Table 3, where F i (.) are linear throughout the operation range of our concern. We are considering a day for which the forecast wind speed, and direction and atmospheric stability class are given. These forecast data are nonuniform over the area. Generally the wind in the west of the region is strong while that by the city is near stagnation. The meteorological conditions and the background level are set deliberately to the extreme so that appreciable pollution effects can be seen . Power Plant I is located primarily in the upwind direction of the city. The computed positions of the three additional monitoring points determined by the proposed algorithm in the prevailing downwind direction and the original three city monitoring points are also shown in Fig. 1. Table 4 shows the total system power demand along with the would-be S02 concentrations (3 hour averages) without any air quality control imposed on the dispatch. Considering C lmax = 0.5 ppm and C 24m a. = 0.1 ppm for S02 (Table 1), it clearly shows that both standards have been violated to various extents at the first , fourth , and sixth monitoring points. The worst violation occurs between hours 12 and 17.
plants. Unlike the fixed ad hoc monetary emission penalties assumed by some previous researchers, our flexible environmental taxes are linked directly to the changing weather and load conditions. This would in effect project less stringent emission requirements over the entire generation schedule. The proposed methodology not only is more efficient but also suggests a more rational tax structure (i.e., weather and load dependent) for the governmental regulatory agencies to impose environmental taxes. This observation is further justified by Chapman's study2l which presented a critical examination of the "sulfur emission tax" imposed by the U.S. government. His general conclusions are that (i) the tax would cause significant reductions in emissions and damages, (ii) it has little effect on electricity demand growth, and (iii) it results in greater social benefits than costs, in particular if the U.S. Clean Air Act is not implemented 2 l The two-mode (short- and long-term) power dispatch considered here is also very promising from the implementation point of view. In fact in an environmental/economic power dispatch algorithm, the Gaussian plume and a socalled "transient models" are used by the Tennessee Valley Authority24 for long- and short-term dispatching, repectiveIy. One of the logical extensions to the present work is the inclusion of an online, preferably hourly or daily , updating of the background S02 concentrations. This would require a great deal of additional data on the various other sources: emissions, traffic flows, mixing heights. solar radiations and so on.
For the long-term problem with environmental con straints, we need to impose the constraint (5) with C lmax = 0.5 ppm , and C24max = 0. 1 ppm. The new schedule is given in Table Sa. Daily averages of the pollution concentrations for monitoring point I and point 6 turn out to be the binding constraints.
8. REFERENCES 1.
U. S. Environmental Protection Agency, Guide for air pollution episode avoidance, Office of the Air Programs, Publication No. AP-76 , Research Triangle Park, N.C.. June,I971.
The environmental fuel impost nit for the three plants is presented in Table 5 b. It can be seen that Plants I and 3 are penalized by the impost. The values of such impost are high at hours 1-2 and 9-19. The former is due to poor weather conditions, the latter to heavy background and great power demands. The fuel imposts nit' i= 1 ,2, .. ,N and t= 1,2, ... can be incorporated with the fuel cost c i for optimizing the short term dispatching in which the air quality constraints are not explicitly considered. The S02 daily average level in the area before irr,posimg, constraints (5) is shown in Fig. 2. That after the imposing, in Fig. 3.
2.
S. H . Schurr, Energy research needs, National Technical Information Service. PB-207 516 , U.S. Department of Commerce , Springfield, Va., October, 1971.
3.
U. S. National Air Pollution Control Administration, "Air Quality Criteria for Sui fur Oxides," NAPCA Pub. AP-50, Government Printing Office. Washington D. c., January, 1969.
4.
M. R. Gent and J. W. Lamont, "Minimum emission dispatch," IEEE Trans. Power App. Syst .• PAS-90, November-December, 1971, pp. 2650-2660.
5.
J. K. Delson, "Controlled emissions dispatch," IEEE PES Winter Meeting. paper T74-156-6. New York, N. Y., January, 1974
6.
0. E . Finnigan and A. A. Fouad. "Economic dispatch with pollution constraints," IEEE PES Winter Meeting, paper C-74-155-8, New York, N. Y., January, I974.
7.
J. W. Lamont, K. F. Sim, and E.P. Hamilton Ill, A multi-area environmental dispatching algorithm, Proc. 9th IEEE PICA , New Orleans. La. , June , 1975 , pp. 242-246.
8.
R. L. Sullivan, "Minimum pollution dispatching ," IEEE PES Summer Meeting, paper C72-468-7, San Francisco, Calif. , July, 1972.
9.
R. L. Sullivan and D. F. Hackett, "Air quality control using a minimum pollution dispatching algorithm ," Environm . Science and Tech. 1. , 8, 1974, pp. 679-680.
10.
P. G. Friedman, Power dispatch strategies for emission and environmental control, lnstr. in the Power
The redistribution of power plant generation levels reveals the fact that most of the pollutants created by the oil-fired Plant 1 and the coal-fired Plant 3 during the peak hours were eliminated by shifting their loads to the second plant which burns a less polluting fuel . i.e. oil, remote from the city, and has a more favorable weather condition. For the example considered, the dispatching algorithm with air quality constraints has reduced the peak S02 level by 67 % compared with the conventional dispatching program . 7. CONCLUSIONS An online power dispatch with background urban emission and air quality constraints is presented. The emphasis is placed on the dynamic dispersion of power plant emmision in surrounding regions which include urban areas. The binding air quality constraints as applied to the long-term dispatch provide a set of "environmental imposts" or "taxes" which may be used as an additional cost for the generation of power. This self-imposed tax, in our opinion. is a very practical scheme for curtailing the air pollution surrounding the power
Real-time urban power Primary Standards
Indust ., 16, 1973, pp. 59-64.
S. R. Carpenter, T. L. Montgomery, J. M. Leavitt, W. C. Colbauch and F . W. Thomas, "Principal plume dispersion models: TVA power plants, J . Air Pol. Cont. Assoc., 21, August, 1971.
11.
M. F. Ruane, J. Gruhl, F. C. Schweppe, B. A. Egan, D. H. Fyock, and A. A. Slowik, "Supplementary control systems-a demonstration," IEEE PES Summer Meet ing, paper F7 5-474-7, San Francisco, California, July, 1975 .
12.
13.
K. C. Chu, M. Jamshidi and R. E. Levitan, "An approach to online power dispatch with ambient air pollution constraints, IEEE Trans. on Automatic Control, AC-22 , June,) 977 .
14.
L. J. Shieh, B. Davidson, and 1. P. Friend, "A model of diffusion in urban atmospheres : S02 in Greater New York ," Proc . Symp. on Multi-source Urban Diff. Models , EPA, 1970, pp. 10.1-10.39.
15.
16.
D. B. Turner, "A diffusion model for an urban area," J. Appl. Meteorol. , 3, February, 1964, pp. 83-91.
17.
C. C. Shir and L. J. Shieh, "A generalized urban air
0. G. Sutton, "Theory of eddy diffusion in the atmosphere," Proc. Roy. Soc., SeT. A (London) 135, Augun, 1968 , pp. 575-582 .
19.
F. N. Frenkiel, "Application of statistical theory of turbulent diffusion to micrometeorology," J . Meteorol., 9, August, 1952, pp. 252-259.
20.
Y. Ogura, "Theoretical distribution functions of matters emitted from a fix point," Meteorol. Society Japan J., 32 (Series 11), January, 1954, pp. 22-26.
21 .
U. S. Federal Register, 36, no. 84 (Part 11), April 30, 1971 , p. 8187.
22.
L. K. Kirchmayer, Economic Operation of Power Systems. New York: John Wiley, 1958, Chapter 4.
23.
D. Chapman, "A sulfur emission tax and the electric utility industry," Energy Systems and Policy, I, 1974, pp.I-30.
24.
J. M. Leavitt, L. A. George and R. E. Clark, "Sulfur dioxide emission limitation (SDEL) program at TV A power plants," J. of Air Pollution Control, 26, December, 1976, pp.II33-1140.
Fuel Cost oil $15 / bl.
2 3
oil $15 / bl. coal
0 . 8~ / kg.
Sulfur Content
8.323 kg. S02 / bl.
Max. Freq.
ppm
Max. Freq.
0.03
annual avg.
0.02
annual avg.
0.14
24hr. avg. once/ yr.
0.10
24hr. avg. once/yr.
0.50
3hr. avg. once/yr.
Hour
Station I
Station 2
Station 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0 .032 0.027 0.029 0.046 0 .065 0.051 0.060 0.096 0.109 0.113 0.111 0.105 0.072 0.060 0.058 0.056 0 .054 0.052 0 .054 0.056 0 .060 0.071 0.101 0.111
0.000 0.000 0.000 0.002 0.004 0 .008 0.030 0.045 0.050 0.055 0.058 0.029 0.015 0.015 0.015 0.018 0.020 0.025 0.023 0.020 0.018 0.018 0.019 0.020
0.025 0.029 0.026 0.025 0.025 0.050 0.101 0 .126 0.139 0.126 0.101 0 .076 0.078 0.080 0.083 0.084 0.082 0 .083 0.083 0.086 0.091 0.083 0.063 0.050
Table 2.
Fuel Consumption Rate Fi(Pit) (per hr.)
8.323 kg. SO/ bl.
ppm
Average Levels of Background S02 in the Urban Area (ppm)
pollution model and its application to the study of S02 distributions in the St. Louis metropolitan area," J. Appl. Meteorol., 13, no. 2, March, 1974, pp. 185-204. 18.
Average Hourly Background S02 Levels (ppm)
Transmission Loss Coefficient Matrix B (Mw)-I
29.2+.813Plt+ ·00148PIt2 20.29+ 1.28IP2t+ .Oo'I86P2t2
57.00 gm. S02/ kg. 3200+298P3t + .32P3t2
Secondary Standards
Table I. Air Quality Standards for Sulfur Dioxide
J. J. Roberts, E. S. Croke and A. S. Kennedy, "An urban atmospheric dispersion model," Proc. Symp. on Multi-Source Urban Diff. Models, EPA, 1970, pp. 6.1-6.71.
Power plant i
313
[ 8650 10-5 • -2.112 -1.215
Table 3. System Operation Data for the Example
-2.112
Power Output Range Pimin:5Pi:5Pimax (Mw) 400 :5 Pit :5 1200
10.500
-121'] -.531
100 :5 P2t :5 1500
- .531
5.813
80 :5 P3t :5 900
K.
314
-c.
Chu, M. Jamshidi and R. E. Levitan
-
N
W+E
140 120 IJ)
~
COAL-FIRED POWER PLANT OIL - FIRED POWER PLANT ,.'-,, AIR QUALITY MONITORY POINT '., URBAN AREA TRANSMISSION LINE
[:=J
~. -
S
100
'E I
~
80
a:: 0
z
60 40 20 00
6
20
40
60
80
100
120
140
160
180
200 220
EAST (miles) Figure 1 Locations of power plants and the city in the illustrative example
Power and S02 Moving Average Schedule: Cost = $ 851,154 Hour
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Power Power Output (MW) Demand At Plant (MW) 2 3 1281 1162 1030 1112 1039 1089 1628 1834 1996 2321 2484 2508 2353 2275 2157 2027 2071 2318 2100 2055 1747 1639 1418 1297
400 400 400 400 400 400 498 615 706 907 990 1026 913 881 812 720 745 907 769 733 558 501 400 400
100 100 100 100 100 100 287 387 468 621 722 713 651 598 537 488 510 619 518 506 352 296 169 100
824 696 555 642 564 618 900 900 900 900 900 900 900 900 900 900 900 900 900 900 900 900 900 843
Line Loss (MW) 44 34 25 30 26 29 58 68 79 109 128 131 112 105 93 82 85 109 88 84 63 58 51 45
Three Hour S02 Moving Average Concentration (ppm) at Station 4 2 3 5 6 .029 .036 .060 .071 .077 .076 .092 .107 .112 .113 .106 .101 .105 .119 .140 .158 .175 .188 .204 .233 .265 .275 . 185 .086
Day
.000 .001 .002 .005 .014 .028 .042 .051 .056 .049 .036 .022 .018 .021 .028 .039 .049 .057 .062 .070 .078 .086 .060 .031
.027 .027 .026 .034 .061 .103 .145 .158 .149 .126 .115 .110 .113 .111 .109 .107 .105 .101 .099 .096 .086 .071 .041 .018
.001 .001 .001 .001 .000 .000 .015 .052 .092 .160 .271 .368 .495 .531 .556 .544 .585 .444 .247 .024 .005 .005 .004 .002
.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .025 .038 .052 .043 .040 .027 .011 .000 .000 .000 .000 .000 .000 .000
.003 .007 .006 .005 .000 .000 .006 .029 .031 .101 .418 .619 .886 .850 .979 .888 .679 .350 .103 .009 .007 .003 .001 .001
Twenty-Four Hour S02 Average Concentration (ppm) at Station 2 4 5 3 6 .131 Table 4.
.038
.090
Dispatching Schedule without Environmental Constraints
.183
.010
.249
Real-time urban power
315
Power and S02 MoYing Average Schedule: Cost = $ 1,220,800 Hour
1 2 3 4 5 6 7 8 9 10 Il 12 13 14 15 16 17 18 19 20 21 22 23 24
Power Power Output (MW) At Plant Demand (MW) 2 3 1281 1162 1030 1112 1039 1089 1628 1834 1996 2321 2484 2508 2353 2275 2157 2027 2071 2318 2100 2055 1747 1639 1418 1297
400 400 400 400 400 400 438 478 485 585 677 659 880 486 551 400 400 400 494 654 558 501 400 400
100 100 100 100 100 100 346 526 696 964 1056 1387 1470 1254 1500 1500 1500 1500 807 585 352 296 169 100
824 696 555 642 564 618 900 900 900 900 900 668 237 705 330 350 395 650 900 900 900 900 900 843
Three Hour S02 Moving Average Concentration (ppm) at Station 2 4 5 6 3
Line Loss (MW) 44 34 25 30 26 29 57 70 87 128 149 206 234 171 224 223 224 233 101 84 63 58 51 45
.029 .036 .060 .071 .077 .076 .092 .107 .1l2 .1l2 .102 .092 .087 .092 .106 .116 .123 .124 .128 .137 .153 .166 .116 .058
.000 .001 .002 .005 .014 .028 .042 .051 .056 .049 .036 .022 .018 .019 .024 .032 .038 .042 .043 .047 .051 .055 .038 .020
.027 .027 .026 .034 .061 .103 .145 .158 .149 .125 .112 .104 .104 .101 .099 .097 .095 .093 .093 .091 .083 .068 .039 .017
.001 .001 .001 .001 .000 .000 .011 .033 .054 .088 .144 .232 .297 .316 .277 .243 .215 .152 .077 .009 .004 .004 .004 .002
.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .074 .122 .164 .173 .186 .144 .061 .000 .000 .000 .000 .000 .000 .000
.003 .007 .006 .005 .000 .000 .006 .029 .031 .089 .197 .249 .327 .278 .325 .300 .278 .179 .068 .009 .007 .003 .001 .001
Twenty-Four Hour S02 Average Concentration (ppm) at Station 2 4 5 6 3
Day
.100 Table 5a.
.087
.030
.090
Dispatching Schedule Subject to Environmental Constraints
Hour
Plant 1
Plant 2
Plant 3
1 2 3 4 5 6 7 8 9 10 Il 12 13 14 15 16 17 18 19 20 21 22 23 24
40.660 13.610 0.250 0.002 0.033 0.282 2.968 7.773 13.838 18.699 17 .605 27.929 22.125 39.791 50.305 61.371 67.164 61.097 16.065 4.004 0.151 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.00132 0.00190 0.00802 0.00001 0.00000 0.00000 0.00002 0.00564 0.01899 0.00285 0.03864 0.16046 0.31251 0.13495 0.29189 0.27555 0.29362 0. 18684 0.00221 0.00444 0.00159 0.00013 0.00086 0.00000
Table 5b.
Environmental Fuel Imposts, ($ / fuel unit)
nil
.039
.100
K. -C. Chu, M. Jams hidi and R. E. Levitan
316 150
100 :I:
~ z
o
.002
:I: I~
o
(J)
o .002 -50 -130
-100
o
100
200
WEST - - - - - - - - EAST
Figure 2 CONTOURS OF TWENTY -FOUR HOUR SULFUR DIOXIDE AVERAGE ON DAY WITHOUT ENVIRONMENTAL CONTROLS (ppm)
150
100 :I:
~
o z
.002
:I: I-
~
o(J)
o
-50 -130
-100
o
100 WEST - - - - - - - - EAST
Figure 3 CONTOURS OF TWENTY-FOUR HOUR SULFUR DIOXIDE AVERAGE ON DAY SUBJECT TO ENVIRONMENTAL CONTROLS (ppm)
200