1. Combined Economic and Emission Dispatch using RBF neural network

2. Topics Introduction CEED RBF Algorithms OVERALL PROCESS DESCRIPTION CEED USING LAMBDA TECHNIQUE CLUSTERING TECHNIQUE CEED USING RBF Case studies 3GEN 6GEN 15GEN Conclusion

3. Introduction of work Formulating Combined economic and emission dispatch using RBF network comparing results using BPA network and conventional lambda technique

4. Combined Economic and Emission Dispatch The multi-objective CEED problem is converted into single optimization problem by introducing price penalty factor, h Minimize Φ = F + h pd * E The modified price penalty factor h pd, combines the emission with the normal fuel costs

5. Combined Economic and Emission Dispatch weightages:

6. Price Penalty Factor The price penalty factor for a particular load demand P D : Find the ratio between maximum fuel cost and maximum emission of each generator. sort h i values in ascending order. Add the maximum capacity of each unit (P i,max ) one at a time, starting from the smallest h i unit until ∑P i,max ≥ P D At this stage, h i associated with the last unit in the process is the price penalty factor for the given load. $/Kg

7. Modified Price Penalty Factor The computation steps for h pd : Find the ratio between maximum fuel cost and maximum emission of each generator sort h i values in ascending order Form an array, m by adding P i,max one by one from the lowest h i value unit Add the elements of m i one at a time, starting from the smallest h i unit until Σ m > P D The modified price penalty factor h pd is computed by interpolating the values of h i for last two units by satisfying the corresponding load demand.

8. Numerical example h i = [h 3 h 2 h 1 ] ; h i = [1.1909 2.6221 3.1057] The corresponding maximum limits of generating units are P i,max = [180 150 200] m is formed by adding maximum capacity of the units one by one m = [180 330 530] For P D = 259MW; (180+330) MW >259MW The modified price penalty factor h m is computed by interpolating the values of h i for last two units by satisfying the corresponding load demand. ie, h pd = 1.1909 + ((2.6221- 1.1909)/(330- 180))*(259- 180) = 1.9446

9. Process in general GENERATING PATTERNS FOR TRAINING NETWORK FROM ABOVE METHOD TRAINING OF RBF NETWORK WITH PROPER SELECTION OF CONSTANTS AND WEIGHT INITIALISATION COMPARING RESULTS RUNNING CEED USING CONVENTIONAL LAMBDA TECHNIQUE INITIALISING RBF NETWORK

10. Lambda iterative technique 1.For given P d find h pd 2.Find lambda 3.Find all P 4.Check and keep within limits 5.Find error sum of P and P d 6.Repeat from 3 to 5 with increment/decrement until convergence

11. Flow Chart of Lambda Iteration Method for Combined Economic and Emission Dispatch and generating required training patterns for training neural networks

12. Clustering technique Read input space of ‘n’ patterns group ith input pattern to the centre which is nearest to it Randomly choose no of centers (say ‘k’) and Then randomly choose those k centers from input space Ensure that no repetitions are there Find average of those groups individually and treat them as new centres Check for centres which are actually matching with input pattern and note them Find width for each corresponding centre End of clustering technique and thus new centres are formed Initialise pattern no i = 1 i = = n i = i + 1 NO YES

13. INPUT SPACE

14. Centers are chosen from input space

15. Centers After Clustering Technique

16. RBF STRUCTURE x1x1 x2x2 xnxn y1y1 ymym 11 22 ll w 11 w 12 w1lw1l wm1wm1 wm2wm2 w ml Weights w ij Centers  j of  j Widths  j of  j Training set Kernels

17. Gaussian RBF φ center φ :  is a measure of how spread the curve is: Large  Small 

18. PROCEDURE – CEED USING RBF: Read reqd. data and training patterns Find centres using Clustering technique Find corresponding widths for each centre Intialise weight matrix b/w hidden layer and o/p layer start weight training and repeat process until itermax is reached or reqd convergence is attained Test network and compare results

19. MEMORISING FOR TRAINING Weight training: 1.First run the process with weights randomised with restrictions on itermax and epsilon 2.Repeat above step for a few trials say 6 - 9 trials and memorize all the finalised weights and Errorrate after complete training 3.Choose the best trial that is most successful among all trials 4.then run process using finalised weights after best run trial as initial set of weights instead of taking randomised weights 5.Repeation of above step 4 for itself for a few times (say 5 – 10) improves convergence time

20. Case studies average percentage absolute error (APAE) Where m is no of generators

21. 3gen data: Here tabulated data is as per these equations F = c + bP + aP*P E = C + BP + AP*P S.No P min MW P max MW abcABC 1 352100.0354638.305531243.53110.00683-0.5455140.26690 2 1303250.0211136.327821658.56960.00461-0.5116042.89553 3 1253150.0179938.270411356.65920.00461-0.5116042.89553

22. 3 generator system Power Demand (MW) W1 w2 MethodP 1 (MW) P 2 (MW) P 3 (MW) Total Fuel Cost (Rs/hr) Total Emission Release (Kg/hr) Total cost Rs/hr APAE % 610 0.80 0.20 Lambda iter. 145.2789234.0502230.670930016.1922451.036528188.3322 RBF145.6566233.7527230.3347 30005.1615450.54927928174.9973 0.0043 570 0.20 0.80 Lambda iter. 144.8022212.7760212.421728175.6457389.473519992.2859 RBF145.4145212.3038211.2764 28131.4432388.01810419929.7954 0.1128 630 0.75 0.25 Lambda iter. 152.1468240.1697237.683430962.7347483.0424028824.1774 RBF153.5925239.8800237.4552 31009.6389484.396528875.0603 0.2445

23. 6 generator data Here tabulated data is as per these equations F = a + bP + cP 2 E = A + BP + CP 2 S.No P min MW P max MW abcABC 15020002.00.0037522.983-0.900.0126 2208001.70.0175025.313-0.100.0200 3155001.00.0625025.505-0.010.0270 4103503.250.0083424.900-0.0050.0291 5103003.00.0250024.700-0.0040.0290 6124003.00.0250025.300-0.00550.0271

24. 6GEN SYSTEM for pd = 347MW w1 = 0.5 w2 = 0.5 S.N o Lambda iter RBF 1 148.8221148.2532 2 63.371663.2481 3 33.315732.6584 4 35.000034.5196 5 30.000030.0827 - 6 36.401836.3468 Through RBF APAE = 0.6330 % Lambda iterRBFDIFF TOTAL FUEL COST $/hr 1040.1959611032.840539-7.355422 TOTAL EMISSION lb/hr 494.605464490.589418-4.016046 TOTAL COST $/hr 997.402970989.849605-7.553365

25. 6GEN SYSTEM for pd = 217MW w1 = 0.3 w2 = 0.7 S.N o Lambda iter RBF 1 94.271694.6084 2 37.501737.4304 3 22.466822.2899 4 21.601421.2436 5 19.997220.0274 6 21.161221.5034 Through RBF APAE= 0.0848 % Lambda iterRBFDIFF TOTAL FUEL COST $/hr 583.012387583.2593660.246979 TOTAL EMISSION lb/hr 250.622047250.7929720.170925 TOTAL COST $/hr 478.844577479.1259340.281357

26. The 75-bus Uttar Pradesh State Electricity Board (UPSEB), Indian Utility system Here tabulated data is as per these equations F = aP 2 + bP + c E = AP 2 + BP + C S.No P min MW P max MW abcABC 110015000.00080.814000.0036-0.8124.300 21003000.00141.380400.0035-0.1027.023 3402000.00161.566200.0330-0.5027.023 4401700.00161.606900.0034-0.3022.070 5402400.00161.566200.0380-0.8124.300 6101200.00181.742200.0330-0.5027.023 7101000.00181.775500.0034-0.0329.040 8201000.00181.742200.0039-0.0229.030 9605700.00121.179200.0030-0.0227.050 10302500.00171.694700.0034-0.3022.070 11402000.00161.620800.0034-0.2523.010 128013000.00040.409100.0035-0.0321.090 13509000.00070.677000.0038-0.4124.300 14101500.00151.491000.0034-0.2023.060 15204540.00101.002500.0036-0.1029.000

27. BPA result for 15gen Nodes(3,44,15) 437 patterns Alpha = 0.85 Eta = 0.05 Epsilon = 0.003 iter = 2000 Error_rate = 0.0057178 Iter = 1200 Error rate = 0.007008 runtime = 289.6560

28.  Nodes(3,49,15)  437 patterns  Alpha = 0.997  Eta = 0.00023  Epsilon = 0.003  iter = 324  Error_rate = 0.004999  runtime = 108.9850 RBF result for 15gen Before memorizing the weights showing error rate Vs no of iterations

29. RBF result for 15gen after memorising weights  Nodes(3,49,15)  437 patterns  Alpha = 0.997  Eta = 0.00023  Epsilon = 0.003  iter = 73  Error_rate = 0.004994  runtime = 58.9850

30. 15 GEN SYSTEM: for pd = 5800 MW w1 = 0.7 w2 = 0.3 S.No Lambda iter RBF 1 399.7628402.1623 2 300.0000300.1345 3 200.0000200.2726 4 170.0000171.7689 5 240.0000241.0690 6 120.0000121.5109 7 100.0000100.0940 8 100.0000100.0060 9 359.0913360.1946 10 250.0000252.0347 11 200.0000199.3489 12 460.6124464.0438 13 399.7611402.0469 14 150.0000152.9520 15 334.9539336.2252 Through RBF apae = 0.5391% Lambda iterRBFDIFF TOTAL FUEL COST $/hr 5638.2836085671.82615633.542548 TOTAL EMISSION lb/hr 6852.9466006920.14015167.193551 TOTAL COST $/hr 6017.2554686061.035340 43.779872

31. 15 GEN SYSTEM: for pd = 6200 MW w1 = 0.6 w2 = 0.4 S. No Lambda iter RBF 1 331.1324331.1961 2 297.7298290.7176 3 200.0000201.1689 4 170.0000171.0384 5 240.0000241.4921 6 120.0000121.5157 7 100.0000100.2106 8 100.000099.8010 9 297.4392297.4031 10 250.0000252.1001 11 200.0000198.9616 12 381.5344381.9169 13 331.1302331.1220 14 150.0000152.2316 15 277.4469277.3163 Through RBF apae = 0.1735% Lambda iterRBFDIFF TOTAL FUEL COST $/hr 5182.5501705186.150039 3.599869 TOTAL EMISSION lb/hr 6089.017525 6132.894039 43.876514 TOTAL COST $hr 5212.1861225227.81061715.624495

32. Conclusion Combined economic and emission dispatch is formulated using RBF network. –Centres were apart –Memorising weights and centres, results in faster convergence Network is tested for 3gen, 6gen, 15gen systems Can be combined with Unit Commitment Problem for complete study

33. References  An RBF Network With OLS and EPSO Algorithms for Real-Time Power Dispatch by Chao-Ming Huang and Fu-Lu Wang IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 22, NO. 1, FEBRUARY 2007 R. Ramanathan, “Emission constrained economic dispatch,” IEEE Trans. Power Syst., vol. 9, no. 4, pp. 1994–2000, Nov. 1994. P. S. Kulkarni, A. G. Kothari, and D. P. Kothari, “Combined economic and emission dispatch using improved backpropagation neural network,” Elect. Mach. Power Syst., vol. 28, no. 1, pp. 31–44, Jan. 2000. P. S. Kulkarni, A. G. Kothari, and D. P. Kothari, “Application of radial basis function neural network for economic dispatch,” J. Inst. Eng. (India): Elect. Eng. Div., vol. 83, pp. 81–86, Sep. 2002. Solutions to Practical Unit Commitment Problems with Operational, Power Flow and Environmental Constraints I. Jacob Raglend and Narayana Prasad Padhy IEEE 2006 Economic Power Dispatch Of Power System With Pollution Control Using Multiobjective Particle Swarm Optimization Tarek Bouktir, Rafik Labdani and Linda Slimani June 2007 University of Sharjah Journal of Pure & Applied Sciences Volume 4, No. 2

34. Thank you

36. Run time comparision Lambda iterative (SEC) RBF (SEC) RUNTIME pd = 5800 MW w1 = 0.7 w2 = 0.3 0.18700.0100 RUNTIME pd = 5800 MW w1 = 0.7 w2 = 0.3 0.15600.0

37. Acid Rain Damages Lakes, Streams, and Forests Acid deposition occurs when emissions of SO2 and NOx react in the atmosphere to create acidic gases and particles which reach the Earth in wet and dry forms. Effects of acid deposition include: –Acidification of lakes and streams, making them unable to support fish and other aquatic life; –Damage to forests through acidification of soil, depletion of soil nutrients, and direct injury to sensitive tree leaves and needles Despite substantial emissions reductions over the last 20 years, high levels of sulfur and nitrogen deposition still enter acid-sensitive lakes and streams, leading to high levels of acidity. Under current emissions rates, nitrogen saturation is expected to get worse Nitrogen saturation contributes to greater forest and grassland susceptibility to fire

38. Year 2004 Utility Greenhouse Gas Emissions Coal 65,484,849 tons CO 2 Oil & petcoke 33,404,545 tons CO 2 Natural gas 44,846,881 tons CO 2  Total fossil fuel143,736,276 tons CO 2 All emissions data from eGrid. Does not include 1,265,244 tons CO 2 emissions from burning of non-biogenic solid waste such as plastics and tires in waste-to-energy facilities. Fossil-fuel electricity generation accounts for about 45% of Florida’s greenhouse gas emissions

39. Year 2004 Net Generation by Source  Fossil-fuel generation Coal 61,982,540 MWh Coal 61,982,540 MWh Oil & petcoke 37,232,873 MWh Oil & petcoke 37,232,873 MWh Natural gas 76,624,773 MWh Natural gas 76,624,773 MWh Interchange power 18,649,000 MWh Interchange power 18,649,000 MWh Subtotal 194,489,186 MWh (83% of grand total) Subtotal 194,489,186 MWh (83% of grand total)  Other generation Biomass 4,950,744 MWh Biomass 4,950,744 MWh Nuclear 31,215,576 MWh Nuclear 31,215,576 MWh Hydroelectric 265,258 MWh Hydroelectric 265,258 MWh Other waste & phosphate* 2,862,650 MWh Other waste & phosphate* 2,862,650 MWh  Grand Total 233,783,414 MWh Interchange data from Florida Reliability Coordinating Council; all other data from eGrid. eGrid assigns 70% of generation from solid waste to biomass; 30% to other waste (plastics, tires, etc.). *Includes waste heat cogeneration in phosphate industry. Interchange data from Florida Reliability Coordinating Council; all other data from eGrid. eGrid assigns 70% of generation from solid waste to biomass; 30% to other waste (plastics, tires, etc.). *Includes waste heat cogeneration in phosphate industry.

40. Year 2004 Average CO 2 Emission Rates for Florida Fossil-Fuel Units Coal 2,113 lb/MWh Oil & petcoke1,794 lb/MWh Natural gas1,171 lb/MWh  Weighted avg.1,635 lb/MWh

41. CO 2 Emission Rates for Fossil-Fuel Generating Units Compared  Year 2004 statewide average emission rate: 1,635 lb/MWh 1,635 lb/MWh  Statewide average emission rate to meet 135 million ton cap with total generation of 325 million MWh, 83% of which supplied by fossil fuel (values selected for illustrative purposes; not a DEP-presumed scenario) 1,000 lb/MWh  Emission rates achievable by today’s new units: Natural gas combined cycle 800 lb/MWh Natural gas combined cycle 800 lb/MWh Pulverized coal or IGCC1,750 lb/MWh (w/o carbon capture & storage) Pulverized coal or IGCC1,750 lb/MWh (w/o carbon capture & storage)