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# Final Review

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The presentation given for my undergraduate project, which deals with optimization and sizing of solar panels and wind turbines of a grid connected hybrid system for a remote area, taking into consideration, the cost and the CO2 emission..

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### Final Review

1. 1. Optimization of a Gridconnected Hybrid PV-Wind System SUBMITTED BY C.S.SUPRIYA M.SIDDARTHAN IV YEAR EEE GUIDED BY DR. M. VARADARAJAN SARANATHAN COLLEGE OF ENGINEERING
2. 2. Objective of the ProjectTo design an optimum PV-wind hybrid energy system, interconnected to the grid (especially for remote areas) so as to:o minimize the electricity production cost (\$/KWh)o ensure that the load is served reliablyo minimize the power purchased from the grid
3. 3. Scope of the ProjectThe assumptions made for this formulation are:o the converter which converts the dc power from the PV panels and wind turbines is assumed to be idealo the system is always connected to the grid; isolated PV panels and/or wind turbines are not taken into account; no battery is consideredo operation of wind and PV generators at their maximum power operating points is ensured through Peak Power Trackers
4. 4. Overall Scheme
5. 5. Mathematical Model of PV Modules- Power OutputPower output of a PV panel is given as: Ps ηISnwhere, η is the conversion efficiency of PV panel I is the irradiance (kW/m2)
6. 6. Mathematical Model of PV Modules- Cost functionInitial and maintenance costs are given as: Sic ScSn Sic(1- λs) Sn Smc Sy Sywhere,Sc is the cost per 1 m2 of PV panelλs is reliability coefficient of PV panelsSy is lifetime of PV panelsSn is number of PV panels to be determined
7. 7. Graphical Representation of Power Output of Wind Generators
8. 8. Mathematical Model of Wind Generators- Power OutputThe power output can be mathematically written as follows:Pw=0 (Wout<WS<Win)Pw ξ(WS- Win) Wn x 10-3 (Win<WS<Wrs)Pw=WrpWn (Wrs<WS<Wout)where,Win is the cut-in speed (m/s)Wout is the cut-out speed (m/s)WS is the wind speed (m/s)Wrp is the rated power (W)ξ is the slope between Win and Wrs (W/m/s)
9. 9. Mathematical Model of Wind Generators- Cost functionInitial and maintenance costs are given as: WcWn Wic(1- λw) Wn Wic Wmc Wy Wywhere,Wc is the cost per one generator of wind turbinesλw is reliability coefficient of wind turbinesWy is lifetime of wind turbinesWn is number of wind turbines to be determined
10. 10. Objective FunctionThe objective function is to minimize the total cost of a grid connected hybrid PV and wind system: Min (Tc) = Min (Sic+Smc+Wic+Wmc+CpUp)where, Sic, Smc are initial and maintenance costs of PV panels used (\$) Wic, Wmc are initial and maintenance costs of wind turbines used (\$) Cp is the cost/kWh of power drawn from utility (\$) Up is the number of units of electric power to be drawn from the grid (kWh)
11. 11. Objective Function (cont.)Thus the objective function can be written as: ScSn Sc(1 λs) Sn 2 WcWn Wc(1 λw) Wn 2min CpUp Sy Sy 2 Wy Wy 2
12. 12. ConstraintsThe constraints are set so as to minimize magnitude of the difference between generated power (Pgen) and the power demand (Pdem) ΔP Pgen Pdemwhere, Pgen = Ps+ Pw+ UpPs, Pw, Up are the power outputs of solar panels, wind turbines and the power taken from the grid respectively.
13. 13. Constraints (cont.)The total generated and demanded energy (Egen, Edem) over a year: 8760 Egen (Ps)( T ) (Pw)( T ) (Up)( T ) n 1 8760 Edem (Pdem)( T ) n 1For generation and load to balance over a given period of time, the curve of ∆P versus time must have an average of zero over the same time period (in this case, over a year) ΔE ΔPdt Egen Edem
14. 14. Constraints (cont.)Hence the constraints can be written as follows: 8760 8760 (Ps)( T ) (Pw)( T ) (Up)( T ) (Pdem)( T ) n 1 n 1Since ∆T=1 hour in this case, the constraints can be further modified as: 8760 8760 8760 8760 Ps Pw Up Pdem n 1 n 1 n 1 n 1Therefore, by substituting the various terms for Ps, Pw, the constraints can be written as: 8760 8760 8760 8760 ηISn ξ(WS Win) Wn 10 3 Up Pdem n 1 n 1 n 1 n 1
15. 15. Procedure to balance the demand and generationAfter obtaining the results yearly optimization, for every hour, Sn and Wn are fixed as obtained above and Up is varied to meet the demand if Ps+Pw<Pdem, Up=Pdem-Ps-Pw if Ps+Pw>Pdem, Up=0; the excess power is dumped into controlled resistors
16. 16. Implementation of Quadratic ProgrammingThe objective function and constraint obtained can be written in matrix form as follows: Sc(1 λs) 0 0 Sy 2 Sn Sn Wc(1 λw) Sc Wc min Sn Wn Up 0 0 Wn Cp Wn Wy 2 Sy Wy 0 0 0 Up Upsubject to: Sn (ηI) (ξ (WS Win) 10 3 ) 1 Wn Pdem Up
17. 17. Implementation of Quadratic Programming (cont.)The above formulation is of the form: min (0.5 XT H X +fT X) sub to: Aeq X = beqwhere, Sc(1 λs) Sc 0 0 Sn Sy 2 Sy Wc(1 λw) Wc X Wn H 0 0 f Wy 2 Wy Up 0 0 0 Cp Aeq (ηI) (ξ(WS Win) 10 3 ) 1 beq Pdem
18. 18. Carbon EmissionApart from cost, our objective is also to reduce the amount of CO2 emitted from the systemCarbon emission is reduced by increasing the use of renewable sources and thereby, reducing the power consumption from gridAmount of CO2 emitted from grid 0.98 kg/kWh
19. 19. Case Study I Hourly average data for load demand, insolation and wind speed of a day are taken and the same is projected for a year Using quadratic programming, yearly optimization is run by fixing maximum number of panels and turbines arbitrarily based on minimum and maximum demands; graphs are obtained Maximum number of panels and turbines are fixed on the basis of ∆P curve against number of modules Optimization is run again, similar graphs are obtained and results are tabulated Region of optimal operation is obtained based on the cost versus carbon emission curves for increasing number of each module
20. 20. Conventional Grid System
21. 21. Grid Connected PV System – Using 32 Panels
22. 22. Grid Connected Wind System – Using 4 Turbines
23. 23. Grid Connected Hybrid System – Using 8 Panels and 4 Turbines
24. 24. Fixing Maximum Number of ModulesMaximum Panels: 74 Maximum Turbines: 8
25. 25. Grid Connected PV System – 74 Panels
26. 26. Grid Connected Wind System – 8 Turbines
27. 27. Grid Connected Hybrid System – 5 Panels and 8 Turbines
28. 28. Comparison of Results – Case Study I Grid Grid Grid Grid systemConfiguratio connected connected connected (Convention n / Type of hybrid wind system PV system al) analysis systemCost per year 1044.6 607.578 2331.5 5716.3 (\$)Power drawn from grid 2954.7 6455.2 9197.8 17,013 (kWh) Per year emission of 2895.9 6326.1 9013.8 16,672 CO2 (kg)
29. 29. Optimal Region of Operation
30. 30. Case Study II Hourly average data for load demand, insolation and wind speed of a year are taken Using quadratic programming, yearly optimization is run by fixing maximum number of panels and turbines arbitrarily based on minimum and maximum demands; graphs are obtained Maximum number of panels and turbines are fixed on the basis of ∆P curve against number of modules Optimization is run again, similar graphs are obtained and results are tabulated Region of optimal operation is obtained based on the cost versus carbon emission curves for increasing number of each module
31. 31. Conventional Grid System
32. 32. Grid Connected PV System (Power Demand and Generation) – Using 75 Panels
33. 33. Grid Connected PV System (Power Demand and Split-up of Generation) – Using 75 Panels
34. 34. Grid Connected Wind System (Power Demand and Generation) – Using 10 Turbines
35. 35. Grid Connected Wind System (Power Demand and Split-up of Generation) – Using 10 Turbines
36. 36. Grid Connected Hybrid System (Power Demand and Generation) – Using 100 Panels and 10 Turbines
37. 37. Grid Connected Hybrid System (Power Demand and Split- up of Generation) – Using 100 Panels and 10 Turbines
38. 38. Fixing Maximum Number of ModulesMaximum Panels: 135 Maximum Turbines: 13
39. 39. Grid Connected PV System (Power Demand and Generation) – 135 Panels
40. 40. Grid Connected PV System (Power Demand and Split-up of Generation) – 135 Panels
41. 41. Grid Connected Wind System (Power Demand and of Generation) – 13 Turbines
42. 42. Grid Connected Wind System (Power Demand and Split-up of Generation) – 13 Turbines
43. 43. Grid Connected Hybrid System (Power Demand and Generation) – 8 Panels and 13 Turbines
44. 44. Grid Connected Hybrid System (Power Demand andSplit-up of Generation) – 8 Panels and 13 Turbines
45. 45. Comparison of Results – Case Study IIConfiguratio Grid Grid Grid Grid system n / Type of connected connected connected (Convention analysis hybrid wind system PV system al) systemCost per year 1690 1440.4 4213 13098 (\$)Power drawn from grid 9922.2 10597 22054 38982 (kWh) Per year emission of 9723.8 10597 21612 38202 CO2 (kg)
46. 46. Optimal Region of Operation
47. 47. Conclusion On basis of cost, the grid-wind system may seem to be the best But carbon emission is also a major criterion to be taken into account Besides, the cost of grid-hybrid system is not too high compared to grid-wind system Thus grid-hybrid system is concluded to be the best configuration which makes maximum use of renewable sources
48. 48. Future Scope If a contract could be signed by incorporating a selling price for the excess power produced, there would be a considerable reduction in the cost Introduction of more efficient PV panels can further decrease the cost of grid-PV system and particularly that of grid-hybrid system Thus, the grid-hybrid system would become the best type of configuration in terms of cost as well in near future
49. 49. References[1] Ashok, S., “Optimised Model for Community-Based Hybrid Energy System” RENEWABLE ENERGY, VOL. 32, NO.7, JUNE 2007, PP: 1155–1164.[2]Bagul, A.D., Salameh, Z.M., Borowy, B., “Sizing of Stand-Alone Hybrid PV/Wind System using a Three-Event Probabilistic Density Approximation.” JOURNAL OF SOLAR ENERGY ENGINEERING, VOL. 56, NO.4, 1996, PP: 323-335.[3]Chedid, R., and Rahman, S., “Unit Sizing and Control of Hybrid Wind-Solar Power Systems” IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 12, NO. 1, MARCH 1997, PP: 79-85.[4]Chedid, R., Saliba, Y., “Optimization and Control of Autonomous Renewable Energy Systems” INTERNATIONAL JOURNAL ON ENERGY RESEARCH, VOL. 20, NO. 7, 1996, PP: 609- 624.[5]Karaki, S.H., Chedid, R.B., Ramadan, R., “Probabilistic Performance Assessment of Autonomous Solar-Wind Energy Conversion Systems.” IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 14, NO. 3, SEPTEMBER 1999, PP: 766-772.[6]Kellogg, W.D., Nehrir, M.H., Venkataramanan, G. and Gerez, V., “Generation Unit Sizing and Cost Analysis for Stand-Alone Wind, Photovoltaic and Hybrid Wind/PV Systems” IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 13, NO. 1, MARCH 1998, PP: 70-75.
50. 50. References (cont.) [7] Kellogg, W.D., Nehrir, M.H., Venkataramanan, G. and Gerez, V., “Optimal Unit Sizing for a Hybrid PV/Wind Generating System.” ELECTRIC POWER SYSTEM RESEARCH, VOL. 39, 1996, PP: 35-38.[8] Muralikrishna, M., Lakshminarayana, V., “Hybrid (Solar and Wind) Energy Systems for Rural Electrification” ARPN JOURNAL OF ENGINEERING AND APPLIED SCIENCES, VOL. 3, NO. 5, OCTOBER 2008, PP: 50-58[9] Musgrove, A.R.D., “The Optimization of Hybrid Energy Conversion System using the Dynamic Programming Model – RAPSODY.” INTERNATIONAL JOURNAL ON ENERGY RESEARCH, VOL. 12, 1988, PP: 447-457.[10] Ramakumar, R., Shetty, P.S., and Ashenayi, K., “A Linear Programming Approach to the Design of Integrated Renewable Energy Systems for Developing Counntries” IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. EC-1, NO. 4, DECEMBER 1986, PP: 18-24.[11] Senjyu, T., Hayashi, D., Urasaki, N., and Funabashi, T., “Optimum Configuration for Renewable Generating Systems in Residence Using Genetic Algorithm” IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 2, JUNE 2006, PP: 459-466. [12] Wang, C., Nehrir, M.H., “Power Management of a Stand-Alone Wind/Photovoltaic/Fuel Cell Energy System” IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 23, NO. 3, SEPTEMBER 2008, PP: 957-967.
51. 51. References (cont.)[13] Yang, H.X., Burnett, J., Lu, L., “Weather Data and Probability Analysis of Hybrid Photovoltaic Wind Power Generation Systems in Hong Kong.” RENEWABLE ENERGY, VOL. 28, 2003, PP: 1813-1824. [14] Yokoyama, R., Ito, K., Yuasa, Y., “Multi-Objective Optimal Unit Sizing of Hybrid Power Generation Systems Utilizing PV and Wind Energy.” JOURNAL OF SOLAR ENERGY ENGINEERING, VOL. 116, 1994, PP: 167-173. [15] Energy Analysis of Power Systems - World Nuclear Association [Online], 2009[Cited July 2009]; Available from: http://www.world-nuclear.org/info/inf11.html[16] Singiresu. S. Rao, Engineering Optimization- Theory and Practice, 3rd edition, New Age International (P) Ltd.; 1996