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..

1. Optimization of a Grid
connected Hybrid PV-Wind
System
SUBMITTED BY
C.S.SUPRIYA
M.SIDDARTHAN
IV YEAR EEE
GUIDED BY
DR. M. VARADARAJAN
SARANATHAN COLLEGE OF ENGINEERING

2. Objective of the Project
To 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 reliably
o minimize the power purchased from the grid

3. Scope of the Project
The 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 ideal
o the system is always connected to the grid; isolated PV
panels and/or wind turbines are not taken into account; no
battery is considered
o operation of wind and PV generators at their maximum
power operating points is ensured through Peak Power
Trackers

4. Overall Scheme

5. Mathematical Model of PV Modules- Power Output
Power output of a PV panel is given as:
Ps ηISn
where,
η is the conversion efficiency of PV panel
I is the irradiance (kW/m2)

6. Mathematical Model of PV Modules- Cost function
Initial and maintenance costs are given as:
Sic
ScSn Sic(1- λs) Sn
Smc
Sy Sy
where,
Sc is the cost per 1 m2 of PV panel
λs is reliability coefficient of PV panels
Sy is lifetime of PV panels
Sn is number of PV panels to be determined

7. Graphical Representation of Power Output of
Wind Generators

8. Mathematical Model of Wind Generators- Power
Output
The 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. Mathematical Model of Wind Generators- Cost
function
Initial and maintenance costs are given as:
WcWn Wic(1- λw) Wn
Wic Wmc
Wy Wy
where,
Wc is the cost per one generator of wind turbines
λw is reliability coefficient of wind turbines
Wy is lifetime of wind turbines
Wn is number of wind turbines to be determined

10. Objective Function
The 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. Objective Function (cont.)
Thus the objective function can be written as:
ScSn Sc(1 λs) Sn 2
WcWn Wc(1 λw) Wn 2
min CpUp
Sy Sy 2 Wy Wy 2

12. Constraints
The constraints are set so as to minimize magnitude of the
difference between generated power (Pgen) and the power
demand (Pdem)
ΔP Pgen Pdem
where, Pgen = Ps+ Pw+ Up
Ps, Pw, Up are the power outputs of solar panels, wind
turbines and the power taken from the grid respectively.

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 1
For 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. Constraints (cont.)
Hence the constraints can be written as follows:
8760 8760
(Ps)( T ) (Pw)( T ) (Up)( T ) (Pdem)( T )
n 1 n 1
Since ∆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 1
Therefore, 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. Procedure to balance the demand and generation
After 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. Implementation of Quadratic Programming
The 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 Up
subject to:
Sn
(ηI) (ξ (WS Win) 10 3 ) 1 Wn Pdem
Up

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 = beq
where,
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. Carbon Emission
Apart from cost, our objective is also to reduce the amount of
CO2 emitted from the system
Carbon emission is reduced by increasing the use of
renewable sources and thereby, reducing the power
consumption from grid
Amount of CO2 emitted from grid 0.98 kg/kWh

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. Conventional Grid System

21. Grid Connected PV System – Using 32 Panels

22. Grid Connected Wind System – Using 4 Turbines

23. Grid Connected Hybrid System – Using 8 Panels
and 4 Turbines

24. Fixing Maximum Number of Modules
Maximum Panels: 74 Maximum Turbines: 8

25. Grid Connected PV System – 74 Panels

26. Grid Connected Wind System – 8 Turbines

27. Grid Connected Hybrid System – 5 Panels and 8
Turbines

28. Comparison of Results – Case Study I
Grid Grid Grid Grid system
Configuratio
connected connected connected (Convention
n / Type of
hybrid wind system PV system al)
analysis
system
Cost 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. Optimal Region of Operation

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. Conventional Grid System

32. Grid Connected PV System (Power Demand and
Generation) – Using 75 Panels

33. Grid Connected PV System (Power Demand and
Split-up of Generation) – Using 75 Panels

34. Grid Connected Wind System (Power Demand and
Generation) – Using 10 Turbines

35. Grid Connected Wind System (Power Demand and
Split-up of Generation) – Using 10 Turbines

36. Grid Connected Hybrid System (Power Demand and
Generation) – Using 100 Panels and 10 Turbines

37. Grid Connected Hybrid System (Power Demand and Split-
up of Generation) – Using 100 Panels and 10 Turbines

38. Fixing Maximum Number of Modules
Maximum Panels: 135 Maximum Turbines: 13

39. Grid Connected PV System (Power Demand and
Generation) – 135 Panels

40. Grid Connected PV System (Power Demand and
Split-up of Generation) – 135 Panels

41. Grid Connected Wind System (Power Demand and
of Generation) – 13 Turbines

42. Grid Connected Wind System (Power Demand and
Split-up of Generation) – 13 Turbines

43. Grid Connected Hybrid System (Power Demand
and Generation) – 8 Panels and 13 Turbines

44. Grid Connected Hybrid System (Power Demand and
Split-up of Generation) – 8 Panels and 13 Turbines

45. Comparison of Results – Case Study II
Configuratio Grid Grid Grid Grid system
n / Type of connected connected connected (Convention
analysis hybrid wind system PV system al)
system
Cost 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. Optimal Region of Operation

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. 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

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