Computer-Methods-in-Power-Systems.pptx

Fast Decoupled Load Flow (FDLF)
CMPS by Dr. Imran sharieff
By
Dr. Imran Sharieff
Associate Professor,
EEE Dept.,
VCE

CONTENTS
1. Fast Decoupled Load Flow (FDLF)
2. Numerical Example of FDLF solved using MATLAB

Principle of Decoupling
An important and useful property of power system is that the change in real power is
primarily governed by the charges in the voltage angles, but not in voltage magnitudes.
On the other hand, the charges in the reactive power are primarily influenced by the charges
in voltage magnitudes, but not in the voltage angles.

(a)Under normal steady state operation, the voltage magnitudes are all nearly equal to 1.0.
(b) As the transmission lines are mostly reactive, the conductances are quite small as compared to
the susceptance (Gij << Bij).
(c) Under normal steady state operation the angular differences among the bus voltages are quite
small , i.e. δi − δj ≈ 0 (within 5 − 10 degrees).
(d)The injected reactive power at any bus is always much less than the reactive power consumed
by the elements connected to this bus when these elements are shorted to the ground (Qi <<
BiiVi
2 ).
Assumptions taken for FDLF method

Jacobian Matrix from FDLF (polar) method:


Q P 
P P 
J 
J
 V 
 3 4 
J2 

 V 
J 
J1
3
2


Q
 0
V

P
 0; J
 According to principle of decoupling J
The reduced Jacobian Matrix is
 4 
0
 J 
J1 0 
J 

Evaluation of J1:
Case 1: When both P and δ belong to same bus-i
i ii
n
ik
i k ik
ii
i ii
n
i
i
 V B
V
P
J  i 
 V 2
B Q
i ii i
k1
2
k1
i
1
k i )
V V Y Sin(
 V Y Sin
VkYik Sin(ik k i )

n
n
Qi  Vi   Vk  Yik  Sin(ik  k  i )
k 1
Evaluation of Jacobian Sub-Matrices J1 and J4.
Pi  Vi  Vk  Yik  Cos(ik  k  i )
k 1
Power flow equations in polar form
2
Q i   Vi Bii )
( Vi  Vi  1; i ii
i
i
 V B
P
 1

Case 2: When both P belongs to bus-i and δ belongs to bus-j
ij
i j ij
j
i
P
J    j  i )
1
 ViVjYijSin(ij )
 Vi Bij
 VV Y Sin(

j
i
Vj  1)
(    0; i ij
j
 V B
Pi
 2
2
1
From &
i
 [B']V
Pi
 i
V
  [B']1 Pi
A

Evaluation of J4:
Case 1: When both Q and V belong to same bus-i
ii
i ii
i
J
 Vi Bii Qi
 Vi Bii
V

Qi
4
n
VkYik Sin(ik k i )
k1
i
 2VY Sin
i ii
i
i
 V B
Q
V 3
Case 2: When both Q belongs bus-i to and V belongs to bus-j
j
J
V

Qi
4
 ViYijSin(ij )
 Vi Bij
 ViYijSin(ij  j i )
i ij
j
i
 V B
Q
V 4

From 3 & 4
i
 [B'']V
Qi
V
i
V
1 Qi
V  [B'']
B
From & B
A
  [B']1 Pi
Vi
V  [B'']1 Qi
Vi
The above two equations are FDLF equations, by evaluating these equations in every iteration, the
unknown states, i.e. δs and Vs are obtained.
Here B' and B'' are susceptance matrices which can be directly obtained from Y-bus.
 B' corresponds to susceptances of unknown δs (Both PV and PQ buses) and B'' corresponds to
susceptances of unknown Vs (Only PQ buses).

2. Example of FDLF method.
G
Bus 1 Bus 2
V1= 1.05 ∠0
Bus 3
400MW+ j250 MVAR
|V3|= 1.04
Pg= 200MW
G
Solve load flow of above power system using FDLF method.
Line Data
S.No Line Z=R+jX
1 1-2 0.02+j0.04
2 1-3 0.01+j0.03
3 2-3 0.0125+j0.025

Step 1: Form Y-bus neglecting line resistances.
Line Data
S.No Line Z=R+jX Z≈jX Y=1/jX
1 1-2 0.02+j0.04 j0.04 -j25
2 1-3 0.01+j0.03 j0.03 -j33.33
3 2-3 0.0125+j0.025 j0.025 -j40



 j73.33
 j33.33
j25 j33.33 
j25  j65 j40 
j40
 j58.33
Y31
Y   
Y12 Y13 
21 22 23
Y32 Y33 

Y11
Y  Y Y

Step 2: Identify unknowns and related power flow equations.
 
3  3 
P2 
Unknowns  ;Equations  P 
2 

V2 
 
Q2 

The unknowns and corresponding power flow equations are related by:
 



  3
3

V2 

B''

Q2 

 P  
B'
P2 

  
2 
Power
Mismatches
Vector
Corrections
Vector
FDLF
Sub-Matrices

 
0.0205
0.0126
 
 40  73.33
0.0126
; [B'']1
[0.0054]
[B']1

0.0232

; B''[65]
B'
 65 40
The FDLF Sub-Matrices are obtained from Y-bus as:
P 2
3
23
23 3 2
22
2
2 22 2
2,Calculated
 0  4 pu  4 pu
P2,Given  P2,Generation  P2,Load
) Y V Cos Y V V Cos(   )
 Y21V1V2Cos(21 1 
Step 3: FDLF Iterations
Given data from system at 100 MVA base
V1=1.0 pu; δ1=0.0 ; PL2=4.0 pu ; QL2=2.5 pu; V3=1.04 pu; Pg3=2.0 pu;
Initial guess:- δ2=0.0; δ3=0.0; V2=1.0;
Power Mismatches
P2 P2,Given  P2,Calculated

Similarly,
P3  P3,Given  P3,Calculated
Q
P
Q2  Q2,Given Q2,Calculated
Where
2
3
23
23 3 2
22
2
2,Calculated 21 1 2 21 1 2 22 2
33
2
33 3
3
2
23
3,Calculated
 0  2.5pu  2.5pu
Q2,Given  Q2,Generation Q2,Load
P3,Given  P3,Generation  P3,Load  2  0  2pu
) Y V Cos(
  )
Y V V Sin(
 Y VV Sin(   ) Y V Sin
 )
 
 Y31V1V3Cos(31 1 3 ) Y23V2V3Cos(
Substituting the initial guess values and given values, we get
P2,Calculated  P3,Calculated  0  P2  4.0;P3  2.0;
Q2,Calculated  2.85pu  Q2  2.5 (2.85)  0.35pu


 

 
 




 0.0111
 0.0683
 0.0111
 0.0683
 1.04 
 4.0
 0.0205 2.0 
 0.0126 1.0 
 0.0232
2
 
2

2
 
 3 
 3 
3 
 
(1)
3 
 
(0)
3 
 
(1)
2 

 V3
P    0.0126
 V 
1 2
Iteration 1:
Unknown δs
P2 
   [B']
1
(0)
2
(1)
2
(0)
(1)
2 2
V  1.0pu)
1.0054 (
 0.0054
V  V 

 
0.35
  [0.0154]
 V
 2 
V2  [B'']
1 Q2 
V 
Unknown Vs
 



1.0054 
  0.0111
 0.0683
(1)
3 
2

V2 


 
Unknown States after Iteration 1 = 

 




 
 2 
2
1
(1)
2
(2)
2
2
1
2

2
 
 V 
Q

V   
V  [B'']

 V3
P3 
 V 
P2 
[B'] 
3 
3 
Similarly in Iteration 2
 
(2)
 
(1)
Using MATLAB programming to solve the same problem for 10 iterations we get
2
2  0.0641;
(10)
3  0.0086;
(10)
V (10)
1.0037pu;

Gauss-Siedel method using
MATLAB
By
Dr. Imran Sharieff
EEE Dept.,
VCE

CONTENTS
1. Solving linear equations
2. Solving non-linear equations
3. Solving Power-flow/ Load-flow problems

Solving linear equations using MATLAB
• Take any set of three linear equations, Say
5x-y+2z=12
3x+8y-2z=-25
X+y+4z=6
• Now, to solve the above equations using Gauss-Siedel method, we
modify them as
x=(12+y-2z)/5
y=(-25-3x+2z)/8
z=(6-x-y)/4
• Say, the initial values of (x,y,z) be (0,0,0)

MATLAB code to solve the above equations
% Linear Equation solver using Gauss Siedel Method
clc
clear all
%Initial Values
x=0;
y=0;
z=0;
Y Z')
disp('Iterations X
for i=1:10
x=(12+y-2*z)/5;
y=(-25-3*x+2*z)/8;
z=(6-x-y)/4;
iter=[i x y z];
disp(iter)
end

Output
Iterations X Y Z
GS method converges at 5th iteration.
1.0000 2.4000 -4.0250 1.9063
2.0000 0.8325 -2.9606 2.0320
3.0000 0.9951 -2.9901 1.9988
4.0000 1.0025 -3.0012 1.9997
5.0000 0.9999 -3.0000 2.0000
6.0000 1.0000 -3.0000 2.0000
7.0000 1.0000 -3.0000 2.0000
8.0000 1.0000 -3.0000 2.0000
9.0000 1.0000 -3.0000 2.0000
10.0000 1.0000 -3.0000 2.0000

Solving non-linear equations
• Take any set of two non-linear equations, Say
4sinX+3cosY=5
tanX+10cotY=9
• Now, to solve the above equations using Gauss-Siedel
method, we modify them as
X=sin-1 ((5-3cosY)/4)
Y=cot-1((9-tanX)/10)
• Say, the initial values of (x,y) be (0,0)

MATLAB code to solve the above equations
%Non-linear Equation solver using Gauss-Siedel
clc
clear all
%initial values
x=0;y=0;
disp('Iterations X Y')
for i=1:10
x=asin((5-3*cos(y))/4);
y=acot((9-tan(x))/10);
iter=[i x*180/pi y*180/pi]; % Angle is shown in degrees as x and y are
% in radians
disp(iter)
end

Output
Iterations X Y
GS method converges at 8th iteration
1.0000 30.0000 49.8937
2.0000 50.0714 52.0272
3.0000 52.0487 52.3397
4.0000 52.3509 52.3902
5.0000 52.3999 52.3984
6.0000 52.4080 52.3998
7.0000 52.4093 52.4000
8.0000 52.4095 52.4000
9.0000 52.4096 52.4000
10.0000 52.4096 52.4000

Solving load flow problem using MATLAB
• Problem:
For the power system shown in figure, solve for V2 and V3 using GS
method. The bus data is given in table, values are in pu
G G
Bus Voltage Gen Load Type
(Remarks)
Pg Qg Pl Ql
1 1.20 ∠0 - - - - Slack bus
2 - 0.7 0.5 0.3 0.2 Load bus
3 - 0 0 0.6 0.4 Load bus

MATLAB code to solve the load flow problem
clc;clear all
% Step1 : Obtain Power Injections Pi= Pg- Pl & Qi=Qg-Ql
pi2=0.7-0.3;
qi2=0.5-0.2;
pi3=0-0.6;
qi3=0-0.4;
% Step2: Construct Y bus
Y=[-9i 5i 4i
5i -9i 4i
4i 4i -8i];
% Step 3 (a): Inital values for V2 and V3
V2=1; V3=1;
Continued in next slide

% Step3 (b): Iterative computation of V2 and V3
disp('Iterations V2 d2 V3 d3')
for k=1:20
V2iter=1/Y(2,2)*((pi2-i*qi2)/conj(V2)-Y(2,1)*1.02- Y(2,3)*V3);
%Check for convergence
if(abs(V2iter-V2)<= 0.00001)
return % if the solution is obtained
end
% if it does not converge
V2=V2iter;
V3=1/Y(3,3)*((pi3-i*qi3)/conj(V3)-Y(3,1)*1.02- Y(3,2)*V2);
iter=[k abs(V2) angle(V2)*180/pi abs(V3) angle(V3)*180/pi];
disp(iter)
end

Output
Iterations V2 d2 V3 d3
1.0000 1.0454 2.4366 0.9836 -3.0757
2.0000 1.0335 1.1297 0.9738 -3.7223
3.0000 1.0301 0.8641 0.9710 -3.8829
4.0000 1.0290 0.8022 0.9701 -3.9231
5.0000 1.0287 0.7876 0.9699 -3.9334
6.0000 1.0286 0.7841 0.9698 -3.9362
7.0000 1.0286 0.7832 0.9698 -3.9369 GS method converges at 7th iteration

•Observations
•It can be observed that using Gauss siedel method, solution can be obtained for linear, non-
linear equations and also for load flow problems.
•Advantages of GS method include
•Simple concept
•Ease of programming
•Efficient use of computer memory
•Although GS method is simple, it has certain draw backs like
•Higher number of iterations required
•Convergence is not guaranteed when diagonal elements are not dominant
•Total time take to converge to solution is more although time per iteration is small.
•In GS method convergence is affected by choice of slack bus and presence of series
capacitors.
•For large systems GS method has doubtful convergence and accuracy.

Newton-Raphson Load Flow (NRLF)
using MATLAB
By
Dr. Imran Sharieff
EEE Dept.,
VCE

CONTENTS
1. NRLF using polar co-ordinates
2. An example for NRLF using MATLAB
3. An example for NRLF from Textbook

1. NRLF using polar co-ordinates
•Algorithm for NRLF method using polar co-ordinates
1. The voltage and angle (|v| and δ) at slack bus are fixed, assume |v| and δ at all PQ buses
and δ at PV buses. (Generally flat voltage start is assumed, i.e. |v| = 1.0 and δ = 0)
2. Compute ∆Pi (for PV and PQ buses) and ∆Qi (for all PQ buses).If all the values are less than
prescribed tolerance, stop the iterations, calculate slack bus powers (P1 and Q1) and print
the entire power flow solution including line flows.
3. If the convergence criterion is not satisfied , evaluate elements of the jacobian matrix.
4. Solve for corrections of voltage angles and magnitudes.
5. Update voltage angles and magnitudes by adding the corresponding changes to the
previous values and return to step 2.
Case 1 (PV bus changes to PQ bus) : In step 2 if reactive power limits of generator bus are violated (i.e. Qg
is greater than Qmax or Qg is less than Qmin), PV bus is changed to PQ bus during that iteration and the value
of Q is taken as its upper/lower limit Qmax/Qmin depending on type of violation.
Case 2 (PQ bus changes to PV bus) : In step 5, if the voltage limits of PQ bus are violated (i.e. |V| is greater
than |V max| or |V| is less than |V min|), PQ bus is changed to PV bus during that iteration and the value of V is
taken as its upper/lower limit |Vmax|/|Vmin| depending on type of violation.

Question. Explain the terms correction vector, mismatch vector and jacobian
matrix by taking an example of a 4-bus system with one PV-bus, one Slack-bus
and two PQ-buses.
G
Test system with 4 buses
Explanation can be done using NRLF algorithm shown in earlier slide.
• Construct a 4 bus system
G
Bus-1
Slack Bus
Bus-3
PQ Bus
Bus-4
PQ Bus
Bus-2
PV Bus

G G
Bus-4
Bus-3
Test system with 4 buses with known parameters
Bus-1
Slack Bus
V1, δ1
PQ Bus
P3 ,Q3
PQ Bus
P4, Q4
Bus-2
PV Bus
P2, V2
Specified/Known Values at different buses

G G
Bus-4
Bus-3
Test system with 4 buses with unknown parameters
Bus-1
Slack Bus
P1,Q1
PQ Bus
V3,δ3
PQ Bus
V4, δ4
Bus-2
PV Bus
Q2,δ2
Unknown Values

 The voltage and angle (|v| and δ) at slack bus are fixed, assume |v| and δ at all PQ buses and δ at PV
buses.
Assume |V3|=|V4|=1.0 p.u., δ2=δ3= δ4= 0. (Flat voltage start)
 Calculate P2, P3, P4, Q3 & Q4 using load flow equations. i.e.
4
4
k1
k i )
Qi,calculated  Vi Vk Yik  Sin(ik
k i )
Pi,calculated Vi Vk Yik Cos(ik
k1
 Obtain the power mismatches ∆P2, ∆P3, ∆P4, ∆Q3 & ∆Q4, using
Pi  Pi,calculated  Pi,specified
Qi  Qi,calculated Qi,specified

The Jacobian Matrix in NRLF method is obtained by partially derivation of the corresponding real
and reactive powers with unknown states. In this case the unknown states are δ2, δ3, δ4, |V3| & |V4|, the
corresponding power flow equations are P2, P3, P4, Q3 & Q4, respectively.
 The angle states (δ’s) are linked with real power flows and the voltage states (V’s) are linked with
reactive power flows.
 The Jacobian Matrix formation is the heart of NRLF method, it can be formed as shown in the next
slide.


3 
3 

Q4


Obtain the elements of Jacobian Matrix
P4 
Q 
Obtain the power mismatch vector  P 
P2 
P’s at all PV and PQ buses
Q’s at all PQ buses






4 
3
3
3
2
4 
4 3
2 3
Q3 
Q3
V4 
 P P P P P 
P3 P3 P3 P3 P3
 P2 P2 P2 P2 P2 
J   4
Q4 Q4 Q4 Q4 
3 3 V3 V4

 Q4

2
   V V 
4 4 4 4

3 3 V3
Q3 Q3 Q3
2
2 3 3 V3 V4 
   V V 
δ2 δ3 δ4 V3 V4
P2
P3
P4
Q3
Q4
Unknown states
Corresponding power
flow equations

• Jacobian matrix can be further divided into four sub-matrices J1, J2, J3 & J4, i.e.






 3 4 
4 
3
3
3
2
4 
3
3
3
2
4 
4 3
2 3
J 
J1 J2 
Q3 Q3 Q3 Q3 Q3 
P4

V3 V4 
P4
P3 P3 P3 P3 P3
 P2 P2 P2 P2 P2 
Q4 Q4 Q4 Q4 
3 3 V3 V4

 Q4

 2
   V V 
  V V
  J
J  

 
 P P
3
P
3
4 4 4
 2
    V V 
• J1 represents ∂P/ ∂δ terms.
•J2 represents ∂P/ ∂V terms.
•J3 represents ∂Q/ ∂δ terms.
•J4 represents ∂Q/ ∂V terms.












3 
4

3 
1
4 
3
3
3
2
4
3
3
3
4 4 4 4

2
4 
3
4
3
2
2 2 2 2 2
3 
4

3 

Q4 

Q
 P 
 P 
P2 
Q3 Q3 Q3 Q3 Q3  
 P P P P P 
P3 P3 P3 P3 P3
 P P P P P

V4


V
• By using both the power mismatch vector and Jacobian matrix, the corrections vector can be found out using
NRLF method as
Corrections  [J]1
mismatches
Q4 Q4 Q4 Q4 
3 3 V3 V4

 Q4

 2
    V V 
    V V 
 2 3 3 V3 V4 
    V V 
    4
 
2 
Corrections
Vector
Power- Mismatches
Vector
Jacobian
Matrix

• The corrections are added to initial values to obtain the new states or the next iterative values.
V r1
V r
• The process is continued until the power mismatches vector is less than tolerance value.
• After the problem is converged, complete load flow solution along with slack bus powers P1 and Q1 and
line flows is printed.
•An example for NRLF method is shown in next slide.
  r
 V r
 r1
  r

An example for NRLF method using MATLAB
G
Bus-1 Bus-2
Bus-3
G
j0.1 pu
Slack Bus
V1=1.0 pu
δ1=0
PQ Bus
PL2=0.9 pu
QL2=0.5 pu
PV Bus
PG3=1.3 pu ; |V3|=1.01 pu
PL3= 0.7 pu ; QL3=0.4 pu
Question. Obtain the power flows using NRLF
method for the 3 bus system shown in the figure.

1. The known states are [δ1, V1, V3]
2. The unknown states are[δ2, δ3, V2]
3. The corresponding power flow equations for unknown states are [P2, P3, Q2].
4. The specified values are |V1|=1.0 pu, δ1=0, P2=-0.9, Q2=-0.5, P3=1.3-07=0.6 pu, |V3|=1.01 pu.
5. Assume the initial values of unknown states, say δ2=0, δ3=0 & V2=1.0.
6. Obtain the Ybus of the system,
1 1 1
13 23
12

9  / 2



 4 / 2
5 / 2 
4 / 2 
10 / 2
15  / 2
5 / 2
5 j    10 / 2
10 j 4 j  14 / 2
 15 j 

 4 j 5 j 9 j

14 j
Y   10 j
 5 j;
 10 j; y   4 j; y 
j0.1 j0.25 j0.2
y 
bus

Q2  Q2,calculated Q2,specified
 Y21V1V2Sin(21 1 2 ) Y22V2V2Sin(22) Y23V2V3Sin(23 3 2 ) Q2,specified
7. The next step is to calculate power mismatch vector, using power flow equations,. i.e.
P2  P2,calculated  P2,specified
 Y21V1V2Cos(21 1 2 ) Y22V2V2Cos(22) Y23V2V3Cos(23 3 2 )  P2,specified
P3  P3,calculated  P3,specified
 Y31V1V3Cos(31 1 3 ) Y32V2V3Cos(32 2 3 ) Y33V3V3Cos(33)  P3,specified

8. The next step is to evaluate the elements of Jacobian matrix J





2

3
2
3 3 3 
2 
3
2

2 2 2

V2 
P P P
P P 
 P
J 
Q2 Q2 Q2
3

2
   V 
  V
23 3 2
23 3
22
21 1
2
2
23 3 2
23 1 3
3
2
23 3 2
21 1 2 23 2 3
21 1 2
2
2
2
3
32 2 3
2
23 3 2
23 3
22
2
3
23 3 2
21 1 2
2
  )
   )


  );

  )

  );

) Y V Sin(
21 1 2 )  2Y22V2Sin(
 Y V Sin(
V
Q
 Y VV Cos(
Q
   ) Y V V Cos(   )
 Y VV Cos(
Q
Y32V3Cos(32 2 3 );
V
P
 Y31V1V3Sin(31 1 3 ) Y32V3V2Sin(
P3
3
 Y32V3V2Sin(32 2 3 );
P3
) Y V Cos(
 Y21V1Cos(21 1 2 )  2Y22V2Cos(
V
P2
 Y23V3V2Sin(23 3 2 );
P2
21 1 2 ) Y23V3V2Sin(
 Y VV Sin(
P2
Elements of
jacobian
matrix

9. The next step is to find the corrections vector for next iteration using NRLF method
2
2
(r)
(r)
3 



Q2 

P
3 
 



V2 

 [J 1
](r)
  P 
 

(0)
2
(0)
2
3 


3 
 

 P
 [J 1
](0)
 P 
 


V2 
 
Q2 

The corrections vector for any rth iteration can be written as

10. The updated values of states are obtained by adding the corrections with initial values, i.e
(0)
2
(0)
2
(0)
2
2
(1) (0)
2 
 
   
3  3  3  3  3 
 
    
 P
[J 1
](0)  P 
  

  
 
    


V2 
 
V2 
 
V2 
 
V2 
 
Q2 

Similarly, the updated values after any rth iteration can be written as
2
2
2
2
2
(r)
(r)
(r)
(r)
3 


P
3 
 

3 
 

3 
 

3 
 


[J 1
](r )  P 
(r1)
  

  


    


V2 
 
V2 
 
V2 
 
V2 
 
Q2 

11. If all the values are less than prescribed tolerance, stop the iterations, calculate slack bus powers (P1
and Q1) and print the entire power flow solution including line flows.
• The problem is solved using Matlab programming shown in next slides

clear all; clc;
disp('NR load flow for 3 bus system:');
% Step 1
% defining the known states
d1 = 0; v1 = 1.0; v3 = 1.01;
% defining the power injections
p2 = -0.9; q2 = -0.5;
p3 = 1.3-0.7;
% Step 2
% deriving the Ybus elements
Y11 = 14; Y21 = 10; Y31 = 4;
Y21 = 10; Y22 = 15; Y23 = 5;
Y31 = 4; Y32 = 5; Y33 = 9;
t11 = -pi/2; t12 = pi/2; t13 = pi/2;
t21 = pi/2; t22 = -pi/2; t23 = pi/2;
t31 = pi/2; t32 = pi/2; t33 = -pi/2;
% Step 3
% assume the inital values of unknowns
d2 = 0; d3 = 0; v2 = 1.0;
X = [d2; d3; v2];
disp(X');
tic
% Step 4
% compute power mismathes (dpq) using the
for m=1:10
% corresponding power functions and jacobian.
fp2 = Y21*v1*v2*cos(t21+d1-d2)+Y22*v2^2*cos(t22)+Y23*v3*v2*cos(t23+d3-d2)-p2;
fp3 = Y31*v1*v3*cos(t31+d1-d3)+Y32*v2*v3*cos(t32+d2-d3)+Y33*v2^2*cos(t33)-p3;
fq2 = -Y21*v1*v2*sin(t21+d1-d2)-Y22*v2^2*sin(t22)-Y23*v3*v2*sin(t23+d3-d2)-q2;
fx = [fp2; fp3; fq2];
% elements of jacobian matrix
J11 = Y21*v1*v2*sin(t21+d1-d2)+Y23*v3*v2*sin(t23+d3-d2);
J12 = -Y23*v3*v2*sin(t23+d3-d2);
J13 = Y21*v1*cos(t21+d1-d2)+2*Y22*v2*cos(t22)+Y23*v3*cos(t23+d3-d2);
J21 = -Y32*v2*v3*sin(t32+d2-d3);
J22 = Y31*v1*v3*sin(t31+d1-d3)+Y32*v2*v3*sin(t32+d2-d3);
J23 = Y32*v3*cos(t32+d2-d3);

J31 = Y21*v1*v2*cos(t21+d1-d2)+Y23*v3*v2*cos(t23+d3-d2);
J32 = -Y23*v3*v2*cos(t23+d3-d2);
J33 = -Y21*v1*sin(t21+d1-d2)-2*Y22*v2*sin(t22)-Y23*v3*sin(t23+d3-d2);
J = [J11 J12 J13; J21 J22 J23; J31 J32 J33]; %jacobian matrix
% power mismatches
dpq=-inv(J)*fx;
% Step 5
Xiter = X+dpq; % NR iteration - calculation of corrections
toc
% Step 6
% Check for convergence criteria
if abs(dpq)<=0.0000000001
disp('iterations')
disp(m)
disp('v2')
disp(X(3))
disp('delta2')
disp(X(1)*180/pi)
disp('delta3')
disp(X(2)*180/pi)
return
end
% Step 7
% if convergence is not satisfied
X=Xiter; % update the values of angles and voltages (unknown states)
d2 = X(1); d3 = X(2); v2 = X(3);
disp(X)
disp('')
end
% Step 8
% if convergence criteia is satisfied print the entire solution including
% slack bus power(p1,q1), q3 for pv-bus and line flows
disp('iterations')
disp(m)
disp('v2')
disp(X(3))
CMPS by Dr. Imran sharieff Ref: Video lectures by Pradeep Yemula

disp('delta2')
disp(X(1)*180/pi)
disp('delta3')
disp(X(2)*180/pi)
%slack bus powers
p1=v1^2*Y11*cos(t11)+v1*v2*Y21*cos(t12+d2-d1)+v1*v3*Y31*cos(t13+d3-d1);
q1=-v1^2*Y11*sin(t11)-v1*v2*Y21*sin(t12+d2-d1)-v1*v3*Y31*sin(t13+d3-d1);
% pv bus 3 reactive power injection q3
q3=-v1*v3*Y31*sin(t13+d1-d3)-v2*v3*Y23*sin(t23+d2-d3)-v3^2*Y33*sin(t33);
qg3=q3+0.4;
%real power flows
p12=v1*v2*Y21*sin(d1-d2);
p21=v1*v2*Y21*sin(d2-d1);
p13=v1*v3*Y31*sin(d1-d3);
p31=v1*v3*Y31*sin(d3-d1);
p23=v2*v3*Y23*sin(d2-d3);
p32=v3*v2*Y23*sin(d3-d2);
%reactive power flows
q12=v1^2*Y21-v1*v2*Y21*cos(d1-d2);
q13=v1^2*Y31-v1*v3*Y31*cos(d1-d3);
q32=v3^2*Y23-v3*v2*Y23*cos(d3-d2);
q21=v2^2*Y21-v1*v2*Y21*cos(d1-d2);
q31=v3^2*Y31-v1*v3*Y31*cos(d1-d3);
q23=v2^2*Y23-v3*v2*Y23*cos(d3-d2);
%----------- Step 9----------------------------------
% line losses
l12=p12+i*q12+p21+i*q21;
l13=p13+i*q13+p31+i*q31;
l23=p23+i*q23+p32+i*q32;
tloss=l12+l13+l23;
Output
Elapsed time is 0.018196 seconds.
iterations
5
v2
0.9667
delta2
-2.7596
delta3
2.3470

The line flows between different buses are calculated using the formulae shown below:
i k
ik
ik
|V |2
|V ||V |
Sin(
X
|Vi ||Vk |
Qik  i
 i k
Cos(i k )
  );
P 
Xik Xik
 The real and reactive power loss in line connecting Bus-i and Bus-k , can be calculated using
Pik,loss  Pik  Pki
Qik,loss  Qik Qki
Plo ss   Pik ,lo ss ;
lines
Qlo ss   Qik ,lo ss ;
lines
 jQloss
 The total transmission loss is equal to: Sl o s s  Ploss

COMPLETE POWER FLOW SOLUTION
G
Bus-1
Bus-3
Bus-2
G
Slack Bus
V1=1.0 pu
δ1=0
PQ Bus
PL2=0.9 pu
QL2=0.5 pu
PV Bus
PG3=1.3 pu ; |V3|=1.01 pu
PL3= 0.7 pu ; QL3=0.4 pu
PG1=0.3 pu
QG1=0.3072
V2=0.9667 pu
δ2=-0.048 rad
=-2.760
δ3=0.0410 rad
=2.340
QG3=0.6816
P12=0.4654+j0.3438
P21=-0.4654-j0.3103
 Line loss in line 1-2 = S12+S21 =j0.0335 pu;
Line loss in line 1-3 = S13+S31 =j0.0072 pu;
Line loss in line 2-3 = S23+S32 = j0.0481
pu;
Total transmission loss = j0.0335+ j0.0072
+j0.0481 =j0.0888 pu or 0.0888 pu (reactive
power loss)

CMPS by Dr. Imran sharieff Ref : Modern Power system analysis by Nagrath & Kothari
2. Example problem from Nagrath and Kothari

Newton-Raphson method using
MATLAB
By
Dr. Imran Sharieff
EEE Dept.,
VCE

CONTENTS
1. Solving non-linear equation with single variable
2. Solving non-linear equations with multiple variables
3. Comparison with GS method

1. Solving non-linear equations with single variable
•Consider a non –linear algebraic equation
f(x)=0
assume the initial value of x be x(0), let Δx(0) be the corrections when added to initial value gives the
solution of above equation, i.e.
f(x(0)+ Δx(0) )=0
Expanding the above equations using taylor series, we have
f(x(0) +Δx(0))=f(x(0))+f`(x(0))+Δx(0) +f``(x(0))(Δx(0) )2+………(h.o.t)=0
neglecting higher order terms (hot), we have
f(x(0) +Δx(0))=f(x(0))+f`(x(0))+Δx(0) =0
Δx(0) =-f(Δx(0) )/f`(Δx(0) )
•The above equation represents the value of corrections required to initial value.

• So the next iterative value will be the sum of initial value and corrections to initial value, i.e.
x(1) =x(0) +Δx(0)
•The generic form of next iterative value using NR method is
Δx(r+1) = x(r) + Δx(r)
or
Δx(r+1) = x(r) – f(x(r) )/f`(x(r) )

Numerical example 1
• Take any non linear equation with one variable x, say
x2-2x=2
• Now, to solve the above equation using Newton-Raphson method, we modify it as
f(x)=x2-2x-2
and its derivative is f`(x)=2x-2
• Say, the initial values of x is x(0) =2.
• The NR method formula is x(r+1)=x(r) - f(x(r))/f`(x(r))
• x(1) = x(0) –f(x(0))/f`(x(0)) = 2-f(2)/f`(2)=2-(-2/2)=3.
• x(2) = x(1) –f(x(1))/f`(x(1)) = 3-f(3)/f`(3)=3-(1/4)=2.75.
• x(3) = x(2) –f(x(2))/f`(x(2)) = 2.75-f(2.75)/f`(2.75)=2.75-(1/4)=2.75-(0.0625/3.5)=2.7321
• iterations will continue till convergence i.e. difference between successive iterations is less than
tolerance value, or |x(r+1) – x(r) |<= ε (say 0.00001)

MATLAB code to solve numerical example 1
fdx')
clc
clear all
% Initial Value
x=2;
disp('Iter x fx
for i=1:10
% Function
fx=x^2-2*x-2;
% Derivative of function
fdx=2*x-2;
%NR Method
xiter=x-(fx/fdx);
% Convergence condition to stop iterations
if abs(xiter-x)<=0.00001
return
end
x=xiter;
iter=[i x fx fdx];
disp(iter) %display results
end

Output
x fx fdx
Iter
1 3 -2 2
2.0000 2.7500 1.0000 4.0000
3.0000 2.7321 0.0625 3.5000
4.0000 2.7321 0.0003 3.4643 NR method converges at 4th iteration
Hence the value of x is 2.7321.

Solving non-linear equations with n variables
•Say the ith equation is
fi (x1,x2,……xn)=0 ; for i=1,2….n
•Say the initial values and corrections be (x (0),x (0),……..x (0)) and (Δx (0), Δx (0),…….. Δx (0)),
1 2 n 1 2 n
respectively, the above equation becomes
f(x (0) + Δx (0), x (0) + Δx (0),,……..x (0) + Δx (0) )=0
1 1 2 2 n n
expanding the above equations using taylor series
f(x1
(0),x2
(0),……..xn
(0))+ [(∂ fi/∂x1) (0)Δx1
(0) +(∂ fi/∂x2) (0)Δx2
(0) +……………..+(∂ fi/∂xn) (0)Δxn ]+ higher order
(0)
terms=0
where (∂ fi/∂x1) (0) , (∂ fi/∂x2) (0) , ………………, (∂ fi/∂xn) (0) are partial derivatives of fi with respect
to x1,x2,……xn evaluated at x (0),x (0),……..x (0)
1 2 n

Neglecting higher order terms, we can write the equations for f1 , f2 ,…. fi…….fn in matrix form as
:
:
:
:
(0)
2
1
(0)
2
(0)
1
(0)
2
(0)
1
 0
(0) 





(0)











2
*



) 





 
2
(0) 
(0)





 
n

n
xn
x
x
xn
f (x(0)
)
f (x(0)
)
n n
 x x
1 2
f (x(0)
)
xn
f (x(0)
)
f (x(0)
)
x1
f (x(0)
)
x
f1(x
x
f1(x )
x
 f1(x )

 fn
 f
 
 
 
f
⁝
2
x2
⁝
⁝ ⁝
 J (0)
*x(0)
 0
f (0)
(0) (0)
f (0)
1
x  J 

Numerical example 2
 2 2 
x2 
2 
f
x1
x x 
• Take any two non linear equations with two variables x1 and x2, say
3x 2-2x 2=-6
1 2
5x 2-7x 2=-43
1 2
• Now, to solve the above equation using Newton-Raphson method, we modify it as
f1=3x 2-2x 2 + 6
1 2
f2=5x 2-7x 2+43
1 2
• Say, the initial values be (x (0) , x (0) )= (1, 1)
1 2
f1 f1 
• The jacobian matrix is defined as J  f
1

1 (0)   0
1

2 *
1
  
(0)


x2
x (0)

x2 
f2 
x1
f2
x x 
 f1 f1 

 f2
 f (0)

• The NR method formula is x(0)
 J (0)
1
f (0)
 J (0)
*x(0)
 0
f (0)



 



1

(0)
1
2 
2
1
1 1
(0)
1
*

 f2
 f (0)

x2 
x1
f f2 
x x 
 f f
x2
x (0)

• The elements of jacobian matrix are 2
2
2
1
1
2
2
2
1
1
1
 14x ;
x
f
10x ;
x
f
 4x ;
x
f
 6x ;
x
f1
 2 
1 14x 
• Jacobian matrix J= 10x
 6x1  4x2 

Iteration 1:

  


  


  
 
 5 
 2.5
10 14 41
(1)
1
 6  4 
1
 7 
(1)   
1
0
0
1
1
  
  
2   2 
(0)
2
(0)
1
(1)


 2   1
(1)
1
1 2
(1)
x2 
x
x2
x (1)

f
f
14x (0)
10x (0)
 4x
6x
x
x
x(1)
 [J (0)
]1
f 0
[x (0)
, x (0)
]  [1,1]
Iteration 2:



  


 
 

 
 3.4 
 
2.05
 15
(2)
(2)
1
 20
1
  25.25 
25  70 100.75
  
(2)
1
1
1
1
1
2   2 
(1) (1)
(1)
2
(1)
1
(2)
  
 
 2 


 2 


 2 
(2)
1
1 2
x
x
x (2)
x
f
f
14x
10x1
 4x
6x
x
x
x(2)
 [J (1)
]1
f 1
[x (1)
, x (1)
]  [2.5,5]
• After 5 iterations the value of x1 and x2 are obtained as (2.0,3.0)

clc
clear all
%Initial values
x=[1;1];
disp('Iter X1
X2')
tic % Time start
for i=1:10
% Functions
f1x=3*x(1)^2-2*x(2)^2+6;
f2x=5*x(1)^2-7*x(2)^2+43;
% Elements of Jacobian Matrix
f1dx1=6*x(1);
f1dx2=-4*x(2);
f2dx1=10*x(1);
f2dx2=-14*x(2); %Continued
% from here
% Formation of Jacobian Matrix
J=[f1dx1 f1dx2; f2dx1 f2dx2];
% NR Method
dx=-1*inv(J)*[f1x;f2x];
xiter=x+dx;
% If condition to stop iterations
if abs(x-xiter)<=0.00001
toc %Time end
return
end
x=xiter;
iter= [i x(1) x(2)];
disp(iter)
end
Matlab program for Numerical example 2 using NR method:

Output:
Iter X1 X2
1.0000 2.5000 5.0000
2.0000 2.0500 3.4000
3.0000 2.0006 3.0235
4.0000 2.0000 3.0001
5.0000 2.0000 3.0000
Elapsed time is 0.000540 seconds..

3. Comparison with GS method
%Matlab program for Numerical example 2
using GS method:
clc
clear all
%Initial value
x=[1;1];
disp('Iter X1 X2')
tic % Time start
for i=1:100
xiter(1,1)=sqrt((2*x(2)^2-6)/3);
xiter(2,1)=sqrt((5*x(1)^2+43)/7);
%If condition to stop iterations
if abs(xiter-x)<=0.00001
toc % Time end
return
end
x=xiter;
iter=[i x(1) x(2)];
disp(iter)
end
•The same numerical example 2 is solved using GS method.
•Initial values are taken as (1,1) in this method also.
•GS iterations are done using the equations
r1 2(x r
)2
 6
x1  2
3
r1 5(x r1
)2
 43
x2  1
7
• The Matlab programming for the same is also shown:
•It has been observed that GS method takes 32 iterations to
obtain the same result as shown in next slide.

Output:
Iter X1 X2
1.0000 + 0.0000i 0.0000 +
1.1547i 2.6186 + 0.0000i
2.0000 1.6036 2.2783
3.0000 1.2084 2.8248
4.0000 1.8220 2.6807
5.0000 1.6705 2.9179
6.0000 1.9173 2.8524
7.0000 1.8504 2.9612
8.0000 1.9611 2.9306
9.0000 1.9302 2.9816
10.0000 1.9816 2.9672
11.0000 1.9671 2.9912
12.0000 1.9912 2.9844
13.0000 1.9844 2.9958
14.0000 1.9958 2.9926
15.0000 1.9926 2.9980
16.0000 1.9980 2.9965
17.0000 1.9965 2.9991
18.0000 1.9991 2.9983
19.0000 1.9983 2.9996
20.0000 1.9996 2.9992
21.0000 1.9992 2.9998
22.0000 1.9998 2.9996
23.0000 1.9996 2.9999
24.0000 1.9999 2.9998
25.0000 1.9998 3.0000
26.0000 2.0000 2.9999
27.0000 1.9999 3.0000
28.0000 2.0000 3.0000
29.0000 2.0000 3.0000
30.0000 2.0000 3.0000
31.0000 2.0000 3.0000
32.0000 2.0000 3.0000
Elapsed time is 0.007903 seconds.

Comparison of GS and NR methods:
Gauss- Siedel
1. It takes more number of iterations to solve
the same problem.
2. The overall program execution time is
slightly more.
3. Time per iteration is less
4. Initial value can be taken randomly.
5. It requires lesser storage memory.
6. Applicable only to small systems.
Newton-Raphson
1. It takes lesser number of iterations.
2. The overall program execution time is
lesser
3. Time per iteration is higher due to
presence of Matrix inversion (J-1)
procedure.
4. Initial value is to be taken carefully
otherwise the problem may not converge.
5. It requires more storage memory.
6. Applicable to any type of system, i.e. large,
medium, small with any number of
variables.

Power System Stability
By
Dr. Imran Sharieff
EEE Dept.,
VCE

CONTENTS
1. Introduction*
2. Power angle curve
3. Swing Equation
4. Methods to improve steady state stability
5. Example 12.1

Power System Stability:
Rotor Angle Stability:

Steady State Stability or Small-Signal Stability:
Transient Stability:

Classification of Power System Stability:

Power-Angle Relation: (P-δ curve)
G
ES  0
V00
jXT


IS
A Single Machine Infinite Bus (SMIB) system
T T
S
jX jX
I

ES cos V  jES sin 
jXT

ES   V

ES (cos   j sin  )  V

sin 
sin 
emax
T
S
e
T
emax
T
S
e
T
S
S
S S
S S
X
E V
X
E V
X
E V
XT
XT
E V
E cos
sin   P
P 
 S
 P
 P 
 jQe
 
E2
VE cos 
 S
sin   j
S S
  Pe





 jX
V  jE sin 
 [E cos  jE sin ]
S  E I*
Complex power transferred from generator to infinite bus
Power Angle Relation
is defined as steady state power
limit or the maximum power that can be
transferred from generator to load bus.
emax
* Here P

sin 
emax
T
S
e
X
E V
sin   P
P 

The Swing Equation
The equation governing the rotor motion is given by:
S.No Linear Rotational
1 S (displacement) θ
2 V (velocity) ω
3 a (acceleration) α
4 M (Mass) J (Moment of
Inertia)
5 F=Ma τ=Jα
6 Power=FV Power=τω

Renewable Energy Sources Lecture Notes
VARDHAMAN COLLEGE OF ENGINEERING
(AUTONOMOUS)
Shamshabad – 501 218, Hyderabad
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
Sem: VII sem Course Code: A2234
Course Outcomes (COs):
After the completion of the course, the student will be able to
CO.1
Apply the principles of Renewable energy sources for the construction of Power generating
station.
CO.2 Analyse various extraction techniques of Renewable energy sources for different applications.
CO.3 Analyse Renewable energy systems for various environmental conditions.
CO.4 Categorize various energy conversion systems and its limitations.

SYLLABUS
UNIT – I
PRINCIPLES OF SOLAR RADIATION : Role and potential of new and renewable source, the solarenergy
option, Environmental impact of solar power, physics of the sun, the solar constant, extraterrestrial and
terrestrial solar radiation, solar radiation on titled surface, instruments for measuring solar radiation and
sun shine,solarradiation data.
SOLAR ENERGY COLLECTION :Flat plate and concentrating collectors, classification of concentrating
collectors, orientation and thermal analysis, advanced collectors.
UNIT-II
SOLAR ENERGY STORAGE AND APPLICATIONS: Different methods, Sensible, latent heat andstratified
storage, solar ponds. Solar Applications- solar heating /cooling technique, solar distillation and drying,
photovoltaic energy conversion.
UNIT-III
WIND ENERGY :Sources and potentials, horizontal and vertical axis windmills, performance
characteristics, Betz criteria
BIO-MASS : Principles of Bio-Conversion, Anaerobic/aerobic digestion, types of Bio-gas digesters,
gasyield, combustion characteristics of bio-gas, utilization for cooking, I.C.Engine operation and
economicaspects.
UNIT-IV
GEOTHERMAL ENERGY :Resources, types of wells, methods of harnessing the energy, potential inIndia.
OCEAN ENERGY :OTEC, Principles utilization, setting of OTEC plants, thermodynamic cycles.
Tidal and wave energy: Potential and conversion techniques, mini-hydel power plants, and their
economics.
UNIT-V
DIRECT ENERGY CONVERSION :Need for DEC, Carnot cycle, limitations, principles of DEC.
TEXT BOOKS:
1.
2.
Renewable energy resources , Tiwari and Ghosal/ Narosa ,second edition (2008), Mc Graw Hill
Company, New Delhi.
Non-Conventional Energy Sources ,G.D.Rai, fourth edition(2009), Khanna Publishers, New Delhi.
REFERENCES:
1. Renewable Energy Sources , Twidell& Weir, fourth Edition (2009), Tata McGraw Hill Education
Private Limited, New Delhi.
Solar Energy, S.P. Sukhatme, Third Edition (2010), Tata McGraw Hill Education Private Limited,
New Delhi.
2.

UNIT-I
PRINCIPLES OF SOLAR RADIATION
Role and potential of new and renewable source
India has a vast supply of renewable energy resources, and it has one of the largest programs in
the world for deploying renewable energy products and systems. Indeed, it is the only country in the
world to have an exclusive ministry for renewable energy development, the Ministry of Non-
Conventional Energy Sources (MNES). Since its formation, the Ministry has launched one of the world’s
largest and most ambitious programs on renewable energy. Based on various promotional efforts put in
place by MNES, significant progress is being made in power generation from renewable energy sources.
In October, MNES was renamed the Ministry of New and Renewable Energy.
Specifically, 3,700 MW are currently powered by renewable energy sources (3.5 percent of total
installed capacity). This is projected to be 10,000 MW from renewable energy by 2012.
The key drivers for renewable energy are the following:
o The demand-supply gap, especially as population increases
o A large untapped potential
o Concern for the environment
o The need to strengthen India’s energy security
o Pressure on high-emission industry sectors from their shareholders
o A viable solution for rural electrification
Also, with a commitment to rural electrification, the Ministry of Power has accelerated the Rural
Electrification Program with a target of 100,000 villages by 2012.
Introduction In recent years, India has emerged as one of the leading destinations for investors
fromdeveloped countries. This attraction is partially due to the lower cost of manpower and good
quality production. The expansion of investments has brought benefits of employment, development,
and growth in the quality of life, but only to the major cities. This sector only represents a small portion
of the total population. The remaining population still lives in very poor conditions.
India is now the eleventh largest economy in the world, fourth in terms of purchasing power. It
is poised to make tremendous economic strides over the next ten years, with significant development
already in the planning stages. This report gives an overview of the renewable energies market in India.
We look at the current status of renewable markets in India, the energy needs of the country, forecasts
of consumption and production, and we assess whether India can power its growth and its society with
renewable resources.
The Ministry of Power has set an agenda of providing Power to All by 2012. It seeks to achieve
this objective through a comprehensive and holistic approach to power sector development envisaging a
six level intervention strategy at the National, State, SEB, Distribution, Feeder and Consumer levels.

Environmental impacts of solar energy:
Every energy generation and transmission method affects the environment. As it is obvious
conventionalgenerating options can damage air, climate, water, land and wildlife, landscape, as well as
raise the levels of harmful radiation. Renewable technologies are substantially safer offering a solution
to many environmental and social problems associated with fossil and nuclear fuels (EC,1995,1997).
Solar energy technologies (SETs) provide obvious environmental advantages in comparison to the
conventional energy sources, thus contributing to the sustainable development of human activities
Not counting the depletion of the exhausted natural resources, their main advantage is related to the
reduced CO2 emissions, and, normally, absence of any air emissions or waste products during their
operation. Concerning the environment, the use of SETs has additional positive implications such as:
* reduction of the emissions of the greenhouse gases (mainly CO2,NO x) and prevention of
toxic Gas emissions (SO2,particulates)
* reclamation of degraded land;
* reduction of the required transmission lines of the electricity grids; and
* improvement of the quality of water resources
The basic research in solar energy is being carried in universities and educational and
researchinstitutions, public sector institution, BHEL and Central Electronic Limited and carrying out a
coordinated program of research of solar energy.
The application of solar energy is
1. Heating and cooling residential buildings
2. Solar water heating
3. Solar drying of agricultural and chemical products.
4. Solar distillation of a small community scale
5. Salt production by evaporation of sea water
6. Solar cookers
7. Solar engines for water pumping
8. Foodrefrigeration
9. Bio conversion and wind energy and which are indirect source of solar energy
10. Solar furnaces
11. Solar electric power generation by
i)
ii)
iii)
Solar ponds
Steam generators heated by rotating reflectors
reflectors with lenses and pipes for fluid circulation
12. solar photovoltaic cells which can be used for conversion of solar energy directly into electricity
(or) for water pumping in rural agriculture purposes.
PRESENTSENERIO:
TPP - 65.34%
HYDRO - 21.53%

NUCLEAR
RENEWABLE
WIND CAPACITY
-
-
-
2.7%
10.42%
14550 MW.
20,000 MW solar by 2022.
Installed power generation capacity of India 181.558 GW
Per capita energy consumption stood at 704 KW.
1/3 GW of installed capacity by 2017
Solar Radiation
Solar energy, received in the form of radiation, can be converted directly or indirectly in to other
forms of energy, such as heat and electricity. The major draw backs of the extensive application of solar
energy of
1. the intermittent and variable manner in which it arrives at the earth’s surface and
2. the large area require to collect the energy at a useful rate.
Energy is radiated by the sun as electromagnetic waves of which 99% have wave lengths in the
range of 0.2 to 4.0 micro meter (1 micro meter = 10-6 meter)
Solar energy reaching the top of the earth’s atmosphere consists of about
 8% ultra violet radiation [short wave length >0.39 micrometer]
 46% visible light [0.39 to 0.78 micrometer]
 46 % infrared [0.78 micro meter above]
Solar constant
The sun is a large sphere of very hot gases, the heat being generated by various kinds of fusion
reactions.Its diameter is 1.39 X 106 km while that of earth is 1.27 X 104 km. the mean distance between
the two is 1.5 X 108 km. although the sun is large, its subtends angle of only 32 min. at the earth’s
surface.
The brightness of the sun varies from its center to its edge. However the calculation purpose the
brightness all over the solar disc is uniform.
The total radiation from the sun is 5762 degrees K
The rate at which solar energy arise at the top of the atmosphere is called the solar constant Isc . This
is the amount of energy received in unit time on a unit area perpendicular to the sun’s direction at the
mean distance of the earth from the sun.
The solar constant value varies up to 3 % throughout the year, because the distance between the
sun and the earth varies little throughout the year.
The earth is close set of the sun during the summer and farthest during the winter.

This variation in distance produces sinusoidal variation in the intensity of solar radiation I that
reaches the earth.
ISC = 1367 watts/m2
𝐼
𝐼𝑆𝐶 365
= 1+0.033 cos 360 𝑛
. where n is the day of the year.
Spectral distribution of solar radiation intensity at the outer limit of the atmosphere
The luminosity of the Sun is about 3.86 x 1026 watts. This is the total power radiated out into
space by the Sun. Most of this radiation is in the visible and infrared part of the electromagnetic
spectrum, with less than 1 % emitted in the radio, UV and X-ray spectral bands. The sun’s energy is
radiated uniformly in all directions. Because the Sun is about 150 million kilometres from the Earth, and
because the Earth is about 6300 km in radius, only 0.000000045% of this power is intercepted by our
planet. This still amounts to a massive 1.75 x 1017 watts. For the purposes of solar energy capture, we
normally talk about the amount of power in sunlight passing through a single square metre face-on to
the sun, at the Earth's distance from the Sun. The power of the sun at the earth, per square metre is
called the solar constant and is approximately 1370 watts per square metre (W m-2).
The solar constant actually varies by +/- 3% because of the Earth's slightly elliptical orbit around
the Sun. The sun-earth distance is smaller when the Earth is at perihelion (first week in January) and
larger when the Earth is at aphelion (first week in July). Some people, when talking about the solar
constant, correct for this distance variation, and refer to the solar constant as the power per unit area
received at the average Earth-solar distance of one “Astronomical Unit” or AU which is 149.59787066
million kilometres. There is also another small variation in the solar constant which is due to a variation
in the total luminosity of the Sun itself. This variation has been measured by radiometers aboard several
satellites since the late 1970's.
The graph below is a composite graph produced by the World Radiation Centre and shows that
our Sun is actually a (slightly) variable star. The variation in the solar constant can be seen to be about
0.1% over a period of 30 years. Some researchers have tried to reconstruct this variation, by correlating
it to sunspot numbers, back over the last 400 years, and have suggested that the Sun may have varied in
its power output by up to one percent. It has also been suggested that this variation might explain some
terrestrial temperature variations. It is interesting to note that the average G-type star (the class of star
the Sun falls into) typically shows a much larger variation of about 4%.

Solar Radiation Measuring Instruments (Radiometers)
A radiometer absorbs solar radiation at its sensor, transforms it into heat and measures the
resultingamount of heat to ascertain the level of solar radiation. Methods of measuring heat include
taking out heatflux as a temperature change (using a water flow pyrheliometer, a silver-disk
pyrheliometer or a bimetallic pyranograph) or as a thermoelectromotive force (using a thermoelectric
pyrheliometer or a thermo electric pyranometer). In current operation, types using a thermopile are
generally used.
The radiometers used for ordinary observation are pyrheliometers and pyranometers that
measure directsolar radiation and global solar radiation, respectively, and these instruments are
described in this section.For details of other radiometers such as measuring instruments for diffuse sky
radiation and net radiation,refer to ”Guide to Meteorological Instruments and Observation Methods”
and “Compendium of LectureNotes on Meteorological Instruments for Training Class III and Class IV
Meteorological Personnel”published by WMO.
Pyrheliometers
A pyrheliometer is used to measure direct solar radiation from the sun and its marginal
periphery. Tomeasure direct solar radiation correctly, its receiving surface must be arranged to be
normal to the solardirection. For this reason, the instrument is usually mounted on a sun-tracking device
called an equatorialmount.
The structure of an Angstrom electrical compensation pyrheliometeris shown in Figure.
This is a reliable instrument used to observe direct solar radiation, and has long been accepted
as a workingstandard. However, its manual operation requires experience.

This pyrheliometer has a rectangular aperture, two manganin-strip sensors (20.0 mm × 2.0 mm
×0.02 mm) and several diaphragms to let only direct sunlight reach the sensorThe sensor surface is
painted optical black and has uniform absorption characteristics forshort-wave radiation. A copper-
constantan thermocouple is attached to the rear of each sensor strip, andthe thermocouple is
connected to a galvanometer. The sensor strips also work as electric resistors and
generate heat when a current flows across them.
When solar irradiance is measured with this type of pyrheliometer, the small shutter on the
front face ofthe cylinder shields one sensor strip from sunlight, allowing it to reach only the other
sensor. Atemperature difference is therefore produced between the two sensor strips because one
absorbs solarradiation and the other does not, and a thermoelectromotive force proportional to this
difference inducescurrent flow through the galvanometer. Then, a current is supplied to the cooler
sensor strip (the oneshaded from solar radiation) until the pointer in the galvanometer indicates zero, at
which point thetemperature raised by solar radiation is compensated by Joule heat. A value for direct
solar irradiance isobtained by converting the compensated current at this time. If S is the intensity of
direct solar irradiance and i is the current, then S = Ki2,
where K is a constant intrinsic to the instrument and is determined from the size and electric
resistance ofthe sensor strips and the absorption coefficient of their surfaces. The value of K is usually
determinedthrough comparison with an upper-class standard pyrheliometer.
Pyranometers:
A pyranometer is used to measure global solar radiation falling on a horizontal surface. Its
sensor has ahorizontal radiation-sensing surface that absorbs solar radiation energy from the whole sky
(i.e. a solid angleof 2π sr) and transforms this energy into heat. Global solar radiation can be ascertained
by measuring thisheat energy. Most pyranometers in general use are now the thermopile type, although
bimetallic pyranometers are occasionally found.

Thermoelectric pyranometer is shown in Figure. The instrument’s radiation-sensing element
has basically the same structure as that of a thermoelectric pyrheliometer. Another similarity is that the
temperature difference derived between the radiation-sensing element (the hot junction) and the
reflectingsurface (the cold junction) that serves as a temperature reference point is expressed by a
thermopile as anthermoelectromotive force. In the case of a pyranometer, methods of ascertaining the
temperaturedifference are as follows:
1)Several pairs of thermocouples are connected in series to make a thermopile that detects the
temperature difference between the black and white radiation-sensing surfaces.
2) The temperature difference between two black radiation-sensing surfaces with differing areas
Isdetected by a thermopile.
3)The temperature difference between a radiation-sensing surface painted solid black and a
metallic block with high heat capacity is detected by a thermopile.
Sunshine recorder
The duration of bright sunshine in a day is measured by means of sun shine recorder. The sun’s
rays are focused by a glass sphere to a point on a card strip held in a groove in spherical bowl mounted
concentrically with the sphere.Whenever there is a bright sun shine the image formed is intensive
enough to burn a part on the card strip. through out the day as sun moves across the sky, the image
moves along the strip. Thus, a burnt trace whose length is proportional to the duration of sun shine is
obtained on the strip.

b
Solar Radiation Data
Most radiation data is measured for horizontal surfaces. As shown in figure. It is seen a fairly,
smooth variations with the maximum occurring around noon is obtained on a clear day.In contrast an
irregular variation with many peaks and valleys may be obtained on a cloudy day.
 Peak values are generally measured in April or may with parts of Rajasthan or Gujarat receiving
over 600 Langley’s per day.
 During the monsoon and winter months, the daily global radiation decreases to about 300- 400
longley per day.
 Annual average daily diffuse radiation received over the whole country is around 175 longlays
per day.
 The maximum value is about 300 langleys in Gujarat in July, while the minimum values between
75 and 100 langleys per day, are measured over many parts of the country during November
and December as winter sets in.
Solar radiation on tilted surface:
The rate of receipt of solar energy on a given surface on the ground depends on the orientation of
the surface with reference to the sun.A fully sun – tracking surface that always faces the sun receives
the maximum possible solar energy at the particular location.
A surface of the same area oriented in any other direction will receive a smaller amount of radiation
because solar radiation is such a dilute form of energy, it is desirable to capture as much as possible on a
ground area.Most of the solar collectors or solar radiation collecting devices are tilted at an angle to
horizontal surface with Y=0 facing south for tilted surface.
Cosθ = Sinδ Sin (ф – s) + Cos δ Cos ω Cos (ф – s)
For horizontal surfaces Cos θZ= Sin ф Sin δ + Cos ф Cos δ Cos ω
Tilt factor for beam radiation
Ύ = Cosθ
Cos θZ
d
2
Ύ = [1+Cos s
]

UNIT-II
SOLAR ENERGY COLLECTION, STORAGE AND APPLICATIONS
Sensible heat storage:
The use of sensible heat energy storage materials is the easiest method ofstorage. In practice,
water, sand, gravel, soil, etc. can be considered asmaterials for energy storage, in which the largest heat
capacity of water, sowater is used more often. In the 70’s and 80’s, the use of water and soil forcross-
seasonal storage of solar energy was reported. But the material’s sensibleheat is low, and it limits
energy storage.
Latent heat-storage:
Latent heat-storage units are storing thermal energy in latent (= hidden, dormant)mode by
changing the state of aggregation of the storage medium. Applicablestorage media are called "phase
change materials" (PCM).. Commonly saltscrystal is used in low-temperature storage, such as sodium
sulfate decahydrate /calcium chloride, sodium hydrogen phosphate 12-water. However, we must
solve the cooling and layering issues in order to ensure the operatingtemperature and service life.
Medium solar storage temperature is generallyhigher than 100 ℃but under 500 ℃, usually it is around
300 ℃. Suitable formedium temperature storage of materials are: high-pressure hot water, organic
fluids, eutectic salt. Solar heat storage temperature is generally above 500 ℃,the materials currently
being tested are: metal sodium and molten salt.Extremely high temperature above 1000 ℃storage, fire-
resistant ball aluminaand germanium oxide can be used.
Chemical, thermal energy storage:
Thermal energy storage is making the use of chemical reaction to store heat. Ithas the
advantage of large amount in heat, small in volume, light in weight. Theproduct of chemical reaction can
be stored separately for a long time. It occursexothermic reaction when it is needed. it has to meet the
needs of belowconditions to use chemical reaction in heat reserve: good in reaction reversibility,
no secondary reaction, rapid reaction, easy to separate the resultant andreserve it stably. Reactant and
resultant are innoxious ,uninflammable, large in heat of reaction and low price of reactant. Now some of
the chemicalendothermic reaction could meet the needs of above conditions. Like pyrolysis
reaction of Ca(OH)2, Using the above endothermic reaction to store heat andrelease the heat when it is
necessary. But the dehydration reaction temperaturein high atmospheric pressure is higher than 500
degrees. I t is difficult to usesolar energy to complete dehydration reaction. We can use catalyst to
decreasethe reaction temperature, but still very high. So it is still in testing time of heat14reserve in
chemistry.
Plastic crystal thermal energy storage:
In 1984, the U.S. market launched plastic crystal materials for home heating.Plastic crystal’s
scientific name is Neopentyl Glycol (NPG), it and the liquidcrystal are similar to three-dimensional
periodic crystals, but the mechanicalproperties are like plastic. It can store and release thermal energy in
theconstant temperature, but not to rely on solid-liquid phase change to storethermal energy, it stores
the energy through the plastic crystalline molecularstructure occurring solid - solid phase change. When

plastic crystals are atconstant temperature 44c, it absorbs solar energy and stores heat during theday,
and releases the heat during the night.
Solar thermal energy storage tank:
Solar pond is a kind of a certain salt concentration gradient of salt ponds, and itcan be used for
acquisition and storage of solar energy. Because of its simple,low cost, and it is suit to large-scale
applied so it has attracted people's attention.After the 60’s, many countries have started study on solar
pond, Israel has alsobuilt three solar pond power plants.
Solar Collectors
Solar collectors are the key component of active solar-heating systems. Solar collectors gather
the sun's energy, transformits radiation into heat, then transfer thatheat to water, solar fluid, or air. The
solar thermal energy can be used in solar waterheating systems, solar pool heaters, andsolar space-
heating systems. There areseveral types of solar collectors:
 Flat-plate collectors
 Evacuated-tube collectors
Residential and commercial building applications that require temperatures below 200°F
typically use flat-plate collectors, whereas those requiring temperatures higher than 200°F use
evacuated-tube collectors.
Flat-plate collectors
Flat-plate collectors are the most common solar collector for solar water-heating systemsin
homes and solar space heating. A typical flat-plate collector is an insulated metal box with a glass or
plastic cover (called the glazing) and a dark-colored absorber plate. These collectors heat liquid or air at
temperatures less than 180°F.Flat-plate collectors are used for residential water heating and hydronic
space-heating installations.
Liquid flat-plate collectors heat liquid as it flows through tubes in or adjacent to the absorber plate. The
simplest liquid systems use potable household water, which is heated as it passes directly through the
collector and then flows to the house. Solar pool heating This home in Nevada has anintegral collector

storage (ICS) system to provide hot water.also uses liquid flat-plate collector technology, but the
collectors are typically unglazed as in figure below.
Unglazed solar collectors typically used for swimming pool heating.
Air flat-plate collectors are used primarily for solar space heating. The absorber plates in air collectors
can be metal sheets, layers of screen, or non-metallic materials. The air flows past the absorber by using
natural convection or a fan. Because air conducts heat much less readily than liquid does, less heat is
transferred from an air collector's absorber than from a liquid collector's absorber, and air collectors are
typically lessefficient than liquid collectors.
Air flat-plate collectors are used for space heating.
Evacuated-tube collectors
Evacuated-tube collectors can achieve extremely high temperatures (170°F to 350°F), making
them more appropriate for cooling applications and commercial and industrial application. However,
evacuated-tube collectors are more expensive than flat-plate collectors, with unit area costs about twice

that of flat-plate collectors.Evacuated-tube collectors are efficient at high temperatures.The collectors
are usually made of parallel rows of transparent glass tubes. Each tube contains a glass outer tube and
metal absorber tube attached to a fin. The fin is covered with a coating that absorbs solar energy well,
but which inhibits radiative heat loss. Air is removed, or evacuated, from the space between the two
glass tubes to form a vacuum, which eliminates conductive and convective heat loss.A new evacuated-
tube design is available from the Chinese manufacturers, such as: Beijing Sunda Solar Energy Technology
Co. Ltd. The "dewar" design features a vacuum contained between two concentric glass tubes, with the
absorber selective coating on the inside tube. Water is typically allowed to thermosyphon down and
back out the inner cavity to transfer the heat to the storage tank. There are no glass-to-metal seals. This
type of evacuated tube has the potential to become cost-competitive with flat plates.
Concentrating collectors
Unlike solar (photovoltaic) cells, whichuse light to produce electricity, concentrating solar power
systems generate electricity with heat. Concentrating solarcollectors use mirrors and lenses to
concentrate and focus sunlight onto a thermalreceiver, similar to a boiler tube. Thereceiver absorbs
and converts sunlight into heat. The heat is thentransported to asteam generator or engine where
it is converted into electricity. There are threemain types of concentrating solarpower systems:
parabolic troughs, dish/engine systems, and central receiver systems.
These technologiescan be used to generate electricity fora variety of applications, ranging from
remote power systems as small as a few kilowatts (kW) upto grid-connected applications of 200-350
megawatts (MW) or more. A concentrating solar power system that produces 350MW of electricity
displaces the energyequivalent of 2.3 million barrels of oil.
Trough Systems
Fig. 1 A parabolic trough
These solar collectors use mirrored parabolic troughs to focus the sun's energy toa fluid-carrying
receiver tube located atthe focal point of a parabolically curved trough reflector (see Fig.1 above).
Theenergy from the sun sent to the tube heatsoil flowing through the tube, and the heatenergy is then
used to generate electricityin a conventional steam generator. Many troughs placed in parallel rows
arecalled a "collector field." The troughs inthe field are all aligned along a northsouth axis so they can
track the sun fromeast to west during the day, ensuring thatthe sun is continuously focused on
thereceiver pipes. Individual trough systemscurrently can generate about 80 MW ofelectricity. Trough
Renewable Energy Sources LectureNotes

designs can incorporatethermal storage—setting aside the heattransfer fluid in its hot phase—
allowingfor electricity generation several hoursinto the evening. Currently, all parabolic trough plants
are"hybrids," meaning they use fossil fuels tosupplement the solar output during periods of low solar
radiation.
Dish Systems
Fig.2 Dish Systems
Dish systems usedish-shaped parabolic mirrors asreflectors to concentrate and focusthe sun's
rays ontoa receiver, which ismounted above thedish at the dish center. A dish/enginesystem is a
standalone unit composed primarily ofa collector, areceiver, and anengine (see Fig.2 above). It works
bycollecting and concentrating the sun's energy with a dishshaped surface onto a receiver thatabsorbs
the energy and transfers it to theengine. The engine then converts thatenergy to heat. The heat is then
convertedto mechanical power, in a manner similarto conventional engines, by compressingthe working
fluid when it is cold, heatingthe compressed working fluid, and thenexpanding it through a turbine or
with apiston to produce mechanical power. Anelectric generator or alternator converts
the mechanical power into electricalpower.
Dish/engine systems use dual-axis collectors to track the sun. The ideal concentrator shape is
parabolic, created either by asingle reflective surface or multiple reflectors, or facets. Many options exist
forreceiver and engine type, including Stirling cycle, microturbine, and concentrating photovoltaic
modules. Each dishproduces 5 to 50 kW of electricity and canbe used independently or linked
togetherto increase generating capacity. A 250-kWplant composed of ten 25-kW dish/enginesystems
requires less than an acre of land.Dish/engine systems are not commercially available yet, although
ongoingdemonstrations indicate good potential.Individual dish/engine systems currentlycan generate
about 25 kW of electricity.More capacity is possible by connectingdishes together. These systems can
becombined with natural gas, and the resulting hybrid provides continuous powergeneration.

Central Receiver Systems
Central receivers (or power towers) usethousands of individual sun-tracking mirrors called
"heliostats" to reflect solarenergy onto a receiver located on top of atall tower. The receiver collects the
sun'sheat in a heat-transfer fluid (molten salt)that flows through the receiver. The salt'sheat energy is
then used to make steam togenerate electricity in a conventionalsteam generator, located at the foot of
thetower. The molten salt storage systemretains heat efficiently, so it can be storedfor hours or even
days before being usedto generate electricity. Therefore, a centralreceiver system is composed of five
maincomponents: heliostats, receiver, heattransport and exchange, thermal storage,and controls (see
Fig. 3). Solar One, Two, “Tres” The U.S. Department of Energy (DOE),and a consortium of U.S. utilities
andindustry, built this country's first twolarge-scale, demonstration solar powertowers in the desert
near Barstow, California. Solar One operated successfully fromThis concentrating solar power system
uses mirrors tofocus highly concentrated sunlight onto a receiver thatconverts the sun’s heat into
energy.ReceiverandgeneratorConcentratorIndividualdish/engine systemscurrently cangenerate about25
kW of electricity.
up
Power tower plantscan potentiallyoperate for 65percent of the yearwithout the needfor a back-
fuel source.Solar Two—a demonstration powertower located in the Mojave Desert—can
generate about 10 MW of electricity.In this central receiver system, thousands of sun-tracking mirrors
calledheliostats reflect sunlight onto thereceiver. Molten salt at 554ºF (290ºC) ispumped from a cold
storage tankthrough the receiver where it is heatedto about 1,050ºF (565ºC). The heated saltthen
moves on to the hot storage tank.When power is needed from the plant,the hot salt is pumped to a
generatorthat produces steam. The steam activates a turbine/generator system thatcreates electricity.
From the steam generator, the salt is returned to the coldstorage tank, where it stored is and canbe
eventually reheated in the receiver. By using thermal storage, power towerplants can potentially
operate for 65percent of the year without the need fora back-up fuel source. Without energystorage,
solar technologies like this arelimited to annual capacity factors near25 percent. The power tower's
ability tooperate for extended periods of time onstored solar energy separates it fromother renewable
energy technologies.Hot saltstorage tankSteamgenerator1,050˚FCold saltstorage tankCondensercooling
tower554˚FSystem boundarySubstationSteam turbineand electric generator

Applications of Solar Energy
Solar energy can supply and or supplement many farm energy requirements. Thefollowing is a
brief discussion of a few applications of solar energy technologies inagriculture.
Crop And Grain Drying
Using the sun to dry crops and grain is one of the oldest and mostly widely usedapplications of
solar energy. The simplest and least expensive techniques is to allow cropsto dry naturally in the field, or
to spread grain and fruit out in the sun after harvesting.The disadvantage of these methods is that the
crops and grains are subject to damage bybirds, rodents, wind, and rain, and contamination by wind
blown dust and dirt. Moresophisticated solar dryers protect grain and fruit, reduce losses, dry faster and
moreuniformly, and produce a better quality product than open air methods.
The basic components of a solar dryer are an enclosure or shed, screened drying trays orracks,
and a solar collector. In hot, arid climates, the collector may not even be necessary.The southern side of
the enclosure itself can be glazed to allow sunlight to dry thematerial. The collector can be as simple as a
glazed box with a dark coloured interior toabsorb the solar energy that heats air. The air heated in the

solar collector moves, eitherby natural convection or forced by a fan, up through the material being
dried. The size ofthe collector and rate of airflow depends on the amount of material being dried, the
moisture content of the material, the humidity in the air, and the average amount of solarradiation
available during the drying season.
There is a relatively small number of large solar crop dryers around the world. This isbecause the
cost of the solar collector can be high, and drying rates are not ascontrollable as they are with natural
gas or propane powered dryers.Using the collector at other times of the year, such as for heating farm
building, maymake a solar dryer more cost effective. It is possible to make small, very low cost dryersout
of simple materials. These systems can be useful for drying vegetables and fruit for
home use.
Space And Water Heating
Livestock and diary operations often have substantial air and water heating requirements.
Modern pig and poultry farms raise animals in enclosed buildings, where it is necessary tocarefully
control temperature and air quality to maximize the health and growth of theanimals. These facilities
need to replace the indoor air regularly to remove moisture, toxicgases odors, and dust. Heating this air,
when necessary, requires large amount of energy.With proper planning and design solar air/space
heaters can be incorporated into farmbuildings to preheat incoming fresh air. These systems can also be
used to supplement
Solar Energy Applications for Agriculture
Natural ventilation levels during summer months depending on the region and weather.Solar
water heating can provide hot water for pen or equipment cleaning or for preheatingwater going into a
conventional water heater. Waterheating can account for as much as 25 percent of a typical family’s
energy costs and up to40 percent of the energy used in a typical dairy operation. A properly-sized solar
waterheatingsystem could cut those costs in half.
There are four basic types of solar water-heater systems available. These systems sharethree
similarities: a glazing (typically glass) over a dark surface to gather solar heat; oneor two tanks to store
hot water; and associated plumbing with or without pumps tocirculate the heat-transfer fluid from the
tank to the collectors and back again.
(a) Drain down systems pump water from the hot water tank through the solar collector,
where it is heated by the sun and returned to the tank. Valves automatically drain thesystem when
sensors detect freezing temperatures.
(b) Drain back systems use a separate plumbing line filled with fluid, to gather the sun’sheat. These
systems operate strictly on gravity. When the temperature is nearfreezing, the pump shuts off and the
transfer fluid drains back into the solar storagetank.
(c) Anti-freeze closed-loop systems rely on an antifreeze solution to operate through coldand winter
months. Anti-freeze solutions are separated from household water by adouble-walled heat exchange.

(d) Bread box batch systems are passive systems in which the storage tank also functionsas the
collector. One or two water tanks, painted black, are placed in a well-insulatedbox or other enclosure
that has a south wall made of clear plastic or glass and titledat the proper angle. This allows the sun to
shine directly on the tank and heat a batchof water. An insulated cover can provide freeze protection.
Greenhouse Heating
Another agricultural application of solar energy is greenhouse heating. Commercial greenhouse
typically rely on the sun to supply their lighting needs, but are not designed to usethe sun for heating.
They rely on gas or oil heaters to maintain the temperaturesnecessary to grow plants in the colder
months. Solar greenhouse, however are designedto utilize solar energy both for heating and lighting.
A solar greenhouse has thermal mass to collect and store solar heat energy, andinsulation to retain this
heat for use during the night and on cloudy days. Asolar green house is oriented to maximize southern
glazing exposure. Its northern sidehas little or no glazing and is well insulated. To reduce heat loss, the
glazing itself is alsomore efficient than single-pane glass, and various products are available ranging
fromdouble pane to cellular glazing. A solar greenhouse reduces the need for fossil fuels forheating. A
gas or oil heater may serve as a back-up heater, or to increase carbon dioxidelevels to induce higher
plant growth.
Passive solar greenhouses are often good choices for small growers, because they are acost-efficient
way for farmers to extend the growing season. In colder climates or in areaswith long periods of cloudy
weather, solar heating may need to be supplemented with agas or electric heating system to protect
plants against extreme cold. Active solargreenhouses use supplemental energy to move solar heated air
or water from storage orcollection areas to other regions of the greenhouse.
Remote Electricity Supply (Photovoltaic)
Solar electric, or photovoltaic (PV), systems convert sun light directly to electricity. Theywork
any time the sun is shining, but more electricity is produced when they sun light ismore intensive and
strikes the PV modules directly (as when rays of sunlight areperpendicular to the PV modules). They can
also power an electrical appliance directly, orstore solar energy in a battery. In areas with no utility lines,
PV systems are often cheaperand require less maintenance than diesel generators, wind turbines, or
batteries alone.And where utilities charge for new lines, a PV generating system is often much
cheaperfor the land owner than paying for a new line.PV allows for the production of electricity–without
noise or air pollution-from a clean,renewable resource. A PV system never runs out of fuel. Solar electric
power comes invery handy on farm and ranches, and is often the most cost-effective and
lowmaintenancesolution at locations far from the nearest utility line. PV can be used topower lighting,
electric fencing, small motors, aeration fans, gate-openers, irrigation valveswitches, automatic
supplement feeders. Solar electric energy can be used to movesprinkler irrigation systems. PV systems
are also extremely well-suitedfor pumping water for livestock in remote pasture, where electricity from
power lines isunavailable. PV is often much less-expensive than the alternative of extending power lines
into these remote areas.
Water Pumping
Photovoltaic (PV) water pumping systems may be the most cost-effective water pumpingoption
in locations where there is no existing power line. They are exceptionally wellsuitedfor grazing
operations to supply water to remote pastures. Simple PV powersystems run pumps directly when the

sun is shining, so they work hardest in the hotsummer months when they are needed most. Generally,
batteries are not necessarybecause the water is stored in tanks or pumped to fields and used in the day
time. Largerpumping systems may include batteries, inverters, and tracking mounts to follow the sun.
When properly sized and installed, PV water pumps are very reliable and require littlemaintenance. The
size and cost of a PV water pumping system depends on the quality ofsolar energy available at the site,
the pumping depth, the water demand, and systempurchase and installation costs, PV systems are very
cost-effective for remote livestockwater supply, pond aeration, and small irrigation systems. For
example, a system thatincludes a 128 watt PV array and a submersible pump can produce 750-1000
gallons ofwater per day from 200 foot drilled well.

UNIT-III
WIND ENERGY
History of Wind-Mills:
The wind is a by-product of solar energy. Approximately 2% of the sun's energy reaching
the earth is converted into wind energy. The surface of the earth heats and coolsunevenly,
creating atmospheric pressure zones that make air flow from high- to lowpressureareas.The
wind has played an important role in the history of human civilization. The firstknown use of
wind dates back 5,000 years to Egypt, where boats used sails to travel fromshore to shore. The
first true windmill, a machine with vanes attached to an axis toproduce circular motion, may
have been built as early as 2000 B.C. in ancient Babylon.By the 10th century A.D., windmills
with wind-catching surfaces having 16 feet lengthand 30 feet height were grinding grain in the
areas in eastern Iran and Afghanistan.The earliest written references to working wind machines
in western world date from the12th century. These too were used for milling grain. It was not
until a few hundred yearslater that windmills were modified to pump water and reclaim much
of Holland from thesea.
The multi-vane "farm windmill" of the American Midwest and West was invented in the
United States during the latter half of the l9th century. In 1889 there were 77 windmillfactories
in the United States, and by the turn of the century, windmills had become amajor American
export. Until the diesel engine came along, many transcontinental railroutes in the U.S.
depended on large multi-vane windmills to pump water for steamlocomotives.Farm windmills
are still being produced and used, though in reduced numbers. They arebest suited for pumping
ground water in small quantities to livestock water tanks. In the1930s and 1940s, hundreds of
thousands of electricity producing wind turbines were builtin the U.S. They had two or three
thin blades which rotated at high speeds to driveelectrical generators. These wind turbines
provided electricity to farms beyond the reachof power lines and were typically used to charge
storage batteries, operate radio receiversand power a light bulb. By the early 1950s, however,
the extension of the central powergrid to nearly every American household, via the Rural
Electrification Administration,eliminated the market for these machines. Wind turbine
development lay nearly dormantfor the next 20 years.
A typical modern windmill looks as shown in the following figure. The wind-millcontains three
blades about a horizontal axis installed on a tower. A turbine connected toa generator is fixed
about the horizontal axis.

Like the weather in general, the wind can be unpredictable. It varies from place to place,and
from moment to moment. Because it is invisible, it is not easily measured withoutspecial
instruments. Wind velocity is affected by the trees, buildings, hills and valleysaround us. Wind is
a diffuse energy source that cannot be contained or stored for useelsewhere or at another
time.
Classification of Wind-mills:
Wind turbines are classified into two general types: Horizontal axis and Vertical axis.
Ahorizontal axis machine has its blades rotating on an axis parallel to the ground as shownin the
above figure. A vertical axis machine has its blades rotating on an axisperpendicular to the
ground. There are a number of available designs for both and eachtype has certain advantages
and disadvantages. However, compared with the horizontalaxis type, very few vertical axis
machines are available commercially.
Horizontal Axis:
This is the most common wind turbine design. In addition to being parallel to the
ground,the axis of blade rotation is parallel to the wind flow. Some machines are designed to
operate in an upwind mode, with the blades upwind of the tower. In this case, a tail vaneis
usually used to keep the blades facing into the wind. Other designs operate in adownwind
mode so that the wind passes the tower before striking the blades. Without atail vane, the
machine rotor naturally tracks the wind in a downwind mode. Some verylarge wind turbines
use a motor-driven mechanism that turns the machine in response to awind direction sensor
mounted on the tower. Commonly found horizontal axis wind millsare aero-turbine mill with
35% efficiency and farm mills with 15% efficiency.
Vertical Axis:
Although vertical axis wind turbines have existed for centuries, they are not as commonas their
horizontal counterparts. The main reason for this is that they do not takeadvantage of the
higher wind speeds at higher elevations above the ground as well ashorizontal axis turbines.
The basic vertical axis designs are the Darrieus, which hascurved blades and efficiency of 35%,
the Giromill, which has straight blades, andefficiency of 35%, and the Savonius, which uses

scoops to catch the wind and theefficiency of 30%. A vertical axis machine need not be oriented
with respect to winddirection. Because the shaft is vertical, the transmission and generator can
be mounted atground level allowing easier servicing and a lighter weight, lower cost tower.
Althoughvertical axis wind turbines have these advantages, their designs are not as efficient
atcollecting energy from the wind as are the horizontal machine designs. The followingfigures
show all the above mentioned mills.
There is one more type of wind-mill called Cyclo-gyro wind-mill with very highefficiency of
about 60%. However, it is not very stable and is very sensitive to winddirection. It is also very
complex to build.

Main Components of a wind-mill :
Following figure shows typical components of a horizontal axis wind mill.
Rotor:
The portion of the wind turbine that collects energy from the wind is called the rotor.
Therotor usually consists of two or more wooden, fiberglass or metal blades which rotateabout
an axis (horizontal or vertical) at a rate determined by the wind speed and the shapeof the
blades. The blades are attached to the hub, which in turn is attached to the mainshaft.
Drag Design:
Blade designs operate on either the principle of drag or lift. For the drag design, the
windliterally pushes the blades out of the way. Drag powered wind turbines are characterized
by slower rotational speeds and high torque capabilities. They are useful for the
pumping,sawing or grinding work. For example, a farm-type windmill must develop high torque
atstart-up in order to pump, or lift, water from a deep well.
Lift Design:
The lift blade design employs the same principle that enables airplanes, kites and birds
tofly. The blade is essentially an airfoil, or wing. When air flows past the blade, a windspeed and
pressure differential is created between the upper and lower blade surfaces.The pressure at the
lower surface is greater and thus acts to "lift" the blade. When bladesare attached to a central
axis, like a wind turbine rotor, the lift is translated into rotationalmotion. Lift-powered wind
turbines have much higher rotational speeds than drag typesand therefore well suited for
electricity generation.

Tip Speed Ratio:
The tip-speed is the ratio of the rotational speed of the blade to the wind speed. The
largerthis ratio, the faster the rotation of the wind turbine rotor at a given wind
speed.Electricity generation requires high rotational speeds. Lift-type wind turbines
havemaximum tip-speed ratios of around 10, while drag-type ratios are approximately 1.Given
the high rotational speed requirements of electrical generators, it is clear that thelift-type wind
turbine is most practical for this application.
The number of blades that make up a rotor and the total area they cover affect
windturbine performance. For a lift-type rotor to function effectively, the wind must
flowsmoothly over the blades. To avoid turbulence, spacing between blades should be
greatenough so that one blade will not encounter the disturbed, weaker air flow caused by
theblade which passed before it. It is because of this requirement that most wind turbineshave
only two or three blades on their rotors.
Generator:
The generator is what converts the turning motion of a wind turbine's blades
intoelectricity. Inside this component, coils of wire are rotated in a magnetic field to
produceelectricity. Different generator designs produce either alternating current (AC) or
directcurrent (DC), and they are available in a large range of output power ratings.
Thegenerator's rating, or size, is dependent on the length of the wind turbine's blades
becausemore energy is captured by longer blades.
It is important to select the right type of generator to match intended use. Most home
andoffice appliances operate on 240 volt, 50 cycles AC. Some appliances can operate oneither
AC or DC, such as light bulbs and resistance heaters, and many others can beadapted to run on
DC. Storage systems using batteries store DC and usually areconfigured at voltages of between
12 volts and 120 volts.
Generators that produce AC are generally equipped with features to produce the
correctvoltage of 240 V and constant frequency 50 cycles of electricity, even when the
windspeed is fluctuating.
DC generators are normally used in battery charging applications and for operating DC
appliances and machinery. They also can be used to produce AC electricity with the useof an
inverter, which converts DC to AC.

Transmission:
The number of revolutions per minute (rpm) of a wind turbine rotor can range between
40 rpm and 400 rpm, depending on the model and the wind speed. Generators typicallyrequire
rpm's of 1,200 to 1,800. As a result, most wind turbines require a gear-boxtransmission to
increase the rotation of the generator to the speeds necessary for efficientelectricity
production. Some DC-type wind turbines do not use transmissions. Instead,they have a direct
link between the rotor and generator. These are known as direct drivesystems. Without a
transmission, wind turbine complexity and maintenance requirementsare reduced, but a much
larger generator is required to deliver the same power output asthe AC-type wind turbines.
Tower:
The tower on which a wind turbine is mounted is not just a support structure. It
alsoraises the wind turbine so that its blades safely clear the ground and so it can reach
thestronger winds at higher elevations. Maximum tower height is optional in most cases,except
where zoning restrictions apply. The decision of what height tower to use will bebased on the
cost of taller towers versus the value of the increase in energy productionresulting from their
use. Studies have shown that the added cost of increasing towerheight is often justified by the
added power generated from the stronger winds. Largerwind turbines are usually mounted on
towers ranging from 40 to 70 meters tall.
Towers for small wind systems are generally "guyed" designs. This means that there are
guy wires anchored to the ground on three or four sides of the tower to hold it erect.These
towers cost less than freestanding towers, but require more land area to anchor theguy wires.
Some of these guyed towers are erected by tilting them up. This operation canbe quickly
accomplished using only a winch, with the turbine already mounted to thetower top. This
simplifies not only installation, but maintenance as well. Towers can beconstructed of a simple
tube, a wooden pole or a lattice of tubes, rods, and angle iron.Large wind turbines may be
mounted on lattice towers, tube towers or guyed tilt-uptowers.
Towers must be strong enough to support the wind turbine and to sustain vibration,
windloading and the overall weather elements for the lifetime of the wind turbine. Their costs
will vary widely as a function of design and height.
Operating Characteristics of wind mills:
All wind machines share certain operating characteristics, such as cut-in, rated and cutout
wind speeds.
Cut-in Speed:
Cut-in speed is the minimum wind speed at which the blades will turn and generate
usable power. This wind speed is typically between 10 and 16 kmph.

Rated Speed:
The rated speed is the minimum wind speed at which the wind turbine will generate its
designated rated power. For example, a "10 kilowatt" wind turbine may not generate
10kilowatts until wind speeds reach 40 kmph. Rated speed for most machines is in the rangeof
40 to 55 kmph. At wind speeds between cut-in and rated, the power output from awind turbine
increases as the wind increases. The output of most machines levels offabove the rated speed.
Most manufacturers provide graphs, called "power curves,"showing how their wind turbine
output varies with wind speed.
Cut-outSpeed:
At very high wind speeds, typically between 72 and 128 kmph, most wind turbines cease
power generation and shut down. The wind speed at which shut down occurs is called thecut-
out speed. Having a cut-out speed is a safety feature which protects the wind turbinefrom
damage. Shut down may occur in one of several ways. In some machines anautomatic brake is
activated by a wind speed sensor. Some machines twist or "pitch" theblades to spill the wind.
Still others use "spoilers," drag flaps mounted on the blades orthe hub which are automatically
activated by high rotor rpm's, or mechanically activatedby a spring loaded device which turns
the machine sideways to the wind stream. Normalwind turbine operation usually resumes
when the wind drops back to a safe level.
Betz Limit:
It is the flow of air over the blades and through the rotor area that makes a wind turbine
function. The wind turbine extracts energy by slowing the wind down. The theoreticalmaximum
amount of energy in the wind that can be collected by a wind turbine's rotor isapproximately
59%. This value is known as the Betz limit. If the blades were 100%efficient, a wind turbine
would not work because the air, having given up all its energy,would entirely stop. In practice,
the collection efficiency of a rotor is not as high as 59%.A more typical efficiency is 35% to 45%.
A complete wind energy system, includingrotor, transmission, generator, storage and other
devices, which all have less than perfectefficiencies, will deliver between 10% and 30% of the
original energy available in thewind.

The following plot gives the relationship between wind speed in KMPH and the powerdensity.
In the last column of the table, we have calculated the output of the turbine assuming thatthe
efficiency of the turbine is 30%. However, we need to remember that the efficiency ofthe
turbine is a function of wind speed. It varies with wind speed.
Now, let us try to calculate the wind speed required to generate power equivalent to 1square
meter PV panel with 12% efficiency. We know that solar insolation available atthe PV panel is
1000 watts/m2at standard condition. Hence the output of the PV panelwith 12% efficiency
would be 120 watts. Now the speed required to generate this powerby the turbine with 30%
efficiency can be calculated as follows:
Turbine output required = 120 Watts/m2
Power Density at the blades = 120/ (0.3) = 400 watts/m2

Computer-Methods-in-Power-Systems.pptx

Computer-Methods-in-Power-Systems.pptx

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