Eee577

EEE577: Term Project

11/10/2011

STUDY OF TRANSMISSION ADEQUACY BY ARIZONA
TRANSMISSION EXPANSION CO. FOR ADDING PV
RESOURCES

A PROJECT REPORT

Submitted by
Supriya Chathadi

In partial fulfillment for completion of the course
EEE577: Power Engineering Operations/Planning

at

Arizona State University, Tempe

[Type text] Page 1


Table of Contents

1. Introduction ......................................................................................................................................... 3
2. The Per Unit System ........................................................................................................................... 3
2.1. Advantages................................................................................................................................... 3
3. DC Power Flow................................................................................................................................... 4
3.1. Assumptions................................................................................................................................. 4
3.2. Formulation .................................................................................................................................. 4
4. Actual Power Flows in the System ..................................................................................................... 5
4.1. Bus Terminology ......................................................................................................................... 5
4.2. Initial Calculations ....................................................................................................................... 5
4.3. Power Flow Calculations ............................................................................................................. 5
5. PV Injection ........................................................................................................................................ 6
5.1. Maximization using linprog ......................................................................................................... 6
6. Line Outage Contingencies ................................................................................................................. 6
7. Results ................................................................................................................................................. 7
8. Additional Concerns ........................................................................................................................... 8
9. Conclusion .......................................................................................................................................... 9
10. References ......................................................................................................................................... 9

Appendix 1: System Representation ........................................................................................................ i
Appendix 2: MATLAB Codes ................................................................................................................ ii
A2.1. Base Case: All Lines under Operation ...................................................................................... ii
A2.2. Line Outage Contingency between Flagstaff & Four Corners .................................................. ii
A2.3. Line Outage Contingency between Flagstaff & Palo Verde .................................................... iii
A2.4. Line Outage Contingency between Flagstaff & Blythe ........................................................... iii
A2.5. Line Outage Contingency between Blythe & Imperial Valley ................................................ iv
A2.6. Line Outage Contingency at One of the Lines between Imperial Valley and Palo Verde ........ v
A2.7. Line Outage Contingency between Palo Verde & Bicknell ...................................................... v

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1. Introduction

A study is performed by Arizona Transmission Expansion Co. (AZTEx) to obtain the transmission
adequacies at certain parts of Arizona on adding high level solar PV resources at suggested sites.

 This report is based on the study where PV resources are added at Bicknell and Blythe.
 The excess generation due to PV injection is dissipated at Imperial Valley and Blythe in
proportion to their present load levels.

An approximate representation of the system base loads and generation, suggested PV injections and
the compensating loads are shown in Appendix 1.

2. The Per Unit System

It is a common practice in power system studies to represent all system parameters as a ratio of a
defined base quantity in the same units, called the per unit representation.

Quantity (Actual units)
Per Unit Quantity =
Base Quantity (Actual units)

Generally, the bases for any two of the system parameters is defined (SB and VB, SB and IB, etc.) are
defined from which all other bases are calculated. For example, when SB and VB are given, the
following expressions can give other base quantities.

SB 3 SB
IB = =
VB 3 VB 3

(VB/ 3 ) 2 VB 2
ZB = =
SB 3 SB

1
YB =
ZB

2.1. Advantages

 Per unit quantities for similar components (generators, transformers, lines) will lie within a
narrow range, regardless of their ratings and sizes.
 They are the same on either side of a transformer, independent of voltage level.
 The relative values of circuit quantities are clearly identified as unnecessary scaling factors
are eliminated.
 Use of the constant is reduced in three-phase calculations.
 Much simpler for calculations and ideal for computer simulations as well.
 It rules out the problem of using different units in different parts of the world by introducing a
universal standard.



3. DC Power Flow

There are a number of ways to perform power flow studies in a system. The simplest formulation is
called „DC Power Flow‟. The name is illusive because there is nothing to do with DC in it.

Some important observations are made from actual load flow studies and few assumptions are made
in order to simplify the calculations and still not vary the results in a large scale.

3.1. Assumptions

 The transmission lines are assumed to be purely inductive as the resistances are much smaller
than the reactances.
 As all machines operate in synchronism, the differences in angles between their voltage
phasors are typically very small (less than 30◦). Thus it is assumed that sin δ ≈ δ.
 It is seen that the per unit voltages operate close enough to 1p.u. This comes up with an
assumption that the voltage magnitudes can be set to 1p.u. at all buses.
 As reactive power flow between two buses is dependent on the difference in their voltage
magnitudes, an assumption can be made that there is no reactive power flow in the system.
 The real power supplied by a bus is much greater than the reactive power supplied and hence
reactive power injection is neglected.

3.2. Formulation

The actual real power flow is given by the equation:

Vi Vj sin ij
Pij 
xij

Based on the assumptions, the power flow equation can be written as:

ij i  j
Pij  
xij xij

The power flow matrix for a system can be written from the above expression as follows:

Pbus  Bbusδ bus
where,

Bbus is called the susceptance matrix, given by the imaginary part of the admittance matrix (Ybus)

 Y 11 Y 12 ... Y1n 
 Y 21 Y 22 ... Y 2 n
Bbus  imag(Y bus)  imag  
 ... ... ... ... 
 
 Yn 1 Yn 2 ... Ynn 

Yii = yi0+yi1+yi2+…+yin

Yij = Yji = -yij



where, yij is the primitive admittance between buses i and j, given by 1
xij

4. Actual Power Flows in the System
4.1. Bus Terminology

For ease of calculation, the buses are numbered from 0 to 5, where 0 indicates the reference bus. The
following conventions are used in the following sections:

Palo Verde (P) – 0 (ref)
Four Corners (FC) – 1
Flagstaff (F) – 2
Blythe (BL) – 3
Imperial Valley (I) – 4
Bicknell (BI) – 5

4.2. Initial Calculations

The reactance of each line can be calculated as the product of reactance per km of the conductor used
and the length of the line. The double line is considered as reactances in parallel.

The base and per unit values for all the line are also calculated and tabulated as follows:

Table 1: Impedance Calculations

SB = 100 MVA = 100MW (no reactive power flows)
Reactance (ohms) Base Reactance (ohms) Per Unit Reactance (p.u)
x12 204 x 0.2908j = 59.2008j 3452/100 = 1190.25 59.2008j/1190.25
x20 80 x 0.0496j = 3.968j 3452/100 = 1190.25 3.968j/1190.25
2
x23 98 x 0.5464j = 53.5472j 345 /100 = 1190.25 53.5472j /1190.25
x34 110 x 0.5464j = 60.104j 3452/100 = 1190.25 60.104j /1190.25
x40 (357 x 0.056j)/2 = 9.996j 5002/100 = 2500 9.996j /2500
2
x50 41 x 0.2903j = 11.8982j 345 /100 = 1190.25 11.8982j /1190.25

4.3. Power Flow Calculations

The values of δ for all buses are found from the expression, δ bus  Bbus Pbus where, Pbus is a
1

matrix showing power injection at various buses. They are given with reference to Palo Verde as
shown below:

δP 0.0000
δFC -0.3382
δF 0.0100
δBL 0.1000
δI 0.1000
δBI -0.0800

Power flows in the lines are found out by increasing the dimension of δbus by adding a zero for the
reference bus, and using the same formula. But, this time the rows of Bbus have entries only at two
sites between which the power flow is calculated.



Consolidated results are shown in section 7.

5. PV Injection

It is desired to inject maximum PV resources at Blythe and Bicknell without overloading any of the
lines (considering the long term rating). The power injection is compensated at Imperial Valley and
Blythe in proportion to their present loads. Thus, their participation factors are calculated as:

25
PFI =  0.926
25  2
2
PFBL =  0.074
25  2

If the power injected at Blythe P1 and that at Bicknell is P2, they are compensated as 0.926(P1+P2) at
Imperial Valley and 0.074(P1+P2) at Blythe.

Same calculations as done in section 4 are done to obtain power flows in terms of P1 and P2.
Optimal values for P1 and P2 are found using linear programming (linprog) in MATLAB. The codes
are shown in Appendix 2.

5.1. Maximization using linprog

Linear programming is defined as:

Min f(x), subject to
Ax ≤ b; Aeqx = beq
lb ≤ x ≤ ub

where, f is called the objective function, x is a vector consisting of decision variables, Ax ≤ b are the
inequality constraints, Aeqx = beq are the equality constraints, lb and ub are the limits for the decision
variables.

The objective in this case is to maximize P1 and P2, with the line flows not exceeding their limits.
The problem can be formulated as given below:

Max (P1+P2) = -Min (-P1-P2)
line flows ≤ line ratings
0 ≤ P1, P2 ≤ ∞

In the constraints, the line flows can be in either direction, thus they might change signs in some
cases. As the direction of line flows cannot be predicted sometimes, it might be necessary to manually
change the signs for the line flows in order to maximize the PV injection. The resulting values of P1
and P2 are the maximum amounts of power which can be injected in terms of PV resources at Blythe
and Bicknell. Results are tabulated in section 7.

6. Line Outage Contingencies

This section deals with the study of (N-1) line outage contingencies. The procedure is basically the
same as illustrated with all lines under operation, except that the results are going to slightly different
because of the difference in Ybus.



On removing the lines one after another, it is seen that the power generations may not suffice the
loads in some cases such as a line outage between Four Corners and Flagstaff or between Palo Verde
and Bicknell, as the generation in Four Corners or Bicknell would be lost. In such cases, it is assumed
that Palo Verde supplies the power loss due to line outage, for the power flows to converge. This is
based on the given suggestion that equivalent generation could be added to another existing
generation site.

The power flow and maximum PV injection results are tabulated in Section 7. It is seen that a
contingency in one of the lines or both between Palo Verde and Imperial Valley is not allowed as the
lines overload even for the base case generation and loads. Thus the study of PV injection cannot be
done for this case.

7. Results

Table 2 gives the line flows in all the lines for including and not including PV injection. For the case
on injecting PV resources, the highlighted values indicate the line which might start overloading if
little more PV resources are added to the system. It is seen that for a line outage between Palo Verde
and Imperial Valley, line overloading occurs even without injecting PV resources.

Table 2: Per Unit Power Flows in All Lines for with/without PV Injection
Per Unit Power PFC-F PP-F PF-BL PI-BL PP-I PBI-P
Flows
(SB = 100MVA)
Condition No With No PV With No PV With No PV With No With PV No With
PV PV PV PV PV PV PV PV
Line ratings 15+15
7.09 7.09 14.8 14.8 4.99 4.99 4.99 4.99 =30 30 10 10
With all lines
7 7 3 1.8010 2 2.8010 0.0002 4.9897 25 29.9998 8 8.1988
under operation
With line outage
- - 9.773 5.1902 1.773 2.8098 0.2271 4.5358 25.23 30 8 8.1872
between Flagstaff
& Four Corners
With line outage
7 7 - - 1 1 3 1.0100 28 30 8 10
between Flagstaff
& Palo Verde
With line outage
7 7 1 1 - - 2 0.9900 27 29 8 10
between Flagstaff
& Blythe
With line outage
7 7 3 1.3551 2 2.3551 - - 25 30 8 8.6449
between Blythe &
Imperial Valley
With line outage at
24.064
one of the lines 7 - 3.9357 - 2.9357 - 0.9357 - (rating - 8 -
between Imperial in this
Valley and Palo case is
15)
Verde
With line outage
7 7 3 1.8162 2 2.8162 0.0002 4.9897 25 29.8162 - -
between Palo
Verde & Bicknell

Table 3 summarizes the maximum amount of PV resources which can be injected at Bicknell and
Blythe for different cases. The study of injecting PV into the system is not possible when a line outage
occurs between Imperial Valley and Palo Verde because of overloading, as shown in Table 2.



Maximum PV can be injected in the system when all lines are under operation, which is about
1078.79 MW.

Table 3: Consolidated Results for Maximum PV Injection at Blythe and Bicknell
Maximum PV Maximum PV Total PV Injection
Injection at Blythe Injection at Bicknell (MW)
(MW) (MW)
With all lines under operation 1058.91 19.88 1078.79
With line outage between 1010.75 18.72 1029.47
Flagstaff & Four Corners
Flagstaff & Palo Verde
Flagstaff & Blythe
Blythe & Imperial Valley
With line outage at one of the
lines between Imperial Valley - - -
and Palo Verde
With line outage between 1058.96 - 1058.96
Palo Verde & Bicknell

8. Additional Concerns

 One of the assumptions of DC load flow studies is to consider that the voltage magnitudes at
all buses are 1 p.u. This comes up with a conclusion that there will be no reactive power flows
between any two buses, as difference in voltage magnitudes between them is zero. Thus
inclusion of reactive power flows, voltage magnitudes, their limits and constraints are all
inter-related. Including reactive power flows or voltage magnitudes automatically gives rise
to the other. The study will become more complex and detailed on doing it. The power flow
equations in this case would be the following:

Vi Vj ij
Pij 
xij

 Vi ( Vi  Vj )
Qij 
xij

The above equations still assume the following:

 The transmission lines are purely inductive.
 δ is very small and hence, sin δ ≈ δ.
 There is no reactive power injection at any bus.

 The active power flow „west of river‟ for the base case is almost negligible. It is 0.0001717
p.u., from Imperial Valley to Blythe. But with PV injection, it is nearly the rating of the line
(4.9897 p.u.). The „worst‟ single line outage is the outage of a line between Imperial Valley
and Palo Verde as one of the lines start overloading for the base case itself. The maximum
active power flow in the line is 0.9357 p.u.



 If it is possible to add another transmission line, it is logical to add a line between Flagstaff
and Imperial Valley. A large amount of power produced by Palo Verde and Bicknell could
not be transmitted efficiently because of the relatively lower ratings on the lines between
Flagstaff and Blythe, Blythe and Imperial Valley. A major share of the system load occurs at
Imperial Valley, thus the transmission lines connecting to it must have compatible ratings. If a
transmission line made of type (3) conductor is added between Flagstaff and Imperial Valley,
a transmission path of Palo Verde to Flagstaff to Imperial Valley would be chosen for
effective transmission of the generated power. Yet another option is to add one more line
between Imperial Valley and Palo Verde, if it is not required to supply more loads
anywhere else.

9. Conclusion

 It is seen that the maximum PV injection is possible when all lines are in service, and it can
be further improved by adding more transmission lines.
 It is seen that the system is not properly designed for an N-1 line outage contingency, and
thus has to be improved

10. References

[1] John J. Grainger, William D. Stevenson, “Power System Analysis”, Tata McGraw-Hill
Publications, January 1994.

[2] Anomynous, “The Power Flow Equations”, available at:
class.ece.iastate.edu/ee458/PowerFlowEquations.doc

[3] Wikipedia, notes appearing on the subject of per-unit systems, available at:
en.wikipedia.org/wiki/Per-unit_system



Appendix 1: System Representation

7 p.u.

Four Corners (2)

8 p.u. Flagstaff (1)
0.074(P1+P2) p.u.

2 p.u. Blythe (3)

P1 p.u.

0.926(P1+P2) p.u. 20 p.u.

Imperial Valley (4) Palo Verde (0) 8 p.u.
25 p.u.

Bicknell (5)

P2 p.u.

Legend

Generation/Load Site

Transmission Line

Base Case Generation/Load

PV Injection/Load Compensation

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Appendix 2: MATLAB Codes
A2.1. Base Case: All Lines under Operation

P=[7;-8;-2;-25;8];
Y=[1190.25/59.2008i -1190.25/59.2008i 0 0 0;
-1190.25/59.2008i (1190.25/3.968i)+(1190.25/59.2008i)+(1190.25/53.5472i) -1190.25/53.5472i 0 0;
0 -1190.25/53.5472i (1190.25/53.5472i)+(1190.25/60.104i) -1190.25/60.104i 0;
0 0 -1190.25/60.104i (1190.25/60.104i)+(1/(3.9984i*10^-3)) 0;
0 0 0 0 1190.25/11.8982i];
B=imag(Y);
del=inv(B)*P;
del1=[del;0];
BB=[-20.1053 20.1053 0 0 0 0;
0 299.9622 0 0 0 -299.9622;
0 -22.2281 22.2281 0 0 0;
0 0 -19.8032 19.8032 0 0;
0 0 0 250.10004 0 -250.10004;
0 0 0 0 -100.0361 100.0361];
PP=BB*del1;
syms P1;
syms P2;
Ppv=[7;-8;P1-2-0.074*(P1+P2);-25-0.926*(P1+P2);8+P2];
delpv=inv(B)*Ppv;
del1pv=[delpv;0];
PPpv=BB*del1pv;
a=vpa(PPpv,4);
disp(a);

A=[-3.532*10^(-18) 8.272*10^(-19);
-0.4548 0.07523;
-0.4548 0.07523;
0.4712 0.001232;
0.4548 0.9248;
0 1];
b=[7.09-7.0;14.8-2.9998;4.99-1.9998;4.99-0.0001717;30-25.0002;10-8];
f=[-1;-1];
lb=[0;0];
[x,fval,exitflag]=linprog(f,A,b,[],[],lb);
if exitflag==1
disp(x);
end

A2.2. Line Outage Contingency between Flagstaff & Four Corners
P=[-8;-2;-25;8];
Y=[(1190.25/3.968i)+(1190.25/53.5472i) -1190.25/53.5472i 0 0;
-1190.25/53.5472i (1190.25/53.5472i)+(1190.25/60.104i) -1190.25/60.104i 0;
0 -1190.25/60.104i (1190.25/60.104i)+(1/(3.9984i*10^-3)) 0;
0 0 0 1190.25/11.8982i];
B=imag(Y);
del=inv(B)*P;
del1=[del;0];
BB=[299.9622 0 0 0 -299.9622;
-22.2281 22.2281 0 0 0;
0 -19.8032 19.8032 0 0;
0 0 250.10004 0 -250.10004;
0 0 0 -100.0361 100.0361];

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PP=BB*del1;
syms P1;
syms P2;
Ppv=[-8;P1-2-0.074*(P1+P2);-25-0.926*(P1+P2);8+P2];
delpv=inv(B)*Ppv;
del1pv=[delpv;0];
PPpv=BB*del1pv;
a=vpa(PPpv,4);
disp(a);

A=[-0.4548 0.07523;-0.4548 0.07523;0.4712 0.001232;0.4548 0.9248;0 1];
b=[14.8-9.773;4.99-1.773;4.99-0.2271;30-25.23;10-8];
f=[-1;-1];
lb=[0;0];
if exitflag==1
disp(x);
end

A2.3. Line Outage Contingency between Flagstaff & Palo Verde

P=[7;-8;-2;-25;8];
Y=[1190.25/59.2008i -1190.25/59.2008i 0 0 0;
-1190.25/59.2008i (1190.25/59.2008i)+(1190.25/53.5472i) -1190.25/53.5472i 0 0;
0 -1190.25/53.5472i (1190.25/53.5472i)+(1190.25/60.104i) -1190.25/60.104i 0;
0 0 -1190.25/60.104i (1190.25/60.104i)+(1/(3.9984i*10^-3)) 0;
0 0 0 0 1190.25/11.8982i];
B=imag(Y);
del=inv(B)*P;
del1=[del;0];
BB=[-20.1053 20.1053 0 0 0 0;
0 -22.2281 22.2281 0 0 0;
0 0 -19.8032 19.8032 0 0;
0 0 0 250.10004 0 -250.10004;
0 0 0 0 -100.0361 100.0361];
PP=BB*del1;
syms P1;
syms P2;
Ppv=[7;-8;P1-2-0.074*(P1+P2);-25-0.926*(P1+P2);8+P2];
delpv=inv(B)*Ppv;
del1pv=[delpv;0];
PPpv=BB*del1pv;
a=vpa(PPpv,4);
disp(a);

A=[-1.13*10^(-16) 2.647*10^(-17);-1.25*10^(-16) 2.927*10^(-17);0.926 -0.074;0 1;0 1];
b=[7.09-7.0;4.99-1;4.99-3;30-28;10.0-8.0];
f=[-1;-1];
lb=[0;0];
if exitflag==1
disp(x);
end

A2.4. Line Outage Contingency between Flagstaff & Blythe
P=[7;-8;-2;-25;8];
Y=[1190.25/59.2008i -1190.25/59.2008i 0 0 0;
-1190.25/59.2008i (1190.25/3.968i)+(1190.25/59.2008i) 0 0 0;

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0 0 (1190.25/60.104i) -1190.25/60.104i 0;
0 0 -1190.25/60.104i (1190.25/60.104i)+(1/(3.9984i*10^-3)) 0;
0 0 0 0 1190.25/11.8982i];
B=imag(Y);
del=inv(B)*P;
del1=[del;0];
BB=[-20.1053 20.1053 0 0 0 0;
0 299.9622 0 0 0 -299.9622;
0 0 -19.8032 19.8032 0 0;
0 0 0 250.10004 0 -250.10004;
0 0 0 0 -100.0361 100.0361];
PP=BB*del1;
syms P1;
syms P2;
Ppv=[7;-8;P1-2-0.074*(P1+P2);-25-0.926*(P1+P2);8+P2];
delpv=inv(B)*Ppv;
del1pv=[delpv;0];
PPpv=BB*del1pv;
a=vpa(PPpv,4);
disp(a);

A=[0.926 -0.074;0 1];
b=[2.99;2];
f=[-1;-1];
lb=[0;0];
if exitflag==1
disp(x);
end

A2.5. Line Outage Contingency between Blythe & Imperial Valley
P=[7;-8;-2;-25;8];
Y=[1190.25/59.2008i -1190.25/59.2008i 0 0 0;
-1190.25/59.2008i (1190.25/3.968i)+(1190.25/59.2008i)+(1190.25/53.5472i) -1190.25/53.5472i 0 0;
0 -1190.25/53.5472i (1190.25/53.5472i) 0 0;
0 0 0 (1/(3.9984i*10^-3)) 0;
0 0 0 0 1190.25/11.8982i];
B=imag(Y);
del=inv(B)*P;
del1=[del;0];
BB=[-20.1053 20.1053 0 0 0 0;
0 299.9622 0 0 0 -299.9622;
0 -22.2281 22.2281 0 0 0;
0 0 0 250.10004 0 -250.10004;
0 0 0 0 -100.0361 100.0361];
PP=BB*del1;
syms P1;
syms P2;
Ppv=[7;-8;P1-2-0.074*(P1+P2);-25-0.926*(P1+P2);8+P2];
delpv=inv(B)*Ppv;
del1pv=[delpv;0];
PPpv=BB*del1pv;
a=vpa(PPpv,4);
disp(a);

A=[ -0.926 0.074;
-0.926 0.074;
0.926 0.926;

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0 1];
b=[14.8-3;4.99-2;30-25;10.0-8.0];
f=[-1;-1];
lb=[0;0];
if exitflag==1
disp(x);
end

A2.6. Line Outage Contingency at One of the Lines between Imperial Valley and
Palo Verde
P=[7;-8;-2;-25;8];
Y=[1190.25/59.2008i -1190.25/59.2008i 0 0 0;
-1190.25/59.2008i (1190.25/3.968i)+(1190.25/59.2008i)+(1190.25/53.5472i) -1190.25/53.5472i 0 0;
0 -1190.25/53.5472i (1190.25/53.5472i)+(1190.25/60.104i) -1190.25/60.104i 0;
0 0 -1190.25/60.104i (1190.25/60.104i)+(2500/19.992i) 0;
0 0 0 0 1190.25/11.8982i];
B=imag(Y);
del=inv(B)*P;
del1=[del;0];
BB=[-20.1053 20.1053 0 0 0 0;
0 299.9622 0 0 0 -299.9622;
0 -22.2281 22.2281 0 0 0;
0 0 -19.8032 19.8032 0 0;
0 0 0 125.05002 0 -125.05002;
0 0 0 0 -100.0361 100.0361];
PP=BB*del1;
syms P1;
syms P2;
Ppv=[7;-8;P1-2-0.074*(P1+P2);-25-0.926*(P1+P2);8+P2];
delpv=inv(B)*Ppv;
del1pv=[delpv;0];
PPpv=BB*del1pv;
a=vpa(PPpv,4);
disp(a);

A2.7. Line Outage Contingency between Palo Verde & Bicknell
P=[7;-8;-2;-25];
Y=[1190.25/59.2008i -1190.25/59.2008i 0 0;
-1190.25/59.2008i (1190.25/3.968i)+(1190.25/59.2008i)+(1190.25/53.5472i) -1190.25/53.5472i 0;
0 -1190.25/53.5472i (1190.25/53.5472i)+(1190.25/60.104i) -1190.25/60.104i;
0 0 -1190.25/60.104i (1190.25/60.104i)+(1/(3.9984i*10^-3))];
B=imag(Y);
del=inv(B)*P;
del1=[del;0];
BB=[-20.1053 20.1053 0 0 0;
0 299.9622 0 0 -299.9622;
0 -22.2281 22.2281 0 0;
0 0 -19.8032 19.8032 0;
0 0 0 250.10004 -250.10004];
PP=BB*del1;
syms P1;
syms P2;
Ppv=[7;-8;P1-2-0.074*P1;-25-0.926*P1];
delpv=inv(B)*Ppv;
del1pv=[delpv;0];
PPpv=BB*del1pv;

Arizona State University v


a=vpa(PPpv,4);
disp(a);

A=[-3.532*10^(-18);
-0.4548;
-0.4548;
0.4712;
0.4548];
b=[7.09-7.0;14.8-3;4.99-2;4.99-0.0001717;30.0-25];
f=[-1];
lb=[0];
if exitflag==1
disp(x);
end

Arizona State University vi

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