100
Chapter 5
AVAILABLE TRANSFER CAPABILITY
CALCULATIONS AND CONTINGENCY ANALYSIS
IN DEREGULATED POWER SYSTEMS
The available transfer capability work is well established [3, 71-89]
and introduction about ATC and contingency is given in chapter 1. In
this chapter, only methods for computation of ATC, problem
formation and algorithm are given. Also computation of ATC for 7-bus
system, 26-bus system, IEEE 118-bus system and case studies of
124-bus real-time Indian utility power system of Andhra Pradesh
State grid are presented and discussed. A brief description of
contingency analysis along with complete results of Andhra Pradesh
State grid is presented.
5.1. METHODS FOR COMPUTATION OF TRANSFER
CAPABILITY
In recent years, there has been a rapidly growing interest for power
engineers to formulate and solve this complex transfer capability
problem. As a result, many methods and techniques have been
developed; very
few
methods
are
practical
for
large
realistic
applications [81]. Only three of them are practical for large realistic
applications. These are follows:
1) Continuation Power Flow (CPF) method [86]
101
2) Optimal Power Flow (OPF) method.
3) Repeated Power Flow (RPF) method.
CPF is first introduced for determining the maximum loadability,
and is also useful for ATC computation. The advantage of CPF is a
successful method even for ill-conditioned power flow equations and
at voltage collapse points. However a major disadvantage is that it
involves complicated implementation of its parameterization, predictor
and corrector and step-size control elements.
OPF and Security-Constrained OPF (SCOPF) are powerful tools [26]
that have been under very active development for the past 30+ years.
OPF can be used to maximize the power transfer between two areas
assuming that all OPF optimized parameters can be centrally
dispatched needs large number of optimal power flows under different
conditions and needs more time.
The RPF method, power flow equations are repeatedly solved at a
succession of points along the specified load/generation increment,
for
TTC
calculation.
Compared
with
SCOPF
and
CPF,
the
implementation of RPF is much easier [71].
There are a number of methods and algorithms [76, 78] for
computing TTC, which are discussed in the chapter 1.
5.2. PROBLEM FORMULATION
Referring to Figure 5.1, a simple interconnected power system can
be divided into three kinds of areas, which are: receiving area, sending
102
area and external area. “Area” can be defined in an arbitrary fashion.
It may be an individual electric system, power pool, control area, subregions, etc. which consist of a set of buses. The transfer between two
areas is the sum of the real powers flowing on all the lines which
directly connect one area to the other area. A base case transfer
(existing transmission commitments) is determined, the transfer is
then gradually increased starting at the base case transfer until the
first security violation is encountered. The real power transfer at the
first security violation is the total transfer capability.
S
S
E
E
S
R
R – Receiving area; S – Sending area;
E – External area; .……transfer path
Figure 5.1.
A simple interconnected power system
The objective is to determine the maximum real power transfers
from sending areas to receiving area through the transfer path.
During a transfer capability calculation, many assumptions [82] may
arise that would affect the outcome. The main assumptions used in
this study are as follows:
103
•
The base case power flow of the system is feasible and
corresponds to a stable operating point.
•
The load and generation are changing very slowly so that the
system transient stability is not jeopardized.
•
The system steady state stability is maintained with sufficient
damping.
•
Bus voltage limits are maintained before the system loses voltage
stability.
Therefore, at this stage only the thermal limits and voltage limits
will be taken into consideration together with generator active and
reactive power limits.
The power flow solution is the most common and important tool in
power system analysis, which is also known as the “load flow”
solution. It is used for planning and controlling to determine the
voltage magnitudes and phase angle of voltages at each bus and
active and reactive power flow in each line. The four quantities
associated with each bus are voltage magnitude, voltage phase angle,
real power injection and reactive power injection.
The Newton-Raphson equations are used in natural power system
form solving for voltage magnitude and angle, given real and reactive
power injections and these can be used in the calculation of transfer
capability [26, 91]. The same thing can express in the mathematical
form as follows [81]:
104
Power Flow Equations:
The complex power injected by the source into the ‘i’ th bus of a
power system is
S i = Pi + jQi = Vi I i* ;
i = 1, 2… n
(5.1)
The load flow problem is handled more conveniently by use of Ii
rather than Ii*. By taking the complex conjugate of equation (5.1),
*
S i = Pi − jQi = Vi * I i
; i = 1, 2… n
(5.2)
Then real and reactive powers can be expressed as
n
Pi =
∑ |V |V |Y |cos (θ
i
j
ij
ij
− δi + δ j )
(5.3)
j =1
n
Qi = − ∑ |V i|V j|Yij| sin (θ ij − δi + δ j )
(5.4)
j =1
and Operational constraints
P Gi
min
≤ P Gi ≤ P Gi
max
(5.5)
Q Gi min ≤ Q G ≤ Q Gi max
(5.6)
S ij ≤ S ij max
(5.7)
V i min
≤ V i ≤ V i max
(5.8)
105
The objective function to be optimized is
Pr =
∑
P km
(5.9)
m ∈ R ,k ∉ R
The control variables in the above formulation are generator real
and reactive power outputs, generator voltage settings, phase shift
angles, transformer taps and switching capacitors or reactors. The
dependent variables in the formulation are slack bus (swing bus)
active and reactive power injections, regulated bus (generator bus)
reactive power injection and voltage angle. All the equality and
inequality constraints considered in this work are given in the above
problem formulation.
5.3.
ALGORITHM
METHOD
FOR
REPEATED
POWER
FLOW
Repeated power flow (RPF) method [81] involves the solution of a
base case, which is the initial system conditions, and then increasing
the transfer. After each increase, another load flow is done and the
security constraints tested. The computational procedure of this
approach is as follows:
Step 1.
Establish and solve for a base case
Step 2.
Select a transfer case
Step 3.
Solve for the transfer case
Step 4.
Increase step size if transfer is successful
Step 5.
Decrease step size if transfer is unsuccessful
106
Step 6.
Repeat the procedure until minimum step size
reached
The flow chart of this method is given in Appendix-C.2.
5.4. METHODS FOR COMPUTATION OF AVAILABLE
TRANSFER CAPABILITY
A report by NERC in 1996 establishes a framework for determining
ATC of the interconnected transmission networks for a commercially
viable wholesale market. The report defines ATC principles under
which ATC values are to be computed and it permits individual
systems, power pools, regions and sub regions to develop their
procedure for determining ATC in accordance with these principles.
Reference [79] discussed some theoretical aspects of ATC and the
problem of its evaluation under open access environment.
In [86], a method based on continuation power flow incorporating
limits of reactive power flows, voltage limits as well as voltage collapse
and line flow limits is described. However, with this method, the
computational effort and time requirement are large. In [81], the
topological information of a system is stored in matrix form and
constants for different simultaneous cases and critical contingencies
have been calculated before hand and used for determination of ATC
values. For very large systems, the method may be quite cumbersome.
In [83], the localized linearity of the system is assumed and additional
load required to hit the different limits are separately calculated and
107
the minimum of all these is taken as ATC. Ashwani Kumar et al. [90]
proposed a simple and efficient non-iterative method to calculate ATC
under bilateral and multilateral contracts based on ACPTDF. The
ACPTDFs have been calculated at base case NRLF results utilizing a
sensitivity-based approach.
METHODS BASED ON DISTRIBUTION FACTORS:
In order
to consider
line
flow (MW) limits
for
static
AC
determination under the system intact, AC power transfer distribution
factors is used. To consider voltage limits in ATC determination under
the normal cases Voltage Distribution Factors [VDF] are used.
1. AC POWER TRANSFER DISTRIBUTION FACTORS
Consider a bilateral transaction ‘tp’ between a seller bus, ‘m’ and
buyer bus, ‘n’. Further consider a line, ‘l’ carrying a part of the
transaction power. Let the line be connected between a bus-i and a
bus-j. For a change in real power transaction between the above seller
and buyer, say, by ‘ ∆ tp’ MW, if the change in transmission line
quantity ‘ql’ is ‘ ∆ ql’, the AC power transfer distribution factors can be
defined as:
(ACPTDF) ql-tp
∆ql
∆t p
(5.10)
The transmission quantity ‘ql’ is taken as real power flow from busi to bus-j.
108
2. VOLTAGE DISTRIBUTION FACTORS
Voltage Distribution Factors (VDFs) are defined as the change in
the bus voltage magnitude ‘ ∆ Vi’ at any bus-i to the change in the pth
transaction, say, by ‘ ∆ tp’ between seller bus and the buyer bus. Let
the base case voltage magnitude at any bus-i be ‘Vi0’ and, after the
change due to a transaction, the new bus voltage be Vi-tp. The voltage
distribution factors are defined as:
∆Vi
VDFi-tp=
∆t p
(5.11)
Where, ∆ Vi = Vi-tp – Vi0
5.4.1. PROBLEM FORMULATION FOR DISTRIBUTATION FACTORS
ATC determination using ACPTDF and Voltage distribution factors:
The distribution factors have been computed with the base case
load flow results using the sensitivity properties of the NRLF Jacobin.
The procedure for calculation of these distribution factors is described
below:
Consider the sensitivity relationship provided by the NewtonRaphson load flow equations in the polar coordinates for a base case
load flow as:
 ∆δ 
 ∆P 
 ∆V  = [ST ]  ∆Q
 
 
(5.12)
Where, ST = [J T ]−1 is a sensitivity matrix and JT is the full Jacobian
defined for all the buses except for the slack bus.
109
At a base case load flow, if only one of the bilateral transactions,
say the pth transaction, between a seller bus, ‘m’ and a buyer bus, ‘n’
is changed by ‘ ∆ tp’, only the following two entries in the mismatch
vector [ ∆ P, ∆ Q ] T of equation (5.12) will be non-zero.
∆ Pm = ∆ tp,
∆ Pn = - ∆ tp
(3.13)
With the above mismatch vector, changes in the voltage angle and
voltage magnitude at all the buses can be computed from equation
(5.12), and hence, a new voltage profile can be calculated. These can
be utilized to compute new values of transmission quantity ‘ql’ and
thus the change in the quantity ‘ ∆ ql’ from the base case. Once ‘ ∆ ql’ is
known for all the lines and change in the voltage magnitude is
computed at all the buses corresponding to a transaction ‘ ∆ tp’, the
ACPTDFs and VDFs for each line and buses, respectively, can be
obtained from (5.10) and (5.11).
ATC from a bus/zone ‘m’ to another bus/zone ‘n’ can be found
using the full AC load flow by varying the amount of transaction until
one or more line flows in the transmission system considered or a bus
voltage at some bus reaches the limiting value. However this method
is
computationally
involved.
Instead,
the
distribution
factors
described above can be used to quickly calculate ATC considering
both the line flow limits and voltage limits, as follows.
110
i)
ATC for base case, between bus/zone ‘m’ and bus/zone ‘n’
using the line flow limit criterion has been calculated using
ACPTDFs as
 (Pijmax − Pij0 )

ij ∈ N l 
ATCmn = min 
 PTDFij,mn

(5.14)
Where,
Pijmax is the MW power flow limit of a line between bus-i and bus-j.
Pij0 is the base case power flow in the line between bus-i and bus-j.
PTDFij-mn are the Power Transfer Distribution Factors for the line
between bus-i and bus-j, when ‘Nl’ is the total no. of lines.
ii) Similarly ATC at base case considering voltage limit violation
can be calculated as:
(V − Vi min )

ATCmn = min  i −t
i ∈ NB 
 VDFi,mn

(5.15)
Where,
Vi-t is the voltage at bus-i under change in the transaction tp.
Vimin is the minimum voltage limit at each bus-i.
VDFi-mn is the voltage distribution factor at bus-i, when the
transaction is taking place between bus/zone ‘m’ and bus/zone ‘n’
and ‘NB’ is the total number of buses.
111
CONTINGENCY ANALYSIS
5.5. INTRODUCTION
With the global development towards the deregulation in the power
system industry, the volume and complexity of the CA results in the
operation and the system studies have been increasing. Not only has
deregulation resulted in much larger system model sizes, but also CA
is computed more frequently in the restructured power markets to
monitor the states of the system under “what if” situations in order to
accommodate the maximum number of power transfers. The net
impact of these changes is a need for more effective CA results are
required to help with the comprehension of the essential security
information, information which could be buried in the enormous and
complex CA data sets [29], [30].
The CA application is based on detailed electrical model of power
system, called the “network model”. This is a simulated model of the
real power system that is prepared by each utility’s system planners
and network engineer specialists. They translate the real world
equipment and connections of a power system (one –line diagram) into
a mathematical model of the power network that is suitable for
solution by computer algorithms. This network model contains the
connection
information
and
electrical
characteristics
of
the
equipment. The algorithm in contingency analysis uses this network
information and the network model to simulate, and calculate the
112
effects of, removing equipment from the power system. With an
initialized power network model, CA now can be executed with a
series of contingency events that is prepared by the CA user. A
“contingency list” contains the each of the elements that will be
removed from the network model, one by one, to test the effects for
possible overloads of the remaining elements. The criteria for selection
of elements for the contingency events are further described below.
In its basic form, CA executes a power flow analysis for each
potential problem that is identified on a contingency list. The voltages,
currents, real and reactive power flows (MW and Mvar) in each part of
the power system can be obtained from power flow solution in
contingency analysis. Results of each contingency test and the
network solution are compared with the limits for every element in the
power system. The lists of violations are saved in the CA data base.
CA actually provides and prioritizes the impacts on an electric
power system when problems occur. Contingency is also called an
unplanned "outage". CA is a computer application that uses a
simulated model of the power system, to evaluate the effects, and
calculate any overloads resulting from each outage event. In other
word, CA is essentially a "preview" analysis tool that simulates and
quantifies the results of problems that could occur in the power
system in the immediate future. This analysis is used as a study tool
for the off-line analysis of contingency events, and as an on-line tool
to show operators what would be the effects of future outages. It
113
allows operators to be better prepared to react to outages by using
pre-planned recovery scenarios.
After a contingency event, power system problems can range from:
• None: When the power system can be re-balanced after a
contingency, without overloads to any element.
• Severe: When several elements such as lines and transformers
become overloaded and have risk of damage.
• Critical: When the power system becomes unstable and will quickly
collapse.
By analyzing the effects of contingency events in advance,
problems
and
unstable
situations
can
be
identified,
critical
configurations can be recognized, operating constraints and limits can
be applied, and corrective actions can be planned.
5.6. METHODS OF CONTINGENCY ANALYSIS
The following are the various methods used for contingency
analysis purpose.
•
DC load flow method of contingency analysis
•
Z-matrix method of contingency analysis
•
Voltage stability index (L-index) computation
•
Decoupled load flow
•
Fast decoupled load flow
114
The tool for detecting overloads is analyzing contingency of the
power system planner which should have execution speed and ease of
detection are the vital considerations. Among the methods mentioned
above, AC power flow calculations methods are accurate when
compared to DC power flow methods but they are a bit complex and
need more execution time.
5.7. RESULTS AND DISCUSSION OF ATC
Results of the ATC for 7-bus, 26-bus, IEEE 118-bus systems and
124-bus Indian utility power system of Andhra Pradesh State grid are
presented and analyzed are given below:
5.7.1. 7-bus System
The computations were done on 7-bus test system with 3-areas as
shown in Figure 5.2. Data for this system is given in Appendix A.1.
Figure 5.2. 7-bus test system
115
The system has been divided into three areas, namely; area A, area
B and area C. Area A includes buses 1, 2, 3, 4 and 5. Area B consists
of bus 6 whereas area C consists of bus 7.
5.7.1.1. Model calculation for PTDF:
The PTDF values are calculated by use of the power world
simulator software with lossless DC approximation and are given in
Table 5.1.
Table 5.1: PTDF values of 7-bus system
S.no. From bus To bus % PTDF
1
1
2
80.41
2
1
3
19.59
3
2
4
2.47
4
2
5
46.47
5
2
6
32.16
6
3
4
18.91
7
4
5
21.38
8
5
7
67.84
9
6
7
32.16
5.7.1.2. Model calculation for ATC:
ATC is calculated by use of the equation (5.14).
 (Pijmax − Pij0 )

ATC = 
ij ∈ N l 
 PTDFij,mn

Consider a transmission line connected between bus 2 and 6, then
the maximum power limit is Pijmax = 160MW,
116
The power flow in the line in base case is Pij0 =74.7MW
and PTDF from Table 5.1 is 0.3216
Then ATC = (160- 74.7)/ (0.3216) = 265 MW
Similarly, ATC is calculated for the remaining part of 7-bus system,
26-bus system, IEEE 118- bus system and 124-bus real-time Indian
utility power system of Andhra Pradesh State grid.
ATC values of 7-bus system are shown in Table 5.2.
Transfer
Table 5.2: 7-bus case, ATC data
Transfer
ATC
areas
A-B
A-C
B-C
Limiting
buses
(MW)
line
1-6
54
1-2
2-6
265
2-6
4-6
281
2-6
1-7
56
1-2
2-7
106
2-5
4-7
152
4-5
6-7
111
6-7
5.7.2. 26-bus system
ATC is calculated from all generator buses to normally heavily
loaded load buses by use of PTDF’s, and variation of ATC is given in
Tables 5.3 to 5.8 for different load conditions vary from 50% to 100%.
Thermal limits used for calculating ATC are given in Appendix A.2.
117
Table 5.3: Variation of ATC from bus 1 to other buses of 26-bus
system
Transfer
buses
NR method
100% load
90% load
75% load
50% load
ATC Limiting ATC Limiting ATC Limiting ATC Limiting ATC Limiting
(MW)
line
(MW)
line
(MW)
line
(MW)
line
(MW)
line
1-3
200 17-18 215 17-18 272 16-17 314 16-17 308 16-17
1-5
238
6-18
195
6-18
180
6-18
1-9
197
2-8
195
7-9
153
1-12
230 17-18 228
2-8
146
1-15
141 17-18 152 17-18 138 13-15 147 13-15 217 16-17
72
6-18
162
6-18
2-8
154 16-20 232
9-10
2-8
108 12-14 215 12-14
1-16
80
17-18
86
17-18 101 15-16
99
15-16 117 16-17
1-17
33
17-18
36
17-18
46
17-18
55
1-17
56
16-17
1-18
235
1-18
208
1-18
223
1-18
197
1-18
329
1-18
1-19
201
6-19
203
6-19
200 16-20
94
6-18
212
6-18
1-24
59
22-24
55
22-24
62
22-24
80
22-24
65
22-24
Table 5.4: Variation of ATC from bus 2 to other buses of 26-bus
system
Transfer
buses
NR method
100% load
90% load
75% load
50% load
ATC Limiting ATC Limiting ATC Limiting ATC Limiting ATC Limiting
(MW)
line
(MW)
line
(MW)
line
(MW)
line
(MW)
line
2-1
666
1-2
672
1-2
691
1-2
670
1-2
723
1-2
2-3
251 17-18 270 17-18 333 16-17 350
2-8
378 16-17
2-5
266 6-18
218
6-18
201
6-18
81
6-18
181
6-18
2-9
193
7-9
194
7-9
139
2-8
112
2-8
232
9-10
2-12
224
2-8
208
2-8
134
2-8
105 12-14 209 12-14
2-15
156 12-15 175 12-15 135 13-15 144 13-15 230 13-15
118
2-16
86
17-18
90
15-16
98
15-16
96
15-16 123 15-16
2-17
34
17-18
37
17-18
47
17-18
52
16-17
2-18
259 1-18
229
1-18
246
1-18
217
1-18
363 16-17
2-19
204 6-19
205
6-19
189
2-8
109
6-18
246
6-18
2-24
59
54
22-24
65
22-24
62
22-24
79
22-24
22-24
54
16-17
Table 5.5: Variation of ATC from bus 3 to other buses of 26-bus
system
Transfer
buses
NR method
100% load
90% load
75% load
50% load
ATC Limiting ATC Limiting ATC Limiting ATC Limiting ATC Limiting
(MW)
line
(MW)
line
(MW)
line
(MW)
line
(MW)
line
3-1
225
3-13
182
3-13
104
3-13
94
12-14 188 12-14
3-5
206
3-13
166
3-13
95
3-13
76
12-14 152 12-15
3-9
193
3-13
157
3-13
86
12-14
62
12-14 124 12-14
3-12
183 12-14 150
3-13
69
12-14
50
12-14 100 12-14
3-15
139 13-15 124 13-15
72
3-13
76
3-13
158
106 15-16
3-13
3-16
84
15-16
78
15-16
77
3-13
80
3-13
3-17
40
17-18
42
17-18
52
16-17
44
16-17
3-18
185 16-17 167 16-17
99
3-13
89
12-14 155 16-17
3-19
195
6-7
160
3-13
91
3-13
69
12-14 138 12-14
3-24
57
22-24
53
22-24
63
22-24
60
22-24
45
78
16-17
22-24
119
Table 5.6: Variation of ATC from bus 4 to other buses of 26-bus
system
Transfer
buses
NR method
100% load
90% load
75% load
50% load
ATC Limiting ATC Limiting ATC Limiting ATC Limiting ATC Limiting
(MW)
line
(MW)
line
(MW)
line
(MW)
line
(MW)
4-1
216
4-12
218
4-12
386
4-12
279
6-7
342 16-17
4-3
194
4-12
195
4-12
346
4-12
357
4-12
359 12-15
4-5
196
6-7
161
6-7
205
6-7
98
6-7
144
6-7
4-9
178 10-12 162 10-12 219
7-9
218
9-10
218
9-10
4-12
299
4-12
313
4-12
4-12
163
4-12
289
line
4-12
162
4-15
118 12-15 133 12-15 178 13-15 190 13-15 190 12-15
4-16
92
15-16
85
15-16
92
15-16
91
15-16 116 15-16
4-17
38
17-18
40
17-18
52
17-18
47
16-17
4-18
214
4-12
215
4-12
240 16-17 178
4-19
177 10-12 162 10-12 232
4-24
56
22-24
52
22-24
62
48
16-17
6-7
206 16-17
6-19
149
6-7
218
6-7
22-24
59
22-24
76
22-24
Table 5.7: Variation of ATC from bus 5 to other buses of 26-bus
system
Transfer
buses
NR method
100% load
90% load
75% load
50% load
ATC Limiting ATC Limiting ATC Limiting ATC Limiting ATC Limiting
(MW)
line
(MW)
line
(MW)
line
(MW)
line
(MW)
line
5-1
106
5-6
100
5-6
110
5-6
288
5-6
275
5-6
5-3
106
5-6
100
5-6
110
5-6
288
5-6
275
5-6
5-6
106
5-6
100
5-6
110
5-6
288
5-6
275
5-6
5-9
106
5-6
100
5-6
110
5-6
232
9-10
232
9-10
5-12
106
5-6
100
5-6
110
5-6
148 12-14 275
5-6
120
5-15
106
5-6
100
5-6
110
5-6
165 13-15 219 16-17
5-16
85
17-18
92 17-18 104 16-17 103 15-16 118 16-17
5-17
34
17-18
37 17-18
5-18
106
5-6
100
5-19
106
5-6
100
5-24
63
22-24
47
17-18
55
16-17
56
16-17
5-6
110
5-6
288
5-6
275
5-6
5-6
110
5-6
237
6-19
272
6-19
69
22-24
66
22-24
85
22-24
58 22-24
Table 5.8: Variation of ATC from bus 26 to other buses of 26-bus
system
Transfer
buses
NR method
100% load
90% load
75% load
50% load
ATC Limiting ATC Limiting ATC Limiting ATC Limiting ATC Limiting
(MW)
line
(MW)
line
(MW)
line
(MW)
line
(MW)
line
26-1
82
11-26 185 11-26 181 11-26 169 11-26 175 11-26
26-3
81
11-26 183 11-26 180 11-26 168 11-26 173 11-26
26-5
76
11-26 170 11-26 168 11-26 156 11-26 162 11-26
26-6
76
11-26 170 11-26 168 11-26 156 11-26 162 11-26
26-9
80
11-26 178 11-26 175 11-26 163 11-26 169 11-26
26-12
80
11-26 179 11-26 176 11-26 128 11-26 170 11-26
26-15
81
11-26 166 12-15 147 13-15 156 13-15 171 11-26
26-16
80
11-26
94
17-18 102 15-16 100 15-16 123 16-17
26-17
34
17-18
37
17-18
26-18
80
11-26 179 11-26 176 11-26 164 11-26 170 11-26
26-19
76
11-26 171 11-26 168 11-26 156 11-26 162 11-26
26-24
61
22-24
56
22-24
47
67
17-18
22-24
53
64
16-17
22-24
55
83
16-17
22-24
121
ATC is varying with variation of load. This variation of ATC depends
upon generators in operation, load variation, bus voltages, variation of
line flows and line limits.
5.7.3. IEEE 118-bus system
ATC is calculated between the areas, and a variation of ATC is
given Tables 5.9. Thermal limits used for calculating ATC of all the
lines is taken as 500MVA.
Table 5.9: Variation of ATC between the areas for different cases
of IEEE 118-bus System
Transfer
areas
Case 1
Case 2
Case 3
Case 4
ATC
Limiting
ATC
Limiting
ATC
Limiting
ATC
Limiting
(MW)
area/line
(MW)
area/line
(MW)
area/line
(MW)
area/line
1-2
750.68 Area 2 67.46 Area 1 231.08 Area 1 49.27 Area 1
1-3
127.24 Area 3 67.46 Area 1 231.00 Area 1 49.27 Area 1
1-4
101.59 Area 4 67.46 Area 1 110.87 Area 4 49.27 Area 1
2-1
465.12 Area 1 232.45 Area 2 288.61 Area 1 133.71 Area 2
2-3
127.24 Area 3 232.45 Area 2 291.71 Area 2 133.71 Area 2
2-4
101.59 Area 4 175.00 Area 4 110.87 Area 4 72.78 Area 4
3-1
465.97 Area 1 560.41 Area 1 134.70 Area 1 225.73 Area 1
3-2
717.31 Area 2 735.76 65-68 133.11 Area 2 234.71 Area 3
3-4
101.59 Area 4 175.00 Area 4 110.87 Area 4 72.78 Area 4
4-1
247.41 Area 4 542.54 Area 4 64.13 Area 4 27.22 Area 4
4-2
247.41 Area 4 694.66 Area 4 64.13 Area 4 27.22 Area 4
4-3
138.91 Area 3 492.06 Area 4 64.13 Area 4 27.22 Area 4
122
5.7.4. CASE STUDY OF APSEB
5.7.4.1. Data collected in March and September 2011
The assessment of ATC using PTDF has been conducted on 124
bus real-time Indian utility power system of Andhra Pradesh State
220-kV transmission grid. For this case study all generating stations
and 400-kV buses are taken as sellers and some of the load busses
are taken as buyers. The sellers and buyers combination is taken
according to the Distribution Companies (DISCOMs) already available
in the State.
In this case study, generation and load data is taken at two
different instants and the analysis was done as two different cases.
They are
1. March 2011
2. September 2011.
Combinations of buses used to calculate ATC are given in Table
5.10. The ATC for these combinations are tabulated in Appendix-B,
Table B.3. The variation of ATC is depending on already committed
dispatches and thermal limits.
Table 5.10: Sets of buses used to calculate ATC for the case of
March 2011 and September 2011
Transfer buses
From
To
1
3,5,6,8,10,13,15,16,18,19,20,21,22,24,30,36,37,39
4
3,5,7,13,15,16,19,22,30,35,37,39
27
3,6,7,10,16,18,19,20,22,24,30,35,39
123
29
5,6,8,10,15,16,18,20,22,24,30,35,36,37,39
30
3,6,7,10,13,15,16,18,19,20,21,22,24,35,36,37,39
35
3,5,6,7,10,13,15,16,18,19,20,21,22,24,30,36,37,39
37
3,5,6,8,10,13,15,16,18,19,20,21,22,24,35,36,39
9
3,5,6,8,10,13,16,18,19,20,21,22,24,36,39,42,43,51,53,57,59
11
3,5,10,13,16,19,22,36,42,43,51,57,59
15
5,6,8,10,16,18,19,20,21,22,24,36,39,42,43,51,53,57,59
20
3,5,6,7,10,13,16,18,19,22,24,36,39,42,43,51,53,57,59
45
3,5,6,7,10,13,16,18,19,20,21,22,24,36,39,42,43,51,53,57,59
46
3,5,6,7,10,13,16,18,19,20,21,22,24,36,39,42,43,51,53,57,59
50
3,5,6,8,10,13,16,18,19,20,21,22,24,36,39,42,43,51,53,57,59
54
3,5,6,7,10,13,16,18,19,20,21,22,24,36,39,42,43,51,53,57,59
56
3,5,6,8,10,13,16,19,22,24,36,42,43,51,53,59
61
3,5,6,7,10,13,16,18,19,20,21,22,24,36,42,43,53,57,59
128
3,5,6,8,10,13,16,18,19,20,21,22,24,36,39,42,43,51,53,57,59
96
95,98,100,101,106,108,109,112,123
97
95,98,100,101,103,106,108,109,112,123
100
95,98,101,103,106,108,109,112,123
102
95,98,100,101,103,106,108,109,112,123
104
95,100,103,106,109,112
105
95,98,101,103,106,108,112,123
106
95,98,100,101,103,108,109,112,123
107
95,98,100,106,109,112,123
111
95,98,100,101,103,106,108,109,123
112
95,98,103,106,109,123
115
95,98,100,101,103,106,108,109,112,123
68
71,77,82,83,86,88,89,125
74
71,77,81,82,83,86,88,89,125
75
71,77,81,82,83,86,88,89,125
78
71,77,81,82,83,86,88,89,125
124
84
71,81,83,86,88,89,125
85
71,81,83,86,88,89,125
87
71,77,81,82,83,86,88,89,125
91
71,81,82,86,88,125
Variation of ATC for above mentioned cases; the difference is more
100MW is shown in from Figures 5.3 to 5.6.
Figure 5.3.
Variation of ATC from March to September 2011
Figure 5.4.
Variation of ATC from March to September 2011
125
Figure 5.5.
Variation of ATC from March to September 2011
Figure 5.6.
Variation of ATC from March to September 2011
From the above figures it is observed that variation of ATC is very
high
from
March
to
September
2011
for
the
following
bus
combinations: 1-20,21; 27-3; 30-3; 35-3,21; 37-21; 11-42,57; 20-3;
50-3; 54-3; 128-20,21,36,39,57; 105-103; 115-100,101,103,108, 112,
123; 68-77 ,82 , 88, 89; 75-71; 84-71; 85-71; 87-89.
The results are certainly useful in an online environment of
deregulated power system to perform the transactions between buyer
and seller.
126
5.7.4.2. Case 3: With zero interstate power transfer
For this case study, total APGENCO, private sector and two
generating stations (bus 1 (2600MW), bus 115 (1500MW)) from CGS
being considered, similarly as the case 1 and 2 but interstate power
from other states as CGS share is set to zero. The analysis was done
at different load conditions varying from 50% to 125% as follows.
ATC is calculated between the areas for different load conditions of
case 3 are tabulated in Table 5.11.
Table 5.11: Variation of ATC between the areas for different cases
of Case 3
Case 3 (a) Case 3 (b) Case 3 (c) Case 3 (d) Case 3 (e)
Transfer
100%(AG)
125%
100%
75%
50%
areas
ATC
ATC
ATC
ATC
ATC
(MW)
(MW)
(MW)
(MW)
(MW)
1-2
1019
1944
1941
1160
353
1-3
1199
1503
1436
1247
353
1-4
1520
1790
537
1057
353
2-1
528
101
36
913
28
2-3
748
101
36
881
1211
2-4
801
101
36
473
673
3-1
734
620
541
458
28
3-2
1019
1428
941
485
358
3-4
795
1359
545
480
368
4-1
607
21
411
224
11
4-2
636
23
1668
216
11
4-3
610
228
1515
1042
111
127
5.7.4.3. Case 4: With interstate power (CGS share) transfer
In this case study, analysis was done with total APGENCO
(8923.86MW), IPPs (3286.3MW) and CGS share (3229.04) being
considered. The details of AP share from CGS are given in chapter 3.
The analysis was also done at different load conditions varying
from 50% to 125% and ATC is calculated between the areas for
different load conditions of case 4 are tabulated in Table 5.12.
Table 5.12: Variation of ATC between the areas for different cases
of Case 4
Case 4 (a) Case 4 (b) Case 4 (c) Case 4 (d) Case 4 (e)
Transfer
100%(AG)
125%
100%
75%
50%
areas
ATC
ATC
ATC
ATC
ATC
(MW)
(MW)
(MW)
(MW)
(MW)
1-2
2061
483
1674
999
486
1-3
1040
483
1531
991
204
1-4
838
483
1572
638
450
2-1
681
491
258
56
427
2-3
1355
692
457
607
612
2-4
1408
610
1018
607
606
3-1
1146
413
553
54
381
3-2
1299
1573
1435
979
697
3-4
869
610
1018
647
510
4-1
676
413
314
56
426
4-2
2576
2174
901
363
513
4-3
675
1168
1155
363
1403
ATC is also calculated for the Case 4(a) (with 100% load, all
generators are operating) and Case 4(c) (with 100% load, some costly
128
generators are off) for the combination of buses are given in Table
5.13. ATC for the given combination is tabulated in Appendix-B, Table
B.22.
Table 5.13: Sets of buses used to calculate ATC for Case 4(a) and
4(c)
Transfer buses
From
To
1
2,3,5,12,24,25,26,27,28,35,129
4
2,3,12
27
1,28,35,37
29
30,31,32,33,34,35,36,38,39,40,42,113
30
6,19,29,31,32,33,34,35,36,38,39,40,42,87,113
31
29,30,32,33,34,35,36,42,87,111,113
32
29,30,31,35
34
29,30,33,35,36
35
1,6,19,28,37
37
1,6,19,28,35
9
6,7,8,16,19,20,21,22,23,35,36,39,42
11
1,2,3,4,12
15
6,9,10,13,16,17,18,19,20,21,23
20
9,15,19,21,35,46,47
45
15,20,21,44,46,47,54,68
46
21,45,47,49,52,54,68,82,84,85
50
45,46,48,49,52,57,61,64,66,72
52
46,48,49,50,61,68,128
129
54
15,21,46,50,52,66,68,82,84,85,77
56
46,48,49,50,52,128
128
46,49,50,52,56
96
31,87,95,98,100,101,102,106
97
85,98,100,101,102,106
100
85,96,97,98,101,102,106
102
98,100,101,108,110,112,115,118,123
104
98,100,101,102,106,112
105
98,100,101,102,106
106
85,87,96,97,98,101,102,108
107
85,87,96,97,98,100,101,102,106,108
111
100,101,102,106,108,110,112,115
112
100,101,106,108,110,111,115
113
29,30,31,102,108,111,112
115
100,101,102,106,108,110,111,112
118
102,106,112,115
66
21,46,49,54,68,71,72,74
68
21,46,49,54,66,71,72,74
72
57,59,66,68,71,74,75,78
74
66,68,69,71,77,78,82
75
66,68,69,71,77,78,82
78
66,71,75,77,80,81,82,85
84
36,39,40,54,85,88,100,101
130
85
39,77,78,81,82,84,87,88,89,100,101,102
87
77,81,82,84,85,100,102
91
39,84,85,88,89
The variation of the ATC for these two cases, the difference is
more than 100MW is shown in Figures 5.7 to 5.11. The change in ATC
is due to some costly generators off and that causes to change the
loading of the lines.
Figure 5.7.
Variation of ATC for Case 4 (a) and Case 4 (c)
Figure 5.8.
Variation of ATC for Case 4 (a) and Case 4 (c)
131
Figure 5.9.
Variation of ATC for Case 4 (a) and Case 4 (c)
Figure 5.10.
Variation of ATC for Case 4 (a) and Case 4 (c)
Figure 5.11.
Variation of ATC for Case 4 (a) and Case 4 (c)
132
From the above figures, it is observed that variation of ATC is very
high, between Case 4(a) and case 4(c) for the following bus
combinations: 29-36; 30-36; 31-36,42,87; 9-35,36; 15-6; 20-46; 4654,84; 50-49,52,57,72; 52-46,49,50; 54-46,50,52,84,85,77; 100-85;
102-100; 112-100; 66-46,49; 72-57; 78-82,85; 84-54,85,100,101; 8577,82,84,100,101,102; 87-77,100,102.
5.7.4.4. Case 5: During summer
In this case study, analysis was done with part of APGENCO
(8923.86MW), IPPs (3286.3MW) and CGS share (3229.04) being
considered. In the summer, most of the hydropower plants are not in
operation due to low head of water. According to the data taken from
GENCO, generators at bus 54 (Nagarjuna Sagar) are operating under
peak load are considered for this case.
The analysis was also done at different load conditions varying
from 50% to 125% as follows. ATC is calculated between the areas for
different load conditions are tabulated in Table 5.14. This variation of
ATC is depends on the generators operating in that particular area
and loading of the lines.
Table 5.14: Variation of ATC between the areas for different cases
of Case 5
Case 5 (a)
Case 5 (b)
Case 5 (c) Case 5 (d) Case 5 (e)
125%
100%
75%
50%
Transfer 100% (AG)
areas
ATC
ATC
ATC
ATC
ATC
(MW)
(MW)
(MW)
(MW)
(MW)
1-2
226
226
739
1066
1-3
1660
1-4
1660
NP
1660
1087
206
1660
235
1281
133
2-1
00
00
297
90
2-3
359
355
981
19
2-4
788
893
1435
1502
3-1
626
219
297
90
3-2
226
219
226
226
3-4
631
219
717
533
4-1
677
307
08
96
4-2
226
226
08
144
4-3
441
448
08
206
5.7.4.5.
ATC Calculations for tie-lines
AP State grid operating at 220kV consists of total 27 tie lines
between the four Areas or DISCOs. There are 10 tie lines between area
1 – area 2 (area 2 – area 1), 2 tie lines between area 1 – area 3 (area 3
– area 1), 1 tie line between area 1 – area 4 (area 4 – area 1), 10 tie
lines between area 2 – area 4 (area 4 – area 2), and 4 tie lines between
area 3 – area 4 (area 4 – area 3) and no tie lines are existing between
area 2 – area 3 (area 3 – area 2).
ATC is calculated for all these tie lines in both the directions is
calculated for the Case 4(a) (with 100% load, all generators are
operating) and Case 4(c) (with 100% load, some costly generators are
off) and are tabulated in Table 5.15.
134
Table 5.15: ATC of tie-lines between areas for Case 4(a) and 4(c)
(with CGS share)
From area 1 to area 2
Transfer buses
S.
Case 4(a)
Case 4(c)
ATC
Limiting
ATC
Limiting
(MW)
line
(MW)
line
28
1080
28-1
1310
28-1
12
11
349
11-12
546
11-12
3
30
19
586
19-9
610
19-9
4
24
25
704
24-25
704
24-25
5
27
28
500
27-28
500
27-28
6
37
28
815
37-28
575
37-28
7
30
36
713
40-84
277
40-84
8
35
42
850
35-38
1094
35-38
9
35
36
681
35-36
299
40-84
10
38
42
479
38-42
581
38-42
From
To
1
1
2
No.
From area 2 to area 1
11
28
1
516
28-1
276
28-1
12
11
12
451
11-12
251
11-12
13
19
30
1637
29-30
675
40-84
14
25
24
896
24-25
896
24-25
15
28
27
1099
27-28
1099
27-28
16
28
37
785
28-37
1024
28-37
17
36
30
1044
35-36
859
35-36
18
42
35
1170
29-35
694
40-84
135
19
36
35
908
35-36
747
35-36
20
42
38
620
35-38
696
38-42
From area 1 to area 3
21
31
113
471
31-113
338
31-113
22
31
101
647
101-31
279
101-31
From area 3 to area 1
23
113
31
375
31-113
508
31-113
24
101
31
996
101-31
1089
40-84
823
101-31
478
40-84
From area 1 to area 4
25
30
87
996
30-87
From area 4 to area 1
26
87
30
1232
40-84
From area 2 to area 3 and from area 3 to area 2
NIL
From area 2 to area 4
27
39
89
1555
89-39
1426
89-39
28
40
84
723
40-84
871
40-84
29
46
120
412
46-120
415
46-120
30
46
84
926
54-46
1250
54-46
31
46
82
758
82-46
767
82-46
32
46
55
615
46-55
731
68-55
33
54
84
1344
84-54
825
84-54
34
57
72
1120
72-57
1474
72-57
136
35
124
69
598
69-124
604
69-124
36
124
71
690
124-71
683
124-71
From area 4 to area 2
37
89
39
782
89-39
913
89-39
38
84
40
250
40-84
97
40-84
39
120
46
692
82-120
697
82-120
40
84
46
1857
54-46
1204
40-84
41
82
46
1870
82-46
1862
82-46
42
55
46
598
68-55
644
66-68
43
84
54
1336
84-54
1855
84-54
44
72
57
764
72-57
394
72-57
45
69
124
534
69-124
528
69-124
46
71
124
642
66-69
632
66-69
From area 3 to area 4
47
99
85
722
85-99
795
97-99
48
95
85
1096
95-85
1474
95-85
49
95
87
1197
95-87
1530
95-87
50
93
92
959
92-93
1112
92-93
From area 4 to area 3
51
85
99
716
85-99
579
85-99
52
85
95
1127
95-85
743
95-85
53
87
95
1242
95-85
819
95-85
54
92
93
1013
92-93
859
92-93
137
The concept of ATC requires the determination of what is available
from a particular condition. If the exact conditions were known in
advance and a specific transaction was in question, the burden would
be significantly less than that encountered in the attempt to predict
what will be available at a future time.
The
ATC
computations
presented
should
give
the
market
participants enough and quick information to make bidding decisions.
In a competitive dynamic power market, ATC depends on the
generation pattern and loading pattern as determined by the bidding
results. Yet market participants also need ATC information before
bidding strategically. The fast ATC calculation method will make more
efficient rounds of bidding for both market participants and ISO.
5.8. RESULTS AND DISCUSSION ON CONTINGENCY
ANALYSIS
There are different methods are available to give contingency
ranking. For this analysis, tie-line MVA Loading is considered for
contingency
ranking.
Contingency
ranking
of
all
the
tie-lines
according to MVA loading is given in Table 5.16.
Table 5.16: Contingency ranking of tie-lines
Power flow
From To
MVA
%MVA Contingency
Circuit
bus bus
(MW) (Mvar) rating loading
rank
40
84
1
-217.1
3.3
400
55.1
1
28
2
-189.8
35
400
48.2
1
28
1
-189.8
35
400
48.2
1
2
138
46
82
1
183.1
-27.5
400
47.4
3
30
19
1
174.4
8.7
400
43.6
4
57
72
2
-169.3
-19.4
400
42.6
5
57
72
1
-169.3
-19.4
400
42.6
35
42
1
163.3
2.4
400
42.3
6
46
120
1
165.6
-12.3
400
41.5
7
27
28
2
150
-7.8
400
37.6
8
27
28
1
150
-7.8
400
37.6
12
11
1
-149
-4.6
400
37.3
9
30
87
1
138.6
38.4
400
35.9
10
54
84
3
92.2
-11
525
35.5
54
84
2
184.3
-22
525
35.5
54
84
1
184.3
-22
525
35.5
38
42
1
119.2
-9.4
400
29.9
12
95
85
1
108.3
-32.8
400
28.2
13
95
87
1
90.1
-31.2
400
23.7
14
39
89
2
-93.1
9.2
400
23.4
39
89
1
-93.1
9.2
400
23.4
46
55
1
79.8
-23.3
400
20.8
16
30
36
1
73.9
19.1
400
20.7
17
31
113
1
-49.4
8.2
400
19.4
18
35
36
1
45.6
51.8
400
19.4
19
31
101
1
73.2
-7.2
400
19.1
20
11
15
139
99
85
1
53.8
-12.1
400
15
93
92
2
56.3
-9.5
400
14.8
93
92
1
56.3
-9.5
400
14.8
37
28
2
40.2
-26.9
400
12.5
37
28
1
40.3
-29.6
400
12.5
24
25
2
48.2
-2.8
400
12.1
21
22
23
24
24
25
1
48.2
-2.8
400
12.1
124
69
1
-18
26.7
400
8.1
25
124
71
1
7.9
-12.7
400
4.3
26
46
84
2
9.7
6.2
400
3.2
46
84
1
9.7
6.2
400
3.2
27
Variation of the ATC compared to base case between the areas
for single line outage at a time is given in the Tables 5.17(a) to 5.17(d).
Table 5.17: (a) ATC between areas with contingencies
Contingency line
Base
1-3
1040
1086
NE
1019
947
1-4
838
834
NE
754
841
2-1
681
675
NE
630
737
2-3
1355
971
1286 1145
1350
System Blackout
Transfer case
40-84 1-28 46-82 30-19 57-72 35-42 46-120
areas
ATC
ATC ATC ATC
ATC
ATC
ATC
ATC
(MW) (MW) (MW) (MW) (MW) (MW) (MW)
(MW)
1-2
2061 1873 NE
1346 1736
1563
1368
976
1023
844
770
728
640
1376
915
140
2-4
1408
1408 1408 1408
1406
1408
1162
3-1
1146
1146
1146
1146
1146
1146
3-2
1299
1288 1323 1341
1296
1284
1334
3-4
869
856
845
795
877
874
808
4-1
676
676
NE
676
676
676
676
4-2
2576
2580 2587 2577
2578
2593
2581
4-3
675
675
676
675
675
NE
675
675
Table 5.17: (b) ATC between areas with contingencies
Contingency line
Base
Transfer case
27-28 12-11 30-87 54-84 38-42 95-85 95-87
areas
ATC ATC ATC ATC
ATC
ATC
ATC
ATC
(MW) (MW) (MW) (MW) (MW) (MW) (MW)
(MW)
1-2
2061 1518 2217 1730 2054 1720 2010
1997
1-3
1040
1101
1128
785
1048
992
1017
1021
1-4
838
852
848
814
807
842
835
637
2-1
681
524
540
682
-66
705
691
687
2-3
1355
1017
1075
1367
-29
1408
1286
1322
2-4
1408
1404
1408
1408
-118
1408
1408
1408
3-1
1146
1079
802
1136
1146
1146
1141
1022
3-2
1299
1269
1255
1325
1296
1294
1203
1087
3-4
869
882
880
857
837
872
830
713
4-1
676
676
676
676
676
676
676
676
4-2
2576
2573
2723
2574
2597
2583
2577
2577
4-3
675
675
675
676
675
675
675
675
141
Table 5.17: (c) ATC between areas with contingencies
Contingency line
Base
Transfer case
39-89 95-87 39-89 46-55 30-36 31-113 35-36
areas
ATC ATC ATC ATC
ATC
ATC
ATC
ATC
(MW) (MW) (MW) (MW) (MW) (MW) (MW)
(MW)
1-2
2061 2235 1997 2235 1156 1895 2033
1854
1-3
1040
1068
1021
1068
1037
1014
917
1007
1-4
838
851
637
851
473
843
838
844
2-1
681
590
687
590
675
663
652
900
2-3
1355
1287
1322
1287
1343
1362
1383
1408
2-4
1408
1408
1408
1408
1362
1408
1408
1408
3-1
1146
1090
1022
1090
1146
1146
1146
1146
3-2
1299
1246
1087
1246
1169
1296
1249
1294
3-4
869
897
713
897
493
873
872
872
4-1
676
676
676
676
676
676
676
676
4-2
2576
2495
2577
2495
2577
2576
2576
2581
4-3
675
676
675
676
675
675
676
675
Table 5.17: (d) ATC between areas with contingencies
Base
Contingency line
Transfer
case 31-101 99-85 93-92 37-28 124-69 124-71 46-84
areas
ATC ATC
ATC
ATC
ATC
ATC
ATC
ATC
1-2
(MW) (MW)
2061 1756
(MW)
2028
(MW)
1959
(MW)
NE
(MW)
2056
(MW)
2036
(MW)
2043
1-3
1040
768
1023
1020
NE
1040
1040
1040
1-4
838
805
837
836
NE
836
831
845
142
2-1
681
2-3
665
686
693
NE
680
681
720
1355 1374
1312
1303
1408
1353
1353
1379
2-4
1408 1408
1408
1408
1408
1408
1408
1408
3-1
1146 1080
1146
742
NE
1146
1146
1146
3-2
1299 1346
1257
954
1281
1296
1303
1287
3-4
869
871
867
723
864
865
860
878
4-1
676
676
676
676
NE
676
676
676
4-2
2576 2576
2577
2577
2578
2576
3577
2582
4-3
675
675
675
675
675
675
675
676
From the above results, out of all these line outages, line 57-72
outage is more severe and causes system blackout. Outage of lines 128 and 37-28, isolate the Area 1 from the remaining system,
calculation of ATC is Not Existing (NE). Outage of line 54-84 causes
the overloading of the line 54-46 by 16% due to that ATC from Area 2
to remaining areas becomes negative.
ATC calculations are extended for the some of the limiting lines
also and all these lines are loaded in between 60 – 70%. Outage of
lines 49-46 is more severe, cause’s system blackout. The details of
variation of ATC for these lines are given in Table 5.18.
143
Table 5.18: ATC Between the areas for other limiting lines
Bas
Contingency line
Transfer case 49-46 102-115 21-47 29-35 100-101 42-35 54-46 97-98
areas
ATC ATC
ATC
ATC ATC
ATC
ATC ATC ATC
(MW) (MW) (MW) (MW) (MW) (MW) (MW) (MW) (MW)
1-2
2061
2052 1343 1269 2086 1563 2048 2048
1040
992
1147 562
1063
978 1040 1042
1-4
838
838
771
441
838
844
843
837
2-1
681
681
132
297
672
728
690
685
2-3
1355
1356
237
719
1366
1376 1388 1352
2-4
1408
1408
504 1312
1408
1408 1408 1408
3-1
1146
1146
300
487
1146 1146 1044
3-2
1299
1238
1344 1347
795
1284 1293 1143
3-4
869
869
790
909
521
874
874
804
4-1
676
676
179
370
676
676
676
676
4-2
2576
2576
2581 2364
2577
2593 2579 2577
4-3
675
675
446
675
675
Blackout
1-3
506
675
675
675
To find secured operating of the system the above given ATC’s are
more useful of the operators of the Andhra Pradesh State electricity
market.
5.9. SUMMARY
In this chapter, basic concepts of ATC and ATC calculations are
discussed. ATC is calculated from all generator buses to normally
heavily loaded load buses for IEEE 26-bus system and between the
144
areas of IEEE 118-bus system for different load conditions, and results
are compared and analyzed. Variation of ATC between different buses
for the data of March, September 2011 is calculated for 124-bus realtime Indian utility system of Andhra Pradesh State grid and ATC is
calculated between the different distribution companies for different
cases considering each company as an area.
And it also presents the concepts of Contingency Analysis (CA) and
methods to analyze the CA problem. Contingency ranking is taken
according to the percentage loading of the lines. For this analysis, tieline MVA Loading is considered for ranking. A 124-bus real time
Indian utility power system of Andhra Pradesh State grid is considered
to find the variation of ATC between the areas for transmission line
outage of each tie-line.