A Comprehensive Two Level Heuristic Approach to
Transmission Expansion Planning
V. S. K. Murthy B, Pradeep Yemula, Student Member, IEEE, and S. A. Khaparde, Senior Member, IEEE
Abstract—The transmission expansion planning (TEP) has long
term effects on system performance. The effects are irreversible.
The conventional optimization techniques have convergence problems for large system and heuristic methods reported so far
are not holistic in nature. This paper proposes a two level
approach. At first level, the usual static solution using linear
approach is proposed. The objective is to minimize the cost
along with overloads. The isolated nodes are handled by ZBUS
formulation as described. The Genetic Algorithm (GA) is used as
a heuristic approach to arrive at results. The plans are shortlisted
with no overloads and least cost. The performance is tested for
high rank contingencies and appropriate system strengthening is
suggested. At second level, further strengthening of the network
on short term basis is done with due consideration to reactive
power balance in the grid. The reactive power support has to be
incorporated since the AC model with reactive power limits can
impose convergence problems. To overcome this, Reactive Power
Compensation (RPC) enhanced FDLF module with integrated
reactive power planning based on set of heuristics is implemented.
The TEP plans need to be evaluated for reactive power balance.
This is accomplished by evaluating voltage stability margin
index (VSMI). It identifies weaker lines prone to reactive power
imbalance. The TEP plan reinforces grid to improve the weaker
section. The proposed methodology is applied to IEEE 46-bus
test system and results are discussed. Power System Simulator
(PSS/E) package along with visualization tools are used for
validating and portraying the results.
Index Terms— contingency analysis, Power System Simulator
(PSS), VSIM, Transmission expansion planning, Tuned FDLF
Module.
I. I NTRODUCTION
ONVENTIONAL transmission expansion planning is
carried out for a future horizon year, where the available
data is base year topology, candidate circuits for expansion,
planned generation and forecasted demand. Reference [1]
gives the basic definition of TEP, its classification based on
the solution methods, treatment of the planning horizon, and
consideration of restructuring in the power sector. Another
significant paper [2] organizes and classifies existing TEP
algorithms in both regulated and deregulated environment.
Expansion planning is a complex problem as it is dynamic
in nature and it is simplified by solving as static transmission
planning.
Traditionally, DC model is used and planning is done only for
C
V. S. K. Murthy B, and Pradeep Yemula are with the Department of
Electrical Engineering, Indian Institute of Technology, Bombay, India, 400076
e-mail: ypradeep@iitb.ac.in, vsk@ee.iitb.ac.in
S. A. Khaparde is Professor, Electrical Department Indian Institute of
Technology, Bombay. e-mail: sak@ee.iitb.ac.in.
c 2008 IEEE
978-1-4244-1762-9/08/$25.00 active power. The problem has been approached in different
ways, including usage of optimization [3]–[6] and heuristic
methods [7]–[10] where, the objective is to arrive at a minimum investment cost plan as best plan while satisfying the
capacity constraints. The usage of the DC model restricts the
planning studies from considering reactive power planning and
losses in the network. References [11], [12] have presented
the formulation of the planning problem using AC model to
address reactive planning issues. Reference [12] presents a
relaxed Short Term Transmission Network Expansion Planning (STTNEP) formulation in conjunction with constructive
heuristic algorithm. The system operators are confronted with
chronic reactive power imbalance in some major parts of the
network. This may be either due to improper reactive power
support or due to improper expansion planning.
This paper gives a two level comprehensive approach to
planning by considering future active power needs along
with contingency studies in Level-1 and reactive power needs
in Level-II. The motivation is to present a comprehensive
methodology incorporating an end to end approach with multiple criteria in a sequential manner. Alternatively, an integrated
approach can be followed where both active, reactive planning
can be done simultaneously in a coordinated way. Although
this approach in principle is more accurate, but for a long
time horizon this may lead to high computation effort and
prone to errors owing to uncertainties. The loss of accuracy can
thus be justified in adopting a sequential approach. Moreover,
in this approach instead of relying on a single “best” plan,
we start with a set of plans and gradually improve to meet
further criteria. Based on a consolidated view of all the plans,
a comparative study is done to choose the final expansion
plan. PSS/E package is used for validating and visualization
of results.
Section-II gives overview of the comprehensive Two Level
Heuristic Approach for TEP. Section-III suggests active power
planning using Z-bus based genetic algorithm and is termed
as Level-1 of planning. Section-IV explains integrated reactive power planning and is termed as Level-2 of planning.
In Section-V,implementation of the proposed method on a
standard TEP test case (46 bus system) is done and the results
are compared with those reported in the literature. Section-VI
concludes the paper.
II. OVERVIEW OF C OMPREHENSIVE T WO L EVEL
H EURISTIC A PPROACH FOR TEP
This section gives an overview of comprehensive two level
heuristic approach for TEP in the form of a flowchart shown
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in Fig 1. This comprehensive approach towards TEP has
following advantages:
•
•
•
•
•
Issues dealing with comprehensive TEP planning are
addressed in a logical order wherein the planning methodology tends to satisfy various operational constraints
while building the network, one after the other. First,
capacity constraints are satisfied followed by security
constraints, then by voltage limit constraints and finally
voltage stability constraints.
The methodology is sequential and follows a repeating
input-process-output format, as seen in the flowchart.
The methodology works on a set of plans and strengthens
them subsequently in every process. The final plan can
be chosen as per planner’s overall criteria.
The methodology is organized into two broad levels i.e.,
active power planning and reactive power planning.
Each component (or process) is implemented as an independent module and hence there is a scope for further
optimizing specific module in future without disturbing
the overall planning process.
The next two sections will detail the proposed methodology
with various intermediate steps shown in the above flowchart
for active and reactive power planning respectively.
III. L EVEL 1: ACTIVE P OWER P LANNING
Medium and Long term TEP mainly focuses on the following three criteria. 1) Minimization of investment cost of transmission expansion, 2) Supplying all the future load demand
and 3) satisfying n-1 contingency criteria. Criteria 1 and 2 are
met in the basic TEP formulation. Additional considerations
suggests contingency analysis have to be carried out to address
criteria 3. In this paper, the first level TEP carries out the
active power planning which is then followed by contingency
analysis to obtain a set of feasible plans with necessary
strengthening to address the (n-1) contingency criteria. The
plans are arranged in increasing order of investment cost which
will be further processed.
Input data is the base year topology, future planned generation capacity additions, future load growth and available
right-of-ways for expansion. DC load flow analysis suffices
for the purpose of planning at this stage as it mainly focuses
on the building the network to carry real power. In this paper a
Z-bus based genetic algorithm method is used to carry out the
conventional expansion planning. This method is explained in
reference [13], [14]. The salient features of this approach are:
1) Adopting overload minimization approach to GA
2) Use of Z-bus for handling isolated nodes. Isolated nodes
are the nodes where a new generation plant or a new
load center is planned in future and there is no initial
connectivity.
3) The overload quantified by simple DC loadflow is used
as a driving signal for genetic algorithm search.
4) The fitness of an individual (plan) is inversely proportional to weighted sum of investment cost and net
overload in the system.
GA provides a set of best solutions with zero overloads and
in increasing order of investment cost.
The next step would be to perform contingency analysis for
each of the expansion plans. This paper proposes a Contingency ranking based heuristic rule for suggesting necessary
improvements so as to make each plan (n-1) secure. The
heuristic is described in Algorithm. 1.
Power System Simulator (PSS/E Version 30.2) is used for
performing above contingency studies and generating contingency ranking reports. Thus, by the end of Level-1, a set of
secure plans addressing active power planning requirements
is achieved. The next section describes the reactive power
planning process which is further carried on these set of plans.
IV. L EVEL 2: R EACTIVE P OWER P LANNING
Fig. 1.
Comprehensive Two Level Heuristic Approach for TEP.
Along with Active power planning, Reactive power planning
should also be considered as an integrated problem while
formulating a planning process because inappropriate reactive
power compensation can lead to either 1) nonconvergence of
the AC loadflow program or 2) unrealistic results due to Q
absorption by generators or 3) unacceptably low voltages in
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Algorithm 1 Contingency Ranking Based Heuristic Rule
while (All plans are not (n-1) secure) do
- Choose a plan which is to be strengthened
- Perform Contingency Analysis on the plan
while (Overloads are detected) do
- Rank the contingencies based on severity of overloads
- Identify most severely overloaded contingency as
location for system strengthening
- Strengthen the system at the identified location
- Again, Perform Contingency Analysis on the plan
end while
end while
- Print the results of strengthening of plans required to make
the system (n-1) secure
the system. The planning so far has only considered the real
power aspects. The power network is meant to carry active
power and if significant reactive power flows are observed
on the transmission lines then valuable transmission resource
is wasted in carrying reactive power [15]. Hence the reactive
power demand is best met locally.
At this stage the future reactive power demand and the
reactive power capabilities of the future planned generators
are also considered as the input data for the algorithm. The
reactive power flow on a line is mainly determined by the
voltage levels of the buses at the either ends of the line. If
there is a demand for reactive VARs at a bus, its voltage dips
and the lines connecting it will have to carry reactive power
to this bus from the adjacent buses, leading to lowering of
bus voltage of adjacent buses as well. Conversely, if the
supply of VARs at bus is excessive, its voltage rises and this
extra reactive power is pushed over the lines to adjacent bus,
spreading high voltage. Hence to minimize the reactive flows
over the lines, the bus voltages must be as close to each other
as possible and also ideally be equal to 1.0 pu.
Reference [16] uses optimal power flow for carrying out
reactive planning for the system and reference [17] uses
enhanced Fast Decoupled Load Flow (FDLF) module for
short term expansion planning. In this work, we extend these
methods to address long term expansion planning issues
which involve the problem of incorporating a large number of
reactive power sources which are not already existing in the
network. Thus, apart from the consideration of time horizon,
the main difference between short-term and medium or longterm planning is the consideration of new Right-of-Ways
(ROWs) and new buses. In the medium or long-term, new
ROWs and new buses are considered for the planning. Reactive
Power Compensation (RPC) enhanced FDLF Module suitable
for medium or long term expansion planning is proposed and
implemented. This permits integrated Reactive power planning
and Load flow analysis. The RPC enhancements applied to
FDLF are described as follows.
A. RPC Enhanced FDLF Module:
In the AC Loadflow program using FDLF Algorithm, low or
high voltage pockets in the system are known only after initial
couple of iterations. To handle this issue, we start monitoring
the voltages after two iterations of the load flow program. In
particular, we track minimum and maximum voltage at each
iterations. If the limiting voltage is beyond permissible value,
then a synchronous condenser is attached at the corresponding
bus which regulates the voltage to the limiting values. For
a bus with over voltage, the synchronous condensor output
will be equal to inductive compensation required to maintain
the voltage at the upper limit. Conversely, the limiting node
with lower voltage, output of synchronous condensor is the
amount of capacitive VARs required to maintain voltage at the
minimum value. To avoid overcompensation in the system, a
tuning variable is defined in the program, which is used to
change the compensation level at each iteration. Depending
on planning scenario, this may or may not be adequate. The
process terminates either when the load flow convergence
criteria is met or when for three successive iterations, the
maximum mismatch consecutively increases. RPC Enhanced
FDLF Module is elaborated in algorithm 2.
Algorithm 2 RPC Enhanced FDLF Module
while (All plans are not processed) do
- Choose a plan for reactive compensation
- Append reactive power data to the chosen plan
- Perform AC load flow
while (AC loadflow not converged) do
- Initiate RPC-FDLF based loadflow algorithm and run
for two iterations
if (voltage violations are identified) then
Perform tuning of reactive compensation at that bus
while (Voltage violations exist) and (Subsequent
iterations do not diverge) do
- Increment reactive compensation in steps at
buses with voltage violations
- Continue RPC-FDLF based loadflow algorithm
for one iteration
- Compare with previous iterations and check for
convergence error
- Continue this loop until voltage violations are
eliminated with sufficient accuracy. If divergence
is detected restart the loop
end while
end if
end while
end while
- Print the results of Reactive Compensation of plans
So far reactive power compensation issue is addressed for
the chosen plans. However, the issue of voltage stability is not
yet considered. According to [18] Voltage instability occurs
when the reactive demand at a certain bus increases to a large
value, which results in voltage dip, which further results in
increase of reactive demand at that bus. This situation builds
until the voltage value goes very low and the system can
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no longer meet the reactive demand at that bus, leading to
a voltage collapse. Once the list of reactive supports is found,
we can take one more step ahead and quantify the voltage
stability margin for the network. Reference [19] defines a
Voltage Stability Margin Index (VSMI) which can be used
to identify weak lines and buses of the network prone to
voltage instability (indicated by low values of VSMI). VSMI
of a line is based on the relationship between voltage stability and prevailing angle difference between sending-end and
receiving-end buses. The advantage of VSMI is that it doesn’t
require the continuation powerflows for estimation of stability
margin and thus involves lesser computational effort and is
aptly suitable for planning studies. The implementation of
VSMI based voltage stability improvement module is detailed
in the algorithm 3.
Algorithm 3 VSMI based voltage stability improvement
while (All plans are not processed) do
- Choose a plan for voltage stability assessment
- Read bus angles and active, reactive power flows over
the lines
- Calculate VSMI indices for all lines
if (VSMI is low) then
- Add a reactive source to supply the corresponding
reactive sink locally
end if
- Generate list of reactive compensation required to
improve voltage stability
- Identify weak areas in terms of voltage instability for
operational use
end while
- Print the results of Reactive Compensation of plans
Although enhancement of reactive compensation for voltage
stability may be relatively uncommon, calculation of VSMI
index is still useful in identification of weak areas which are
prone to voltage instability and hence this information gives
insights for operational purposes.
V. R ESULTS AND D ISCUSSION
The proposed methodology is applied to a standard TEP 46
bus test system. The system data is available in [3] and the
single line diagram of initial network is given in [20]. This
system is chosen for the case study since its a reasonably
large and practical system reported in the literature. But the
data concerning real power planning is only given in the above
reference. In this paper the resistance of lines is derived from
the reactance of the line assuming an X/R ratio of 20. Also the
reactive loading at each bus is not specified for the standard
test system and hence reactive power load is assumed to be
30% of real power load which approximately corresponds to
a power factor of 0.95. The values are chosen in the above
two assumptions as are valid in a typical practical power
transmission network. The test system consists of 46 buses,
12 isolated buses and 79 ROWs for new circuit additions with
a active power demand of 6,880 MW, reactive power demand
of 2,064 MVAR, with maximum generation capacity of 10,545
TABLE I
P ROPOSED N EW L INES
ROW⇓
Plan No⇒
14-22
32-43
20-21
42-43
46-06
25-32
31-32
28-31
24-25
5-6
13-20
8-13
28-43
12-14
21-19
20-23
2-5
19-21
5-11
11-46
21-25
Cost (mn $)
New Lines required for
Zero Overload Min
Investment cost criteria
1
2
3
4
5
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
1
1
1
1
Additional New Lines
required for (n-1) security criteria
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
4
1
1
2
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
166 168 169 169 171
3
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
149 120 142 134 111
MW. Plans are searched considering no generation re-dispatch
and maximum new circuit additions allowed in each corridor
is restricted to three.
As described in Section I, Comprehensive Two Level
Heuristic Approach for TEP was preformed on this test system.
The steps followed are as per the flowchart in Fig 1. At the
end of Active Power Planning five plans were obtained as
shown in Table I. Next Contingency ranking based heuristic
is applied to arrive at 5 plans which are (n-1) secure. As per
this, the additional new lines required at various ROWs along
with total cost are also shown in Table I. With this level 1 of
planning is completed. The network single line diagram with
low investment cost (as per plan 1) at this stage is shown in
Fig 2.
The five plans are further improved with addition of reactive
power support upon implementing the RPC enhanced FDLF
module on these plans. Table II. shows the reactive compensation needed as per the RPC enhanced FDLF module for
each plan, so as to satisfy voltage limit criteria. Voltage limits
of 0.98 pu. to 1.05 pu. are enforced. Table II. also shows the
results reported in literature according to Reference [12]. It can
be observed that although the methodology used in this paper
and [12] are different, the results are more or less confirming.
Fig. 3 shows the comparison of total investment cost of
these five plans for both levels. It is observed that the Plan5 is evolved as the optimal plan at the end of Level-2. The
optimum investment plan at the end of planning is shown in
the fig 4. The real and reactive power losses are 45.9MW and
918MVAR. These are optimum as compared to reference [12].
VI. C ONCLUSION
A comprehensive two level heuristic approach to transmission expansion planning is proposed in this paper. The
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TABLE II
R EACTIVE C OMPENSATION R EQUIRED
Conventionalplanningcost(inmillion$)
Bus no.⇓
Amount of Reactive compensation
in MVAR (all are capacitive VARS)
Plan No⇒
2
5
13
20
21
23
24
25
33
36
38
40
42
43
44
45
Total (MVAR)
Cost (mn $)
1
54
0
150
240
190
212
144
74
48
0
36
24
192
190
80
76
1710
7.372
2
0
92
180
270
224
184
144
86
62
0
54
38
188
154
92
54
1822
7.855
3
80
24
78
292
120
214
144
62
54
0
64
32
224
120
74
46
1628
7.019
4
60
0
180
254
210
146
144
78
72
0
36
42
214
140
60
32
1668
7.191
Results
from
Ref [12]
75
0
75
225
0
225
0
0
75
75
75
150
650
0
0
75
1700
6.500
5
100
0
180
292
270
198
144
80
60
0
54
36
198
180
30
44
1866
8.045
Overallcostforeachplan(inmillion$)
315.47
Plan1
303.97
Plan2
282.55
171.23
169.98
169.36
168.31
166.9
Fig. 3.
311.48
288.56
Plan3
Plan4
Plan5
Cost Comparison of Plans.
1
1
1.004
1
7
1
4
0.988
1.004
0
2
-101
1
1.004
1
1
9
8
0.992
1.004
0.994
5
1
1
1
12
1
0.956
6
1.000
0.994
7
1
0.950
0.965
2
46
1.000
1
14
0.960
1.022
-188
4
0
1
1
13
1
1
1
9
5
1
8
0.976
1.000
1
0.942
1
0
1
-292
0.965
20
1.001
1.000
1
0.972
22
1
19
1.000
17
21
0
1
1.000
1.000
1
23
1
1
1
0
0.975
13
46
18
16
1.000
-198
6
0.981
-270
1
1
12
1.000
1.000
14
0.920
1
1
1
26
1.000
1
0
19
1.000
22
17
21
0.907
1
1
1.000
1.000
1.000
32
25
1.006
0.986
1
1
1.000
1.000
34
1.000
23
1
1
28
27
1
1.000
1
1
18
16
1.000
1
31
0
1
0.904
-81
20
0.984
24 33
1.002
1
-145
0.974
1
1
1
1
0.917
1
26
0.994
1
1
24
0.940
1
1
36
1
32
1.000
25
0.943
0.995
33
34
1
1
1.000
1.000
35
0.959
0
1.000
1.000
-55
31
28
27
0.990
38
1.006
1
37
1.000
43
0
1.000
-180
1
1
1
1
1
35
39
1.001
1.000
1.000
42
-198
0.996
0
36
0
40
1
0.999
-36
1
1
1
1
38
44
45
1
0
37
43
1.000
1
-44
0.990
1.000
1.000
1
1.000
1
1
40
39
0.985
0.993
1.000
42
Fig. 4. Final Optimal Network for 46 bus system at the end of both Active
and Reactive Power Planning.
1
1
1
44
45
0.935
1
0.950
1
Fig. 2. Optimal Network for 46 bus system at the end of Active Power
Planning.
main contribution of the paper is to show that in a sequential
manner it is possible to work with the AC system model for
transmission expansion planning and also the so mentioned
optimal plans in the literature may not be optimal by considering other aspects as explained. The above method can
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be further improved by incorporating other factors like angle
stability, loss of load, inclusion of FACTS devices, etc. The
method has sequential steps viz, planning for active power,
contingency planning, reactive planning, and voltage stability
evaluation. The initial best multiple plans arrived in the first
step are carried forward and improved on in the later steps. The
sequential approach can be converted to combined integrated
approach, where all the above criteria are simultaneously
evaluated and the best set of plans is arrived at. The authors
believe that if the described planning methodology is applied
to a real world system it would yield good overall insight by
virtue of its holistic nature.
VII. ACKNOWLEDGEMENT
This work is supported by Department of Science and
Technology (DST), Ministry of Science and Technology, Government of India under the project no SR/S3/EECE/44/2006.
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V. S. K. Murthy B is currently with Department of Electrical Engineering,
Indian Institute of Technology Bombay, India. His research interests include
Transmission System Expansion Planning.
Y. Pradeep Kumar is currently working towards Ph.D. degree in Electrical
Engineering Department at IIT Bombay, India. His research interests include,
Transmission Expansion Planning, IT application in power systems and power
systems restructuring issues.
Shrikrishna A. Khaparde (M’87-SM’91) is a Professor, Department of
Electrical Engineering, Indian Institute of Technology Bombay, India. He is
a member of the Advisory Committee of Maharashtra Electricity Regulatory
Commission (MERC). He is on the editorial board of International Journal
of Emerging Electric Power Systems (IJEEPS). He has co-authored books
titled, ”Computational Methods for Large Sparse Power System Analysis:
An Object Oriented Approach,” and, ”Transformer Engineering: Design &
Practice,” published by Kluwer Academic Publishers and Marcel Dekker,
respectively. His research area includes distributed generation and power
system restructuring.
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