40220140507005

INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING &
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) Volume 5, Issue 7, July (2014), pp. 45-55 © IAEME
TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 5, Issue 7, July (2014), pp. 45-55
© IAEME: www.iaeme.com/IJEET.asp
Journal Impact Factor (2014): 6.8310 (Calculated by GISI)
www.jifactor.com
45

IJEET
© I A E M E
TRANSMISSION EXPANSION PLANNING AND COST ALLOCATION
WITH AND WITHOUT SECURITY CONSTRAINTS IN A DEREGULATED
POWER SYSTEM
Srujana Raghupatruni Uddavolu
Assistant Professor, Department of Electrical Engineering, Muffakham Jah College of Engineering
and Technology, Hyderabad, India
ABSTRACT
This paper presents a novel approach for static transmission expansion planning and
allocation of the associated expansion costs to individual market entities in a restructured power
system. The approach seeks the optimal addition of transmission lines among the possible candidate
transmission lines minimizing the overall system costs and at the same time satisfying the system
operational and security constraints. Novelty of the approach lies in applying a widely known
technique used for overload security analysis to an area such as Transmission expansion planning.
Transmission expansion costs are allocated using distribution factors to the individual entities in a
fair and transparent manner. The results for modified Garver Test system demonstrate that the
approach with the advantage of its simplicity can be applied to transmission expansion planning and
cost allocation in restructured power system.
Keywords: Open Access, Deregulation, Restructured Power System, Transmission Expansion
Planning (TEP), Security Constraints, Power Flow Tracing.
1. INTRODUCTION
Growing electricity demand driven by fast industrial growth and growing access to electricity
in developing countries has necessitated the increase in generation and need for adequate
transmission capacity. One of the many means of enhancing transmission capacity that involves
significant capital expenditure is that of Transmission Expansion Planning (TEP). Vast number of
influencing parameters including candidate circuits, electricity demand, generation forecast,
operational network topology, etc. are required for an optimal solution of TEP problem. In general,

TEP consists of choosing, from a predefined set of circuits, those that should be built in order to
minimize the investment cost, and to supply the forecasted demand along the planning horizon.
46

The TEP problem is generally considered as non-linear, no-convex optimization problem.
During past few decades, significant number of methods have been proposed to solve TEP problem.
One of the earliest approaches for TEP was proposed by authors in [1], where TEP problem was
formulated as a power flow problem and used a linear programming algorithm to find the most direct
routes from generation to loads. The approach discourages power flow on the right of ways without
existing transmission lines by penalizing them .The transmission line that alleviates maximum
overload emerged as the one chosen for addition. A new interactive method of TEP optimization
approach was proposed by author’s in [11]. A mixed integer linear programming approach to solve
the static TEP problem has been proposed in [12]. The proposed approach considers the line losses in
the optimization framework. However in this method it is generally hard to guaranty the model
feasibility and global optimality of the problem solution. Authors in [13] proposed a new method
known as branch and bound method to solve the TEP optimization problem. The authors have used a
transportation model to represent the transmission network. Authors in [2], proposed a combined
use of linear and dynamic programming. Linear programming was used to find the minimum cost
capacity increments required to meet the changes on demand and generation. Afterwards, they used
dynamic programming to search for a close to optimal sequence of investment (continuous)
decisions. Reference [3] proposed a pure dynamic programming, but due to the computational
effort, its applications were very restricted.
Authors in [4] proposed the use of interactive tools for transmission planning. To rank the
possible additions this approach used a sensitivity analysis with respect to circuit’s susceptances of a
“least effort” index, which is the result of an optimization problem whose solution is identical to a
DC power flow solution. In 1984, Villasana [6] proposed two approaches to be applied in
transmission expansion planning. The first one is formulated combining a DC power flow model
with a transportation model. While the DC model evaluated the power flow for the existing
transmission facilities, the transportation model was used to compute the “overload” flow. This
approach consists in an improvement of the approach proposed in [1]. The second approach used
linear mixed integer formulation.
The use of mathematical decomposition schemes for this problem started with the approach
proposed in [5], where the author has applied a Benders decomposition technique to decompose the
global problem into two sub problems: the Master investment sub problem, which chooses the trial
expansion plan, and the operation sub problem that analyzes the trial investment decisions and
expresses operational violated constraints in terms of investment variables through Benders cuts.
However the hierarchical level II reliability calculations employed for composite system planning
increases the complexity of overall problem.
Many researchers [8],[9] have applied meta-heuristic techniques like GA and simulated
annealing to tackle the TEP problem. However there are some limitations of these evolutionary
optimization approaches. These limitations include large computational burden and constraint
handling problem which becomes more complex for highly constrained problems especially in large
power networks.
Authors in [14] formulated the composite system expansion planning as a nonlinear model
while considering different location based fuel supplying costs. Thought the method employs n-1
contingency criterion, reliability measure has not been studied quantitatively. Authors in [7] have
described an automatic way of finding the least cost method of securing a given power system.
With the advent of electricity markets ,the inability of wheeling electricity through desired path
either due to physical and operating limits of the transmission lines or the absence of transmission
lines in the desired right of way may hamper the prospects of trading electricity as dictated by

economics. In forward markets, it would be beneficial to plan for transmission expansion to ensure
fair competition among the market participants. Transmission expansion planning must therefore,
simulate market behaviour sufficiently to encourage and facilitate fair electricity market
environment.
47

The present paper can be divide into three main sections- the first section (section II)
discusses transmission expansion planning without security constraints ,where the transmission lines
with the overall benefit of being comparatively inexpensive and being able to alleviate maximum
overload are added one at a time till the overload on the network is alleviated. Reliability is of utmost
importance in competitive markets and the second section (section III) deals with TEP to obtain N-1
secure system. As expected, the number of lines that were added for N-1 secure system were higher.
In the the third section (section IV) the transmission expansion costs were allocated to individual
generators and loads using distribution factors [10]. Results are discussed in section V followed by
concluding remarks in section VI.
2. TEP WITHOUT SECURITY CONSTRAINTS
2.1 Method Adopted
The method adopted is similar to overload security analysis, where in instead of removing a
line (as in overload security analysis), line addition is simulated.
The brute force method involves adding one line at a time and performing DC load flow. A much
more efficient approach is to simulate the line addition by using Thevenin’s /Norton’s equivalent. In
this approach the base case network before line addition remains the same for all candidate circuits
as shown in Fig.1.
thkm X k
m
f
km P
f km X = X
q
km
Fig. 1: Thevenin’s equivalent for single topological change
For a line addition between buses k and m, thethakm ( 0
q ) shown in the Thevenin’s
km
equivalent model is computed as defined in (1).
0 0 0
km k m
q = q −q
(1)
(superscript 0 denotes that the values correspond to base case)
Thevenin’s equivalent impedance is evaluated as defined in (2).
thkm kk mm km mk X = X + X − X − X
(2)

f km
km X X
f DP = − P P

=
48

thkm f
P
+
=
q 0
(3)
To find out the effect of the line addition on the rest of the system, the angle changes are
evaluated as defined in (4)-(6).
f f Dq = XDP
(4)
where,
[0 0...... 0 ...0] f
km
f
km
(5)
(the two entries correspond to buses k and m affected)
q f = q 0 + Dq f
(6)
DC load flow is run to get post addition flows using the new angles (
q f ).
From flows obtained, the indices p PI and NI are calculated as defined in (7) and (8)
respectively.
2
P
flowl
max
p
l l
PI
P

(7)
where, l belongs to the set of all the lines that are overloaded to avoid masking effect i.e., the line
that is just below its limit contributes to performance index almost equal to the line just above the
limit.
−
base
p p PI PI
=

os

NI
C t
(8)
Using the procedure described below the optimal solution is arrived at.
2.2 Algorithm
1) DC load flow is run on the base case network (modified Garver Six bus system) to obtain the
flows on all the lines and bus angles prior to the line addition
and performance index, base
p PI is calculated.
2) A line is added amongst the 5 possible right of way using Thevenin’s Equivalent approach
described above and flows are calculated.
3) From the flows, performance index, p PI and a normalized index, NI are calculated.
4) Go to step 2 until normalized index is found out for all possible right of way (ROW).
Add the line with largest value of the normalized index and go to step 1 till all the overloads
on the network are alleviated.

49
3. TEP WITH SECURITY CONSTRAINTS

An important aspect that must be considered when planning a transmission network
expansion is system-security. Contingency analysis looks at the state of the system after some lines
of the network fail. The N-1 contingency analysis looks at the system state after a single line of the
network fails and see if it is secure or not. N-1 contingency analysis requires that after each line fails
independently, the network constraints be satisfied.
When planning a transmission expansion, it is desirable to consider whether or not the
topology modification plan will be secure after any single line outage.
Seifu et. al. [13] have first considered a base case network (optimal expansion plan obtained
from TEP without security constraints) in which there are no overloads. They have then considered a
network expansion plan beyond that network so that it does not have overloads in a single line out
case (N-1 secure).
In the proposed method, the overall network planning for (N-1) security is solved in an
integrated fashion i.e. there is no distinction as base case network planning (without security
constraints) and planning against contingencies. The proposed method considers outage possibility of
any line (excluding radial lines) one at a time and plans the network expansion such that there are no
overloads in any (Nc+1) topology cases.
3.1 Method Adopted
A double line outage kind of approach is used for security constrained transmission
expansion planning to simulate two network changes – a line addition and another line removal.For a
line addition between buses, k and m and line removal between buses, i and j, the Thevenin’s
equivalent model is computed as defined in (9)-(16).
th X
T
f f
km ij P P

0
=
0

km
f
ij
X
X
X
q
0

km

q
0
ij

Fig. 2: Thevenin’s equivalent for double topological change
0 0 0
km k m
q = q −q
(9)
0 0 0
ij i j
q = q −q
(10)
(superscript 0 denotes that the values correspond to base case)
Thevenin’s equivalent impedance is evaluated as,
thij ij ii jj ij ji X = X + X − X − X
, (11)
thkm,km kk mm km mk X = X + X − X − X (12)
thkm,ij thij ,km ik im jk jm X = X = X − X − X + X (13)

f DP = −P P −P P
50

=
X X
, ,
thkm km thkm ij
th X X
thij km thij ij
X
, ,
(14)

q

f
km = X +
X
P

−
0
km
0
1 [ ]
ij
P
f th f
ij
q
(15)
where,

−
+
=
ij
km
x
f x
X
0
0
(16)
To find out the effect of the change in the network topology on the rest of the system, the
angle changes are evaluated as defined in (17)-(19).
f f Dq = XDP
(17)
where,
[0 0...... 0 ... ...0.... ....0] f
ij
f
ij
f
km
f
km
(18)
Therefore,
q f = q 0 + Dq f
(19)
DC load flow is run to get post changes flows using the new angles (
q f ).
From flows obtained, the indices p PI (which is a double summation over number of outage
topologies and base case and number of overloaded lines) and NI are calculated

Nc
P

=
flowlj
j P
= l l
PIp
2
max
0 (20)
Using the procedure described below the optimal N-1 secure solution is arrived at
.
−
base
p p PI PI
=

os

NI
C t
(21)
3.2 Algorithm
1. DC load flow is run for the base case and base
p PI is evaluated.
2. A single line outage simulation is done for all the Nc outage topologies considering one line out
at time and p PI calculated is added to the PIpbase obtained for the base case to get PIpbase for all the
Nc+1 topologies.
3. For all candidate circuit considered one at a time , using double line outage kind of approach
(adding this line and considering Nc+1 outage topologies one at a time) indices p PI , NI are
calculated.
4. The line with highest NI is added and go to step 1 till a network which is N-1 secure is obtained.

5. Redundant lines are removed by carrying out a double line outage simulation if it does not result
in overloads for all the Nc+1 topologies to arrive at the optimal secure expansion plan.
(Radial lines and the line added are not considered for outage)
51
5. RESULTS

The validity of the method is investigated by applying it to the modified “Garver 6-bus test
system for expansion”[1].Table 1 shows the lines added to meet forecasted load without security
constraints. Additional lines are added in Right of Ways (ROW) 3—5,6—2,6—4. The total cost of
the transmission expansion is 1X100 + 3X150 + 2X150 = 850 currency units. Transmission
Expansion Planning without security constraints leaves the system unable to supply certain loads in
case of transmission outages (planned and unplanned).The results for Transmission expansion
planning with security constraints (Table II) shows that additional lines have to be added above those
added in the previous case to make the system N-1 secure. The total cost of transmission expansion
is 1340 currency units for the lines added as shown in Table II. An additional cost of 490 currency
units needs to be incurred.
Using the D and C factors, the transmission expansion costs can be attributed to generators
and loads respectively. Negative costs indicate a certain entity is responsible for
Table I: Results for TEP without security constraints
Line no.
Between buses (k-m)
No. of lines added
Total no. of lines in the
ROW
Flow in the ROW(p.u)
Cost
1 1-2 0 1 -0.5125 --
2 1-4 0 1 -0.3175 --
3 1-5 0 1 0.5300 --
4 2-3 0 1 0.6200 --
5 2-4 0 1 0.0363 --
6 3-5 1 2 1.8700 100
7 6-2 3 4 3.5689 150
8 6-4 2 2 1.8812 150
9 6-5 0 0 0 305
10 6-3 0 0 0 240

52

Table II: Results for TEP with security constraints
Line no.
Between buses (k-m)
No. of lines added
Total no. of lines in the
ROW
Flow in the ROW(p.u)
Cost
1 1-2 0 1 -0.3348 --
2 1-4 0 1 -0.2682 --
3 1-5 0 1 0.3030 --
4 2-3 0 1 0.2735 --
5 2-4 0 1 -0.0675 --
6 3-5 2 3 2.0970 100
7 6-2 3 4 2.9408 150
8 6-4 3 3 1.9357 150
9 6-5 0 0 0 305
10 6-3 1 1 0.5735 240
counter flows and therefore instead of being charged, the corresponding entity will be credited. It
therefore encourages the entities that can reschedule their transactions to reduce/avoid the need for
transmission expansion planning while charging the other entities for the additional transmission
capacity to be added. Tables III and Table IV show the cost allocation without security constraints
for generators and loads respectively. Tables V and Table VI show the cost allocation with security
constraints for generators and loads respectively.
6. CONCLUSION
The optimal design of Transmission lines is an important part of the overall planning task of
electric power systems. A single line outage simulation using Thevenin’s equivalent kind of
approach was used to study the effect of line addition and to arrive at the optimal expansion without
security constraints. Given the right of way where new transmission lines can be added, the solution
gives the right of way in which the new line has to be added.
A novel method for Transmission expansion planning incorporating security aspects so that
the designed network is also secure due single outages has been presented .In the proposed method,
the overall network is solved in an integrated fashion i.e., there is no

53

G6 5.45 =
1 G = 0.5
5 L = 2.4
2 L = 2.4
4 L = 1.6
1 L = 0.8
3 G = 1.65
3 L = 0.4
Fig. 3: Optimal transmission expansion plan without security constraints (newly added lines shown
in red color)
6 G = 5.45
1 G = 0.5
5 L = 2.4
2 L = 2.4
4 L = 1.6
1 L = 0.8
3 L = 0.4
3 G = 1.65
Fig. 4: Optimal transmission expansion plan with security constraints (newly added lines shown in
red color)

40220140507005

Recommended

Recommended

More Related Content

What's hot

What's hot (19)

Viewers also liked

Viewers also liked (20)

Similar to 40220140507005

Similar to 40220140507005 (20)

More from IAEME Publication

More from IAEME Publication (20)

Recently uploaded

Recently uploaded (20)

40220140507005