Transmisison & generation_expansion_planning_ijepes-d-13-00427_r1_accepted

Elsevier Editorial System(tm) for International Journal of Electrical Power and Energy
Systems
Manuscript Draft
Manuscript Number: IJEPES-D-13-00427R1
Title: Computationally Efficient Composite Transmission Expansion Planning: A Pareto Optimal
Approach for Techno-Economic Solution
Article Type: Research Paper
Keywords: transmission expansion planning, generation planning, genetic algorithm, congestion
management, social welfare, linear matrices
Corresponding Author: Dr. Rajiv Shekhar, Ph. D.
Corresponding Author's Institution: Indian Institute of Technology Kanpur
First Author: Neeraj Gupta, Ph. D.
Order of Authors: Neeraj Gupta, Ph. D.; Rajiv Shekhar, Ph. D.; Prem K Kalra, Ph. D.
Abstract: This paper presents an integrated approach for composite transmission expansion planning
incorporating: (i) computationally efficient linear matrices, (ii) a novel Demand/Energy Not Served
(DNS/ENS) and Generation Not Served (GNS) calculation approach, to circumvent the time intensive
iterative procedures. A self-tuning mechanism based on stochastic Roulette wheel (RW) simulation
procedure supports the reduction of network congestion. It establishes a trade-off between technical
and economic criteria using the theory of marginal value (marginal reduction in interruption cost and
marginal increment in the investment) for the incremental updating method. A hybrid of deterministic
(N-1) and probabilistic (critical N-2) contingency scenarios have been simulated for security of the
system. Results show that existing lines and generators capacity are necessary to update for economic
operation for minimizing interruption cost and to achieve optimal investment. Modified 5-bus 24-bus
and 118-bus IEEE systems are taken to show the generalization of Methodology.

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Abstract— This paper presents an integrated approach for composite transmission expansion planning
incorporating: (i) computationally efficient linear matrices, (ii) a novel Demand/Energy Not Served
(DNS/ENS) and Generation Not Served (GNS) calculation approach, to circumvent the time intensive
iterative procedures. A self-tuning mechanism based on stochastic Roulette wheel (RW) simulation
procedure supports the reduction of network congestion. It establishes a trade-off between technical and
economic criteria using the theory of marginal value (marginal reduction in interruption cost and
marginal increment in the investment) for the incremental updating method. A hybrid of deterministic
(N-1) and probabilistic (critical N-2) contingency scenarios have been simulated for security of the
system. Results show that existing lines and generators capacity are necessary to update for economic
operation for minimizing interruption cost and to achieve optimal investment. Modified 5-bus 24-bus and
118-bus IEEE systems are taken to show the generalization of Methodology.
Index Terms— transmission expansion planning, generation planning, genetic algorithm, congestion
management, social welfare, linear matrices.
1. Introduction
During the last few decades, rapid changes in the electricity industry around the globe necessitate a robust
and optimal transmission infrastructure to supply electricity. The existing literature provides a wide variety of
TEP methodologies in the complex deregulated environment [1], [2], where, very few technical papers have
discussed composite TEP (generation and transmission planning are carrying simultaneously) [3], [4]. The
methodologies developed for TEP can be classified according to different domains such as (i) modeling, (ii)
optimization method, (iii) reliability, (iv) congestion management, (v) AC power planning, (vi) competition and
electricity market, (vii) uncertainty analysis, (viii) distributed generation (integration of wind farms and other
renewable generators), (ix) environmental impact (x) Coordinated TEP and composite TEP, and (xi) security
constrained TEP. A comprehensive review is presented in [1]-[10]. Some researchers have used above described
domains separately in TEP [1]-[9], however, rarely integrated -even at some extent- on a single platform [9]. In
this regard, a number of technical papers and reports have discussed the transmission system planning issue as a
set of optimization problems [1] – [8], [10]-[14], where variables are discrete, for example, capacity of
generators and lines, location of lines etc. [10]-[13]. Over the last two decades, numerous articles and books
1
Prof. Rajiv Shekhar (Corresponding Author) is with the department of Materials Science & Engineering, Indian Institute of Technology Kanpur, India.
Computationally Efficient Composite Transmission
Expansion Planning: A Pareto Optimal Approach
for Techno-Economic Solution
Neeraj Gupta, 1
Rajiv Shekhar, Prem K. Kalra
*Manuscript
Click here to view linked References

2
have been written on the development of search techniques for optimizing TEP, focusing on both traditional
(linear, quadratic programming, mix-integer, heuristic etc.) and non-traditional optimization techniques (GA,
swarm, meta-heuristic etc.) [1] – [13]. Using these techniques, TEP has, over the years, evolved from cost-based
to value-based approaches [9] – [14]. In the value-based approach, Min-cut-max-flow (MCMF) algorithm and
load flow based curtailment strategy have been used to calculate expected demand/ energy not served
(EDNS/EENS) [1], [3], [8], [12], as reliability measures. The iterative computational requirement of
EDNS/EENS forced planners to find a novel, simplified non-iterative approach [1], [12], [14]. An analytical
review of TEP models and reliability measures are given in [1], [15]. The TEP methodology given in [15]
demonstrates a new non-iterative EDNS/EENS calculation approach, which might be useful in the long term
TEP procedure with MCS based probabilistic contingency analysis. Here minimization of the sum of
investment, operational and interruption costs were carried out to determine optimal TEP [1] – [15]. Most of the
research papers in this regard have used deterministic N-1 contingency based TEP methodology, while very few
publications have reported work based on N-2 and MCS based contingency approach [1], [12], [15].
Developing countries such as India are going through a rapid change of industrial development process,
resulting in a large demand. India plans to install 74 GW generation capacity by 2017 [16]. Clearly, increase in
generation capacity has to be complemented with increased transmission capacity. Moreover, electric power
systems are getting more and more complex due to bottlenecks in transmission networks, primarily because of
uncertain demand growth and increased heterogeneity of power generation processes [1], [14]. The Central
Electricity Regulatory Commission (CERC) in India has estimated that 10.3% to 12.9 % power deficit is due to
unreliable transmission network [16], [17], which, in turn, may also increase the risk of blackouts Thus, a
robust and optimal transmission infrastructure to supply electricity reliably is of prime importance under smart
operation of the power industry. This, in turn, requires analysis of more severe contingency scenarios other
than N-1 contingency scenarios, especially in a country such as India where demand far outstrips supply [1],
[12], [14], [18]. Along with, it should attract the investors for a huge investment by giving them profit
maximizing signal [4], where loss should be minimum due to contingency and congestion in the network. This
E-mail: vidtan@iitk.ac.in and phone: (+91) (512) 259 7016.

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motivates us to propose a techno-economic computational efficient planning methodology (incorporating
demand and probabilistic outage of lines), which incorporates reliability evaluation modeling [7], [12], [13],
[19], congestion management criterion [12], uncertainty analysis, security of the systems, value assessment [12],
and market based approach [3], [16].
The TEP approach followed by previous investigations has several shortcomings [1]-[22]. First, the capacity
of all possible new alternative lines and generators were specified a priori (only locations have been selected
during the optimization process). Second, the calculation procedure of ENS (DNS) is iterative, thus expensive
to implement with probabilistic contingency analysis. Third, transmission service provider‘s and generator‘s
benefits are not incorporated simultaneous with customer‘s profit in the concept of social welfare, for example,
non-zero ENS also implies unutilized generation capacity or generation not served (GNS) and wheeling loss
(WL), the cost of which must be accounted for in TEP. Fourth, the computational efficiency of the algorithm
should be better to analyze sever probabilistic contingency scenarios along with N-1 contingency scenarios.
Fifth, the Techno-Economic planning criteria are rarely available for the composite planning of generators and
transmission network, which results excessive investment. Six, generally during the planning of the power
systems, reliability level is decided ―a priori‖ based on experts knowledge. Thereafter, simulation is carried out
to achieve least cost solution satisfying the decided reliability level. Selection of reliability level does not have
any analytical procedure, which may leads to sub-optimal solution. In the proposed methodology, well known
and globally accepted ―Marginal cost‖ based approach is demonstrated to trade-off reliability (least interruption
cost) and economics (least investment) [16].
Unfortunately, the proposed TEP in [12] is computationally-intensive. For a modified IEEE-5 bus power
system, it takes seven days (calculation is processed on Computer E-series (VPCEC15FG), 2.13 GHz, 4 GB
ram) to give an optimal solution for a case study incorporating 450 GA iterations with 30 population size,
twelve demand scenarios, and 1000 MCS contingency scenarios. A similar exercise for a 24-bus IEEE power
system takes more than 14 days. To make it computationally efficient, linear sensitivity factors have been
incorporated: (1) GPF (generation participation factor) to replace the iterative ELD calculation [23], (2) PTDF
(power transfer distribution factor) matrix to replace multiple DC-load flow calculations [24], (3) LODF (Line
outage distribution factor) and GLODF (generalized line outage distribution factor) matrix for transmission

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lines contingency analysis [25], and (4) BBIM (bus-branch incidence matrix) [16], [26] for the calculation of
ENS and GNS. The overall scheme is implemented on the modified IEEE-5 bus, IEEE-24 bus and IEEE-118
bus test power systems to show the generalization at large networks. Here, equation (8) is used (constrained by
equation (7)) to establish a better trade-off between economics and reliability [16]. The proposed methodology
finds an optimal solution by using the marginal cost (investment) theory [16].
2. Methodology
The proposed methodology has been implemented with the following assumptions:
a. Forecasted peak hourly load curve at all buses is defined to incorporate 8760 seasonal scenarios [16].
b. Single-stage planning of 10 years is demonstrated [12].
c. 8.5% compound load growth is selected for target year [12].
d. Probabilistic N-2 contingencies are incorporated along with N-1 contingency scenarios.
e. Location of generators and possible candidate alternative lines are pre-specified based on topological
conditions, expert knowledge and resource availability [16].
f. Old generators and transmission lines are free to update with new capacities, which are to be calculated by
the planning procedure.
g. Demand is assumed completely elastic and variation of 20% is permitted from mean value over the year
[16].
2.1 Objective Function
The objective function (J) includes sum of operational cost, interruption cost (cost of expected ENS, GNS,
WL, and outage cost of generation), and investment for setting up the new lines and generation capacities.
TN
T1,q q T,
rl,s s q 1
s g
(t) * (t) *
(t) *
8760 EENS EGNS
EWLt 1
Interruption cost w.r.t customer, generators, transmission owner
C *TL C2C *EGO (t)
J
C EENS(t) C EGNS(t)
C EWL(t) 


 
    
 


  
 
nN 8760
p T,p p p
p 1 t 1
g 8760
G,s G,s G.s s s
s 1 t 1
Investment and operating cost in setting up transmission lines
Investment and operating
*OCF *TL *F
C1 C2 *OCF EPG EG
 
 
 
  
 
 
    
 
cost in setting up generation capacity
 
 
 
 
 
 
 
 
 
 
(1)
Subscript T stands for transmission line and G stand for generator, where t is the time at which quantities are
measured. EENS, EGNS and EWL represents Expected Energy Not Served (MWh), Expected Generation Not

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Served (MW) capacity, and Expected Wheeling Loss (MWh), respectively. CEDNS, CEGNS, CEWL, Crl,s are the costs
of EDNS, EGNS, EWL, and revenue loss (rl) of sth
generator due to outage respectively, in units of k$/MWh.
Capital investment cost of qth
transmission line is CT1,q, and CT2 is annual operating and maintenance cost of line
(k$/MW/km). Length of the qth
transmission line (km) TLq. N is the number of transmission lines, where
subscript ‗T‘ belongs to total (updated existing + new) and ‗n‘ belongs to new transmission lines. EGOs(t) is the
expected outage of generator at bus s at time instant t due to force outage rate (FOR). C1 is capital cost of the
particular facility represented by subscripts. First subscript represents type of facility (‗T‘ or ‗G‘), where second
subscript stands for index of facility, i.e., C1T,q and C1G,s are respectively for transmission line (in k$/km) and
generator (in k$/MW). C2 is operating and maintenance cost of the particular facility represented by subscripts,
i.e., C2T,p and C2G,s are respectively for line (in k$/MWh/km) and generator (in k$/MWh, including fuel cost).
EPGs and EGs are proposed expected generation capacity of generator at bus-s calculated from simulation and
pre-speciﬁed capacity of generators at bus-s, respectively. Fp represents capacity of pth
transmission line (MW)
and OCFp=(1-FORp)/FORp is operating cost factor of qth
transmission line computed by forced outage rate
(FOR), based on climatic and geographical conditions. Minimization of fuel cost is reflected in ELD thus does
not included in J.
2.2 Constraints
TEP problem is dealt as constrained optimization problem, a list of equality and inequality constraints are:
0s sG D   (2)
*  fPTDF G T (3)
f (max) f f (min)T >T T (4)
 minG G (5)
RWR N (6)
0 1con,Np . (7)
MEC MI (8)
0 20baseD D * .  (9)
1ib (10)
Equation (2) represents supply-demand constraint, where, equation (3) is used for load flow calculation.
Equation (4) constrained the flow in transmission lines and equation (5) is used for operating generators above
minimum limit. Here, probabilistic RW simulation is used to mitigate congestion in the network (as discussed

6
in section 2.8), where number of total rotations of RW in one complete cycle (RRW) is defined by equation (6),
where N is the number of transmission lines – existing and proposed both - having a congestion probability
greater than 0.1, as shown by equation (7). Equation (8) provides techno-economic solution and establishes a
trade-off between reliability (interruption cost) and economics (investment) of the system. Instead of using
conventional economic load dispatch (ELD) iteratively for all demand scenarios, GPF matrix is used to
calculate optimal operating points of the generators, where change in all demand scenarios from base demand
follows equation (9). Equation (10) is used to remove infeasible chromosome formation in GA population,
where more than one bit in ith
chromosome (bi) should be 1.
2.3 GPF Calculation and Application
To eliminate the iterative computations of economic load dispatch (ELD), GPF model is used. In this
strategy, first the base optimal generation (Gs
base
) of all generators is calculated by ELD for based demand
scenario. Thereafter, other optimal operating points are calculated for the reasonably small changes in loads
(multiple demand scenarios) using GPF by    1/ / 1/s s j
j g
GPF c c

 
  
 
. Here, subscript s stand for bus, cs is the
cost coefficient associated with the quadratic term of the generator‘s cost function at bus s [23], [16] and j
belongs to all generators in the power system. The change in sth
generator‘s power ( sG ) subject to change in
system demand ( D ) is given by *s sG GPF D  . Steps for calculating ELD of generators for multiple demand
scenarios are:
1. GPF for all generators is calculated.
2. Out of all demand scenarios generated from load curves, first scenario is chosen as the base demand. For
this base demand ELD is run to get base
sG for all generators.
3. The base demand is subtracted from all remaining demand scenarios to obtain the change in demand ( D ).
4. Change in optimal power generation is calculated for remaining demand scenarios D .
5. Economic generation at all generator buses are defined without iteration by base
s s sG G G   .
From the simulation we observed that for 8760 demand scenarios, above describe algorithm reduces
computational time by approximately 67%, compare to ELD. Incorporation on PTDF matrix instead of DC-load

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flow procedures for multiple demand scenarios reduced 78% computational time. Many publications have
shown the importance of the PTDF matrix [16], [24].
2.4 GLODF Matrix Calculation and Application
The PTDF matrix approach is much faster than the DC- load flow approach; however, it is still unwieldy for
the outage study of large networks. Power system in Fig. 1 shows that for the outage of two transmission lines,
20 matrix elements of PTDF matrix need to be stored in the memory. In contrast, GLODF matrix requires only
10 matrix elements to be stored, and is therefore computationally efficient for large power systems. The details
of GLODF matrix have been given by Guo et al [25].
Fig. 1. Example of a 5-bus power system
Step by step calculation of power flow in transmission lines is given below:
1. Given base BBIM (considering all lines on-line), where rows represent buses and columns represents
transmission lines. It shows the relationship of buses with the nature of transmission lines (incoming or
outgoing). BBIM element has value 1 and -1, if lines are incoming to bus-s and outgoing from bus-s,
respectively. For unconnected line to bus-s BBIM element has value 0.
2. Consider multiple outages of transmission lines according to probabilistic contingency.
3. Diagonal reactance matrix for online transmission lines (XM) is formed, which has reactance of online
transmission lines on the diagonal.
4. Diagonal reactance matrix for contingent transmission lines (X0) is formed, which has reactance of
contingent (off-line) lines on the diagonal.

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5. Segregate the base case BBIM in two BBIMs ( and ), where BBIM  has number of columns associated
with contingent transmission lines and  has remaining columns associated with on-line transmission lines.
6. GLODF matrix is calculated as, here, E is identity matrix (dimension equal to the number of contingent
lines)
 
1
1 1 1 1
0   

   
 T T
MGLODF X B E X B (11)
7. Power flow in remaining (online) lines after outage of multiple transmission lines is calculated as:
 , , ,
      
     
post pre pre
f M f M f OT T GLODF T (12)
Here, ,
pre
f MT and ,
post
f MT are the pre- and post- contingency power flow in on-line transmission lines,
respectively. ,
pre
f OT is the pre-contingency power flow in contingent transmission lines. The above descried
approach is very efficient to calculate change in lines flow for 8760 demand scenarios.
2.5 Linear calculation approach for ENS, GNS and WL
Method presented in [9] to calculate ENS and GNS are explored here and derived as:
   , , , , , , , ,s f s i c s i f s j c s j
i cm j cn
Diff T T T T
 
      (13)
Here, cm is constrained in-coming lines and cn is constrained out-going lines at bus-s Diffs is the sum of
overflow in in-coming and out-going transmission lines and can have one of the three values given below:
: 0
: 0
0 :
s s
s s s
GNS if Diff
Diff ENS if Diff
Otherwise


 


(14)
We construct the vector Tover
to represent overflow in transmission lines, where the kth
element is defined as
, , , , , , , ,
, , , ,
:
0 :
f k s c k s f k s c k sover
k
f k s c k s
T T if T T
T
if T T
 
 

(15)
Tf,k,s = amount of power flow in kth
transmission line (either incoming or outgoing transmission lines to any
bus ‗s‘). Sum of the elements of vector Tover
represents WL for a particular demand scenario (this provides
monetary loss to transmission owner, which he realized due to the constraint in the network. He might make
some profit from this, if wheel on the network). For all buses, equation (13) can be represented in matrix form
[25] as
[Diff] = [BBIM][Tover
] (16)

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Diff is a matrix for multiple demand scenarios. After contingency of transmission lines BBIM is replaced with
 Using the above formulation to access reliability of power systems, ENS, GNS and WL calculation algorithm
for multiple demand scenarios is given in the steps outlined below. Here it is assumed that BBIM is given for
the network in normal operating scenario, and post contingency power flow in lines have been calculated for all
demand scenarios, using above models.
1. For the given multiple contingencies,  is calculated.
2. Power flow in transmission lines are calculated by GLODF matrix if there is no generator contingency,
otherwise GPF and reformed PTDF matrices are used.)
3. Tover
is calculated using equation (15).
4. The multiplication of the Tover
with  gives a matrix Diff shown by equation (16).
5. Apply equation (14) to form matrices GNSs
and ENSs
.
6. Sum of columns of GNSs
and ENSs
matrices represents the system GNS and ENS, respectively for each
demand scenario.
From the simulation results shown in [16], it is noted that the matrix model for calculating ENS and GNS does
not alter the output of the simulation presented in [12]; however it is computationally more efficient and save
approximately more than 85% comparative to linear optimization based load curtailment strategy (LCS). Since
for each load scenario LCS has to run multiple times for computing ENS, however, proposed algorithm
calculates ENS in a single step.
2.6 Contingency Analysis
Generally, N-1 contingency analysis is carried out under composite TEP methodologies [1], [21], [27].
Although, N-1 secured system is economic (less investment) but not reliable for more than single outage of
lines/generators, which are very frequent in highly developing countries like Indian and China. In these
countries demand growth is very uncertain with heterogeneity in generation process, which changes operating
scenarios frequently. This forces more stress on the transmission network and results in more than single outage
of lines frequently [17], [18], [27]. N-1 contingency secured power system resist for all single outage (off-
peak/peak time), but unable to maintain reliability under more than single contingency. Thus, in a highly

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deregulated power system, to maintain grid code efficiently against vulnerable operating scenarios, a highly
reliable network is of prime importance. Our proposed methodology is comparatively fast and thus N-1
contingencies are incorporated with critical (highly probable) N-2 contingencies. It must be pointed out
that higher contingency scenarios (N-3, N-4, Monte Carlo simulation) can be incorporated very easily in the
proposed methodology Process of finding a set of contingency scenarios (Z) for simulation is as follows:
1. Outage probability of all transmission lines is known.
2. All transmission lines are the elements of set {X} for N-1 contingency analysis.
3. Make a set of all combinations of two transmission lines {Y_2}.
4. Calculate outage probability of all elements in set {Y_2}, where each element is the combination of two
lines.
5. Rank the elements of set {Y_2}, in higher to lower outage probability sequence.
6. Calculate average outage probability of the set {Y_2}.
7. Select all elements of set {Y_2}, which are above than average outage probability to form a set {Y}.
8. All lines are removed from the set {X}, which are also included in the set {Y}. For example in Fig. 1, set for
single outage analysis of lines {X} = {TL 1, TL 2, TL 3, TL 4, TL5, TL 6, TL 7}. If we chose a set {Y} =
{(TL 1, TL 4), (TL 1, TL 6)} for severe N-2 contingency analysis. Then, new set {Xn} = {TL 2, TL 3, TL5,
TL 7}. Here three lines (TL 1, TL4 and TL 6) are removed from the set X.
9. Final contingency set {Z} is the union of set Y and Xn, Thus in upper example, {Z} = {(TL 1, TL 4), (TL 1,
TL5), TL 2, TL 3, TL5, TL 7}.
A similar procedure is used to generate severe probabilistic N-2 contingency scenarios for generators outage
analysis along with N-1 contingencies. Reliability of the reduced network (after each contingency scenario) is
checked for all demand scenarios by calculating EENS, EGNS and EWL. During the contingency analysis,
condition of islanding is taken care off, since system islanding may be the cause of ill-conditioned PTDF,
GLODF matrices. In this case, to simulate methodology properly, at least on transmission line is placed from
islanded bus to nearby grid connected bus. Thereafter, capacity of that line is defined by proposed methodology.

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2.7 Detection of Islanding after Contingency of Lines
In power systems operation islanding is always undesirable. Since Islanded system may suffer from deficit
generation or surplus of economic generators. This may lead to social loss by increasing electricity price.
Therefore, in this paper, Islanding is checked for each contingency scenario, and if islanding is realized by the
network an extra line is permitted to remove islanding. Isolation of demand or/and generator buses or a part of
power system from the power grid (islanding) is detected by an efficient method described by Sun et al. [26].
The incidence matrix (A) is used to compute islanding, where ai,j element will be ‗1‘ if line is connected
between ‗i‘ and ‗j‘ nodes, otherwise ‗0‘. In the matrix A, the sum of elements in a row gives the number of
connected transmission lines to the associated bus, which is called degree of bus (BD). A bus is ―islanded‖ from
the grid if it has zero BD. However, the problem is to identify islanding in the system when all buses have non-
zero BD. For that we use either the upper or lower triangular matrix (AU
or AL
) of A. Now consider AU
, where the
last row is removed (reduced AU
matrix). Here, we calculate the sum of ‗1‘s in each row (IL). A non-zero sum
signifies that the associated bus is connected to the grid. According to Fig. 1, for the outage of three lines (TL
4, 5 and 6), the resulting A and AU
matrices are given below.
1 2 3 4 5
1 0 1 1 0 0 2
2 1 0 1 0 0 2
3 1 1 0 0 0 2
4 0 0 0 0 1 1
5 0 0 0 1 0 1
Dbus B
A
  
 
   
  
 
 
   
The number of islanded regions can be defined as the addition of one to the number of zeros in IL vector.
Here, one zero in IL suggests the presence of two ―islands‖ in the power system the detailed analysis is shown
in [26]. Here, bus-1, bus-2 and bus-3 are in one island, while bus-4 and bus-5 are in other island.
2.8 Techno-Economic Solution Mechanism (A Pareto Approach) for Capacity Selection
Composite TEP design problem involves simultaneous solution of multiple conflicting objective functions [28],
[29]. The most common objectives which arise in power systems planning are to minimize the overall
investment (economics) and simultaneous maximization of the reliability of system (continuity of supply).
Tradeoff between two quantities are explained by Fig. 2, where a number of plausible solutions (points ‗A‘,

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‗B‘, ‗C‘ and ‗D‘) of a hypothetical composite TEP design are shown. Solution point ‗A‘ shows that the system
is economical (minimum investment), however less reliable (large interruption cost), on the other hand, solution
point ‗B‘ provides highly reliable system (least interruption cost) with high investment cost (uneconomical).
Both solution points are useful particular planner criterion according to developed and developing countries
(developed countries require more economic solution). Solution point ‗C‘ cannot be the choice of planner –not a
good solution (higher investment with less reliability). In multi-objective planning strategy these multiple
solutions form a pareto-optimal front (shown by long dashed line in Fig. 2), where any point may be the
solution. To achieve this strategy two level (bi-level) optimization procedure [27] is carried out. In first level,
GA generates a chromosome where each bit shows the location of candidate lines. In second level marginal
value of the investment is checked with respect to the marginal value of the interruption cost (measure of
reliability), and if both are equal pareto-optimal solution point is selected for the generated chromosomes. This
is achieved stochastically using roulette wheel simulation and congestion management strategy as described in
next section.
Fig. 2. A typical two conflicting objective problem in Power system planning (solution points A, B and D are
pareto-optimal optimal solution)
2.9 Roulette Wheel Simulation for congestion management
It can be noticed from the previous studies that the TEP for the given generation capacities is divided into two
sections. The first one concerns with the location selection of transmission lines, while the second is associated
with finding the appropriate capacities of selected transmission lines. Given generation plan cannot be optimal
or at this non-optimal plan new transmission lines for plan cannot be optimal. If we want to optimize overall
power system, generation planning should be simultaneously calculated along with TEP. Thus, third section of
the composite TEP belongs to optimal capacity of the generators.

13
First issue is resolved with the help of optimization procedures, assuming the capacity of the lines a priori.
But now, a more sophisticated approach to resolve both the issues have been introduced, namely, RW selection
based on stochastic approach. This procedure is prominently and effectively applied in genetic algorithm (GA)
optimization procedure [12] and adopted for composite TEP to manage the congestion stochastically. It
improves the planning efficiency and optimality and can be used with any optimization formulation (linear or
non-linear or meta-heuristic) and generalized for any size of the network. After calculating power flow in all
lines multiple times (equal to the number of operating scenarios) all congested transmission lines -- where
power flow is greater than their respective transmission capacities -- have value 1, while the un-congested lines
are assigned a value 0. Congestion probability of each transmission line is then computed. Now, an imaginary
RW [12], [16] is constructed where each transmission line in the network is represented by a separate segment
on the surface of RW. The area of each segment is proportional to the congestion probability of associated
congested line (RW is rotated N times). At the end of each rotation, the segment at which the pointer stops, and
the corresponding transmission line, is noted. After rotation of N times, capacity of all lines is updated
according to
o
N N N NF F m F   (17)
FN
0
is base capacity of the Nth
transmission line, mN is number of times out of N that the roulette pointer stops
at the segment corresponding to the Nth
transmission line, and NF represents value by which the transmission
capacity is increased in the Nth
transmission line. The updated capacity of the network has strong correlation
with the congestion probability, thus efficiently and optimally reduces congestion after each iteration of
network capacity assignment. It is important to ensure that the transmission capacities are not over-specified
because it would result in superfluous investment. Consequently, the process of capacity updating of a
transmission line is terminated, once the probability of congestion goes below 0.1. In every step, after the RW is
rotated N times, the marginal expected cost  1
/i i
EC EC FMEC 
   and marginal investment
 1
/i i
inv invT T FMI 
  are calculated, where  , , 1N i N iF F F    . ECi
and ECi-1
are expected cost in ith
iteration
and expected cost in (i-1)th
iteration, respectively. FN is updated network capacity of the network in one
complete simulation of RW selection and dFN is change in the capacity of the network. i
invT and 1i
invT 
are

14
transmission investment in ith
iteration and transmission investment in (i-1)th
iteration, respectively. Final
outcome of TEP is in fact subjected to the economies of scale i.e., if long-run marginal social cost is below or
equal to the long-run investment, TEP is appropriate. Thus, when MEC equals MI, an optimal solution has been
found where the total cost is minimized. This method provides a tuning mechanism for better Techno-economic
planning, where pareto optimal solution has been found.
2.10 Genetic Algorithm (GA)
GA is very well known optimization search method to solve complex power system planning problem, where
most of the design variables are discrete (binary). In TEP the states of transmission lines are represented as
binary variable, where 1 and 0 represent the active and inactive lines respectively. In GA every chromosome has
multiple bits, where each bit represents a particular transmission line and generator. The length of each
chromosome is equal to the number of bits which is the sum of number of new alternative transmission lines:
the candidates to be planned. Initial population is generated randomly keeping constraints like all bits in the
chromosome should not be 0. In this paper generated population has thirty chromosomes. From the second
iteration of GA, the population generation follows the law of natural selection which has sequential process
such as selection, reproduction, crossover and mutation as described in [16]. If the generated chromosomes are
similar in new population, then mutation with high mutation probability is carried out until all chromosomes get
different. This is required to avoid the multiplicity of the similar simulation. As a result, the new chromosomes
are available to compute associated fitness value to achieve optimal solution. The process of creating new
population is continued until one of the stopping criteria is satisfied, i.e., maximum number of iterations,
solution is achieved, does not change the value of objective function in consecutive 50 iterations. Two level (bi-
level) optimization procedures [27], [28] are used to find the global optimal solution. In level-I, GA is used to
generate candidate lines, where, capacity of the respective selected lines and generators are optimized in level-II
as shown in Fig. 3.
3. Proposed TEP algorithm
Proposed composite TEP methodology is described below and corresponding flow chart is shown in Fig. 3:
1. Initial population of chromosomes having the length equal to the set of proposed lines is generated. Each

15
chromosome satisfies criteria defined by equation (10).
2. Demand matrix (D) for 8760 demand scenarios are generated for target year and accordingly economic
power generation matrix G is calculated using GPF model. Both matrices will have 8760 columns and
number of demand and generation buses, respectively.
3. One chromosome from GA population is taken and base capacity (Fj
0
) of 25 MW is updated initially to all j
candidate lines and total investment in calculated.
4. Base PTDF, BBIM, GPF matrices, power flow in lines are calculated for all 8760 demand scenarios using
ELD (conventional model).
5. From the multiple contingency cases, one case is taken and thereafter lines and generators are removed
accordingly from the network.
6. If system is in islanding mode, connect one line from islanded bus to the nearby bus, connected to network
(to secure uninterrupted power supply).
7. Power flow (Tf) in all online transmission lines are calculated using PTDF, LODF and GPF matrices for
8760 demand scenarios and stored for further calculation, under three contingency cases
a) For no outage of generators (only lines outage), power flow in all online lines are calculated by GLODF.
Procedure is described above.
b) For outage of slack generator (replace the slack generator with the next higher capacity generator) and/ or
others generators (no outage of lines), calculate G for remaining generators using GPF and new PTDF
matrix. Calculated Tf in the network.
c) For the case where generator and line outage occurs are considered, step (b) is followed.
8. ENS, GNS and WL is calculated using equation (14)-(16) and values are stored.
9. Go to step 5 until last contingency scenario is taken.
10. EENS, EGNS and EWL and corresponding expected cost (EC) is calculated.
11. Marginal expected cost (MEC) and marginal investment (MI) are calculated, and If MEC is equal to MI,
then go to step 18.
12. The probability of congestion for each active line is calculated using stored data in step 7.
13. Imaginary RW is constructed. Active lines with pcon,j ≤ 0.1 are not considered to update

16
14. Capacities of the transmission lines are updated according to equation (17)
15. Impedance of the transmission lines are updated according to updated capacity
16. Expected generation is calculated from the data stored in step 7 for all 8760 demand scenarios and
contingency cases, and required optimal generation is calculated by  1.6* 3* ( )R
i i iG ERG std ERG  ,
incorporating 16% reserve margin. Here, ERGi is difference of expected and existing capacity of ith
generator and std is standard deviation of generation distribution to incorporate maximum uncertainty.
17. Investment in the updated lines and generators capacity is calculated and go to step 5.
18. Compute associated objective function by equation (1).
19. Go to step 3 until whole population is analyzed.
Fig.3 Flow chart of the proposed TEP methodology Fig.4. IEEE 24-bus power system
20. Genetic algorithm sequential process like selection, reproduction, crossover and mutation is applied to

17
generate new population of best candidate lines.
21. When stopping criteria met, GA is terminated and at this point optimum solution is found.
4. Case Study
The proposed methodology is first compared with the procedure described in [12]. For that both methodologies
are applied on the same network (modified 5-bus IEEE test power system, given in [12]), here, we have
observed that except computational time there is no change in the optimal solution. Methodology presented in
[12], has limitation to apply on large power systems for multiple contingency scenarios. Though, the presented
methodology is free from computational inefficiency, thus applied on 24-bus IEEE power system (Fig.4) and
118-bus IEEE Power system. We have also observed that without optimizing the capacity of generators,
transmission investment is high enough to give uneconomic solution (lead to over investment). Therefore, in
this paper, capacity of the proposed generators has been simulated for multiple transmission network plans. To
show the effect of generation planning simultaneously with TEP, simulations were carried out on the same
power system (modified 5-bus IEEE test power system), with similar operating scenarios as shown in [12]. In
modified 5-bus power system, pre-specified capacity of generation was 250 MW, 150 MW, 200 MW and 250
MW, respectively at bus 1, 2, 6 and 7, however calculated optimal value (using the proposed methodology) is
184 MW, 211 MW, 187 MW and 240 MW respectively. It shows that the specified generation capacities at
buses 1 and 2 vary significantly from the pre-specified generation capacities. On the other hand investment in
transmission network is minimized further. To show comparison, simulation is carried out first to set up new
lines where generation capacity is not optimized (denoted by WOG in Fig. 5). Thereafter, optimization of the
generation capacity has been achieved simultaneously with TEP (denoted by WG in Fig. 5). It is evident from
the results (shown in Fig. 5) that the generation planning along with TEP decreases the overall updated
transmission and generation capacities by more than 30 %, and thus the total investment. This strategy gives
appropriate signal to the generator‘s investors that under outage of lines they will be online always to play
efficiently in market, because capacity is calculated using step 16 (given in section 3). This planning strategy
increases the reliability of power network with decreasing investment.

18
Fig. 5. Comparison of TEP, without generation planning (WOG) and with generation planning (WG)
To show the applicability of the proposed methodology on a large power system, a 24 bus-IEEE power
system, is used. It has 10 generators (with 1800 MW total capacity) and 35 existing transmission lines,
capacities of which are given in Fig. 4. Here it is noted that only existing generators are planned to update with
new capacity for the total system forecasted demand of 4259 MW. Total number of new alternative lines (NTL)
is 82, shown in [16]. Due to its computational efficiency, the proposed TEP methodology is able to handle a
relatively higher number of critical N-2 contingency cases along with N-1 contingencies. Updated and new
transmission capacities are given in Table-I. Associate proposed economic generation capacity is shown in
Table-II. In the methodology to realize discrete values of the transmission lines step increment ( NF ) is taken
as 25 MW. Here, generator‘s optimal capacity is calculated based on ELD, thus, approximated to the nearby
standard value after simulation. Here, we can observe that 12 new lines have to be set-up with capacity update
of 18 existing lines comprising total capacity of 3650 MW. Here to follow economies of scale of the
transmission lines 50 MW lines are replaced by 75 MW capacities, where the total investment is $77.67m.
Required number of parallel transmissions lines are also shown in Table-I. These are constrained by the ROW
constraints; all existing transmission routes except TL 12, 20, 29, 31, 32 and 34 (can have maximum three
parallel lines) are constrained for only two parallel line, and new routes can have maximum three parallel lines.
Table-I
New lines and updated capacity of existing lines
Capacity # of proposed
parallel lines
Existin
g
Updated Total
TL 1 75 75 150 1*75
TL 3 75 50 125 1*75
TL 12 75 150 225 2*75
TL 14 100 100 200 1*100

19
TL 16 75 50 125 1*75
TL 17 75 75 150 1*75
TL 19 100 50 150 1*75
TL 20 75 150 225 2*75
TL 21 50 50 100 1*75
TL 23 100 100 200 1*100
TL 24 75 100 175 1*100
TL 28 50 100 150 1*100
TL 29 75 150 250 2*75
TL 31 100 200 300 2*100
TL 32 75 175 250 2*100
TL 33 100 75 175 1*75
TL 34 75 125 200 2*75
NTL (1-3) 0 100 100 1*100
NTL (1-8) 0 75 75 1*75
NTL (2-4) 0 150 150 2*75
NTL (3-9) 0 125 125 2*75
NTL (6-7) 0 125 125 2*75
NTL (7-8) 0 150 150 2*75
NTL (7-9) 0 100 100 1*100
NTL (13-16) 0 225 225 1*100+2*75
NTL (14-15) 0 225 225 1*100+2*75
NTL (15-19) 0 125 125 2*75
NTL (15-21) 0 100 100 1*100
Total updated network capacity 3650
TL (Existing Transmission Line), NTL (New Transmission Line)
Table-II
Required Expected Economically Optimal Capacity of the Generators in MW
Bus 1 2 7 13 15 16 18 21 22 23
Existing 150 150 200 250 100 250 250 200 150 350
Updated 400 350 400 550 350 450 375 425 400 450
Total 550 500 600 800 450 700 625 625 550 800
EMP ($) 7 8 7 7 7 6.5 7 7.2 7.8 7.3
EMP = Expected Marginal Price
The remaining expected cost in the system, comprising EENS (74 MWh), EGNS (81 MW), and EWL (88
MW) costs etc. is $37.33m. This condition is most economic condition which is calculated by step-10 of the
methodology. Total investment in the generators is $1767.62m. Methodology based on GA is generally
expensive but due to its advantageous features, it is accepted and here simulation took 11 hours approximately
on core i3 processor with 4 GB RAM in MATLAB environment (using MatPower [30]). Solution gives
approximately flatter than expected marginal price profile at buses (Table-II). Since methodology follows
congestion management and resulting system is efficiently secured for unseen contingencies without loss of
economic market.

20
The proposed methodology is also tested on an IEEE 118-bus power system, given in [16]. This system has
54 existing generators, 91 loads and 186 existing transmission lines. FOR, lines length, impedances and existing
capacity of each transmission line is given in [16]. Total existing capacity of the transmission network is 29,600
MW with 10,000 mile circuit length to meet the load of 4,827 MW and 8,090 MW generation. Generation has
enough excess capacity to meet the 8.5% compound load growth. Here, 10 new generators (NG) are proposed to
be planned at the buses (31, 46, 87, 90, 102, 103, 107, 110, and 118). Capital cost to update old and new
generators per MW capacity, outage cost and O&M cost is also given for each generator (existing and new) in
[16]. A total of 167 candidate alternative lines are available [16], from which 53 new lines, totalling 7875 MW,
are selected after simulation. To achieve optimal solution at pareto-optimal front, 24 existing transmission lines
((from bus-to bus) 8-5, 8-9, 9-10, 30-17, 26-25, 34-37, 55-56, 63-59, 60-61, 64-65, 68-116, 77-78, 80-97, 88-89,
94-100, 101-102, 110-111, 105-108, 104-105, 105-106, 89-90, 63-64, 24-70, 22-23) are required, also, to update
with 2900 MW capacity. Due to ROW constraints limit on lines capacity are 300 MW, however, most of the old
lines have reached the prescribed maximum limit. Simulation took 128 hours to give optimal results with the
same processor mentioned above. In the final solution, the remaining EENS, EGNS and EWL are 300 MW, 305
MW and 310 MW, respectively. The value of objective function is $770m with investment in transmission and
generation system is $230m and $400m, respectively. The total cost including cost of EENS, EGNS and EWL is
$140m. Proposed generation capacity of new 10 generators are 173, 100, 173, 258, 368, 173, 173, 182, 47, 173
MW respectively calculated for the security of system duringN-1 and N-2 critical contingencies. Some old
generators (thirteen) are required to update along with new generators to secure economic operation of the
power system during the contingencies, with 300, 275, 100, 104, 100, 165, 190, 197, 275, 355, 95, 76, 155 MW
capacity at buses 10, 26, 25, 49, 46, 55, 65, 66, 80, 89, 100, 113, 116, respectively. Here updating of existing
generators ensures the operational economics. Further noticed that the update of old transmission lines and
generation capacities along with new lines and generators achieve optimally economic solution with higher
reliability level. In this scheme marginal price of all generator buses are approximately flat due to use of
economic load dispatch strategy.
5. Conclusion
A new probabilistic composite TEP methodology which does not require a priori specification of generation

21
and transmission lines capacities has been presented. Proposed methodology gives perfect alignment between
generation planning and TEP. To speed-up the TEP methodology four linear matrices have been introduced in
this paper, i.e., GLOF, PTDF, GPF and BBIM to remove DC-load flow calculations for multiple demands and
changing network topology due to contingencies. Proposed methodology is validated with the results presented
in [12] on modified IEEE 5 bus network. It shows that updating the existing generators and lines are necessary
for economic operation of the power system. Also it reduces the involved investment in the network. Since a
matrix model of calculating ENS, GNS and WL are proposed which reduced computation time drastically.
Results of the proposed TEP methodology have also been shown on an IEEE 24-bus and IEEE 118-bus power
systems. Results shown conclude the generalization and practical importance of the methodology for the large
power systems planning. GA based method secure the nonlinear optimization for discrete variables and security
checked is done for N-1 and probable N-2 contingency cases. Case study has been shown that probabilistic
congestion based model flatter the price profile of all generator buses. Thus, an economic market can be
established. Here, we can observe several lower capacity transmission lines. In real situation, these lines may be
uneconomical due to difficulties in acquiring ROW(s) to construct new transmission lines, and the economies of
scale. Avoiding of low size transmission lines can be achieved by pruning the "smaller capacity" transmission
lines, which is described in detail in a forthcoming paper. To make the proposed methodology more realistic,
important aspect of power system e.g. congestion cost, re-dispatch cost [15], [16] and AC-load flow analysis
[22] needs to be included with multi-stage [10] composite TEP, which is the scope of further papers.
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