Security Constrained UCP with Operational and Power Flow Constraints

ACEEE International Journal on Electrical and Power Engineering, Vol. 1, No. 1, Jan 2010

Security Constrained UCP with Operational and
Power Flow Constraints
S. Prabhakar karthikeyan1, K.Palanisamy1, I. Jacob Raglend2 and D. P. Kothari3
1
S.Prabhakar Karthikeyan, & K.Palanisamy are with the School of Electrical Sciences, VIT University,
Vellore- 632014, INDIA. (e-mail:spk25in@yahoo.co.in , kpalanisamy79@yahoo.co.in )
2
I Jacob Raglend is with the Christian College of Engineering and Technology, Oddanchatram, Dindigul District,
Tamil Nadu, India. (e-mail: jacobraglend@rediffmail.com)
3
Dr .D.P.Kothari is currently Vice Chancellor, VIT University, Vellore-632014. INDIA, (e-mail: dpk0710@yahoo.com)

Abstract— An algorithm to solve security constrained unit bound method, lagrangian relaxation, interior point
commitment problem (UCP) with both operational and power optimization etc. are able to solve UCP with success in
flow constraints (PFC) have been proposed to plan a secure varying degree. Carlos E. Murillo-Sanchez and Robert J.
and economical hourly generation schedule. This proposed Thomas describe a parallel implementation of the
algorithm introduces an efficient unit commitment (UC)
approach with PFC that obtains the minimum system
Lagrangian relaxation algorithm with variable duplication
operating cost satisfying both unit and network constraints for the thermal UCP with AC power flow constraints [1].
when contingencies are included. In the proposed model N.P. Padhy made a comparative study for UCP using
repeated optimal power flow for the satisfactory unit hybrid models [2]. Finardi and Silva proposes a model for
combinations for every line removal under given study period solving the UCP of hydroelectric generating units [3]. Wei
has been carried out to obtain UC solutions with both unit and Fan, Xiaohong Guan and Qiaozhu Zhai proposed a new
network constraints. The system load demand patterns have method for scheduling units with ramping constraints [4].
been obtained for the test case systems taking into account of Xiaohong Guan, Sangang Guo and Qiaozhu Zhai
the hourly load variations at the load buses by adding discovered how to obtain feasible solution for the security
Gaussian random noises. In this paper, the proposed
algorithm has been applied to obtain UC solutions for IEEE
constrained unit commitment (SCUC) problems within the
30, 118 buses and Indian utility practical systems scheduled Lagrangian relaxation framework [5]. Qing Xia proposed
for 24 hours. The algorithm and simulation are carried the optimization problem of UC and economic dispatch
through Matlab software and the results obtained are quite with security constraints can be decomposed into two sub
encouraging. problems, one with integer variables and the other with
continuous variables [6]. Yong Fu, Mohammad
Index Terms—Unit commitment, Dynamic Programming, Shahidehpour and Zuyi Li proposes an efficient SCUC
Newton Raphson, Lagrangian multiplier, Economic dispatch, approach with ac constraints that obtains the minimum
optimal power flow, Contingency Analysis. system operating cost while maintaining the security of
I. INTRODUCTION power systems [7]. Bo Lu and Mohammad Shahidehpour
In power system operation and control, due to variations of consider network constraints in SCUC and decomposed the
load demand and non-storable nature of the electrical problem into master problem for optimizing UC and sub
energy, given the hourly load forecasting over a period of a problem for minimizing network violations [8]. Zuyi Li and
day or a week ahead, the system operators should schedule Mohammad Shahidehpour introduce a SCUC model with
the on/off status, as well as the real power outputs of the emphases on the simultaneous optimization of energy and
generating units to meet the forecasted demand over the ancillary services markets [9].
time horizon. The resultant UC schedule should minimize Dynamic programming is used to compute the minimum
the system production cost during the period while running cost for a given combination of units according to
simultaneously satisfying the load demand, spinning the enumeration technique for a given load [10-13]. The
reserve, ramp constraints and the operational constraints of review of unit commitment problem under regulated system
the individual unit. Scheduling the on and off times of the has been given in [15-16] and [17] gives the review of UCP
generating units and minimizing the cost for the hourly under deregulated market. In every hour all the possible
generation schedule is the economics to save great deal of combination of units that satisfies the unit and network
money by turning units off (decommiting) when they are constraints are checked by removing one line at a time and
not needed. By incorporating UC schedule, the electric proceed until all the lines are removed once. The state
utilities may save millions of Dollars per year in the which converges for optimal power flow for every line
production cost. The system security is still the most removal is stored and the best combination which gives
important aspect of power system operation and cannot be minimum production cost are selected and stored. Then
compromised. Various numerical optimization techniques proceed further until the UC schedule for the entire time
have been employed to approach the UC problem. horizon is obtained and the total production cost (TC) is
Traditional and conventional methodologies such as obtained and minimized respectively. In a power system,
exhaustive enumeration, priority listing, dynamic the objective is to find the real and reactive power
programming, integer and linear programming, branch and
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scheduling for each generating unit in such a way to MS it - Start-up maintenance cost at tth hour ($/h)
minimize TC. The UC schedule for the generating units
considering only the unit constraints may not satisfy the Similarly the start down cost SDit = kP Gi (4)
PFC and leads to insecure operation of the network. So to k is the proportional constant
obtain the practical UC solutions the model must consider Subject to the following constraints:
both the operational and PFC. For secure operation, the UC NG
schedule is obtained by including contingencies in the
network. Contingency analysis is performed by removing a
Equality Constraints- Power balance ∑P
i =1
Gi = PDt + PLt
line from the power system and checks for PF convergence, (5)
if it converges remove the next line and proceed until all Inequality Constraints: System spinning reserve constraint
the lines are removed once and select the state which NG
converges for every line removal. Repeated OPF for the
satisfactory unit combinations under given study period be ∑P
i =1
max
Gi I ≥ PDt + PRt
it

carried out to obtain UC solutions with unit and network (6)
constraints including contingencies. The results obtained Minimum up-time
using contingency analysis gives a secure UC schedule
because they are converged for OPF when any line from 0 < Tiu ≤ No. of hours units Gi has been on
the system is removed during the operation. This paper (7)
presents the UC schedule for different IEEE bus systems
and Indian utility practical system with power flow (PF) Minimum down-time
constraints and when contingency analysis are done on the 0 < Tid ≤ No. of hoursunits Gi has been off
system for 24 hours.
II. PROBLEM FORMULATION (8)
UC is an optimization problem of determining the schedule Maximum and minimum output limits on generators
of generating units within a power system with a number of PGi ≤ PGi ≤ PGi
min max

constraints. The objective of the UCP is the minimization (9)
of the TC for the commitment schedules is Ramp rate limits for unit generation changes
NG
PGit − PGi ( t −1) ≤ URi as generation increases
T
TC = ∑ ∑
i =1 t =1
FC it ( PGi ) + STit + SD it $ / hr
(10)
(1) PGi ( t −1) − PGit ≤ DRi as generation decreases
Where N G - Total number of generator units (11)
T - Total number of hours considered PDt , PRt , PLt - Demand, Spinning reserve, total system
FCit ( PGi ) - Fuel cost at ith hour ($/h) and represented by
losses at t th hour
an input/output (I/O) curve that is modelled with a
polynomial curve (Normally quadratic) Tiu , Tid - Minimum up-time and Minimum down-time in
FC it (PGi ) = α i + β i PGi + γ i P 2
Gi $ / hr hours
(2) URi , DRi - Ramp-up and Ramp-down rate limit of unit i
γ i , βi , αi are the cost coefficient of generator (MW/h)
Power Flow Equality Constraints:
PGi - Real Power generated by the ith generator. Power balance equations
Nb
( )
− −
STit , SDit - Start-up cost and start down cost at tth hour
($/h)
PGi − PLi − ∑V
j =1
i V j Yij cos θ ij − δ i + δ j = 0

The start up (12)
STit = TS it Fit + (1 − e ( Dti ASit ) BS it Fit + MS it Nb
( )
− −
(3) QGi − Q Li + ∑j =1
Vi V j Yij sin θ ij − δ i + δ j = 0
th
TS it - Turbines start-up energy at i hour (MBTu)
(13)
Fit - Fuel input to the ith generator Power Flow Inequality Constraints:
Dit - Number of hours down at tth hour PGi ≤ PGi ≤ PGi , i = 1,........, N G
min max

(14)
AS it - Boiler cool-down coefficient at tth hour
Q Gi ≤ Q Gi ≤ Q Gi , i = 1,........, N G
min max

BS it - Boiler start-up energy at tth hour ($/h) (15)

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− min − − max

V i ≤ V i ≤ V i , i = 1 ,........, N L
solution, the voltage magnitude and phase angle of all
buses are determined. The total transmission power loss
(16)
including Bmn is given by
φ imin ≤ φ i ≤ φ imax
NG NG NG
PL = ∑∑ Pi Bij Pj + ∑ B0i Pi + B00
(17)
MVA f ij ≤ MVA f ijmax , i = 1,......... , N TL
i =1 j =1 i =1
(18) (19)
Nb , NG - Number of total buses, number of generator c. After getting the loss coefficient perform economic
buses dispatch i.e., the power generated in each ‘ON’ generator
unit using Lagrangian multiplier method.
N L , N TL - Number of load buses, number of transmission
d. Read the total demand, cost characteristics and MW
lines limits along with loss co-efficients. The condition for
min max
PGi , PGi - Limits of real power allowed at generator i. optimum dispatch
min max dC i ∂ PL (20)
QGi , QGi - Limits of reactive power allowed at + λ = λ , i = 1K N G
dP Gi ∂ P Gi
generator i. N G (21)
PGi , QGi - Real and reactive power generation at bus i ∑ P Gi = P Dt + P Lt
i=1

PLi , QLi - Active and reactive power loss at bus i Equation 19 can be written as
⎛ ⎞
⎜ ⎟ (22)
Vi , δ i - Voltage magnitude, Voltage angle at bus i ⎜ 1 ⎟ dC i = λ, i = 1, K , N
⎜ ∂ PL ⎟ dP G
Yij - ijth elements of Y-bus matrix ⎜1 − ⎟ Gi
⎝ ∂ P Gi ⎠
MVA f ij - Apparent power flow from bus i to bus j dC i (23)
Li = λ, i = 1, K , N G
max dP Gi
MVA f ij - Maximum rating of transmission line
where Li is the penalty factor of plant.
connecting bus i and j.
III. Implementation of contingency analysis based UCP f. For an estimated value of λ, PGi are found from the cost
with operational and power flow constraints quadratic function.
⎛ (k ) ( ⎞
1. Initialize the unit characteristics for the N unit system ⎜ λ (1 − B 0 i ) − β i − 2 λ ( k ) ∑ B ij P Gjk ) ⎟
with system constraints. ⎜ ⎟
P Gik )
(
= ⎝ ⎠
j≠i

2. Find all the available states that satisfy the load (k )
2 γ i + λ B ii ( )
demand for 24 hours. Each state corresponds to the “ON” (24)
and “OFF” conditions of the generator units and (k )
ΔP (25)
represented as 1 and 0. Δ λ (k ) = (k )
⎛ dP Gi ⎞
3. Calculate the transitional generation cost for the states
satisfying the system constraints along with contingencies
∑ ⎜
⎝ dλ ⎠
⎟

on their transit from the present stage to the succeeding
stage with the help of following steps: λ(k +1) = λ(k ) + Δλ(k )
For each satisfying state perform contingency analysis by NG
removing one line from the system and carry out the Δ P (k ) = PDt + PLtk ) −
(
∑ PGik )
(
optimal power flow solution using a hybrid Lagrangian i =1
multiplier and Newton Raphson power flow algorithms. g. Check the slack bus power generated from the cost
Perform contingency analysis for each satisfying state quadratic function and the slack bus power obtained from
repeatedly until all the lines are removed once except the the power flow solution.
lines which are connected only either to the load bus or h. If they lie with in a tolerance limit say 0.001, do the
generator bus and carry out optimal power flow for every load flow with the PGi obtained from the economic
contingency for that state. Prepare the data base for the dispatch and determine the generation cost using the
system including line data, bus data, generator data and tap cost characteristic equation
setting of the transformers.
a. Form Ybus using line resistance, reactance, and shunt
C i = α i + β i PGi + γ i PGi
2
(28)
elements [14]. If they are not with in the tolerance limit, then with the
Obtain the power flow solution for the states got from power generation obtained from economic dispatch using
step 2 using Newton-Raphson method for power flow cost quadratic equation is given as the P specified in the
subject to the power-flow equations. load flow analysis for the next iteration. Once again the
b. Calculate the Bmn loss coefficients using V and losses can be obtained from the new power flow solution
and repeat the economic dispatch.
δ obtained from the PF solution. From the power flow
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Start that hour. Repeat the above steps for 24 hours with the
generated load profile and tabulate all the transitional cost
of the satisfying states for each stage.
Read the unit characteristics of the N unit system, line, bus and
generator data and load profile for 24 hours
k. Choose the state with minimum transitional cost for
each stage that satisfies the unit constraints. Calculate TC
by the summation of all the minimum transitional cost
Find all the possible states that satisfy load demand and obtained between each stage and print the results. The flow
spinning reserve for every hour
chart for this algorithm has been given in Figure 1.

For each satisfying state perform contingency analysis by IV. SIMULATION AND RESULTS
removing a line and perform OPF along with ED. If it
converges repeat until contingencies are checked in every
Three case studies consisting of an IEEE 30, 118 bus
line and select that state. systems and Indian utility 75 bus system have been
considered to illustrate the performance of UC schedule
with contingency analysis in the network. The UC schedule
For that state without any contingencies perform OPF using obtained considering contingency analysis is very realistic
Newton Raphson method as it has the capability to withstand when contingency
exists in a particular line. The contingency analysis is not
performed on the lines which are completely dedicated for
Check MVA limits violation and calculate Bmn loss co-
generating and supplying the loads. The unit combination
efficients which satisfies the load demand and spinning reserve are
allowed to perform OPF for every contingency and the unit
combination for which OPF converges for every line
Perform Economic dispatch using Lagrangian multiplier
removal is selected. For that unit combination OPF is
method.
performed without considering any contingencies and store
the dispatch and transitional cost. The commitment
schedules and the transitional cost at each stage with
contingency analysis, with and without power flow
If slack bus power obtained
from ED and NR method ≤
constraints (PFC) for the above case studies have been
tolerance tabulated from Table 1 to 3. Loads at different buses are
assumed to be variable and have been generated using
No Gaussian random noise function for the twenty four hours
Yes during power flow simulations because in practice the loads
do not vary uniformly.
Store the generation cost, state, dispatch for checking
ramp constraints for all the possible states for every hour Case a. IEEE 30 bus system
The IEEE 30 bus system has six generating units and the
characteristics of generators, unit constraints and the hourly
Choose the minimum generation cost for every hour, state load distribution over the 24 hour horizon. The network
which satisfies minimum up and down time, ramp topology and the test data for the IEEE 30 bus system are
constraint. Add shut down, start up, cold and hot start cost
if necessary given in http:// www.ee.washington.edu/research/pstca. For
every hour, all the possible combinations that satisfy the
load demand and spinning reserve constraints are selected
Sum all the transitional cost from each hour and display and these states are allowed to perform OPF for all the
the results with state, dispatch, transitional cost, total possible contingencies that can happen in that network. If
minimum generation cost the state converges for OPF for every line removal, then
select that state and perform OPF without any
End contingencies and store that state. Similarly all the states
that satisfy OPF for every contingency in the system and
Figure1 Flow chart for the proposed algorithm
demand on that hour are stored. This procedure has to
continue for the specified time horizon. Select the state that
possess minimum cost and satisfies the unit constraints for
The state which converges for power flow when all the the entire time horizon. Finally the complete unit
lines are removed once from the system is selected. For that commitment schedule with minimum TC has been
state perform power flow and economic dispatch without obtained. The TC obtained by considering contingency in
any contingencies in the system and store the transitional the network are 916.2 $/day more than the generation cost
cost. obtained without PFC and 512.5 $/day more than the
j. The same procedure is followed for all the states that generation cost obtained with PFC. UC schedule without
satisfy the load demand and spinning reserve constraints for PFC and performing contingency analysis may not be
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practical, since the states must include the system network 1.4
x 10
4

losses and also converge for optimal power flow. This is Transitional cost without PF
Transitional cost with PF
the reason for the cost being minimum when power flow 1.3 Transitional cost with CA

constraints and contingency analysis are not considered. 1.2
The transitional generation cost for every hour have been

T rans itional Cos t in $/hr
compared and plotted with CA, with and without PFC in 1.1

Figure 2. 1

1000
Transitional cost without PF 0.9
Transitional cost with PF
900 Transitional cost with CA
0.8
800
Transitional Cos t in $/hr

0.7
0 5 10 15 20 25
700
Time in Hours

600 Figure 3. Transitional cost for IEEE 118 bus

500

400

300

200
0 5 10 15 20 25
Time in Hours

Figure 2. Transitional cost for IEEE 30 bus

Table 1. IEEE 30 bus UC schedule
Period Load UC without PFC Trans cost UC with PFC Trans Cost Security Constrained UC Trans cost
1 166 101101 492.3680 101101 506.0666 101101 506.5560
2 196 101101 514.4198 101101 535.2034 101101 536.4296
3 229 101101 623.0319 111101 799.0942 101111 828.0507
4 267 111101 898.2148 111001 838.9670 111110 961.8205
5 283.4 111101 766.8436 111011 987.8135 111110 804.9445
6 272 111101 728.0110 111011 765.0130 111110 762.8829
7 246 111101 642.2775 111011 670.6727 111110 669.4243
8 213 111101 539.1919 111011 558.4164 111110 557.2563
9 192 111101 476.9293 111011 491.5142 111100 542.7611
10 161 110101 432.1891 111011 398.9967 111000 479.9059
11 147 110101 363.5154 111011 359.6488 110000 404.7152
12 160 110101 399.3866 111011 396.1338 110000 415.5276
13 170 110101 427.6901 111011 425.1014 110000 447.9513
14 185 110100 497.5949 111011 469.9788 110000 498.2986
15 208 110100 538.8728 111011 542.1670 110000 579.6063
16 232 110100 616.7335 111011 621.9727 111000 748.7215
17 246 110100 663.7953 111011 670.6739 111001 791.2400
18 241 111100 738.3682 111011 653.0992 111001 659.6339

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19 236 111100 609.1311 111011 635.7233 111001 641.7818
20 225 111100 573.9276 111011 598.2173 111001 602.9092
21 204 111100 508.6984 111011 529.3179 111001 531.0425
22 182 111000 524.2561 111011 460.8624 111001 460.6676
23 161 111000 378.1085 111011 398.9961 111001 397.0433
24 131 111000 295.4216 111010 338.9695 111000 335.9958
Total Minimum cost in $ / day 13248.9 13652.6 14165.1

Table 2. IEEE 118 bus UC schedule
Trans Trans Security Constrained
Period Load UC without PFC UC with PFC Trans
cost cost UC cost
1 3170 1111101111111101100 8026.0 1111101011111111101 10820 1111101011111111110 10833
2 3200 1111101111111101100 7978.8 1111101011111111101 10839 1111101011111111110 10809
3 3250 1111101111111101100 8134.8 1111101011111111101 11062 1111101011111111110 11043
4 3300 1111101011111101100 8334.4 1111101011111101100 12070 1111101011111111110 12226
5 3460 1111101011111101100 8791.1 1111101011111101100 12367 1111101011111111110 12578
6 3640 1111101011111101100 9400.9 1111101011111101100 12890 1111001011111101110 13092
7 3686 1111001011111101100 9595.8 1111001011111101110 13319 1111001011111101110 13154
8 3640 1111001011111101100 9386.8 1111001011111101110 13010 1111001011111101110 13010
9 3560 1111001011111101100 9116.9 1111001011111101110 12775 1111001011111101110 12775
10 3440 1111001011111101100 8719.5 1111001011111101100 12307 1111001011111111110 12603
11 3250 1111001011111111100 8229.8 1111101011111111110 11449 1111101011111111110 11223
12 3200 1111001011111111100 7960.6 1111101011111111110 10809 1111101011111111110 10809
13 3175 1111001011111111110 8016.6 1111101011111111110 10707 1111101011111111110 10707
14 3210 1111001011111111110 8012.0 1111101011111111110 10850 1111101011111111110 10850
15 3420 1111001011111101110 8703.8 1111101011111101100 12326 1111101011111111110 12483
16 3620 1111001011111101110 9337.9 1111101011111101100 12827 1111101011111101110 13013
17 3620 1111001011111101110 9337.9 1111101011111101100 12827 1111101011111101110 12983
18 3580 1111001011111111100 9333.2 1111101011111101100 12702 1111001011111111110 13024
19 3460 1111001011111111100 8791.4 1111101011111101100 12367 1111001011111111110 12539
20 3270 1111001011111111100 8179.7 1111001011111111111 11483 1111001011111111111 11205
21 3210 1111001011111111100 7991.7 1111001011111101111 10796 1111001011111101111 10796
22 3153 1111001011111101100 7813.8 1111101011111101110 10855 1111101011111101110 10855
23 3148 1111001011111101110 7927.0 1111101011111101110 10608 1111101011111101110 10608
24 3166 1111001011111101110 7869.3 1111101011111101110 10673 1111101011111101110 10673
Total Minimum cost in $ / day 204989.5 282737.1 283889.1

Case b. IEEE 118 bus system.

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The proposed algorithm has been applied to IEEE 118 bus more than the generation cost obtained without power flow
with 19 generating units. The network topology and the test constraints and 1152 $/day more than the generation cost
data for the IEEE 118 bus system has been taken from obtained with power flow constraints. The transitional
http://www.ee.washington.edu/research/pstca.UC schedules generation cost for every hour have been compared and
for an IEEE 118 bus with CA, with and without PFC are plotted with CA, with and without power flow constraints
given in Table 2. The total generation cost obtained by are given in Figure 3.
considering contingency in the network are 78899.6 $/day
Table 3. UP 75 bus UC schedule
Period Load UC without PFC Trans UC with PFC Trans Cost UC with CA Trans cost
cost
1 3352 111110111111111 3845.1 111110111111111 4090.9 111111111101111 4113.1
2 3384 111110111101111 3918.0 111110111101111 4170.1 111111111101111 4117.4
3 3437 111110111101111 3954.3 111110111101111 4213.9 111111110101111 4296.1
4 3489 111110011101111 4091.7 111110011101111 4355.5 111111110101111 4376.8
5 3659 111110011101111 4332.9 111110011101111 4626.5 111111110001111 4772.5
6 3849 111110011101111 4669.0 111111011101111 5072.8 111111110011111 5217.8
7 3898.1 111110011101111 4755.6 111111011111111 5225.6 111111110011111 5131.7
8 3849 111110011101111 4669.0 111111011111111 4954.0 111111110011111 5037.8
9 3764 111110011101111 4517.3 111111011111111 4808.3 111111111011111 4935.0
10 3637 111100011101111 4351.6 111111011111111 4565.6 111111111011111 4575.7
11 3437 111100011101111 3956.2 111111011101111 4264.1 111111111111111 4476.6
12 3384 111100001101111 3925.2 111111011101111 4116.7 111111111101111 4169.4
13 3357 111100001101111 3820.1 111111011101111 4069.2 111111111101111 4069.9
14 3394 111100001101111 3882.0 111111011101111 4136.1 111111110101111 4219.4
15 3616 111100001101111 4264.0 111111001101111 4606.0 111111110101111 4595.1
16 3828 111100001101111 4638.6 111111001111111 5098.4 111111110101111 4997.5
17 3828 111100001101111 4638.6 111111001111111 4918.4 111111110101111 4997.5
18 3786 111101001101111 4677.7 111110001111111 4874.8 111111110101111 4917.0
19 3659 111101001101111 4337.8 111110001111111 4609.9 111111110001111 4772.5
20 3458 111100001101111 4020.1 111110001111111 4248.0 111111110001111 4316.6
21 3394 111100001101111 3882.0 111110001111111 4134.5 111111110001111 4199.6
22 3334 111100001001111 3864.4 111111001111111 4141.0 111111110001111 4090.7
23 3329 111100001001111 3771.1 111111001111111 4019.2 111111111001111 4139.1
24 3348 111100001001111 3802.8 111110001111111 4084.0 111111111001111 4059.4
Total Minimum cost 100584.8 $/day 107403.5$/day 108594.4$/day

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52 48 49

70 72 G
G G G G 11
6 7 3
5
51 40

69
5400
32 31 33 18 64 Transitional cost without PF
71 68 37 5200 Transitional cost with PF
27 66 20
62 39 60 Transitional cost with CA
25
19

61
38 22
5000
G 36
59 58
G 1

Transitional Cost in $/hr
26
14
17
4800
57
43
53
29
G
G 23 46
2
4600
8 G 9
75

G G 74 16
4
34
10
35
4400

28 54
30
56
G 4200
24 12

65
67 41 50
G
13
4000
47
21 63

42 3800
55

G
15 3600
45 73
0 5 10 15 20 25
44
Time in Hours

Figure 4. One line diagram of Indian utility system Figure 5. Transitional Cost of Indian Utility System

Case c. Indian Utility (Uttar Pradesh State) 75 bus system commitment schedule obtained by incorporating both
The 75-bus Uttar Pradesh State Electricity Board (UPSEB) network and unit constraints, also with the commitment
Indian Utility system with fifteen generating units is shown schedule obtained without incorporating network
in Figure 4. The data in per unit (p.u) is on 100 MVA base. constraints. Since exhaustive enumeration technique is
UC schedules for the 75 bus system with CA, with and used, it guarantees the optimality of the solution. The
without power flow constraint are given in Table 3. The effectiveness of this method has been demonstrated on an
total generation cost obtained by considering contingency IEEE 30, 118 buses and on Indian utility system and may
in the network are 8009.6 $/day more than the generation also be extended to large systems. The results achieved are
cost obtained without PFC and 1190.9 $/day more than the quite encouraging and indicate the viability of the proposed
generation cost obtained with PFC. The solution results in technique to deal with future UC problems.
this study indicate that the proposed algorithm is applicable VI. REFERENCES
to the day-ahead UC calculation of large scale power [1]. Carlos E. Murillo-Sanchez, Robert J. Thomas, “Parallel
systems. The transitional generation cost for every hour Processing Implementation of the Unit Commitment Problem with
have been compared and plotted with CA, with and without Full AC Power Flow Constraints”, Proceedings of the 33rd Hawaii
International Conference on System Sciences, 2000.
power flow constraints are given in Figure 5. The platform [2]. N. P. Padhy, “Unit Commitment using Hybrid Models, A
used for the implementation of this proposed approach is on Comparative Study for Dynamic Programming, Expert systems,
INTEL[R], Pentium [R] 4 CPU 1.8 GHz, 256 MB of RAM Fuzzy Systems and Genetic Algorithm”, Electric Power and
and simulated in the MATLAB environment. The solution Energy System, vol. 23, pp. 827-836, 2000.
results in this study indicate that the proposed algorithm is [3]. E. C. Finardi, E. L. da Silva, “Unit Commitment of Single
applicable to the day-ahead UC calculation of large scale Hydroelectric Plant”, Electric Power System Research, vol. 75,
power systems. pp. 116-123, 2005.
[4]. Wei Fan, Xiao Hong Guan, Qiaozhu Zhai, “A New Method
for unit Commitment with Ramping Constraints”, Electric Power
System Research, vol. 62, pp. 215-224, 2002.
V. CONCLUSION [5]. Xiao Hong Guan, Sangang Guo, Qiaozhu Zhai, “The
This paper presents an approach to solve security Conditions for Obtaining Feasible Solutions to Security
constrained UCP by accommodating both unit and network Constrained Unit Commitment Problems”, IEEE Trans. On Power
constraints. This algorithm would give realistic results as Systems, vol. 20, no. 4, pp. 1746-1756, Nov. 2005.
the entire unit and network constraints are included. The [6]. Qing Xia, Y. H. Song, Boming Zhang, Chongqing Kang,
commitment schedule holds well even if there is any Niande Xiang, “Effective Decomposition and Co-ordination
contingency in any of the lines in the network as the Algorithms for Unit Commitment and Economic Dispatch with
Security Constraints”, Electric Power System Research, vol. 53,
selected unit combination has been converged for OPF for
pp. 39-45, 2000.
every contingency occurred in the system. The security
constrained UC schedule has been compared with the

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© 2010 ACEEE
DOI: 01.ijepe.01.01.03


[7]. Yong Fu, Mohammad Shahidehpour, “Security Constrained [12] D.P.Kothari and I.J.Nagrath, “Modern Power System
Unit Commitment with AC Constraints,” IEEE Trans. On Power Analysis”, 3rd Edition, McGraw Hill, New York, 2008.
Systems, vol. 20, no. 2, pp. 1001-1013, May 2005. [13]D.P.Kothari and J.S.Dhillon, “Power System Optimization”,
[8]. Bo Lu, Mohammad Shahidehpour, “Unit Commitment with Prentice Hall of India Pvt. Ltd., Second Edition, New Delhi, 2005.
Flexible Generating Units”, IEEE Trans. On Power Systems, vol. [14]. Hadi Sadat, “Power System Analysis”, Tata McGraw-Hill
20, no. 2, pp. 1022-1034, May 2005. Publishing Company Limited, 2002.
[9]. Zuyi Li, Mohammad Shahidehpour, “Security Constrained [15] N.P.Padhy, (2004). Unit Commitment- A Bibliographical
Unit Commitment for Simultaneous Clearing of Energy and Survey, IEEE Trans. On Power Systems, vol. 19, no. 2, pp. 1196-
Ancillary Services Markets”, IEEE Trans. On Power Systems, vol. 1205.
20, no. 2, pp. 1079-1088, May 2005. [16] Subir Sen and D. P Kothari, “Optimal Thermal Generating
[10]. N.P.Padhy, “Unit Commitment- A Bibliographical Survey”, Unit Commitment: A Review”, International Journal on Electric
IEEE Trans. On Power Systems, vol. 19, no. 2, pp. 1196-1205, Power and Energy Systems, Vol. 20, No 7, pp 443-451, 1998.
May 2004. [17] Narayana Prasad Padhy, “Unit Commitment Problem under
[11]D.P.Kothari and I.J.Nagrath, “Power System Engineering”, Deregulated Environment-A Review”, Proceedings of IEEE
Tata McGraw Hill, Second Edition, New Delhi, 2007. Power Engg. Soc. General Meeting, 2003.

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© 2010 ACEEE
DOI: 01.ijepe.01.01.03

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