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Placement of UPFC for Minimizing Active Power Loss and Total Cost Function by PSO Algorithm Arup Ratan Bhowmik
Ajoy Kumar Chakraborty, P.N.Das
Dept. of Electrical Engineering National Institute Of Technology, Agartala Tripura, India
[email protected]
Keywords— Flexible AC Transmission Systems (FACTS); Line Loss Sensitivity Index; Active Power Loss Minimization; Cost Function Minimization; PSO; UPFC.
I.
INTRODUCTION
Present electric power system network undergoes surprising fast changes in terms of demand/generation arrays and trading actions that hinder the system operation as well as security. In that context, FACTS controllers could be an appropriate alternative to redirect power flows through the lines and can afford strategic profit for transmission system management through better service of existing transmission facilities by increasing system reliability and stability [1]. Though FACTS devices endorse many advantages, their installation price is very high. Therefore, to confirm the full potential of application for maintaining the stability and reliability of existing system, optimal placement of these controllers must be ascertained. For the last few years, among all FACTS devices, interests in UPFC have risen amongst researchers as it offers significant flexibility by controlling voltage magnitude, phase angle and impedance simultaneously. On the other hand, it can also control the real and reactive power flow in the line [2]. Several researches were made on the optimal placement of UPFC in different power system network by considering different criteria [2] [3] [4]. A sensitivity index based approach was proposed for the suitable placement of Thyristor Controlled Series Capacitor (TCSC) and UPFC to enhance the power system loadability [5]. Saravanan et al. [6] used PSO technique for finding the optimal allocation of TCSC, SVC and
,(((
UPFC to attain utmost system loadability with least cost of installation. Singh et al. [7] suggested sensitivity based approach for the suitable locations of UPFC to increase power system loadability. Majumder et al. [8] proposed minimization of power losses using FACTS devices with Modified Simulated Annealing and PSO techniques. M. Kowsalya et al. [9] proposed particle swarm optimization to find the global optimum solution for the loss minimization by optimally placed UPFC in the power system network. In this paper, PSO technique has been applied to find out the optimal site selection of UPFC for better operation of the power system network in terms of line loss sensitivity factors and to attain minimum active power loss and total generation cost while satisfying all other power system constraints. The approach has been applied and tested under simulated condition on modified IEEE 14-bus system. II.
MODELING OF UPFC FOR OPTIMAL PLACEMENT
The UPFC is used for the static and dynamic compensation of ac transmission systems. It consists of two voltage source converters (VSCs) as shown in fig. 1. These back-to-back converters, labelled ‘converter 1’ and ‘converter 2’ in the figure, share a common dc link including a dc storage capacitor. The real power exchanged at the ac terminal is transformed into dc power which appears at the dc link [2]. Series transformer
Transmission line I T+ Iq Shunt Transformer
Abstract—In this paper Particle Swarm Optimization (PSO) technique has been used to minimize the active power loss and the total cost function, which includes the generation costs and the UPFC investment cost, through optimally placing the Unified Power Flow Controller (UPFC) in the power system network. Three objective functions are taken as the indexes of the system performance; identification of most suitable buses using line loss sensitivity index, minimization of active power loss and total generation cost by employing PSO. For the validation and comparison purposes of the proposed techniques, simulations are carried out on modified IEEE 14-bus power system. Results validate that the static performances of the power system can be successfully improved due to the optimal allocation of single UPFC controller.
Dept. of Electrical Engineering National Institute Of Technology, Agartala Tripura, India
[email protected],
[email protected]
I DC link Converter 1
Converter 2
Fig. 1. Basic Circuit arrangement of UPFC
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The basic responsibility of converter 1 is to provide or absorb the real power demanded by converter 2 at the common dc link. This dc link power demand of converter 2 is transformed back to ac by converter 1 and coupled to the transmission line through a shunt transformer. The basic scheme of the UPFC is shown in fig.2.
k
k
k
g ij +jbij =
1 . rij +jx ij
Bus j
V T< ĭ T
k
Where C1 , C 2 are the real power and C3 , C 4 are the reactive power loading sensitivity respectively, Where
III.
PROBLEM FORMULATION
The Active Power Loss minimization problem may be formulated as follows:
rij + j x ij
Bus i
Objective I: Minimize U(x);
IT + j Iq jB/2
Subject to V(x) = 0; and P(x) < 0; where, jB/2
UPFC
Where U(x) is a function of the sum of branch losses, V(x) is the functional equality constraints, P(x) is functional inequality constraints and the limits of the control variables, x is the state variable vector, xi and xu are the lower and upper limits of variable x respectively.
Fig. 2. Equivalent Circuit of UPFC
The real and reactive power with the system loading (Ȝ) is determined by the following equation [7],
¦P .
Pi = PGi − PDi0 (1 + λ ) =
Two objective functions are used in this topic. They can be written as follows-
(1)
ij
xi < x < xu
u1 ( x) = PL .
j∈Nb
(7)
Where PL= sum of line active power losses in the system. 0 Qi = QGi − QDi (1 + λ ) =
¦Q
ij
.
(2)
j∈Nb
PDi0 and Q0Di are the real and reactive power demands. PGi and Q Gi are the real and reactive power Where
generations at bus-i respectively. The real power loss sensitivity index is determined using equation (1),
C1k = −2Vi gij cos(∂i ) + Vj [ gij cos(∂ j ) − bij sin(∂ j )]/ PDi0 .
ª ΔP º u2 ( x) = « » + PL . ¬ ΔQ ¼ 2
(8)
The functional equality constraints, v(x) is,
ΔPi = PGi − PDi − Pi .
(9)
ΔQi = QGi − QDi − Qi .
(10)
(3)
C2k = −2Vi gij sin(∂i ) +Vj [−gij sin(∂ j ) + bij cos(∂ j )]/ PDi0 . (4) The reactive power loss sensitivity index is set according to equation (2), 0 C3k = (Vi (− gij sin(∂ i ) + bij cos(∂ i ))) / QDi .
(5)
0 C4k = (Vi ( gij cos(∂ i ) + bij sin(∂ i ))) / QDi .
(6)
The inequality constraints, p(x) represents system and equipment technical limits
Vmin ≤ V ≤ Vmax .
(11)
X UPFC min ≤ X UPFC ≤ X UPFC max .
(12)
φmin ≤ φ ≤ φmax .
(13)
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∂ min ≤ ∂ P ≤ ∂ max .
(14)
Where the state variable vector ‘X’ is defined as,
wmin is the final value of inertia weight equal to 0.4. A. Flowchart Using PSO Technique:
ªV º «X » X = « UPFC » . «φ » « » ¬∂ ¼ At a time one objective function (i.e. either considered.
Where w is the inertia weight, itermax is the maximum number of iterations, “ iter ” is the current iteration number, wmax is the initial value of inertia weight equal to 0.9 and
(15)
Start
Read agents, velocities
u1 or u2 ) is
Compute Ploss
Objective II: Minimize C (t) = C1 (f) + C2 (Pg) Subject to A (f, g) = 0; and B (f)
If constraint is violated, evaluated value = Ploss + Penalty
≥ 0; D (g) ≥ 0;
Where C(t) is the overall cost objective function which includes the investment cost of UPFC C1 (f) and the generation cost C2 (Pg), A (f, g) represents the conventional power flow equations , B (f) and D (g) are the inequality constrains for FACTS devices and the optimal power flow respectively; f, Pg are vectors that represent the variables of FACTS devices and the active power outputs of the generators; and lastly g represents the operating state of the power system
Set Pbest for agent. For best evaluated value, gbest=evaluated value
Calculate velocities and agents
Calculate Ploss and new evaluated value
IV.
PARTICLE SWARM OPTIMIZATION
PSO is a popular non-conventional optimization technique with high global searching capability and is recently used for searching nonlinear multidimensional search spaces. The main reason behind its wide spread in power system is its simplicity and generating high quality solutions within very short duration. PSO has the same flexibility as compared to the other heuristic algorithms for controlling the stability between the global and local investigation of the search space [10]. PSO finds the best possible solution with a population of particles where each particle represents a candidate solution to the problem [8]. The change in position depends on previous, best individual, best global and a random velocity position. The term individual best, global best and random velocity are responsible for changes in particle position during iterations are associated with values called inertial weights. In general, maximum number of iterations for termination of the search process and inertia weights is set according to the following equation:
w = wmax −
wmax − wmin .iter itermax .
(16)
If new evaluated value is better than Pbest, agent = Pbest. For best Pbest, gbest = Pbest and store gbest Yes if i < n No
Stop
Fig. 3. Flow Chart of PSO Technique.
V.
RESULTS AND DISCUSSION
Using equation (3)-(6), the sensitivities of modified IEEE 14-bus system were measured. The lines having maximum sensitivities are shown in the Table I. From Table I, it can be concluded that real power loading sensitivity is more negative (i.e.-191.163) when UPFC is connected between bus 4 and 9. The reactive power loading sensitivity is also more negative (i.e. 1298.17) for the line 4-9 with UPFC. Therefore, the optimal location of UPFC is chosen when it is connected
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between buses 4-9. After identifying the suitable buses a load flow is performed using GA and PSO techniques respectively and the results are given in Table II and III. The total system power losses after installing UPFC at its best possible position using PSO method are given in table IV. Different operating conditions are simulated for the determination of the optimal FACTS sites. The total number of generation is 200 and there are 20 individuals in each generation. TABLE I.
LINE LOSS SENSITIVITY INDICES OF IEEE 14 BUS SYSTEMS
Line k
C1k
Ck 2
C3k
Ck 4
6-13
-31.346
-68.789
-352.287
139.954
4-9
-15.982
-191.163
-1298.17
711.169
4-2
-78.238
-80.569
-158.945
123.128
4-3
-84.472
-82.884
-219.692
164.924
1-5
87.457
97.828
-232.761
172.682
2-3
-27.726
-67.724
-365.135
69.643
TABLE II.
COMPARATIVE PERFORMANCE OF DIFFERENT CASE STUDIES Case Study
PSO Method
Initial loss (p.u)
0.5806
Final loss (p.u)
0. 0124
Total loss reduction (p.u)
0. 5682
Simulation time in sec
254.1740
TABLE III.
Total Loss Reduction (p.u)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
With UPFC
Without UPFC
4-9
0.5201
0.8429
0.5353
0.8229
4-3
0.5732
0.8432
TABLE IV. From 1 1 2 2 2 3 4 4 4 5 6 6 6 7 7 9 9 10
POWER FLOWS WITH UPFC To 2 5 3 4 5 4 5 7 9 6 11 12 13 8 9 10 14 11
13 14
VI.
0.048 0.161
0.52 0.73
CONCLUSIONS
Simultaneous optimization of the positions of the FACTS devices, their types and rated values is a very difficult optimization problem in large power system network. The algorithm applied in this paper is a general optimization method, which is suitable to solve such combinatorial problems. It always gives the best solutions and it is faster than the classical optimization methods also. In this paper, sensitivity based factors has been used for optimal position of UPFC for better operation of the power system network in terms of line loss sensitivity factors and to attain minimum active power loss and total system cost while satisfying all other power system constraints. Furthermore, since the total cost function, which includes the generation costs and the UPFC investment costs, is minimized, the UPFC investment costs can be provided by sparing of the generation costs. This algorithm is practical and easy to be implemented into the large power system analysis. REFERENCES
13-6
Branch
12 13
[1]
TOTAL POWER LOSS WITH AND WITHOUT UPFC
Line k (i to j)
19 20
Losses P (MW)
Q (MVar)
5.977 3.487 2.453 1.910 1.092 0.813 0.657 0.211 0.012 0.019 0.174 0.071 0.283 0.022 0.349 0.459 0.832 0.977
16.45 13.34 9.53 6.72 3.54 1.74 0.52 0.84 2.82 3.44 0.99 0.37 0.58 0.51 0.77 0.88 0.02 0.45
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