30 hns system with single and multiple TCSC devices. The pmposed model ... day congestion management problem with help of FACTS devices efficiently.
Power Flow Control and Transmission Loss Minimization Model with TCSC for Practical Power Networks Abdel-Moamen M. A.
Narayana Prasad Padhy
is to pool power plants and load centers io order to supply the load at a required reliability, maximum efficiency and at lower cost. As power transfers grows, the power system can become increasingly more difficult to operate, and the system becomes more insecure with unscheduled power flows and higher losses. In this context, as well as the rapid development of self-commutated semiconductor devices, have made it possible to design power electronic equipments. These equipments are well known as Flexible AC Transmission Systems (FACTS)-devices, and introduced in 1988 by Hingorani [ 5 ] . The objective of FACTS devices is to bring a system under control and to transmit power as ordered by the control centers, it also allows increasing the usable transmission capacity to its maximum thermal limits. By Using FACTS devices it is possible to control the phase angle, the voltage magnitude at chosen buses and /or line Index Terms- FACTS devices, TCSC and Newton’s Optimal impedances of a transmission system. Power flow is Power Flow. electronically controlled and it flows as ordered by control center and consequently the losses odand cost will he I. INTRODUC~ON optimized. It has been observed that installation of FACTS PTIMAL Power Flow (OPF) is a static nonlinear devices increases the network‘s controllability. But the ‘programming problem aimed at scheduling the controls existing conventional OPF algorithms have to he modified of the power system in a manner that optimizes a certain such that power system analysis is possible for modern power objective function while satisfying a set of physical and industry with FACTS devices. operational constraints imposed by equipment limitations and For last two decades researchers developed new algorithms security requirements. OPF was horn in 1962 [ I ] and took a and models for power flow and optimal power flow long time to become a successful algorithm that could be incorporating FACTS devices, so that cheap power can be applied in every days use. Over the last three decades, many made available to the customers without violating system successful OPF techniques have been developed [2-4] such as, constraints. Still research is in progress to meet the present the generalized reduced gradient method, successive linear day congestion management problem with help of FACTS programming solutioo, successive quadratic programming, the devices efficiently. Various algorithms have been reported to Newton method, the P-Q decomposition approach, the Interior solve power flow and optimal power flow (OPF) for power Point Method (IPM), Genetic Algorithm (GA), Evolutionary systems equipment with various FACTS devices. New control Programming etc. After obtaining the OPF solution, the variables and control objective equations are usually added in implementation of the optimal control variables will bring the conventional power flow equations. Several papers have reported the OPF incorporating FACTS devices. system to the “optimum” state. Noroozian and Anderson [6] have proposed a method for In the present day scenario private power producers are increasing rapidly to meet the increase demand due to heavily solving the power flow control problem incorporating FACTS loaded customers. The purpose of the transmission networks devices based on decomposition and locally measurable variables. Taranto et al. [7] have proposed a decomposition method for representing FACTS devices in optimal power AMel-Mcamn M . A and Nvrayana Prarad Padhy. are wilh the Deparurent flow (OPF) model. The proposed approach was first proposed of Elecuical Engineering, Indian InSliNte of Technology, Rmrkee - 241667, to solve the optimal active power flow dispatch problem India (miml~sd~ceBiilr.crnel.iil I npprcbc(Niitr.vroclin ) incorporating FACTS devices. This methodology is based on Abstract- In this paper, optimal power flow (OPF) model has been developed and analyzed with Thyristor ContmUed Series Compensator (TCSC) for practical power networks using Newton’s optimization technique. The minimiration of total system real power losses is an objective with controlling the power flow of specifled transmission lines. This model has considered the optimal settings generators, transformers and TCSC devices. The optimal transmission losses and corresponding generation schedules with optimal TCSC setting parameters for different case studies have also been reported. The performance of the proposed algorithm has been tested for IEEE30 hns system with single and multiple TCSC devices. The pmposed model converges very fast and independent of initial conditions. It has also been observed that the proposed algorithm can he applied to larger systems and do not suffer with computational ditllcnlties.
~~~~
0-7803-7989-6/03/$l7.00 02003 IEEE
880
mathematical decomposition and network compensation techniques. This method can deal with the representation of series compensators and phase shifters, but this method did not consider the specified line flow constraints. Hiyama. ef a/. [SI, presented an application of a fuzzy logic control scheme for TCSC module to enhance overall stability of electric power systems and also to increase the maximum power transmission through the existing AC transmission lines. Gotham and Heydt [9] presented the modeling of FACTS devices for power flow studies and the role of that modeling in the study of FACTS devices. Also they proposed a simultaneous method to solve the combined set of power flow equation and FACTS control equations. Ge and Chung [IO] described a method to incorporate the power flow control using FACTS for the optimal active power flow problem. Povh [ 111 presented that FACTS controller can essentially improve long-distance ac transmission. This technology has been extended by a large number of further FACTS elements, which can be effectively used for load flow control in power systems. Ambriz-Perez et a/ [12] solved the OPF incorporating FACTS devices using Newton’s method, leading to highly robust iterative solutions. Fuerte ef a/ [ 131 proposed simultaneous methods to solve the combined set of power flow equations and FACTS control equations. Lu and Abur [14] presented a systematic procedure to place and operate TCSCs in a power system. First the “Single Contingency Sensitivity (SCS)” criterion for a given branch flow is defined. This criterion is then used to develop a branch’s prioritizing index in order to rank branches for possible placement of TCSCs. Finally, optimal settings for TCSC parameters are determined for important contingencies. Billinton et al [I51 presented power system reliability enhancement using a TCSC. Chung and Li [ I61 presented an improved genetic algorithm (GA) to solve optimal power flow (OPF) problems in power system with FACTS. In the solution process, GA coupled with full AC power flow, selects the best regulation to minimize the total generation fuel cost and keep the power flows within their secure limits. The optimization process with GA is presented with case study examples of an IEEE test system to demonstrate its feasibility and effectiveness. The proposed optimal power flow algorithm for transmission loss minimization incorporating TCSC devices is capable of handling multiple TCSC devices and independent of the system size. The algorithm uses sparse Newton optimization [17] and due to which the mathematical complexity has been reduced drastically without compromising optimality.
w
L
Fig.]. Model of TCSC Under those assumptions, the TCSC shown in Fig. I , steady state voltage and current equations can be obtained [ I81 from the analysis of a parallel LC circuit with a variable inductance. And hence the expression for TCSC equivalent reactance, as a function of the TCSC fuing angle a i s given by, x, = -x,+ K,(Zo+sinza-K, cos2o ( i ~ t a n ( ~-tan01 u) (1)
Land C are variable inductance and capacitance of TCSC. The general transfer admittance matrix for the TCSC is formulated by applying KCL and KVL to the electric circuit shown in Fig. I . For each branch, compute the elements of the branch admittance matrix where
;[=I:
;][
(4)
and V , = IV, le’’,
V , = IV, le”,
(5)
where I, and I, are the currents flow on branches ff and r f respectively. (V, land IV, I are the bus voltages magnitudes on nodesfand f. 0, and 0,are the bus voltages angles on nodes f and t.
1
* - Y,, = -
Y
-
xTCSC
Yf =Yr, =--
1 TCSC
Now the TCSC power flow equations from nodefto node IS, are n
TCSC
The TCSC linearized power flow equations with respect to firing angle a are
11. PROBLEM FORMULATION
(9)
A. TCSC Power Flow Model
Assuming that a loop current is trapped in the reactorcapacitor circuit and that the power system can be represented by an ideal, sinusoidal current source.
where
881
111. NUMEIUCAL RESULTS The effectiveness of proposed approach will be illustrated using the IEEE 30 test systems. It will be assumed that the impedance of all TCSCs can vary within &75% of the corresponding branch impedance. In this section, the analysis the TCSC linearized power flow equations with respect to shows that the operation mode of TCSC is automatically set to capacitive or inductive modes. Fig. 2 depicts the TCSC voltage magnitude IVA and voltage angle Bare equivalent impedance at the fundamental frequency (f =5OHz) as function of firing angle ( a )corresponding to a capacitance C=0.00020 pu and a variable inductance L0.0150 pu. For all cases in this paper, the convergence tolerances are 1.0e-8 (0.OOOl MWMvar) for maximal absolute bus power mismatch. A . 30-Bus System
Cases studies for IEEE 30 bus system [I91 shown in Fig. 3. have been carried out to determine the effectiveness of the proposed model. The system has 6 generation, 4 LTC transformers, and 41 transmission lines. TCSC device has been installed on branch number. 2, 3, 6, and 12 one by one based on the optimal power flows (Table 1) on those lines such as 24.20.394,45.004 and 14.208 MW respectively. It has k e n found that the base case power flows are sometimes very B. OPF with TCSC Now the OPF formulation has been modified with the variable close to the maximum rating of the lines and other case it may parameters of TCSC devices and the objective function is be very much underutilized. So an attempt has been made to defined as the minimization of total system real power losses, control the power flows in the above-mentioned lines and the and at the same time, some constraints, including entire power MW flows are specified to 24.0701. 20.5467.45.151 and 19.923M W flow equations, generation limits, voltage ranges, line transfer respectively. Further the model has been applied to multiple capability and TCSC impedance etc., has to he satisfied. The FACTS devices (two, three and four) for the above-specified total system real power losses typically is considered as power flows. Table 2., 3 and 4 presents the optimal quadratic functions or as a piecewise linear approximation. transmission losses generation schedules, value of firing For a quadratic function, the OPF problem can be formulated angle, TCSC reactance and under specified power flow using one, two, three and four FACTS devices respectively. as: power flow equations from node t to nodef Sf just exchange the subscriptsfand f in above equations. , is equal to S, and S, is For the power equations at node f S equal to Sf The above differentiations have been used in the Jacobian and Hessian matrix formulation of the proposed model.
Minimize Subject to:
f (4
(13)
s(x) = 0 h(x) 5 0
(14)
x;nm~X~Xmax
where x is the vector of control and state variables of the system, represented by the magnitude 1VI and angle 6 o f voltages, and tap (TAP) in the On Load-Tap Changing. The objective functionflx) represents the real power losses in the transmission (PL). This function is non-separable and permits no simplification. The equality constraints, ~ ( x ) represent . the real (P(x))and reactive (Q(x)) power flow equations, which are obtained by means of the conservation of energy principle at all buses of the system. The inequality constraints, h(x), represent the functional constraints of power flow, e.g. limit of real and reactive PFs in the transmission lines and transformers, limits of reactive , and x,,, are power injections for reactive control buses. x the upper and lower limits of the state variables and control systems. In the proposed model the OPF solutions have been obtained using Newton's method [17]. TARLE I
882
bus 1
To bus 3
24,0008-1.8252i
Spcifi edP,, 26
24.0701
130
3
2
5
20.3938-2.5021i
17
20.5467
65
6
2
6
45.004- 3.6331
23
45.151
65
12
6
10
14.208+13.9661
14
19.923
32
Line
From
#
2
PowertIaw(S,,) MVA
MNN RESULT
IS"
TABLE 4 IFEEE 30-BUSS Y S E M W l l H MULn-TCSC L N S
Three TCSCs
MVC ~
I
~
VI
2.38~6 1.0500 1.0477 1. 0305 1.0379
-5.938 0.179 4.505
-1.656 0.073 4.500
M
3.6&12 1.0500 1.0476 1.0300 1.037I 1.0896 1.0766 __ 51.60 80.00 50.00 35.00 30.00 40.00 1.781 -1.604 0.297 -4.425 __
6.277 14. 046 38.364
5.849 12.944 38.317
18.862 16.845 38.349
1.0476 1.0292 1.0362
1.0476 1.0292 1.0363
1.0808
1.0781 51.61 TABL F E E E 30-BUS SYSTI
80.00
\1THONE
SC INST
Line 2 1.0500 1.0476 1,0290 1.0361 1.0799 1.0764 51.64
Line 3 1.0500 1.0477 1.0294 1.0365 1.0799 1.0769 51.64
80.00
80.00
0.0575
Line 6 1.0500 1.0477 1.0295 I .0366 1.0801 1,0769 51.64 80.00 50.00 35.00 30.00 40.00 7.820 -10.000 0.351 -4.404 13.544 __ 0.0365
286.638
286.639
286.632
3.238
3.239
3.232
967.995
967.977
I aTCSC
1.0500 1.0477 1.0293 1.0364 1.0799 1.0767 51.65 80.00 50.00 35.00 30.00 40.00 7.739
50.00 35.00 30.00 40.00 7.703
.IO.wO
-10.000
0.297 -4.428
0.211 -4.448 4.711 -0.0345
!86.647
50.00 35.00 30.00 40.00 7.769 -10.000 0.352 -4.413 15.638 -
286.643
2&3
VI V2
-2
V5 V,
o
2&6 1.0500 1.0476 1.0476 1.0292 1.0292 1.0364 1.0364 1.0500
80.00 50.00 Pm 35.00 Pm, 30.00 40.00 7.752 T , ~ -10.0oo T7< 0.295 Ti
Pm P,
i - i :; 2
80.00 50.00 3.5.00 30.00 40.00 7.776 -10.0~ 0.282
I
Line 12 1.0500 1.0478 1.0298 1.0372 1.0838 1.0744 51.63
3&6 1.0500 1.0476 1.0300 1.0372
80.00 50.00 35.00 30.00
80.00 50.00 35.00 30.00
40.00 8.166 -10.000 0.687 4.283 13.668
80.00
21.261 18.580
50.00 35.00 30.00 4.682 -3.450 0. 119 -4.460 134.105 __ -0.3277
1
2; 24:;
14.577 12.685 38.37 -0.0197 -0.0252 -0.0363 xmc(w' 0.0466 0.0286 -0,3322 ~ P (MW) G 1286.637 1286.638 286.627
I
C%d(de@ee)
I
I
c40,y3 (MWI 3.237
1 3.238 1
1
3.227
e C m I ($/hr))967.9901967.993 967.967
-1o.000 K L g
0.499
I
3&12 1.0500 1.0476 1.0293 1.0365 1.0894 1.0754 51.62 80.00 50.00 35.00 30.00 40.00 2.736 -2.289
I
0.061
~
0.0961 0.0709 -0.3335 ~
286.609
286.m
286.594
3.209
3.200
3.194
967.922
967.900
967.886
Y
38.49
38.41 0.0392 0.0542 0.0688 -0.3290 -0.3235 286.616 1286.623 286.623
1
3.216
80.00
50.00 35.00 30.00 40.00 1.879 -1.547 0.481 -4.359 13.271 20.939 18.555 38.366 0.0340 0.1277 0.0920 -0.3323
i
~
68412 1.0500 1.0477 1.0295 1.0365 1.0775 1.07M) 51.62 80.00 50.00 35.00 30.00 40.00 9.379 -5.739 0.128
16.670 0.0983
I
35.00 30.00 40.00
~
-
1 I 4.4.: ;4l: ;:$;
-2.470 0.008
I
,3,6&1: 1.0500 1.0477 1.0304 1.0378 1.0899 1.0773 51.59
~
I III I II I 2E
35.00 30.00 40.00
0.0377 0.1333 0.0923
40.00
~
2&12 l.0500 1.0475 1.0290 1.0360
30.00
~
~
967.991
~
50.00 35.00
~
1 3.223 1
3.223
1 967.938 1967.9551 967.957
1
Fig. 3. The IEEE 30-bus system 1V. CONCLUSION
This paper has presented an OPF model incorporating multiple TCSC using Newton's algorithm. This model is capable of solving power networks of any sire and converges with minimum number of iterations and independent of initial conditions. the IEEE 30 bus systems have been used to demonstrate the proposed method over a wide range of power flow variations in the transmission system. It has also been observed that the proposed algorithm is efficient and suitable for better range of power control.
883
V. REFERENCES I., “Contribution a I‘ktude du Dispatching Economique,” Bulletin de la Socidtd. Franpise des Elecrriciena, Ser. 8 Vol. 3, pp. 4 3 1 4 7 , August 1962.
VI. BIOGRAPHIES
[I1 Carpentier
[21 Huneault M. and Galiana F.D.:”A Survey of the Optimal Power Flow Literature,” IEEE transactions on Power Systems, Vol. 6. N0.2, pp. 762.170, May 1991. [31 Wood A.J. and Wolknkrg B.F. “Power Generation, Operation, and Control”. John Wiley and Sons, New York, 1996. 141 Momoh 1A. Ehawary ME., Adapa R, “A Review of Selected Optimal Power Flow Literature to 1993, P m I, Pan 11, IEEE transactions an Power System Vo1.14, No. 1 ,pp.96-111, Feb.99 151 Hingorani N.G. “Power Electronics in Electrical utilities: Role of Power Electronics in Future Power Systems”, Proceedings of rhe IEEE VOI. 76 NO.4, pp.4~1-4a2.~ p r i 1 1 ~ 8 8 . 161 Noroozian M. Angquist L., Ghandhari M., Andersson G. ‘%nproving Power System Dynamics by Series-Connected FACTS Devices”, IEEE Transactions on Power Deliver),, vol. 12. No. 4, pp.1635-1641, October 1997. 171 Taranto G.N., Pinto L.M.VG., Pereira MVF.,“Representation of F A m S Devices in Power System Economic Dispat&”,/EEE transgcrions on power s3,slems vo1,7, N ~ 2,. pp,572.576, ~ ~ ~ [SI Hiyama,T. er 01. ‘%oordinated Fuzzy Logic Control for Series Capacitor Modules and PSS to Enhance Stability of Power System”, IEEE Tmnsacrions on Power Delivery ~01.10,No. 2, 1098-1104April. 199.5. [91 Gotham D.1. and Heydt G.T.,: ’%wer Flow Control and Power Flow Studies for Systems with FACTS Devices.” IEEE transactions on Power System vo1.13, No. I, pp. 60-65 Feh.1998. [IO] Ge S.Y. and Chung T.S. ‘Optimal Active Power Flow Incorporating FACTS Devices with Power Flow Control Constraints”, Elecrrical Power& Energy Systems vo1.20, No. 5 , pp.321-326 May. 1998. [I 11 Dusan Povh, ”Use of HVDC and FACTS, Proceedings of rhe IEEE, vol. 88, No. 2, pp. 235-245, February 2000. 1121 Ambriz-Perez H., Acha E., Fuerte-Esquivel C.R.: “Advaced SVC Model for Newton-Raphson Load Flow and Newton Optimal Power Flow Studies” IEEE rransacrions on Power Systems, vol. I S , NO.l, pp.129-136, February 2000. [I31 Fuerte CR., Acha E., Tan SG., Rico J1,:”Efficient Object OTiented Power Systems Software for the Analysis of Large-Scale Networks Conlaining FACTS-Controlled Branches” IEEE rransacrions on Power Systems, vol. 13, N0.2, pp.464-472. May1998. [I41 Lu Yunqiang and Ahur Ah,:“Improving System Static Security via Optinwl Placement of Thyrister Controlled Series Capacitor (TCSC)”, IEEE, PES, WM, Columbus, Ohio, USA., Ian. 2001. [ I S ] Billinton R., Firuzabad M.F., Faried S.O. “Power System Reliability Enhancement using a thyristor Controlled Series Capacitor”, IEEE transactions on Power Systems vo1.14, No. I, pp.369-374, February. 1999. [I61 Chung T.S., Li Y.Z. “A Hybrid CA Approach for OPF with Consideration of FACTS Devices”, IEEE Power Engineering Review, vol. 21, N0.2, pp. 47-50, February2001. [I71 Sun I David, Ashley Bruce, Bewer Brian, Hughes Art, T h e y E. William,:”Optimal Power Flow by Newton Approach”, IEEE transacrions on Power Apparatus and System volPAS 103, No. LO, pp.2864-2875, October 1984. 1181 AMel-Moamen, M. A.; Padhy, N.P. “Newton-Raphson TCSC Model for Power Flow Solution of Practical Power Networks” l E E E PES, SM, Vol: 3, pp: 1488 -1493,2002 1191 Alsac 0. and Stott B.:”Optimal Power Flow with Steady-State Security”, IEEE transacrions on Power Apparatus and Systems, VoL PAS- 93, No. 3, pp.745-751, Mayllune 1974. [20] Power Systems Test Case, The University of Washington Archive. htlp:liwu.w.cc.washinglan.edu/rcsc3rcl, 2ooO. .
I-Rahim received the B. Sc. degree and the M S c . degree both in Electrical Engin-ng from Assuit University. Egypt in 1991 and 1998. respectively. He joined Aswan High Institute of Energy as an Assistant Lecturer. Aswan, Egypt in 1993. He is currently working towards the Ph.D.degree at the d e p a r t ” of Electrical Engineefing. Indian Institute of Technology, Rmkee. India. His research interests include power systemeconomicsand FACTS. obtained his Degree in Electrical Engineering and Masters in Power System Engineering with Distinction in 1990 and 1993, respectively. In 1997. hc obtained his Ph.D. degree in Electrical En&ering from Anna University, Chennai, India. He joiad Birla Institute of Technology & Science (BITS) as an Assistant Professor, Electrical En@neenngD e p a n t in 1997. He is presently working as Assistant Professor in the D e p a n ” of Electrical Engineering, Indian Institute of Technology. Roorkee. He taught course in Basic Electrical Enaneering, Power System and Artificial Intelligence. His field of interest is Power System Privatization, Resrmcruring and Deregulation. Artificial 9 2 , Intelligence Applications to Power System Operation and optimization Problems,
