Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥٠٠ OPTIMUM POWER GENERATION FOR IRAQI SUPER HIGH VOLTAGE SYSTEM Dr. Samir S. Mustafa Kirkuk Technical Institute Abstract Iraqi super grid power system consists of six generating power plants : Baji, Sad Al-Mosul, Haditha, Mussayab, Nasiriya and Hartha. A Matlab5.3 package has been used to calculate the optimum generation of the system generators which gives minimum losses in comparison with the total losses according to the same data which were recorded in National Control Center. The losses reduction became 30.96% . Gradient method has been employed for the solution of optimal power flow. The partial derivative of active and reactive losses with respect to injected power were used as an indicator on optimum power generation. Keywords- Optimum, Power Generation. �رة ,/@3(� أ �DE أ &�!: �� أ ��اق�� ��)Fأ � أ �3 � �ون ()'&%. د �� ��,� كآ�آ3/ ا ,�0� ا ��/� أ �56� �< ��اق *���ن � ?l �4-"ت *� � أ� !"# � : ������ أ &%$ أg-�ة أ � �f<�o�l&f#G)" ا DfG"!� أ ��>�fI�F �fار �j أ DG"!� أf� ��gDf� *Lf % . p#) nS��F �F�D4�٣٠.٩٦ أ '>"("ت أ rZ4-"ت أ�� � ا� �< �� � ا� �<�B� J4.�ل أ� �f وا ��#"���f .ا?��Gام �I9�o ا ��رج "�# DfG"!� ا �fIرة ا �f!�g *L ا?��Gام أI�(J"ق ا �)�I4� >�ه"(D'� إ ; ا �Iرة ا�* ����>"ت آ�V)� ��; ا�AB /�رة ��9 � j<�S ا�. Introduction Many different mathematical techniques have been employed for the solution of optimal power flow. The majority of the techniques in the references ( Selman2005), (Antonio2002), (Quek2002), (Pjiac2003), (Kristiansen2002) and (Stevenson1985) use one of the following methods: 1- Lambda iteration method. 2- Gradient method. 3- Newton’s method. 4- Linear programming method. 5- Interior point method. Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥٠١ Optimal power flow (OPF) has been widely used in planning and real-time operation of power systems for active and reactive power dispatch to minimize generation costs and system losses and improve voltage profiles. The primary goal of OPF is to minimize the costs of meeting the load demand for a power system while maintaining the security of the system (Claudio2001). The cost associated with the power system can be attributed to the cost of generating power (megawatts) at each generator, keeping each device in the power system within its desired operation range. This will include maximum and minimum outputs for generators, maximum MVA flows on transmission lines and transformers, as well as keeping system bus voltages within specified ranges. OPF program is to determine the optimal Operation State of a power system by optimizing a particular objective while satisfying certain specified physical and operating constraints to achieve these goals, OPF will perform all the steady-state control functions of power system. These functions may include generator control and transmission system control. For generators, the OPF will control generator MW outputs as well as generator voltage. Optimization and security are often conflicting requirements and should be considered together. All the optimization problems can easily be transcribed into the following standard form (Yong1999) and (John2003): min f )( x subject to: gi 0)( ≤x i = 1, …, ng hk(x) = 0 k = 1, …, mh Where { } ℜ∈= n xxx ... 1 (design variables). f(x) the objective function. gi(x) inequality constraints. hk(x) equality constraints. We assume that only part ( Gi P ) of the total net power is controllable for the purpose of optimization. The objective function can then be defined as the sum of instantaneous operating costs over all controllable power generation: f (x)=∑ i iGi Pc )( (1) where ci is the cost of producing PGi. The minimization of system losses is achieved by minimizing the power injected at the slack node. Note that Baji generator has been chosen as slack node. The minimization of the objective function f (x) can be achieved with reference to the Lagrange function (L). The nonlinear power loss equation is: Ploss = ∑ = N i 1 ∑ = N j 1 [ ])cos(VV2VVGij jiji 2 j 2 i δδ −−+ (2) Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥٠٢ The linearized sensitivity model relating the dependent and control variables can be obtained by linearizing the power equations around the operating state. Despite the fact that any load flow techniques can be used, N-R load flow is most convenient to use to find the incremental losses. The change in power system losses, L P∆ , is related to the control variables by the following equation ( Selman2005) L P∆ = m LL V P V P ∂ ∂    ∂ ∂ .. 1    ∂ ∂ ∂ ∂ ++ wm L m L Q P Q P .. 1                 ∆ ∆ ∆ ∆ + + wm m m Q Q V V 1 1 M (3) Electric power systems designed with generating units that are widely scattered and interconnected by long transmission lines may suffer significant losses. The losses depend on the line resistance and currents and are usually referred to as thermal losses. While the line resistances are fixed, the currents are a complex function of the system topology and the location of generation and load. Using the load data collected on 2/1/2003 in Table 1 which can be obtained from the Iraqi Control Center (Afaneen2004) algorithm was applied to determine the best placement of new units in order to maximize power available and minimize losses on the system for a given load (William2002) The analysis objective is to find the partial derivatives (sensitivity) of active power loss with respect to active and reactive power injected at all buses except slack bus. [ ] [ PPSEN L ∂∂= / ]QP L ∂∂ / (4) The results of sensitivity vector [ ]SEN are used as an indicator to the efficiency of the system to reduce losses in case of installing generation units or shunt capacitors at these buses. The following matrix [D] is the partial derivative of real losses with respect to voltage magnitude at load buses and voltage angles at all buses except slack bus (samir2007). [ ]                           ∂∂ ∂∂ ∂∂ ∂∂ ∂∂ ∂∂ = ∂ ∂ = +1 3 2 3 2 / / / / / / NLloss loss loss Nloss loss loss VP VP VP P P P x f D δ δ δ (5) The components of [ ]D are calculated as follows: [ ]∑ ≠ = −=∂∂ N ij j jijiijiloss VVGP 1 )sin(2/ δδδ (6) Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥٠٣ [ ]∑ ≠ = −−=∂∂ N ij j jijiijiloss VVGVP 1 )cos(2/ δδ (7) The mathematical analysis needs also Jacobian matrix [ ]Jac which is used before in power flow problem, then: [ ] [ ] [ ]DSENJac T = (8) then [ ] [ ] [ ]DJacSEN T 1− = (9)       sen sen Q P =             ∂ ∂ ∂ ∂ Q P P P L L = [ ]           ∂ ∂ ∂ ∂ − V P P Jac L L T δ1 (10) where Psen = partial derivative of real losses with respect to real power injected at load buses. Qsen = partial derivative of real losses with respect to reactive power injected at load buses. [ ]J is the Jacobian matrix of Newton-Raphson load flow. Then Psen =             ∂ ∂ ∂ ∂ +1 2 NL P Ploss P Ploss (11) And Qsen =             ∂ ∂ ∂ ∂ +1 2 NL Q Ploss Q Ploss (12) Iraqi National Super Grid Iraqi national super grid contains six generating sets of various types units, thermal and hydro turbine kinds, with different capabilities of MW and MVAR generation and absorption. The load and generation of INSG system on the 2 nd of January 2003 are tabulated in Table 1 machines parameters and lines are tabulated in Tables 2 and 3 (Afaneen1998) A software package under Matlab5.3 has been developed to perform electrical power system analysis on a personal computer. The software is capable of performing admittance calculations, load flow studies, optimal load flow studies of electric power systems. The sensitivity of each power plant to reduce losses with respect to power generation is calculated according to equation (10).The results were shown in Tables (1-5). As shown in these Figures, increasing power generation at each bus reduces system losses if sensitivity value at that bus is negative. On the other hand increases power generation at each bus increases system losses if sensitivity value is positive. The values of power generation which give minimum losses at SDM, HAD, MSB, NSR, and HRT power plants are 250, 425, 950, 700, and 450 Mw respectively. Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥٠٤ Notice that increasing power generation at each bus reduce system losses if sensitivity value at that bus is negative, and increase system losses if sensitivity is positive. System power losses with respect to sensitivity of each power plant shown in Figures 6, 7, 8 & 9. Calculations of optimal power generation Optimal power generation for all generation plants can be obtained by increasing real power of each generator with small amounts at the same time, as shown in Figure 11. Increasing active power for each generator is stopped when sensitivity at that generator bus becomes zero or positive. The over all process continues until the sensitivities for all buses become zero or positive. The procedure is done using the package under Matlab. The results show that optimum power generations give minimum losses equal to 25.95Mw where shown in Table 4. Also the results show that total losses with ordinary generation is equal to 37.592Mw using the data of ordinary generation and loads on the 2 nd of Jan. 2003. Optimal losses reduction = ( losses with ordinary Pg – losses with optimum Pg) / losses with ordinary Pg x 100% = 37.592-25.95 / 37.592 = 30.96 % Conclusions Using sensitivity analyzing gives us a good indicator about the buses which are sensitive to reduce system total losses .Increasing power generation at each generation plant reduces system losses if sensitivity value at that bus is negative. On the other hand increasing power generation at each bus increases system losses if sensitivity value is positive. The results show us that optimum generation in the generation plants give minimum total losses in the Iraqi national super grid without exceeding the constrains of voltages, active and reactive power, as shown in Table 5. References • Afaneen A. Abood Automated Mapping Facilities Management Geographic Information System of a Power System, M. Sc. Thesis, University of Technology, Baghdad, 1998. • Afaneen A. Abood, Implementation of Geographic Information System (GIS) in Real-Time Transient Stability, Ph.D. thesis, University of Technology, Baghdad, 2004. • Antonio J. and Maria J., “Optimal Power Flow Algorithm Based on TABU Search for Meshed Distribution Networks”, www.pscco2.org, 2002. • Claudio C., “Comparison of Voltage Security Constrained Optimal Power Flow Techniques”, Proc. IEEE-PES Summer meeting Vancouver, BC, July 2001. • Etienne J., “A Reduced Gradient Method with Variable Base Using Second Order Information, Applied to the Constrained and Optimal Power Flow”, www.system.seurope.be/pdf, 2000. • John R., “Engineering Design Optimization”, www.me.uprm.edu/vgoyal/inme 4058, 2003. • Kristiansen T., “Utilizing Mat Power in Optimal Power Flow”, www.ksg.haward.edu, 2002. • Pajic S., “Sequential Quadratic Programming-Based Contingency Constrained Optimal Power Flow”, M. Sc. Thesis, Worcester polytechnic institute, www.wpi.edu. April 2003. Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥٠٥ • Quek R., “Power Transfer Capability Assessment”, www.innovexpo.itee.uq.edu.au/ 2002. • Samir S. Mustafa, Minimum Power Losses Based Optimal Power Flow Iraqi National Super Grid and its Effect on Transient Stability, Ph.D thesis, University of Technology, Baghdad, 2007. • Stevenson W. D., “Elements of Power System Analysis”, McGraw-Hill Book co. 4 th edition, 1985. • William R., "Optimal Placement of Distributed Generation", www.pscco2.org, 2002, USA. • Yong T. and Lasseter R., "OPF Formulation in Market of Retail Wheeling", www.pserc.cornell.edu, 1999. Table1: INSG System Load Data Generation Load Bus Bar Number Bus Bar Name Type MW MVAR MW MVAR 1 BAJ Slack 570.592 100.4455 200.00 98.00 2 SDM P,V 700.00 - 23.2248 5.00 2.00 3 HAD P,V 500.00 - 0.8474 100.00 60.00 4 QAM P,Q .00 .00 60.00 40.00 5 MOS P,Q .00 .00 300.00 180.00 6 KRK P,Q .00 .00 70.00 40.00 7 BQB P,Q .00 .00 150.00 80.00 8 BGW P,Q .00 .00 500.00 360.00 9 BGE P,Q .00 .00 500.00 360.00 10 BGS P,Q .00 .00 100.00 50.00 11 BGN P,Q .00 .00 300.00 200.00 12 MSB P,V 600.00 420.6564 120.00 70.00 13 BAB P,Q .00 .00 100.00 50.00 14 KUT P,Q .00 .00 100.00 60.00 15 KDS P,Q .00 .00 200.00 100.00 16 NAS P,V 650.00 - 69.1434 100.00 54.00 17 KAZ P,Q .00 .00 350.00 200.00 18 HRT P,V 380.00 35.9855 38.00 22.00 19 QRN P,Q .00 .00 70.00 30.00 Total 3400.592 463.8716 3363 2056 Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥٠٦ Table2: Machine's Parameters Table3: INSG System Line Data From To R (P.U) X (P.U) B (P.U) BAJ4 SDM4 0.00542 0.0487 1.4384 MOS4 SDM4 0.00143 0.0124 0.36439 MOS4 BAJ4 0.00399 0.03624 1.074 BAJ4 HAD4 0.00364 0.03024 0.8676 QAM4 HAD4 0.0035 0.03 0.7413 BGE4 BQB4 0.00076 0.00689 0.2043 BAJ4 KRK4 0.00182 0.01654 0.49031 BAJ4 BGW4-2 0.0055 0.05004 1.4826 BAJ4 BGW4-1 0.00483 0.04393 1.3017 HAD4 BGW4 0.00483 0.04393 1.3017 BGW4 BGN4 0.00093 0.00847 0.25099 BGN4 BGE4 0.00029 0.00265 0.0788 KRK4 BGE4 0.00481 0.04373 1.29581 BGE4 BGS4 0.00105 0.00955 0.28309 BGW4 BGS4 0.00144 0.0131 0.38816 BGS4 MSB4-1 0.00121 0.0102 0.30944 BGS4 MSB4-2 0.00121 0.0102 0.30944 BAB4 MSB4-1 0.00077 0.00648 0.19666 BAB4 MSB4-2 0.00077 0.00648 0.19666 Node Name Armature ARG (Per Transient XD (Per Inertia Constant BAJ4 0.0 0.0122242 132 SDM4 0.0 0.037 91.008 HAD4 0.0 0.04948 36.096 MSB4 0.0 0.017225 104 NSR4 0.0 0.0285 99.94 HRT4 0.0 0.0508 47.5 Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥٠٧ BGS4 KUT4 0.00245 0.02236 0.6625 BGS4 KDS4 0.00292 0.02659 0.788 KDS4 NSR4 0.00383 0.03486 1.03314 KAZ4 NSR4 0.00439 0.03999 1.1849 KUT4 NSR4 0.00433 0.0394 1.1674 KAZ4 HRT4 0.00119 0.01083 0.32104 QRN4 HRT4 0.0013 0.01182 0.35022 QRN4 KUT4 0.00628 0.05713 1.6927 Table4: Active Power Generations which Give Optimal Losses Reduction Table5: Limits of Generation and Load Buses Qgeneration [Mvar] Voltage [P.V] Bus Bar Qmin Qmax Vmin Vmax 1 - 200 200 0.95 1.05 2 - 257.15 433.82 0.95 1.05 3 - 183.68 309.87 0.95 1.05 4 0 0 0.95 1.05 5 0 0 0.95 1.05 6 0 0 0.95 1.05 7 0 0 0.95 1.05 8 0 0 0.95 1.05 9 0 0 0.95 1.05 10 0 0 0.95 1.05 11 0 0 0.95 1.05 12 - 220.42 371.85 0.95 1.05 Generation Bus Number Generation [Mw] BAJ 571 SDM 250 HAD 350 MSB 1000 NSR 500 HRT 400 Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥٠٨ 13 0 0 0.95 1.05 14 0 0 0.95 1.05 15 0 0 0.95 1.05 16 - 238.77 402.83 0.95 1.05 17 0 0 0.95 1.05 18 - 139.6 235.5 0.95 1.05 19 0 0 0.95 1.05 Figure (1): Ploss vs. Pinjection at Bus 17 (KAZ) Figure (٢): Ploss vs. Pinjection at Bus 19 (QRN) 0 20 40 60 80 100 120 140 160 180 36.7 36.8 36.9 37 37.1 37.2 37.3 37.4 37.5 37.6 Plosses[Mw] Pinjection[Mw] bus 17 max loss reduction=2.34% 0 20 40 60 80 100 120 140 160 180 200 36.8 36.9 37 37.1 37.2 37.3 37.4 37.5 37.6 37.7 37.8 37.9 38 bus 19 optimum reduction=1.71% Ploss[Mw] Pinjection[Mw] Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥٠٩ 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0 5 10 15 20 25 30 35 40 Max Loss Reduction% Bus No. Figure3:Loss Reduction for Injecting Real Power at some Buses Figure4: Ploss vs. Qinjection for Bus 4 (QAM) 0 5 10 15 20 25 30 35 40 45 50 37.59 37.6 37.61 37.62 37.63 37.64 37.65 37.66 bus 4 (no loss reduction) Ploss[Mw] Qinjection[Mvar] Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥١٠ Figure5: Ploss vs. Qinjection for Bus 5 (MOS) Figure 6: Relationship between Sensitivity and System Losses at Bus 2 (MOS) 0 50 100 150 200 250 300 37.35 37.4 37.45 37.5 37.55 37.6 37.65 Ploss[Mw] bus 5 optimum loss reduction=0.59% Qinjection[MVAR] 0 100 200 300 400 500 600 700 800 31 32 33 34 35 36 37 38 39 bus 2 Ploss[Mw] Pgeneration[Mw] Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥١١ Figure 7: Relationship between Sensitivity and System Losses at Bus 3 (HAD) Figure 8: Relationship between Sensitivity and System Losses at Bus 12 (MSB) -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 33.5 34 34.5 35 35.5 36 36.5 37 37.5 38 38.5 bus 12 ploss[Mw] sensitivity -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 33.5 34 34.5 35 35.5 36 36.5 37 37.5 38 38.5 bus 12 ploss[Mw] sensitivity Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥١٢ Figure 9: Relationship between Sensitivity and System Losses at Bus 16 (NSR) Figure10: Relationship between Sensitivity & System losses at Hartha Bus18(HRT) -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 37 37.5 38 38.5 39 39.5 40 Ploss[Mw] sensitivity -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 37 37.2 37.4 37.6 37.8 38 38.2 38.4 38.6 38.8 39 Ploss[Mw] sensitivity From a Subroutine calculating losses using eq.٢ Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٥١٣ Figure11: Flow chart illustrating optimization program using sensitivity analyzing Form vector       ∂ ∂ x f using eq.5 Form vector       ∂ ∂ u f =       ∂ ∂ v p Calculate Gradient of F [ ] λ×      ∂ ∂ +      ∂ ∂ =∇ T u g u F F Form vector       ∂ ∂ u g =the partial derivative of injected power Calculate the sensitivity ( λ ) [ ]       =       ∂ ∂ −== − SEN SEN T Q P SEN x f JacSEN * 1 λ Form Hessian matrix (H)which represent the second partial derivative for Ploss w.r.t control variables Calculate variable incremental [ ] [ ] [ ]FHU ∇×−=∆ −1 [ ] op U ε:∆ Develop variables [ ] 11 ++ ∆+= KKK UUU max1min UUU K ≤≤ + To a Subroutine to calculate Pi&Qi injection power Calculate load flow and transmission line losses End K=K+1