Application of Genetic Algorithms for Optimal Reactive Power Planning of Doubly Fed Induction Generators

Transcription

1 Application of Genetic Algorithm for Optimal Reactive Power Planning of Doubly Fed Induction Generator P. SANGSARAWUT, A. OONSIVILAI and T. KULWORAWANICHPONG * Power Sytem Reearch Unit, School of Electrical Engineering Suranaree Univerity of Technology 111 Univerity Avenue, Suranaree Ditrict, Nakhon Ratchaima THAILAND * Correponding author {thanatchai@gmail.com} Abtract: - Thi paper decribe optimal reactive power control of a doubly fed induction generator (DFIG), which i widely ued in a ditributed generating plant. Although it tructure i imilar to that of induction motor, it reactive power control i more complicated. In thi paper, teady-tate power tranfer equation are derived and developed for a doubly fed tructure of the induction generator. When a ditributed power plant equipped with DFIG i connected to a regional power grid, reactive power injection from the plant reult in ditribution ytem performance, e.g. voltage drop, power loe, etc. By uing genetic algorithm, optimal reactive power injection can be achieved in order to minimize total power lo in power ditribution ytem. The 37-node IEEE tandard tet feeder i ued to evaluate it performance. A a reult, optimal reactive power control of DFIG can reduce total power loe and alo improve voltage profile in power ditribution ytem. Key-Word: - Optimal reactive power planning, doubly fed induction generator, optimization, genetic algorithm 1 Introduction A ditributed generator (DG) i a mall generator (normally le than 15 MW) [1], cattered throughout an electric power ditribution ytem to erve local load. It i widely ued in a renewable energy plant. The renewable plant ha been increaingly intalled due to everal reaon: i) it can be located cloer to cutomer, ii) high efficiency of modern ditributed generating plant i available for a mall ize capacity of ranging from 10 kw 15 MW, iii) it i required horter intallation time and cheaper invetment cot, iv) it improve ditribution reliability, etc [2]. The ue of DG in the future require ditribution ytem engineer to take into account it impact in the ytem planning. To intall a new DG at a particular location, invetment and operating cot are very important in power ditribution planning. Therefore, one of the planner goal i to minimize overall cot [3-5]. When the ditribution power network tructure i aumed to be invariable during the planning period, change in load energy demand or the appearance of new load over hort period could require ome action from exiting reactive power equipment or invetment for network upgrade might be neceary. In thi circumtance, DG ha a built-in function to inject deired reactive power to the grid at the point of connection. Thi lead to the advantage of reducing power loe and can be a valuable option for the planning engineer to reduce invetment for the grid upgrade. However, their intallation in non-optimal location or izing can reult both in an increaing of power loe and in a reducing of reliability level [6]. Analyi of reactive power control for ditributed generator at a given location in order to determine an appropriate range of complex power exchange indicate optimal izing of DG intallation. In thi paper, a doubly fed tructure of induction generator [7] i invetigated. Determination of optimal DG rating i one of contrained optimization problem that can be olved by nonlinear optimization technique uch a equential quadratic programming (SQP) or intelligent method like genetic algorithm (GA) [8]. In thi paper, Section 2 provide problem formulation of the reactive power planning problem. Brief of power ditribution network and doubly fed induction generator model i alo included. Section 3 give olution methodology decribed tep-by-tep, particularly the exploitation of GA and the formulation of penalty function. Simulation reult and concluion are in Section 4 and 5, repectively. ISSN: Iue 3, Volume 9, March 2010

2 2 Problem Formulation Thi ection decribe formulation of reactive power planning. It conit of two major part: i) power lo model of the power ditribution ytem and ii) reactive power control via DFIG. Both part are coupled and mut be olved accordingly. Although olution from the power network i directly involved total power loe, reactive power olution of DG obtained from the power network olver mut not be exceeded the reactive power limit of the DFIG. The following give brief decription of both part. Power Network Solution Power flow calculation i to determine a et of voltage olution that atify the power mimatch equation at every node. The main information obtained from thi calculation are phaor voltage of load bue, reactive power injection by generator bue, complex power flow through tranmiion line, total power loe, etc [9]. Connected generator at generator bue can be modeled a either PV bu or PQ bu. If the voltage magnitude at the point of connection i regulated, the PV bu model can be ued. With obtained voltage olution, the reactive power injected from DFIG can be computed. Reverely, if the reactive power injection i treated a a control variable, DFIG will be aigned a a PQ bu generator with a pecified reactive power value. Therefore, the voltage magnitude of the DFIG connection can be obtained. Power network olution mut atify a et of nodal power mimatch equation. Given that there i a total of n bue in the ytem and one of them i aigned a the lack bu. Power flow equation of bu k (real and reactive power) can be imply expreed a follow. Where n ( ) (1) P = V VY co θ + δ -δ cal,k k i ki ki i k i=1 n ( ) (2) Q = V VY in θ + δ -δ cal,k k i ki ki i k i=1 P cal,k and Q cal,k are calculated real and reactive power of bu k V k i the voltage magnitude of bu k δ k i the phae angle of bu k Y ki i the magnitude of the k th -row, i th - column admittance matrix element θ ki i the phae angle of the k th -row, i th - column admittance matrix element The olution of the power network can be obtained by employing ome efficient iterative method, e.g. Gau-Seidel or Newton-Raphon method, in order to olve the power mimatch equation, ΔP k = P cal,k P ch,k = 0 and ΔQ k = Q cal,k Q ch,k = 0 for all node, where P ch,k and Q ch,k are cheduled real and reactive power of bu k. By applying the Talor Serie expanion, the NR method eparately approximate the real and reactive power flow equation by collecting the firt two term and neglecting other higher-order term but there i till ome interaction between them. Briefly, (2) and (3) repreent real and reactive power mimatch equation at bu k after approximation. By collection of the real and reactive power mimatche of a total of n-1 bue, olution updating equation of the Newton-Raphon power flow method can be written in (4). In addition, (4) can be reduced to the compact matrix form, o-called Jacobian matrix equation of the power flow olution method a decribed in (5). Where ΔP J J Δδ 1 2 = ΔQ J J Δ V 3 4 J 1 J 4 are Jacobian ub-matrice (4) (5) By rearranging (5), phae angle and magnitude of the voltage phaor of n-1 bue can be updated according to the following equation. ISSN: Iue 3, Volume 9, March 2010

3 Δδ J J ΔP = Δ V J J Δ Q ( k+ 1) ( k) ( k) = +Δ i i i (6) δ δ δ (7) ( k+ 1) ( k) ( k) i i i V = V +Δ V (8) where R = r + r / and X = x +x g 1 2 g 1 2 Briefly, expreion of real and reactive power exchange between the DFIG and the upply grid can be written in (11) and (12). Thee two equation will be ued a pecial contraint during the proce of the power network optimization. Reactive Power Control of a Doubly Fed Induction Generator A DFIG ha a pecial feature and differ from a conventional induction generator in which it rotor circuit i connected to an adjutable ac ource [10] a hown in Fig. 1. Fig. 2 how the per-phae teady-tate equivalent circuit of the DFIG. It real and reactive power tranfer equation can be directly derived from thi circuit. Analyzing the DFIG i imilar to that of a conventional induction generator. Only a controlled external ource E i added in the rotor circuit. Starting with complex power tranfer from the induction generator a decribed in the following expreion, and I S g * = Pg - jq g = V t * I g (9) g = E θ E V 0 ( + j ) t coθ inθ Vt = (10) R + j X R + jx g g g g ( a) V t ( b) V t ( c) V t Fig. 1. Doubly fed induction generator ytem + V t - I g r 1 jx 1 jx 2 jx m ( a E ) ( b E ) ( c E ) E r 1 / Fig. 2. Per-phae teady-tate equivalent circuit of the DFIG P = VE r VE 2 r ( ) ( ) 2 δ δ ( ) r ( r+ 2 ) 1 +x+x ( 1 2 ) t t 2 r+ 1 co + x+x 1 2 in -r+ 1 Vt g 2 2 VE VE ( ) δ ( ) ( ) t t r x 2 1+x2 co - r 1+ ind- x 1+x2 Vt g 2 2 Q = r ( r+ 2 ) 1 +x+x ( 1 2 ) 2 (11) (12) From the above equation where all machine parameter are fixed, there are three variable that can be controlled: i) E, ii) δ and iii) lip (). In ome application, contant peed operation might be held. Therefore, controlling through E and δ are more generalized. Thee two variable can be achieved by a pecially deigned voltage controller of the back-to-back converter a in Fig. 1. With regulating the real power injection from the DFIG, reactive power can be varied according to E and δ adjutment. When contant real power generation i taken into account, a pecified value ISSN: Iue 3, Volume 9, March 2010

4 of the reactive power yield only one pair of E and δ. Thi reult in Fig. 3 repreenting δ in horizontal axi without howing E. Fig. 3. DFIG reactive power control of contant real power operation where r 1 = 3.4 Ω, r 2 = 0.43 Ω, x 1 = 3.5 Ω, x 2 = 0.35 Ω, = 4.0% 3 Optimal Reactive Power Planning Minimizing the overall power loe in during normal operation of an electric power ditribution ytem require ome efficient optimization technique. It can be formulated a follow. Minimize m 2 lo = i i i=1 P I r Subject to Pch,k - P cal,k = 0,k = 1,2,...,n Q Q = 0,k = 1,2,...,n ch,k cal,k ( ) ( ) Equation 3 = 0 Equation 4 = 0 min max g g g Q Q Q Vmin Vi V max,i = 1,2,...,n Emin E Emax δ δ δ min max Where r i denote the reitance of feeder i I i denote the current flowing through feeder i m i a total number of feeder line P g i a fixed value of DFIG real power Q g i a control variable To olve the above contrained optimization problem, a penalty function combining the objective function together with all contrained i applied. The quadratic function i ued to penalize all the above contraint. In thi paper, genetic algorithm will be employed. It can be decribed a follow. Genetic algorithm [8, 11-14] are one of the well-known intelligent earch mechanim baed on the Darwinian principle of natural election. It conit of bit tring repreenting the control variable and three genetic operator: i) election or ISSN: Iue 3, Volume 9, March 2010

5 reproduction, ii) croover and iii) mutation. The algorithm tart with a random creation of an initial population. During each generation, the tring within the current population are evaluated for their fitne value via the objective function. A new population, o-called offpring, i then created uing thee three genetic operator. Thi tochatic proce i intended to generate a new and better population from the old population. Auming the algorithm converge, a et of olution with better fitne i obtained. Thu, the optimal olution i found. It can be ummarized tep-by-tep a follow. Given that a population et ha N member and each member conit of M variable. Each individual member of the population i called a chromoome. 1. Initialization: Generate an initial population by uing random proce and then evaluate their correponding fitne function. 2. Evolution: Apply the genetic operator to create an offpring population. 3. Fitne tet: Evaluate the fitne value for the generated offpring population. 4. Convergence check: Check for violation of all termination criteria. If not atified, repeat the evolution proce. problem. To reduce programming complication, the Genetic Algorithm (GADS TOOLBOX in MATLAB [15]) i employed to generate a et of initial random parameter. With the earching proce, the parameter are adjuted to give the bet reult. 5 Simulation Reult To evaluate the propoed reactive power control cheme, the 37-node IEEE tandard tet feeder [16] a hown in Fig. 4 wa ued for tet. All day operation and reactive power compenation performed by the DFIG at a pecific location in order to minimize the total power loe were ituated. Four tet cae cenario were conducted a: i) bae cae of no DFIG intalled, ii) DFIG intalled at node 8, iii) DFIG intalled at node 25 and iv) DFIG intalled at node 8 and 25. In addition, the real power injection by the DFIG i fixed for each cae by 5 MW and 10 MW. Therefore, there i a total of eight tet cae cenario. Applying genetic algorithm, the optimal olution for each cae can be obtained. Furthermore, thee olution are compared with the olution obtained by a cae of zero reactive power injection and the bae cae. All reult can be hown in Table 1 and 2 a follow. It can be ummarized in Fig. 4. Fig node IEEE tandard tet feeder Fig. 4. Flowchart of the GA procedure [11] In thi paper, the GA i elected to build up an algorithm to olve optimal reactive power flow Table 1 Optimal olution in which each P g = 5 MW wa fixed Location Without DFIG Q g = 0 Mvar Optimal Q g Bu MWh MWh MWh Bu MWh MWh MWh Bu 8 & MWh MWh MWh ISSN: Iue 3, Volume 9, March 2010

6 Table 2 Optimal olution in which each P g = 10 MW wa fixed Location Without DFIG Q g = 0 Mvar Optimal Q g Bu MWh MWh MWh Bu MWh MWh MWh Bu 8 & MWh MWh MWh Moreover, with 30 trial of each cae, the bet olution of which obtained from each can be illutrated in Table 3 6. Table 3 Optimal olution in which P g = 5 MW wa intalled at bu 8 Hour Total load (MW) Before intallation Power loe (MW) Unity power factor Optimal Q g Optimal Q g (Mvar) Total Loe ISSN: Iue 3, Volume 9, March 2010

7 Table 4 Optimal olution in which P g = 5 MW wa intalled at bu 25 Hour Total load (MW) Before intallation Power loe (MW) Unity power factor Optimal Q g Optimal Q g (Mvar) Total Lo ISSN: Iue 3, Volume 9, March 2010

8 Table 5 Optimal olution in which P g = 5 MW wa intalled at bu 8 and 25 Power loe (MW) Optimal Q g (Mvar) Hour Total load Before Unity power (MW) Optimal Q intallation factor bu bu Total Lo ISSN: Iue 3, Volume 9, March 2010

9 Table 6 Optimal olution in which P g = 10 MW wa intalled at bu 8 Hour Total load (MW) Power loe (MW) Optimal Q g Before Unity power Optimal (Mvar) intallation factor Q g Total Lo ISSN: Iue 3, Volume 9, March 2010

10 Table 7 Optimal olution in which P g = 10 MW wa intalled at bu 25 Power loe (MW) Total load Optimal Q g Before Unity power Hour (MW) Optimal Q (Mvar) intallation factor g Total Lo ISSN: Iue 3, Volume 9, March 2010

11 Table 8 Optimal olution in which P g = 10 MW wa intalled at bu 8 and 25 Hour Total load (MW) Power loe (MW) Unity Before power intallation factor Optimal Q g (Mvar) Optimal Q bu bu Total Lo A a reult, when reactive power injected from the DFIG i well controlled, operation with minimum power loe can be expected. For a cae of P g = 5 MW, the maximum power lo reduction i jut over 40 MWh. Whilt, about 60 MWh energy reduction i obtained from the other cae. Imagine that Suranaree Univerity of Technology (SUT) conume 2 MW average power demand per hour, i.e. a total of 48-MWh electric energy i conumed every day. The total amount of energy lo reduction from the propoed reactive power control cheme i ufficient to feed the SUT campu for a whole day. 6 Concluion Thi paper preent effect of a doubly fed induction generator on power lo reduction in an electric power ditribution ytem. Appropriate adjutment of the reactive power injection from an available DFIG reult in total power loe and voltage ditribution along feeder line. In addition, real and reactive power tranfer of a DFIG are included to formulate a contrained optimization problem. With both contraint the obtained olution i verified for practical ue due to the limitation of voltage fed by the back-to-back converter. Genetic algorithm are very ueful in thi problem due to it ability of finding a near global ISSN: Iue 3, Volume 9, March 2010

12 olution. From atifactory reult, optimal reactive power control of a doubly fed induction generator can coniderably reduce total power loe of the electric power ditribution feeder. It i confirmed by the reult of the 37-node IEEE tandard tet feeder decribed in thi paper. 7 Acknowledgment The author would like to acknowledge the financial upport of the reearch grant (IRD ) ponored by Suranaree Univerity of Technology, during a period of thi work. Reference: [1] G. Celli, F. Pilo, Optimal Ditributed Generation Allocation in MV Ditribution Network, 22 nd International Conference on Power Indutry Computer Application (PICA 2001), May 2001, pp [2] T. Niknam, A.M. Ranjbar, A.R. Shirani, A.R. Mozafari, A. Otadi, Optimal Operation of Ditribution Sytem with Regard to Ditributed Generation: A Comparion of Evolutionary Method, Fourtieth IAS Annual Meeting on, October 2005, pp [3] M. Mardaneh, G.B. Gharehpetian, Siting and Sizing of DG Unit Uing GA and OPF Baed Technique, IEEE Region 10 Conference (TENCON 2004), November 2004, pp [4] D. Chattopadhyay, K. Bhattacharya, J. Parikh, Optimal Reactive Power Planning and It Spot- Pricing: an Integrated Approach, IEEE Tranaction on Power Sytem, Vol. 10, pp , 1995 [5] R.E. Brown, J. Pan, X. Feng, K. Koutlev, Siting Ditributed Generation to Defer T&D Expanion, Tranmiion and Ditribution Conference and Expoition, 28 October - 2 November 2001, pp [6] C. Wang, M.H. Nehrir, Analytical Approache for Optimal Placement of Ditributed Generation Source in Power Sytem, IEEE Tranaction on Power ytem, Vol. 4, pp , 2004 [7] M.S. Vicato, J.A. Tegopoulo, Steady State Analyi of A Doubly-Fed Induction Generator Under Synchronou Operation, IEEE Tranaction on Energy Converion, Vol. 4, pp , 1989 [8] D.E. Goldberg, Genetic Algorithm in Search Optimization and Machine Learning, Addion-Wiley, 1989 [9] H. Saadat, Power Sytem Analyi, McGraw-Hill, 2004 [10] A. Tapia, G. Tapia, J.X. Otolaza, J.R. Saenz, R. Criado, J.L. Beraategui, Reactive Power Control of a Wind Farm Made up with Doubly Fed Induction Generator Part I, IEEE Porto Power Tech Conference (PPT 2001), Sep 2001, pp [11] The MathWork Inc., Genetic Algorithm and Direct Search TOOLBOX, CD-ROM Manual, [12] N. Naewngerndee and T. Kulworawanichpong, Voltage-dependent Parameter Refinement for Singlephae Induction Motor uing Genetic Algorithm, The WSEAS Tranaction on Sytem and Control, Iue 1, Vol. 4, pp , [13] P. Pao-La-Or, T. Kulworawanichpong, A. Oonivilai, Bi-objective Intelligent Optimization for Frequency Domain Parameter Identification of a Synchronou Generator, The WSEAS Tranaction on Power Sytem, Iue 3, Vol. 3, pp , [14] B. Fahimnia, R. Molaei, M. Ebrahimi, Genetic Algorithm Optimization of Fuel Conumption in Compreor Station, The WSEAS Tranaction on Sytem and Control, Iue 1, Vol. 3, pp. 1 10, [15] K. Somai, A. Oonivilai, A. Srikaew, and T. Kulworawanichpong, Optimal PI controller deign and imulation of a tatic var compenator uing MATLAB SIMULINK, The 7th WSEAS International Conference on POWER SYSTEMS, Beijing, China, pp [16] Ditribution Sytem Analyi Subcommittee.: IEEE 37-node Tet Feeder. IEEE Power Engineering Society ISSN: Iue 3, Volume 9, March 2010