Research on method of total transfer capacity based on immune genetic algorithm Dong Liang, Jianjun Xu, Zhigang Sun

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1 Research o method of total trasfer capacity based o immue geetic algorithm Dog Liag, Jiaju Xu, Zhigag Su Departmet of Electrical Iformatio Egieerig, Northeast Petroleum Uiversity, Daqig , Chia Keywords: power system, immue geetic algorithm, total trasfer capacity (TTC) Abstract: I this paper the sum of the load active power icremetal has bee used for the objective fuctio to create a mathematical model. The iequality costraits problems of geerator group like power costraits ad ode voltage costraits, that are trasformed to o-costrait coditios by itroducig the pealty fuctio. The optimizatio methods are programmed by MATLAB, ad each module of the program are described; Basic process based o immue geetic algorithm to calculate the total trasfer capacity (TTC) of power system is give. I order to verify the correctess of the model ad algorithm proposed i this paper, IEEE-30-ode system is take as testig system. By the calculatio of each lie TTC of a grid lie, the practicality of the proposed method has bee achieved greatly. Itroductio I recet years, the power geeratio capacity has bee icreasig at the rate of 10% per year i Chia. So the electrical shortage pheomea have bee reduced largely. The total trasfer capacity (TTC) problems have bee solved by a large umber of domestic ad foreig experts ad scholars with a variety of differet ways. Disbrach distributig factor method was used for TTC as well as power trasmissio ad geerator outage distributig factor methods [1]. The oliear system ad reactive power voltage were cosidered by cotiuatio power flow method, which was superior to DC power flow [2]. The cotiuous quadratic programmig method was adopted to figure out TTC [3]. The optimal power flow ad the static voltage stability restrait were both requested for the computatio [4]. The maximum ecoomic beefit was joied ito the calculatig coditios [5]. The Newto's ad the iteral pealty fuctio method are combied for the calculatio of the probability of the available trasfer capability [6]. I this paper, the immue geetic algorithm is applied to the solutio of total trasfer capacity of power system. Model for total trasfer capacity based o immue geetic algorithm Equality costraits Pi PDi Vi Vj ij cosij Bij siij 0 j1 (1) Qi QDi Vi Vj ij siij Bij cosij 0 j1 where P i, Q i are the active ad reactive power of the geerator i. P Di, Q Di are the load active ad reactive power of the ode i. is the total umber of odes. V i, i are the voltage amplitude ad phase of the ode i. ij i j, ij j Bij are the correspodig elemets of system odal admittace matrix. Iequality costraits. The voltage amplitude of each ode must be maitaied aroud the rated voltage. Thus the safe ad steady operatio of power system ad power quality ca be guarateed. The costrait of power grid operatio is composed of the active ad reactive output

2 costraits of geerator. Here, the active power output of geerator P i ad lie capacity P ij are selected as the cotrol variables. Ad the ode voltage V i ad reactive power output of geerator Q i are selected as the state variables [7-8]. The power costraits of geerator sets: max Pi Pi Pi, i S (2) max Qi Qi Qi The costrait of ode voltage: mi V max i Vi Vi, i S (3) The costrait of lie capacity: mi P P P max,, i j S (4) ij ij ij where S is the muster of all the odes. S is the muster of odes i the power trasmissio zoe. The subscripts *, mi ad max are respectively the per-uit value of basic power flow, the miimum ad maximum of the variable. Calculatio for total trasfer capacity based o immue geetic algorithm The module for power flow. The P-Q decompositio was chose as the key method for solvig the TTC based o immue geetic algorithm i this paper. Durig the flow calculatio, if the covergece ca`t be caught withi the set iteratios, the the idividual fitess value is take as 0, that is equivalet to the objective fuctio beig take as a very large value. Whe happeed the pathological etwork, the P-Q decompositio method ca`t coverge, ad the idividual o behalf of that etwork ca`t be a fial solutio [9-10]. Here for the P-Q decompositio mathematical equatios. Iterative correctio equatios are: P1 V1 B11 B1 V1 1 (5) P V B 1 B V Q1 V1 B11 B1 m V1 Qm V m Bm1 B mm V m The above equatio ca be abbreviated as: ' P V BV (7) '' Q V B V (8) where ' B ad '' B are symmetric real matrix, which are remaied uchaged i the iterative process. The equatios for every ode Pi, Qi are: i i i j ij ij ij ij j1 P P V V cos Bsi (9) Q Q V V si B cos (10) i i i j ij ij ij ij j1 1. Eter the origial data. The iput data are odes ad braches i the desig of this program. 2. Form the admittace matrix. The odes are processed by optimized sortig ad the idexed list of sparse storage of o-diagoal elemets for the admittace matrix is costructed. Therefore, the coefficiet matrix has bee obtaied ad came to the admittace matrix. 3. Form the factor table. It comes from the triagular factorizatio of B ' ad B ''. 4. Set the iitial voltage. PV ad PQ odes eed to set the iitial voltage. 5. Determie whether to meet the covergece coditio. PV ad QV are both the judgmets i this paper. (6)

3 The basic flow of algorithm. The TTC calculatio procedures based o immue geetic algorithm are as follow: 1. Iput the iitial data The iput data mai iclude geerator parameters, load parameters, lies, etc.al. I this paper, the data eed to verify are basic ode data, the upper ad lower limits of ode voltages, actual operatig data of geerator ad the allowed output limits of geerator. 2. Calculate the basic power flow The basic power flow has bee solved accordig to the origial data, while each brach ode variable uder the basic flow is obtaied. Thus, the lie active ad reactive power, each ode voltage amplitude ad phase agle ca be verified. 3. eerate the iitial atibodies If it`s the primary respose, the all the iitial atibodies are. If ot, the half the iitial atibodies are geerated radomly i the solutio space, the others are from the memory uit. 4. Calculate the atibody fitess The objective fuctio is take as the fitess fuctio i the paper, so the affiity values of atibody are draw by the calculatio results of the power flow. Sice this objective fuctio is used for seekig the maximum problem, so the approximatio of atibodies ad optimal solutio is proportioal to the value of the objective fuctio. 5. eetic operatio I accordace with the proposed geetic algorithm, the followig are wet o: cloig, crossover ad mutatio. 6. Determie whether the atibody diversity meet the requiremets By calculatig the affiity A ad iformatio etropy H we ca determie whether the diversity of atibodies meets the requiremets. If met the proceed to step 7, if ot retur to step Update based o the aggregate fitess The atibodies fitess ad cocetratio are evaluated comprehesively by calculatig the aggregate fitess. The atibodies of excellet fitess also ca suppress much high cocetratios of atibodies. 8. Update the memory cell The atibodies are arraged accordig to the size of fitess value, where the lower fitess atibodies i the memory set are replaced by the top atibodies. Such memory cells always cotai the higher fitess atibodies. But their solutio distributio is relatively good ad icrease the covergece speed greatly. 9. Determie whether the termiatio coditio is satisfied Firstly, the optimal solutio should be searched withi the limits of certai geetic geeratio. If the solutios searched is still optimal after may iteratios, the jump out of the evolutio. If the optimal solutio chages, the the cotiue search work should be requested util meetig the costat optimal solutio after may iteratios. Secodly, if the optimal solutio has`t be foud after the maximum iteratios, the the curret suboptimal solutio should be output. Case study The verificatio system is IEEE -30 ode system. The system has 6 geerators ad 41 lies. It ca be divided ito 3 zoes, as follows Fig. 1. The Beder decompositio, traditioal geetic algorithm ad immue geetic algorithm are used to calculate the TTC betwee every zoes. The fial result is take from the average value of each thirtieth separately. The results are show i Table 1: Show i Table 1, the calculatio results of traditioal geetic ad immue geetic algorithm based o the group optimizatio search is superior to those of Beder decompositio used aloe. The traditioal geetic algorithm is easy to fall ito local optimal solutio, while the result of immue geetic algorithm is more accurate tha geetic algorithm. We ca also get from Table 2, the computig time o immue geetic algorithm takes much shorter

4 Zoe Zoe Zoe3 26 Fig. 1 IEEE-30-ode system Fig.2 TTC covergece curve of geetic algorithm Table 1 total trasfer capacity calculatios zoe TTC /MW eetic algorithm Immue geetic algorithm Beder decompositio Table 2 Zoe 1 Zoe 2 to the TTC ad computig time averages Algorithm The average of TTC /MW Computig time /s Immue algorithm Immue geetic algorithm As show i Figure 2, whe the traditioal geetic algorithm is cosiderig, the curve of geeratios from 110 to 125, 129 to 148, 145 to 155 ad 155 to 173 are showig a similar level of situatio. Therefore, after a cosiderable umber of iteratios, the traditioal geetic algorithm ca be avoided ito local optimal value ad obtaied the global optimal value. However, due to the slow calculatig speed of traditioal geetic algorithm, the curve slope i the iitial search is very small. The TTC i the first 20 geeratios ca reach 45 (MW). Ad it ca`t reach 100 (MW) util passig 90 geeratios. Whe we are goig to calculate the trasfer data, i order to improvig the accuracy ad speed of calculatio process further, the immue geetic algorithm has bee proposed by author for TTC. Based o the combiatio of immue theory ad geetic algorithm, the populatio are iitialized by immue theory ad the capacity of coquerig the limit value is superior to geeral algorithm. The curve i Fig. 3 is a better covergece curve of the modified geetic algorithm. We ca fid the improved iitial populatio algorithm achieves the desired effect by the positios of iitial poits. Immue geetic algorithm Fig.3 TTC covergece curve of immue geetic algorithm Fig.4 Covergece curve compariso chart of two algorithms

5 The immue geetic algorithm has characteristics of learig, memory, ad adaptive capacity, so the populatio quality ca be optimized sigificatly ad the covergece speed is also improved. As show i Fig. 4, the covergece speed of immue geetic algorithm has bee faster tha the traditioal algorithm sice the begiig of the process. By comparig the two curves ca be foud the immue algorithm has stroger ability to overcome the local miima. As show i Figure 2, the covergece curve of the traditioal geetic algorithm from 110 to 125, 129 to 148, 145 to 155 ad 155 to 173 are showig slight dowward tred, which is similar to level situatio. As a result, the search stagatio come out o the four stages of 15, 19, 10 ad 18 geeratios. The rapidity ad practicability based o the traditioal geetic algorithm are affected greatly. However, the immue geetic algorithm has the stroger search capacity ad more rapid covergece speed. The covergece curve of immue geetic algorithm appears cotiual small-scale fluctuatios i the first 12 geeratios to the 35th. After several geeratios ca the curve still escape from local optima ad quickly move to the area close to the optimal solutio, so that the immue geetic algorithm has very strog ability to overcome local miima. It does ot appear the pheomeo of log-term search stagatio. I a sum, compared with traditioal geetic algorithm, the immue geetic algorithm has the advatages of more accurate calculatios, shorter iteratios ad good prospects i the applicatio of the total trasfer capacity. 5 Coclusio I this paper, the total trasfer capacity state of the power system has bee itroduced, which cotais the TTC theory ad its basic calculatig methods. The geetic algorithm ad immue geetic algorithm are both adopted ad compared to calculate the TTC about IEEE-30-ode system ad a practical power grid. Overall, the followig coclusios we ca get: 1. The objective fuctio is the maximum load icremet ad the pealty fuctio is used for the state variables from costrait to o-costrait. So a mathematical model of the total trasfer capacity has bee established. Meawhile, the immue geetic algorithm is applied to TTC. 2. The total trasfer capacity issue is a importat factor o the security ad ecoomic operatio of the power system. Comparig with the geeral algorithm for TTC, lots of existed problems ca be solved by the immue geetic algorithm excelletly, such as log computig time, poor accuracy ad so o. The applicatio of immue geetic algorithm has developed a broad space for the total trasfer capacity. Ackowledgmets This work was supported by the Natural Sciece Foudatio of Heilogjiag Provice (E201260). Refereces [1] C Ejebe, J Waight, M Saots Nieto, et al. Fast calculatio of liear available trasfer capability. IEEE Tras. o Power System, 2013, 28(3): [2] LIU Hua-zhi, LI Yag, CHEN Xiao. Available trasfer capacity calculatio based o cotiual power flow for trasmissio etwork. Electric Power Autoatio Equipmet. 2003, 23(12): 5-8. [3] DIAO Qihua, Mohamed Shaaba, NI Yixi. Iter-area total trasfer capacity calculatio usig sequetial quadratic programmig method i power market. Automatio of Electric Power Systems, 2000, 24(24): 5-8. [4] PAN Xiog, XU uo-yu. OPF based ATC calculatio with static voltage stability costraits. Proceedigs of the CSEE, 2002, 22(11): [5] LI Wei-xig, LI Zhi-mi, UO Zhi-zhog, WAN Peg. Available trasfer capacity calculatio based o maximizig system beefit. Automatio of Electric Power Systems, 2004, 28(20): [6] LI uo-qig, LI Xue-feg, et al. A probability ATC computatio by a combiatio of NEWTON with SUMT iterior poit method. Proceedigs of the CSEE, 2003, 23(8): [7] wo-chie L. Short-term eeratio Schedulig Usig Improved Immue Algorithm [J]

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