Determining Transmission Losses Penalty Factor Using Adaptive Neuro Fuzzy Inference System (ANFIS) For Economic Dispatch Application

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1 7 Determnng Transmsson Losses Penalty Factor Usng Adaptve Neuro Fuzzy Inference System (ANFIS) For Economc Dspatch Applcaton Rony Seto Wbowo Maurdh Hery Purnomo Dod Prastanto Electrcal Engneerng Department, Sepuluh Nopember Insttute of Technology Kampus ITS, Keputh Sukollo, Surabaya-60 Abstract - Ths Research project proposes an Adaptve Neuro Fuzzy Inference System (ANFIS) methodology for penalty factors calculaton. Transmsson loss penalty factor are commonly appled n the economc dspatch of generaton. The purpose of the penalty factor s to reflect nto the economc loadng the effect of losses realzed n delvery of power across the transmsson network to the load. The economcs of generator are non lnearly based by ts electrcal locaton relatve to the load. The farther electrcally a generator s from the load, the loss penalty wll be the larger. n searchng target. The combnaton of both method wll cover the weaknes each other. 2. ECONOMY DISPATCH 2. Economc Dspatch Power system can be represented as fgure below: Keywords: Economc dspatch, Losses, penalty factor and ANFIS. INTRODUCTION Economc Dspatch s a mportant procces that should be done for supplyng the Electrc Load. In the frame work of gettng smple calculaton and faster calculaton, frequenly, t s calculated wth neglectng the transmsson losses. The Impact of neglectng transmsson losses s the result of the calculaton can t get optmal result[]. It means there s posblty that the farther and low cost generator unt wll tend to produce hgher output, and the nearer and hgh cost generator unt wll tend to produce lower output. Ths condton wll cause hgher power losses n the transmsson lne. Therefore, we apply penalty factor to economc Dspatch n the frame work of consderng transmsson losses. Ths method wll apply the hgher penalty factor to long dstance generator unt and lower penalty factor to short dstance generator unt. The mplcaton of ths method s that the output power from long dstance generator unt wll be lower than before [3]. Ths paper proposes a alternatve methode for determnng penalty factor usng Adaptve NeuroFuzzy Inference System (ANFIS). ANFIS Combnes two method, that s neural networks (NN) and fuzzy logc (FL). Fuzzy logc has strong pont on the hgh speed target searchng but t has to be set when facng dfferent condton. In other hand, neural networks method has strong pont on adaptng to dfferent condton but t has low speed Fg. N thermal unt commtted to serve a load of P load The fgure above state objectve functon, constrant and LaGrange equaton that can be formulated below: Lagrange Equaton : δl F T + λφ δl Lagrange Equaton F T Objectve Functon λ Lagrange Multpler φ Constrant Objectve functon s equal to the total cost for supplyng the ndcated load. The problem s to mnmze F T subject to the constrant that the sum of the power generated must equal the receved load. Objectve Functon : F T F + F 2 + F 3 +..F N Σ F (P ) Constrant : φ P load + P loss (P,P 2 P N ) - Σ P Optmum operaton can be reached f the dervatve of Lagrange Functon wth respect to power output s equal to zero. Then δ L 0 δ P

2 8 δl df δp loss λ 0 δp dp δp δp δp loss df dp ( P ) λ It means that the mnmum cost of operatng condton occur f the ncremental cost rates multpled wth penalty factor of all the unts s equal to undetermned value, λ. The frst equaton s penalty factor, pf, whch represent level of the unt causng transmsson losses Pf δploss δp And the Incremental loss for bus : δploss δp If economc dspatch neglected the transmsson losses consderaton, then the ncremental cost rates of all unt should be equal to undetermned value, λ. Ths concept can be extended to nvestgate the mpact of penalty factor. For Pf > (Increment of P cause hgher transmsson losses) df ( P ) Pf dp t means unt, relatvely, causes hgher losses n power system network. For Pf < (Increment of P cause lower transmsson losses). t means unt, relatvely, causes lower losses n power system network. The statement above can be descrbed as a graph usng ncremental cost curve at Fg. 2. Rule : If x s A and y s B, then f p x + q y + r Rule 2: If x s A 2 and y s B 2, then f 2 p 2 x + q 2 y + r 2 Fg. 3(a) llustrates the reasonng mechansm for ths Sugeno model, the correspondng equvalent ANFIS archtecture s shown n Fg. 3(b), where nodes of the same layer have smlar functon, as descrbe next. Fg. 3 (a) Two nput frst-order Sugeno fuzzy model; (b) ANFIS archtecture Layer Every node n ths layer s an adaptve node wth node functon O l, μ A (x), for,2, or O l, μ B (y), for 3,4 where x or y s the nput node and A or B -2 s a lngustc label (such as small or large ) assocated wth ths node. In other word O \, s the membershp grade of a fuzzy set A(A, A 2, B or B 2 ) and t specfes the degree to whch the gven nput x or y satsfes the quantfer A. Here the membershp functon for A can be any approprate parameterzed membershp functon, such as the generalzed bell: μ A ( x) 2b x c + a where {a, b, c ) s the parameter set. As the values of the parameters change the bell shaped functon vares accordngly, thus exhbtng varous forms of the membershp functon for fuzzy set A. Parameters n ths layer are referred to as premse parameter. Fg. 2 Concept of economc dspatch usng ncremental curve 2.2 ANFIS Theory For smplcty, we assume that the fuzzy nference system under consderaton has two nputs x and y and one output z. For a frst order Sugeno fuzzy model, a common rule set wth two fuzzy fthen rules s the followng: Layer 2 Every node n ths layer s a fxed node wth node labeled Π, whose output s the product of all the ncomng sgnals O 2, ϖ μ A (x)μ B (y),,2. Each node output represents the frng strength of a rule. In general, any other T-norm operators that perform fuzzy AND can be used as the node functon n ths layer

3 9 Layer 3 Every node n ths layer s a fxed node wth node labeled N. The th node calculates the rato of the th rule s frng strength to the sum of all rules frng strength _ w O 2, w,2 w + w For convenence, outputs of ths layer are called normalzed frng strength. Layer 4 Every node n ths layer s an adaptve node wth node functon O 4, ϖ f ϖ (p x + q y + r ) 2 where ϖ s a normalzed frng strength from layer 3 and {p x + q y + r } s the parameter set of ths node. Parameters n ths layer referred to as consequent parameters. Layer 5 The sngle node n ths layer s a fxed node wth node labeled Σ, whch computes the overall output as the summaton of all ncomng sgnals. All Output O 5, _ w f w f w Reasonng mechansm The reasonng mechansm (learnng rules) that used n ANFIS s hybrd learnng rules. Table 2. Reasonng mechansm Forward Pass Backward Pass Parameter premse Fxed Gradent Descent Parameter Least Square consequent Estmator Fxed Sgnal Node Output Sgnal Error 3. THE SIX BUS ANFIS APPLICATION The System conssts of three unts for supplyng load. Fuel Cost equaton of each unts s: F (P ) 23, +,669 P + 0,00533 P 2 R/h F 2 (P 2 ) 200,0 + 0,333 P 2 + 0,00889 P 2 2 R/h F 3 (P 3 ) 240,0 + 0,833 P 3 + 0,0074 P 3 2 R/h Fg. 4 Sngle lne dagram 6 bus Maxmum and mnmum power of each generator unts s : 50,0 MW P 200 MW 37,5 MW P 2 50 MW 45,0 MW P 3 80 MW The sx bus system conssts of transmsson lnes and the data of mpedances can be shown at Table. Table Data of lne transmsson Impedances From To bus bus R (pu) X (pu) B (pu) Data of the sx bus system are entered to computer program whch has algorthm below: A. ANFIS Tranng step. Enterng data such as maxmum and mnmum capacty of each generator unt, Type of bus, actve and reactve power of each bus, per unt mpedances of transmsson lne 2. Startng load flow calculaton usng Newton Raphson Method. Ths calculaton uses applcaton software, Matpower. 3. Calculatng ncremental transmsson losses (P loss ) usng senstvty analyss method. 4. Developng structure of ANFIS. Appled Structure of ANFIS n ths research s : 5.

4 0 a. Sugeno fuzzy model b. Membershp functon s gauss wth 4 nput for each membershp functon c. The appled Defuzzfcaton s weght average. d. The Input of ANFIS s power output of each generator unt and the output of ANFIS s penalty factor. The Archtecture of ANFIS can be shown from Fg. 5 No Load Pf. Pf. 2 Pf Usng penalty factor above, we calculate economc dspatch whch the result s shown below. Table 3 Transmtted power and generaton cost of each unt No Load Unt. Unt. 2 Unt. 3 Losses Cost Fg. 5. ANFIS Archtecture B. ANFIS Applcaton Step. Enterng power system load. 2. Enterng generated actve power of each generator unt. 3. Determnng penalty factor usng ANFIS. 4. Calculatng economy dspatch to fnd transmsson losses and the generaton cost. 4. SIMULATION AND ANALYSIS 4. Determnng Penalty Factor Usng Matrx B mn Method In ths secton, penalty factor s determned usng matrx Bmn. It wll be compared wth calculated penalty factor usng ANFIS method. Penalty factor s calculated based on data from Table. and load data vary from 80 MW untl 480 MW. The result can be shown from Table 2. Table 2 Determned Penalty factor usng Matrx B mn Method No Load Pf. Pf. 2 Pf Determnng Penalty Factor Usng ANFIS Method Usng ANFIS method, penalty factor can be determned and the results are shown n Table 3. Penalty factor s calculated based on data from Table. and load data vary from 80 MW untl 480 MW. Table 4 Determned Penalty factor usng ANFIS method No Load Pf. Pf. 2 Pf

5 No Load Pf. Pf. 2 Pf Usng penalty factor above, we calculate economc dspatch whch the result s shown below. Table 5 Transmtted power and generaton cost of each unt No Load Unt. Unt. 2 Unt.3 Losses Cost CONCLUSIONS generaton cost of load 440 MW where the dfferent s 2 %. 4. Ths research prove that ANFIS method can be a alternatve method to solve economc dspatch wth consderng transmsson losses. 6. REFERENCES [] Allen J. Wood, Bruce F. Wollenberg, Power Generaton, Operaton And Control, Jhon Wley & Sons Inc, 996. [2] J. S. Roger Jang, Neuro-Fuzzy and Soft Computng, Prentce-Hall Inc, 997 [3] Rony Seto W, Perhtungan Penalty Factor Rug-rug Transms Dengan Jarngan Saraf Truan Untuk Aplkas Economy Dspatch Pada Sstem Tenaga Lstrk, Report book of Research Insttute of ITS, BIOGRAPHIES Rony Seto Wbowo, receved bachelor of Engneerng (ST) n 999 from ITS. He has joned Electrcal Engneerng Department, Sepuluh Nopember Insttute of Technology snce 999. Hs areas of nterest nclude Economc Dspatch, Generaton schedulng and Load Forecastng. Maurdh Hery Purnomo, receved Bachelor of Engneerng n 984 from ITS, M.Eng n 995 and Dr n 998 from Osaka Cty Unversty. He has joned Electrcal Engneerng Department, Sepuluh Nopember Insttute of Technology snce 985. Hs areas of nterest nclude artfcal Intellgent and power system analyss. Dod Prastanto, receved bachelor of Engneerng (ST) n 2003 from ITS Based on the data analyss of ths research, we can conclude :. Penalty factor data show that penalty factor for unt and 3 s less than and penalty factor for unt 2 s more than. It means that unt and unt 3 wll tend to produce hgher output than economc dspatch wthout consderng transmsson losses and unt 2 wll tend to produce lower out than economc dspatch wthout consderng transmsson losses 2. Result of Smulaton show that determned penalty factor usng ANFIS method s better than determned penalty factor usng B mn matrx. It can be ndcated from the generated transmsson losses. For load 440 MW, the dfferent transmsson loses s 7.28 MW or 6,5%. 3. Based on generaton cost consderaton, there s no sgnfcant dfferent between ANFIS method and matrx B mn. It can be ndcated from