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SEARCH TELKOMNIKA , Vol.10, No.2, June 2012, 257~264 e-ISSN: 2087-278X (p-ISSN: 1693-6930) Accredited by DGHE (DIKTI), Decree No.: 51/Dikti/Kep/2010

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Optimum Reactive Power Dispatch for Alleviation of Voltage Deviations 1

Abraham Lomi

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, Dhadbanjan Thukaram

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Department of Electrical Engineering, Institut Teknologi Nasional (ITN) Malang, Indonesia Jl. Raya Karanglo Km. 2, Malang, Indonesia, Ph./Fax: +62-341-417636/417634 2 Department of Electrical Engineering, Indian Institute of Science, Bangalore, India CV Raman Avenue, Bangalore, India, Ph./Fax: +91-80-22932361/2360 0444 1 2 e-mail: [email protected] * , [email protected]

Abstrak

Paper ini mempersembahkan suatu algoritma optimasi non-linear untuk mengurangi kondisi naik turunnya tegangan pada operasi sehari-hari dari suatu jaringan daya listrik. Pengendalian tegangan untuk beban yang bervariasi dan kondisi pembangkitan dapat dicapai dengan mengkoordinasikan peralatan kompensasi shunt (SVC), trafo OLTC, dan eksitasi generator. Algoritma yang dikembangkan untuk pengendalian tegangan menggunakan teknik non-linear least square minimization. Hasil-hasil yang diperoleh sebagai ilustrasi menggunakan sistem 6-bus Wa rd-Hale dan sistem modifikasi IEEE 30-bus. Kata kunci : least square minimization, OLTC, optimisasi, pengendalian tegangan, SVC

Abstract

This paper presents a non-linear optimization algorithm for alleviation of under-voltage and over- voltage conditions in the day-to-day operation of power networks. Voltage control for varying load and generation conditions can be achieved by coordinated control of switchable shunt VAR compensating (SVC) devices, on load transformer taps (OLTC) and generators excitation. The proposed algorithm for voltage control uses a non-linear least square minimization technique. Results obtained for 6-Bus Ward- 1 of 8 Report (/report/reactive-power-dispatch-for-alleviation) Hale system and a modified IEEE 30-Bus system are presented for illustration purposes.

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Keywords : least square minimization, OLTC, optimization, SVC, voltage control

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Introduction The objective of an energy control center (ECC) is to ensure secure and economic operation of a power system. For the secure operation of power system it becomes essential to maintain network voltage profile within specified limits. In the day-to-day operation, power systems may experience both over-voltage and under-voltage violations. These violations occur due to inadequate reactive power supply for different loading conditions and network configurations. These violations can be relieved by co-ordinated control and switching of voltage/reactive power control devices like: (i) Switchable shunt VAR compensating (SVC) devices. (ii) On load tap change (OLTC) transformers. (iii) Generators excitation. Various algorithms [1-3] employing linear and non-linear optimization techniques have been reported in literature for voltage correction. These algorithms involve intensive numerical computations. This chapter presents a non-linear optimization algorithm for alleviation of undervoltage and over-voltage conditions in the day-to-day operation of power networks. The proposed algorithm for voltage control uses a non-linear least square minimization technique [4] . Least squares based estimation algorithm used extensively for power system state TELKOMNIKA , Vol.10, No.2, June 2012, 257~264 e-ISSN: 2087-278X (p-ISSN: 1693-6930) estimation (PSEE). Least squares minimization gives maximum likelihood estimate when measurement errors obey the Gaussian distribution.

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Accredited by DGHE (DIKTI), Decree No.: 51/Dikti/Kep/2010 257 Received January 11, 2012; Revised April 13, 2012; Accepted April 17, 2012 Optimum Reactive Power Dispatch for Alleviation of Voltage Deviations Abraham Lomi 1 * , Dhadbanjan Thukaram 2 1 Received January 11, 2012; Revised April 13, 2012; Accepted April 17, 2012 Department of Electrical Engineering, Institut Teknologi Nasional (ITN) Malang, Indonesia Jl. Raya Karanglo Km. 2, Malang, Indonesia, Ph./Fax: +62-341-417636/417634 2 Department of Electrical Engineering, Indian Institute of Science, Bangalore, India CV Raman Avenue, Bangalore, India, Ph./Fax: +91-80-22932361/2360 0444 e-mail: [email protected] 1 * , [email protected] 2 Abstrak Paper ini mempersembahkan suatu algoritma optimasi nonlinear untuk mengurangi kondisi naik turunnya tegangan pada operasi sehari-hari dari suatu jaringan daya listrik. Pengendalian tegangan untuk beban yang bervariasi dan kondisi pembangkitan dapat dicapai dengan mengkoordinasikan peralatan kompensasi shunt (SVC), trafo OLTC, dan eksitasi generator. Algoritma yang dikembangkan untuk pengendalian tegangan menggunakan teknik non-linear least square minimization. Hasil-hasil yang diperoleh sebagai ilustrasi menggunakan sistem 6-bus Ward-Hale dan sistem modifikasi IEEE 30-bus. Kata kunci : least square minimization, OLTC, optimisasi, pengendalian tegangan, SVC Abstract This paper presents a non-linear optimization algorithm for alleviation of under-voltage and over- voltage conditions in the day-to-day operation of power networks. Voltage control for varying load and generation conditions can be achieved by coordinated control of switchable shunt VAR compensating (SVC) devices, on load transformer taps (OLTC) and generators excitation. The proposed algorithm for voltage control uses a non-linear least square minimization technique. Results obtained for 6-Bus Ward- Hale system and a modified IEEE 30-Bus system are presented for illustration purposes. Keywords : least square minimization, OLTC, optimization, SVC, voltage control Copyright © 2012 Universitas Ahmad Dahlan. All rights reserved. 1. Introduction The objective of an energy control center (ECC) is to ensure secure and economic operation of a power system. For the secure operation of power system it becomes essential to maintain network voltage profile within specified limits. In the day-to-day operation, power systems may experience both over-voltage and under-voltage violations. These violations occur due to inadequate reactive power supply for different loading conditions and network configurations. CLICK HERE TO DOWNLOAD NOW! These violations can be relieved by co-ordinated control and switching of voltage/reactive power control devices like: (i) Switchable shunt VAR compensating (SVC) devices. (ii) On load tap change (OLTC) transformers. (iii) Generators excitation. Various algorithms [1-3] employing linear and non-linear optimization techniques have been reported in literature for voltage correction. These algorithms involve intensive numerical computations. This chapter Previous post Next post presents a non-linear optimization algorithm for alleviation of under-voltage and over-voltage Arthur A. Lee Bentley, III, Acting U.S. Soft Tissue Lasers In Dental Hygiene conditions in the day-to-day operation of power networks. The proposed algorithm for voltage Attorney Et Al (/Arthur-A-Lee-BentleyPdf (/Soft-Tissue-Lasers-In-Dentalcontrol uses a non-linear least square minimization technique [4] . Least squares based Iii-Acting-U-S-Attorney-Et-Al) Hygiene-Pdf) estimation algorithm used extensively for power system state estimation (PSEE). Least Jul 27, 2017 Jul 27, 2017 squares minimization gives maximum likelihood estimate when measurement errors obey the Gaussian distribution. e-ISSN: 2087-278X Optimum Reactive Power Dispatch for Alleviation of Voltage Deviations (Abraham Lomi) 258The main objective of this paper is to detail a developed linear programming approach for least squares formulation of optimum reactive power dispatch. Results obtained for 6-Bus Ward-Hale system and a modified IEEE 30-Bus system are presented for illustration purposes. 2. Formulation of Optimization Problem The optimization technique used is Least square minimization. The objective function used is minimization of sum of the squares of voltage deviations from pre-selected desired values. The control variables considered are switchable shunt reactive power (SVC), OLTC transformers and generators excitation. Consider a system where, n total number of buses 1,2…, g generator buses ( g ) g+1, g+2, …, g+s SVC buses ( s ) and g+s +1, … , n the remaining buses ( r = n-g-s ), and t number of on load tap changing transformer. The objective function is expressed as min [ ] 21)( )( ∑ += −= ngical xidesi V V X J (1) where X is the vector of control variables [ ] [ ] .,...,,,...,,,..., 111 sgggt t QQV V T T X ++ ΔΔΔΔΔΔ= The condition for minimization of )( X J is 0)( =Ñ X J x . Defining [ ] ∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂= ++++++++++ sgngngnnt nnsgggggggt gg QV QV V V V V T V T V QV QV V V V V T V T V H LLLMMMLLL 111111111111 (2) We have [ ] −−−=Ñ ++ calndesncalgdesgt x V V V V H X J M 11 2)( (3) To make )( X J x Ñ equal zero, Newton's method is applied which gives the corrections required for the control variables [ ] )()( 1 X J X X J X x x Ñ− Ñ=Δ − ∂ ∂ (4) The Jacobian of )( X J x Ñ is calculated by treating H as constant matrix. TELKOMNIKA e-ISSN: 2087278X TELKOMNIKA Vol. 10, No. 2, June 2012 : 257 – 264 259 [ ] [ ] −−−=Ñ ++ calndesncalgdesgt x V V V V H X X X J M 11 2)( ∂ ∂ ∂ ∂ X X J n ∂∂Ñ )( = [ ] [ ] H H t 2 (5) Hence, substituting Equations (3) and (5) in (4), we obtain, [ ] [ ] { } [ ] −−=Δ ++− calndesncalgdesgt t V V V V H H H X M 111 22 [ ] [ ] −−=Δ ++ calndesncalgdesgt t V V V V H X H H M 11 (6) 2.1. Computation of H Matrix The element of H matrix cannot be defined directly and so is evaluated as sensitivity matrix. The relation between the net reactive power change at any bus due to change in the transformer tap setting and voltage magnitudes can be written as, ΔΔΔΔ = ΔΔΔ RS GT RS G V V V T A A A A A A A A A A A A QQQ 1211109 8765 4321 (7) where [ ] t gG QQQ ΔΔ=Δ ,..., 1 [ ] t sggS QQQ ++ ΔΔ=Δ ,..., 1 [ ] t nsg R QQQ ΔΔ=Δ ++ ,..., 1 [ ] t t T T T T ΔΔ=Δ ,..., 1 [ ] t gG V V V ΔΔ=Δ ,..., 1 [ ] t sggS V V V ++ ΔΔ=Δ ,..., 1 [ ] t nsg R V V V ΔΔ=Δ ++ ,..., 1 The sub matrices A 1 to A 12 are the corresponding terms of partial derivatives ∂ Q / ∂ T and ∂ Q / ∂ V . Transferring the control variable to the RHS and dependent variables to the LHS we obtain, ΔΔΔ = ΔΔΔ S GT R RG QV T S S S S QV Q 4321 (8) where S 1 = [ ] [ ][ ][ ] [ ] 314121 B B B B B − −+ (9) e-ISSN: 2087-278X Optimum Reactive Power Dispatch for Alleviation of Voltage Deviations (Abraham Lomi) 260 S 2 = [ ][ ] [ ] 5142 B B B − − (10) H = [ ] 43 S S (11) S 3 = [ ] [ ] 314 B B − (12) S 4 = [ ] [ ] 514 B B − (13) B 1 = [ ] 21 A A , B 2 = [ ] 43 A A −− , B 3 = 10965 A A A A , B 4 = −−−− 121187 A A A A , B 5 = − 0 I , Size of various sub-matrices are: S 1 : (g) x (t + g), S 2 : (g) x (s), S 3 : ( s + r ) x ( t + g ), S 4 : ( s + r ) x ( s ), H : ( s + r ) x ( t + g + s ), B 1 : (g) x (t + g), B 2 : g x (s + r), B 3 : (s + r) x (t + g), B 4 : (s + r) x (s + r), B 5 : (s + r) x (s) and I : is an identify matrix of size ( s x s ). Matrices S 3 and S 4 are voltage sensitivities of load and matrices S 1 and S 2 are sensitivities of generator Q injections to different reactive power controllers. 2.2. Algorithmic Steps In day-to-day operational power systems, for a particular load and set of network conditions, an optimal combination of real power generation schedule has to be obtained from an active power optimization algorithm. The control variables are to be initialized in the P-optimization algorithm. The following steps are followed to obtain the optimal reactive power allocation in the system. Step 1: Read the system data. Step 2: Form network matrices. Step 3: Perform initial power flow (assumed available from state estimator). Step 4: Compute the voltage error vector caldeserr V V V −= Step 5: If all the voltage errors are within the specified tolerance go to step 11. Step 6: Compute [ H ] matrix using Equation (11). Step 7: Solve for control variables using Equation (6). Step 8: The control variables are adjusted for a suitable step size. Step 9: Control variables are updated and checked for their limits. If no scope for Controller change exist then go to step 11. Step 10: Perform power flow and go to step 1. Step 11: Print the results. 2.3. Hard and Soft Constraints Equipment constraints including SVC, OLTC settings and generator outputs should not exceed its rating due to equipment safety and other operational constraints. Hence SVC, OLTC settings and generators excitation/Q outputs are treated as hard constraints. In case of any voltage violations exist in the system than they must be completely alleviated, if possible, else reduced by suitable control action. Hence the system voltage is considered as a soft constraint.

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