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Simple Hybrid Model for Efficiency Optimization of Induction Motor Drives with Its Experimental Validation

Simple Hybrid Model for Efficiency Optimization of Induction Motor Drives with Its Experimental... Hindawi Publishing Corporation Advances in Power Electronics Volume 2013, Article ID 371842, 8 pages http://dx.doi.org/10.1155/2013/371842 Research Article Simple Hybrid Model for Efficiency Optimization of Induction Motor Drives with Its Experimental Validation 1 2 Branko Blanuša and Bojan Knezevic FacultyofElectricalEngineering,UniversityofBanja Luka,Patre 5, 78000 BanjaLuka, Bosnia andHerzegovina Faculty of Mechanical Engineering, University of Banja Luka, Bulevar Stepe Stepanovica 75, 78000 Banja Luka, Bosnia and Herzegovina Correspondence should be addressed to Branko Blanuˇsa; bbranko@etfbl.net Received 28 December 2012; Revised 14 February 2013; Accepted 14 February 2013 Academic Editor: Jose Pomilio Copyright © 2013 B. Blanuˇsa and B. Knezevic. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. New hybrid model for efficiency optimization of induction motor drives (IMD) is presented in this paper. It combines two strategies for efficiency optimization: loss model control and search control. Search control technique is used in a steady state of drive and loss model during transient processes. As a result, power and energy losses are reduced, especially when load torque is significant less related to its rated value. Also, this hybrid method gives fast convergence to operating point of minimal power losses and shows negligible sensitivity to motor parameter changes regarding other published optimization strategies. This model is implemented in vector control induction motor drive. Simulations and experimental tests are performed. Results are presented in this paper. 1. Introduction improvement of IMD can be implemented via motor u fl x level and this method has been proven to be particularly Induction motor is a widely used electrical motor and a eeff ctive at light loads and in a steady state of drive. Also great energy consumer. The vast majority of induction motor u fl x reduction at light loads gives less acoustic noise derived drives are used for heating, ventilation, and air condition- from both converter and machine. From the other side low ing (HVAC). These applications require only low dynamic u fl x makes motor more sensitive to load disturbances and performance, andinmostcases only voltagesourceinverter degrades dynamic performances [3]. is inserted between grid and induction motor as cheapest Drive loss model is used for optimal drive control in solution. eTh classical way to control these drives is constant loss model control (LMC) [3–7]. These algorithms are fast V/f ratio, and simple methods for efficiency optimization because the optimal control is calculated directly from the can be applied [1]. From the other side there are many loss model. But power loss modeling and calculation of the applications where, like electrical vehicles, electric energy has optimal control can be very complex. Often the loss model is to be consumed in the best possible way and use of induction not accurate enough. motors. es Th e applications require an energy optimized Search strategy methods have an important advantage control strategy [2]. compared to other strategies [8–11]. It is completely insen- One interesting algorithm which can be applied in a drive sitive to parameter changes, while effects of the parameter controller is algorithm for efficiency optimization. variations caused by temperature and saturation are very In a conventional setting, the efi ld excitation is kept expressed in two other strategies. eTh online efficiency constant at rated value throughout its entire load range. If optimization control on the basis of search, where the u fl x is machine is underloaded, this would result in overexcitation decremented in steps until the measured input power settles and unnecessary copper losses. us Th in cases where a motor down to the lowest value, is very attractive. Algorithm is drive has to operate in wider load range, the minimization applicable universally to any motor. Besides all good charac- of losses has great significance. It is known that efficiency teristics of search strategy methods, there is an outstanding 2 Advances in Power Electronics problem in its use. For many applications ux fl convergence to magnetizing ux fl and not specifically taken into account. itsoptimal valueistoo slowly.Also, ufl xisnever reachedits Only conductive losses in the inverter are dependent on the optimal value then in small steps oscillates around it. magnetizing ux, fl and these can be presented in the next form: For electrical drives that work in periodic cycles, it is 2 2 2 𝑃 =𝑅 𝑖 =𝑅 (𝑖 +𝑖 ). (3) INV INV 𝑠 INV 𝑠𝑑 𝑠𝑞 possible to calculate the optimal trajectory of magnetization u fl x, using optimal control theory, so that power losses in Based on the previous considerations, the losses in the one working cycle are minimal [12]. eTh se methods give good induction motor drive, dependent on the magnetizing ux, fl results if the working conditions do not change. can be expressed as follows: Hybrid method combines good characteristics of two 2 2 𝑃 =(𝑅 +𝑅 )𝑖 +(𝑅 +𝑅 +𝑅 )𝑖 optimization strategies SC and LMC [3, 13–15]. It was 𝛾 INV 𝑠 INV 𝑠 𝑟 𝑠𝑑 𝑠𝑞 enhanced attention as interesting solution for efficiency (4) 2 2 2 +𝑐 𝜔 𝜓 +𝑐 𝜔 𝜓 . optimization of controlled electrical drives. During tran- eddy hys 𝑠 𝑠 𝑠𝑑 𝑠𝑑 sient process LMC is used, so fast u fl x changes and good Take into account expression for output power: dynamic performances are kept. Search control is used for efficiency optimization in a steady state of drive. Loss 𝑃 =𝑑𝜓𝜔 𝑖 , (5) out 𝑠𝑑 𝑠𝑞 model of IM in d-q rotational system and procedure for where 𝑃 is output power and 𝑑 is constant which depends out parameter identification in a loss model based on Moore- on the characteristics of Park’s rotating transformation (in Penrose pseudoinversion is given in Section 2.New hybrid this case it is 1.5), and the relation model is presented in Section 3. Qualitative analyses of this method with simulation and experimental results are given 𝑃 =𝑃 +𝑃 (6) in 𝛾 out in Section 4. At the end, obtained results are presented in expression for input power can be written in the next form: Conclusion. 2 2 2 2 2 𝑃 =𝑎𝑖 +𝑏𝑖 +𝑐 𝜔 𝜓 +𝑐 𝜔 𝜓 +𝑑𝜓𝜔 𝑖 , (7) in 𝑠𝑑 𝑠𝑞 1 𝑠 𝑠𝑑 1 𝑠 𝑠𝑑 𝑠𝑑 𝑠𝑞 2. Power Loss Modeling where 𝑎=𝑅 +𝑅 , 𝑏=𝑅 +𝑅 +𝑅 , 𝑐 =𝑐 , 𝑐 =𝑐 , 𝑠 INV 𝑠 INV 𝑟 1 eddy 2 hys and 𝑑 is positive constant. eTh process of energy conversion within motor drive con- Two typical cases are differed: verter andmotor leadstothe powerlossesinthe motor windings and magnetic circuit as well as conduction and (1) linear dependence of magnetizing ux fl from the mag- commutation losses in the inverter [6]. netizing current, The losses in the motor consist of hysteresis losses and (2) nonlinear dependence of magnetizing ux fl from the eddy current losses in a magnetic circuit (iron losses), losses magnetizing current. in the stator and rotor windings (copper loss), and stray In the algorithms for loss minimization, magnetizing flux losses. In nominal operating conditions the iron losses are is less than or equaltothe nominalvalue,soitisusedinthe typically 2-3 times smaller than the copper losses, but at linear part of magnetization characteristics. low loads, these losses are dominant. These losses consist Starting from the expressions (4) and taking into account of hysteresis and eddy current losses. Eddy current losses expression (5), the power losses can be expressed as a function are proportional to the square of supply frequency, and of 𝑖 , 𝑇 ,and 𝜔 as follows: hysteresis losses are proportional to supply frequency. Both 𝑠𝑑 em 𝑠 components of iron losses are dependent of stator ux fl level, 2 2 2 2 2 em so next expression is suitable to represent these losses: 𝑃 (𝑖 ,𝑇 ,𝜔 )=(𝑎 + 𝑐 𝐿 𝜔 +𝑐 𝐿 𝜔 )𝑖 + . 𝛾 𝑠𝑑 em 𝑠 1 2 𝑠 𝑚 𝑠 𝑚 𝑑 2 (𝑑𝐿 𝑖 ) 𝑚 𝑠𝑑 2 2 2 𝑃 =𝑐 𝜓 𝜔 +𝑐 𝜓 𝜔 , (1) (8) 𝛾 Fe eddy 𝑠𝑑 𝑠 hys 𝑠𝑑 𝑠 Slip angular speed can be defined as follows: where 𝑐 is eddy current and 𝑐 is hysteresis loss coeffi- eddy hys cients. 𝑖 𝑠𝑞 (9) 𝜔 =𝜔 −𝜔 ≈ , Copper losses areappearedasaresult of thepassing the 𝑠𝑙 𝑠 𝑇 𝑖 𝑟 𝑠𝑑 electric current through the stator and rotor windings. eTh se where 𝑇 is time rotor constant. losses are proportional to the square of current through stator Based on expression (8) power losses can be given as and rotor windings, and they are given by function of magnetizing current 𝑖 and operating conditions 𝑠𝑑 2 2 (𝜔, 𝑇 ): 𝑝 =𝑅 𝑖 +𝑅 𝑖 . (2) em 𝛾 Cu 𝑠 𝑠 𝑟 𝑠𝑞 2 2 2 2 𝑃 (𝑖 ,𝑇 ,𝜔) = (𝑎 + 𝑐 𝐿 𝜔 +𝑐 𝐿 𝜔) 𝑖 𝛾 𝑠𝑑 em 1 𝑚 2 𝑚 𝑠𝑑 The total additional losses typically do not exceed 5% when thedrive workswithlight loads. Thiscaseisthe most (2𝜔𝐿 +𝑐 𝐿 )𝑇 𝑚 2 𝑚 em important for the power loss minimization algorithms, so + (10) 𝑑𝑇 stray losses are not considered as a separate loss component. Losses in the drive converter consist of the losses in 𝑏 𝑐 1 em 1 the rectiefi r and the conductive and switching losses in the + ( + ) . 2 2 2 2 𝑑 𝐿 𝑇 𝑖 𝑚 𝑟 inverter. eTh losses in the rectifier are independent of the 𝑠𝑑 𝑏𝑇 Advances in Power Electronics 3 2 2 2 2 2 2 𝑇 Putting 𝑘 =𝑎 + 𝑐 𝐿 𝜔 +𝑐 𝐿 𝜔 , 𝑘 =(𝑇 /𝑑 )(𝑏/𝐿 + 𝑊=[𝑎 𝑏 𝑐 𝑐 𝑑] , input signal and the input power are 1 1 𝑚 2 𝑚 2 em 𝑚 1 2 averaged in the period 𝑇=𝑄𝑇 : 𝑐 /𝑇 ),and 𝑘 =(2𝐿𝜔 +𝑐 𝐿 )𝑇 /𝑑𝑇 (10)can be written 1 𝑟 3 𝑚 2 𝑚 em 𝑟 as follows: (𝑛+1)𝑇 (𝑛+1)𝑇 (𝑛+1)𝑇 2 2 ∫ 𝑃 (𝑡 ) = 𝑎 ∫ 𝑖 (𝑡 ) + 𝑏 ∫ 𝑖 (𝑡 ) in 𝑑 𝑞 2 𝑛𝑇 𝑛𝑇 𝑛𝑇 𝑃 (𝑖 ,𝑇 ,𝜔) = 𝑘 𝑖 + +𝑘 . (11) 𝛾 𝑑 em 1 𝑠𝑑 3 (𝑛+1)𝑇 𝑠𝑑 2 2 +𝑐 ∫ [𝜓 (𝑡 ) 𝜔 (𝑡 ) 𝑑𝑡] 𝑑 𝑠 𝑛𝑇 Parameter 𝑘 is a function of 𝑇 which is time variant 3 𝑟 (𝑛+1)𝑇 especially duetotemperature changes. Time rotorconstant +𝑐 ∫ [𝜓 𝑡 𝜔 𝑡 𝑑𝑡] ( ) ( ) is continuously updated in the algorithm for parameter 2 𝑑 𝑠 𝑛𝑇 identification, so the parameter 𝑘 too. (𝑛+1)𝑇 First and second derivations of 𝑃 in a function of 𝑖 are 𝛾 𝑠𝑑 +𝑑 ∫ [𝜔 (𝑡 ) 𝑖 (𝑡 ) 𝜓 (𝑡 ) 𝑑𝑡]⇒ 󳨐 𝑞 𝑠𝑑 𝑛𝑇 𝛾 𝑘 𝑌 =𝑎𝐴 +𝑏𝐵 +𝑐 𝐶 +𝑐 𝐶 +𝑑𝐷 . 𝑁 𝑁 𝑁 1 𝑁1 2 𝑁2 𝑁 =2𝑘 𝑖 −2 , 1 𝑠𝑑 𝜕𝑖 (15) 𝑠𝑑 2 2 (12) Values 𝐴 ,𝐵 ,𝐶 ,𝐶 ,and 𝐷 , 𝑁 = 1, ...,𝑀 suc- 𝜕 𝑃 𝜕 𝑃 𝑁 𝑁 𝑁1 𝑁2 𝑁 𝛾 𝑘 𝛾 =2𝑘 +6 ,𝑘 >0, 𝑘 >0, >0, cessively form the columns 𝑃(:, 1), 𝑃(:, 2), 𝑃(:, 3), 𝑃(:, 4) ,and 1 1 2 2 4 2 𝜕 𝑖 𝑖 𝜕 𝑖 𝑠𝑑 𝑠𝑑 𝑠𝑑 𝑃(:, 5) of matrix 𝑃 . 𝑀×5 for 𝑖 ≤𝑖 ≤𝑖 . 𝑠𝑑 min 𝑠𝑑 𝑠𝑑 max Vector 𝑌 is formed from 𝑀 averaged values of input power 𝑌 , 𝑁 = 1, ...,𝑀 .Vector 𝑊 is calculated by applying 𝑁 𝑔 Value 𝑖 is chosen to be 𝐼 ,and 𝑖 is determined Moore-Penrose pseudoinversion (Figure 1) as follows: 𝑠𝑑 max 𝑑𝑛 𝑠𝑑 min based on characteristics of drive and requirements for elec- 𝑇 −1 tromagnetic torque reserve. In this case 𝑖 = 0.5𝐼 ,where 𝑎 𝑏 𝑐 𝑐 𝑑 (16) 𝑠𝑑 min 𝑑𝑛 𝑊 = [ ] = (𝑃 𝑃 ) .𝑃𝑌 𝑔 𝑔 𝑔1 𝑔2 𝑔 𝐼 is nominal value of 𝑖 current. On the basis of expressions 𝑑𝑛 𝑠𝑑 in (12), it can be concluded that in the steady state of drive and That is 𝑊 is approximate solution of the matrix equations known operating conditions exists accurate value of 𝑖 which 𝑃𝑊 = 𝑌 ,which givesaminimumvalue ‖𝑃𝑊 − 𝑌‖ or 𝑠𝑑 gives minimal losses as follows: minimum mean-square error. eTh choice of 𝑄 is of great importance for the process of parameters identification (see ( 15)) because the input power ∗ 4 2 𝑖 = √ . (13) u fl ctuations should be sufficient in the period 𝑇=𝑄𝑇 . 𝑠𝑑 LMC 𝑆 Otherwise 𝑃 𝑃 matrix will be singular or aspire singularity, that is, det (𝑃 𝑃 ) will be close to 0. The process of determining Basedonthe speciefi d optimalvalue of 𝑑 component stator the parameters in the loss model is repeated during the currentvectorand commandofelectromagnetic torque, 𝑞 operation of electric drive. component of the stator current is determined as follows: 3. Hybrid Model for Efficiency Optimization ∗ em 𝑖 = . (14) 𝑠𝑞 LMC 𝑠𝑑 LMC Electrical drive with block for efficiency optimization is shown in Figure 2. Electric drive is supplied from the primary 2.1. Parameter Identica fi tion in a Loss Model. This proce- power network 3×380 V. This voltage is rectied fi , and the volt- dure of parameter identification is a mainly based on the age and current in DC link are measured. eTh drive inverter procedures described in [6, 7]. In order to determine the is current regulated (CR) voltage three-phase inverter. Refer- parameters in the model losses, 𝑎, 𝑏, 𝑐 ,and 𝑐 ,itisnecessary ence and measured 𝑑 and 𝑞 components of stator current are 1 2 to measurethe inputpower andknowthe exact valueofthe kept in the current controllers. eTh se controllers are realized output power. eTh exact value of the output power is needed in rotational 𝑑, 𝑞 coordinate system as a linear PI controller. to determine correct information of the losses in the drive Outputs of controller are 𝑑 and 𝑞 componentofstatorvoltage. andtoavoid coupling betweenloadpulsation andworkof These voltages are transformed ( B-transformation) in three- ∗ ∗ ∗ optimization controller. Also, the samples of the values that phase reference voltages V , V ,and V .Thesevoltagesare 𝑎 𝑏 𝑐 define input powers V , 𝑖 (𝑃 = V 𝑖 )are available scaled and lead to PWM modulator, where control signals DC DC in DC DC in the controller, and these values are used for protect and of inverter switches are generated. This drive works as speed control functions (dynamic braking, the so-s ft tart operation, controlled drive. Speed reference and measured speed are PWM compensation, etc.). led into speed controller. Speed controller is realized as PI The proposed procedure of parameter identification is controller in incremental form, with proportional coefficient shown in Figure 1. eTh samples that exist in the expres- in a feedback local branch. eTh output of speed controller sion (7) are memorized at each period. Usually the 𝑇 is reference value of electromagnetic torque. Reference value is 100–200 𝜇 s. Due to high-frequency components that do of stator current 𝑑 component is determined in a block for not contribute to identicfi ation of the relevant parameters efficiency optimization and 𝑞 componentofstatorcurrent 𝑑𝐿 𝜕𝑃 𝑑𝑡 𝑑𝑡 𝑑𝑡 4 Advances in Power Electronics 𝑗=𝑄 (:, 𝑃 1) = 𝑢 𝑢 (𝑛𝑇 + 𝑗)𝜏 (:, 𝑃 1) 2 1 1 ∑ 𝑇 𝑠𝑑 [𝐴 ···𝐴 ] 𝑛0 𝑛0+𝑀 𝑗=1 𝑗=𝑄 (:, 𝑃 2) = 𝑢 (𝑛𝑇 + 𝑗)𝜏 𝐵 𝑢 (:, 𝑃 2) 2 2 𝑛 𝑇 𝑇 0.25 𝑠𝑞 [𝐵 ···𝐵 ] ∣det(𝑃 𝑃)∣ 𝑗=1 𝑛0 𝑛0+𝑀 𝑗=𝑄 𝑃 (:, 𝑃 3) = 𝑢 𝑢 (𝑛𝑇 + 𝑗)𝜏 𝐶 3 (:, 𝑃 3) 2 2 3 𝑛1 𝜓 𝜔 ∑ 𝑠𝑑 𝑠 𝑄 [𝐶 ···𝐶 ] 𝑗=1 𝑛0 𝑛0+𝑀 𝑊 =[𝑎 𝑏 𝑐 𝑐 𝑑 ] [𝑎 𝑏 𝑐 𝑐 𝑑 ] = 𝑔 𝑔 1𝑔 2𝑔 𝑔 𝑔 𝑔 1𝑔 2𝑔 𝑔 𝑔 𝑗=𝑄 𝑢 (𝑛𝑇 + 𝑗)𝜏 (:, 𝑃 3) = 𝑇 −1 𝑇 𝑢 4 (:, 𝑃 4) 2 𝑛2 4 (𝑃 𝑃) 𝑃 𝑌 𝜓 𝜔 𝑠 𝑇 𝑠𝑑 𝑗=1 [𝐶 ···𝐶 ] 𝑛20 𝑛20+𝑀 𝑗=𝑄 𝑢 𝑢 (𝑛𝑇 + 𝑗)𝜏 𝐷 (:, 𝑃 4) = (:, 𝑃 5) 5 5 𝑖 𝜓 𝜔 𝑠𝑞 𝑠𝑑 ∑ [𝐷 ...𝐷 ] 𝑄 𝑛0 𝑛0+𝑀 𝑗=1 𝑗=𝑄 𝑢 (𝑛𝑇 + 𝑗)𝜏 𝑌= 𝑢 𝑛 𝑃 (DC) 𝑇 in [𝑌 ···𝑌 ] 𝑗=1 𝑛0 𝑛0+𝑀 Figure 1: A method for determining the parameters 𝑎, 𝑏, 𝑐 ,𝑐 and, 𝑑 from the input signal. 1 2 vector on the basis of 𝑑 stator current vector component and 3.2. Search Controller. Search algorithmisusedinsteady electromagnetic torque reference (see (14)). Position of rotor state, which is detected in the SSC block. Error that exists ufl xvectorisdeterminedinindirectvectorcontrol block between the current reference 𝑖 that is generatedinthe LMC (IVC). model and in the search model appears as a consequence of Hybrid model for efficiency optimization consists from inverter and stray losses which are not included in the model. 3blocks, LMC, SC, and steady state control (SSC) block. The applied search algorithm is simple. Since the current 𝑖 𝑠𝑑 LMC is used during transient states caused of external speed is very close to the value which gives minimal losses, small ∗ ∗ or torque demand [3]. Optimal control (𝑖 ,𝑖 )is step of magnetization current Δ𝑖 = 0.01𝐼 is chosen. 𝑠𝑑 𝑑𝑛 𝑠𝑑 LMC 𝑠𝑞 LMC For two successive values of the 𝑖 current, power losses calculated directly from loss model for a given operational 𝑠𝑑 are determined. Sign of Δ𝑖 is maintained if power losses are conditions what obtains power loss optimization and good 𝑠𝑑 reduced. Otherwise, the sign of Δ𝑖 is opposite in the next dynamic performances. SC is used in a steady state for a 𝑠𝑑 step: constant output power. On the basis of speed reference and measured speed, SSC 𝑖 (𝑛 ) =𝑖 (𝑛−1 ) − sgn (Δ𝑃 (𝑛−1 ))Δ𝑖 . (17) blockdenfi esits output andcontrolsswitches( Figure 2). If 𝑠𝑑 𝑠𝑑 𝛾 𝑠𝑑 transient states is detected, LMC is active, and its outputs are When the two values of magnetization current 𝑖 and 𝑠𝑑1 forwarded to indirect vector control (IVC) block and current 𝑖 were found, so the sign of power loss is changed between 𝑠𝑑2 regulators. When steady state is detected in SSC block, last these values, and new reference of 𝑖 current is specified as: 𝑠𝑑 value of magnetizing current during transient state is used as starting point for search algorithm. 𝑖 +𝑖 ∗ 𝑠𝑑1 𝑠𝑑2 (18) 𝑖 = . 𝑠𝑑 SC In this way, there are no oscillations of 𝑖 current, air gap 3.1. Loss Model Controller. Optimal control calculation in 𝑠𝑑 u fl x, and electromagnetic torque, which are characteristics of LMC for a given operational conditions is described in the search algorithm. Section 2. Expressions for 𝑑 and 𝑞 component of stator current are defined by ( 8)and (10). 4. Simulation and Experimental Results This method is sensitive to parameter changes due to temperature changes and magnetic circuit saturation, what 4.1. Simulation Results. Hybrid method for efficiency opti- consequently leads to error in a current references calcu- mization of IMD has been studied through computer sim- lation. So, algorithm for parameter identicfi ation is always ulation in MATLAB-Simulink. active, and parameters in the loss model are continuously Speed reference and load torque are shown in Figure 3. updated (Figure 2). eTh steep change of load torque appears with the aim MATRICA (𝑀×5) Advances in Power Electronics 5 𝑠𝑞𝑆𝐶 in 𝑃 =𝜔 ∗ 𝑇 ∗ out em 𝑆𝐶 𝑖 𝑠𝑑𝑆𝐶 𝑠𝑑 1/𝑧 𝑑 PI current controller ∗ SW3 SW1 Steady state control 𝐶𝑠𝑑𝑀𝐿 𝑖 ∗ 𝑠𝑞 𝑞 PI current controller 𝐶𝑠𝑞𝑀𝐿 SW2 𝑐 𝑐 𝑎𝑏 1 2 𝑑 Loss model parameter em + Δ𝜔 identification 𝜃 Speed Torque 𝑠 PI speed 𝐼 𝑉 𝐶 3 reference estimator controller em 𝜓 𝑖 𝑖 𝜔 𝜔 𝑃 𝑠𝑑 𝑠𝑞 𝑠 𝑠𝑑 in 𝑠𝑑 3Φ 2Φ 𝑠𝑞 ∗ ∗ 𝑣 𝑣 1 ∗ ∗ 𝑞 2Φ 3Φ 2 𝑖 𝑖 𝑖 ∗ 𝑎 𝑏 𝑐 −1 𝜃 𝑣 𝑠 𝐵 Power supply Incremental CRPWM 𝑖 𝑣 3 × 230 V Rectifier encoder DC DC 50 Hz VSI interface Encoder Power calculation in Figure 2: Overall proposed block diagram of efficiency optimization controller in IMD. of testing the drive behavior in the dynamic mode and its robustness for a sudden load perturbations. Graphs of magnetization current (𝑖 )and active component(𝑖 )of 𝑠𝑑 𝑠𝑞 stator current vector for a given operating conditions and 0.8 appliedhybridmethodare shownin Figure 4. Graphs of power loss for nominal u fl x and hybrid method Speed reference p.u. 0.6 are given in Figure 5. It is obvious that the use of hybrid methodsgives signicfi antly less powerlossesthanwhenthe flux is maintained at nominal value for a light load of drive. 0.4 Load torque p.u. 4.2. Experimental Results. The experimental tests have been 0.2 performed on the setup which consists of the following: (i) induction motor (3 phases, Δ380 V/𝑌220 V, 3.7/2.12 A, cos 𝜙 = 0.71 ,1410r/min,50Hz), 0 2 4 6 8 10 12 (ii) incremental encoder connected with the motor shaft, Time (s) (iii) three-phase drive converter (DC/AC converter and Figure 3: Speed reference and load torque [p.u.]. DC link), (iv) PC and dSPACE1102 controller board with TMS320C31 floating point processor and peripherals, (v) interface between controller board and drive con- Parameters of used induction motor are given in the verter. appendix of the paper. 𝐴𝑀 𝐿𝑀 6 Advances in Power Electronics 1.4 1.2 0.8 𝑞 0.6 𝑑 0.4 0.2 02468 10 12 Time (0.5 s/div) 0 2 4 6 8 10 12 Figure 6: Power losses for nominal magnetization ux fl and opera- Time (s) tional conditions shown in Figure 3. Current 𝑖 p.u. Current 𝑖 p.u. Figure 4: Graphs of 𝑑 and 𝑞 component of stator current for a given operating conditions. Nominal flux 02468 10 12 Time (0.5 s/div) Hybrid method Figure 7: Power losses when the hybrid method is applied and operational conditions shown in Figure 3. 0 2 4 6 8 10 12 Time (s) Based on graph in Figure 6,itcan be concludedthat Figure 5: Graph of power loss for nominal flux and applied hybrid method. the speed drop for a step change of load is small and speed response is strictly aperiodic. 5. Conclusion The algorithm observed in this paper used the MATLAB- Simulink software, dSPACE real-time interface, and C lan- Algorithms for efficiency optimization of induction motor guage. Handling real-time applications is done in ControlD- drive are briefly described. Detailed theoretical analysis of esk. power losses in induction motor is presented. Algorithm for All experimental tests and simulations have been done parameter identification in the loss model based on Moore- in the same operating conditions of the drive, and some Penrose pseudoinversion is presented. Also, hybrid algorithm comparisons between algorithms for efficiency optimization for efficiency optimization has been applied. According to the are made through the experimental tests. Graphs of power theoretical analysis, performed simulations, and experimen- losses for nominal u fl x and when the hybrid method is tal tests we have arrived to the following conclusions. applied are shown in Figures 6 and 7,respectively. Graphs of If load torque has a value close to nominal or higher, magnetization current for a given operational conditions are magnetizing ux fl is also nominal regardless of whether an shown in Figure 8, and speed response is shown in Figure 9. algorithm for efficiency optimization is applied or not. Power losses (W) and stator currents Power losses (10 W/div) Power losses (10 W/div) Advances in Power Electronics 7 2.5 0.75 kW (nominal mechanical power) cos 𝜙 = 0, 71 (power factor) 2 1410 r/min (nominal mechanical speed) 𝑅 = 10.4 Ω (stator resistance) 1.5 𝑅 = 11.6 Ω (rotor resistance) 𝐿 =22 mH (stator leakage inductance) 𝛾𝑠 𝐿 =22 mH (stator leakage inductance) 𝛾𝑟 𝐿 = 0, 557 H (magnetization inductance) 𝑚𝑛 𝐽 = 0, 0072 kgm (inertia moment) 0.5 𝐼 = 1.501A(nominalvalue of 𝑖 current) 𝑑𝑛 𝑠𝑑 𝐼 = 2.093A(nominalvalue of 𝑖 current). 0 𝑞𝑛 𝑠𝑞 02468 10 12 Time (0.5 s/div) Nomenclature Figure 8: Magnetization current 𝑖 and active current when the 𝑅 ,𝑅 : Resistance of stator and rotor winding hybrid method is applied and operational conditions shown in 𝑠 𝑟 𝐿 ,𝐿 : Self-inductance of stator and rotor Figure 3. 𝑠 𝑟 𝐿 :Magnetizinginductance 𝜎:Leakagefactor 𝐿 : Stator transient inductance 𝑃:Numberofpolepairs 𝜗 ,𝜔 : Rotor flux angle and angular speed 𝑠 𝑠 𝜗, 𝜔 : Rotor angle and angular speed 𝜔 : slip speed 𝑇 : Elektromagnetic torque em 𝜓 :Magnetizingufl x 𝑠𝑑 𝑖 ,𝑖 : 𝑑 and 𝑞 components of stator current vector. 𝑠𝑑 𝑠𝑞 References 02468 10 12 [1] F. Abrahamsen,F.Blaabjerg,J.K.Pedersen, P. Z. Grabowski, and P. gTh ersen, “On the energy optimized control of standard Time (0.5 s/div) and high-efficiency induction motors in CT and HVAC appli- Figure 9: Speed response when the hybrid method is applied and cations,” IEEE Transactions on Industry Applications,vol.34, no. operational conditions shown in Figure 3. 4, pp. 822–831, 1998. [2] M. Chis, S. Jayaram, and K. Rajashekara, “Neural network- based efficiency optimization of EV drive,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering (CCECE ’97), pp. 454–457, May 1997. For a light load, hybrid method for efficiency optimiza- [3] E.S.Sergaki andG.S.Stavrakakis,“Online search basedfuzzy tion gives significant power loss reduction (Figures 5, 6,and optimum efficiency operation in steady and transient states 7). for DC and AC vector controlled motors,” in Proceedings of There is no oscillation of magnetization u fl x which is the International Conference on Electrical Machines (ICEM ’08), characteristic of the search algorithms (Figures 4 and 8). Vilamoura, Portugal, September 2008. Also, this hybrid method shows good dynamic perfor- [4] F. Abrahamsen, J. K. Pedersen, and F. Blaabjerg, “State-of-Art of mances and no sensitivity to parameter changes (Figure 9). optimal efficiency control of low cost induction motor drives,” Implementation of presented algorithm is simple, and it in Proceedings of Conference on Fuzzy Systems (PESC ’96),pp. can be universally applied to any electrical motor. Changes 920–924, 1996. are only related to different models of power losses. [5] M. N. Uddin and S. W. Nam, “Development of a nonlinear and model-based online loss minimization control of an IM drive,” Appendix IEEE Transactions on Energy Conversion,vol.23, no.4,pp. 1015– 1024, 2008. Parameters of used induction motor [6] B.Blanusa,P.Matic, ´ Z. Ivanovic, and S. N. Vukosavic, “An improved loss model based algorithm for efficiency optimiza- 3phase Δ220/Y380 V (supply voltage) tion of the induction motor drive,” Electronics,vol.10, no.1,pp. 3,7/2,12 A (nominal stator current) 49–52, 2006. Speed (rad/s) Currents , (0.1 A/div) 8 Advances in Power Electronics [7] S. N. Vukosavic and E. Levi, “Robust DSP-based efficiency optimization of a variable speed induction motor drive,” IEEE Transactions on Industrial Electronics,vol.50, no.3,pp. 560– 570, 2003. [8] G.C.D.Sousa,B.K.Bose, andJ.G.Cleland,“Fuzzy logic based on-line efficiency optimization control of an indirect vector-controlled induction motor drive,” IEEE Transactions on Industrial Electronics, vol. 42, no. 2, pp. 192–198, 1995. [9] D. de Almeida Souza, W. C. P. de Aragao Filho, and G. C. D. Sousa, “Adaptive fuzzy controller for efficiency optimization of induction motors,” IEEE Transactions on Industrial Electronics, vol. 54, no. 4, pp. 2157–2164, 2007. [10] S. Ghozzi, K. Jelassi, and X. Roboam, “Energy optimization of induction motor drives,” in Proceedings of the IEEE International Conference on Industrial Technology (ICIT ’04),pp. 602–610, December 2004. [11] Z. Liwei, L. Jun, W. Xuhui, and T. Q. Zheng, “Systematic design of fuzzy logic based hybrid on-line minimum input power search control strategy for efficiency optimization of IM,” in Proceedings of the CES/IEEE 5th International Power Electronics and Motion Control Conference (IPEMC ’06),pp. 1012–1016, August 2006. [12] B. Blanusa and S. N. Vukosavic, “Efficiency optimized control for closed-cycle operations of high performance induction motor drive,” Journal of Electrical Engineering,vol.8,pp. 81–88, [13] C. Chakraborty and Y. Hori, “Fast efficiency optimization techniques for the indirect vector-controlled induction motor drives,” IEEE Transactions on Industry Applications,vol.39, no. 4, pp. 1070–1076, 2003. [14] B. Blanuˇsa, P. Matic, ´ and B. Dokic, ´ “New hybrid model for efficiency optimization of induction motor drives,” in Proceed- ings of 52nd International Symposium ELMAR-2010, pp. 313–317, [15] P. Was, Electrical Machines and Drives, Oxford University Press, 1992. 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Simple Hybrid Model for Efficiency Optimization of Induction Motor Drives with Its Experimental Validation

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Hindawi Publishing Corporation
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Copyright © 2013 Branko Blanuša and Bojan Knezevic. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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10.1155/2013/371842
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Hindawi Publishing Corporation Advances in Power Electronics Volume 2013, Article ID 371842, 8 pages http://dx.doi.org/10.1155/2013/371842 Research Article Simple Hybrid Model for Efficiency Optimization of Induction Motor Drives with Its Experimental Validation 1 2 Branko Blanuša and Bojan Knezevic FacultyofElectricalEngineering,UniversityofBanja Luka,Patre 5, 78000 BanjaLuka, Bosnia andHerzegovina Faculty of Mechanical Engineering, University of Banja Luka, Bulevar Stepe Stepanovica 75, 78000 Banja Luka, Bosnia and Herzegovina Correspondence should be addressed to Branko Blanuˇsa; bbranko@etfbl.net Received 28 December 2012; Revised 14 February 2013; Accepted 14 February 2013 Academic Editor: Jose Pomilio Copyright © 2013 B. Blanuˇsa and B. Knezevic. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. New hybrid model for efficiency optimization of induction motor drives (IMD) is presented in this paper. It combines two strategies for efficiency optimization: loss model control and search control. Search control technique is used in a steady state of drive and loss model during transient processes. As a result, power and energy losses are reduced, especially when load torque is significant less related to its rated value. Also, this hybrid method gives fast convergence to operating point of minimal power losses and shows negligible sensitivity to motor parameter changes regarding other published optimization strategies. This model is implemented in vector control induction motor drive. Simulations and experimental tests are performed. Results are presented in this paper. 1. Introduction improvement of IMD can be implemented via motor u fl x level and this method has been proven to be particularly Induction motor is a widely used electrical motor and a eeff ctive at light loads and in a steady state of drive. Also great energy consumer. The vast majority of induction motor u fl x reduction at light loads gives less acoustic noise derived drives are used for heating, ventilation, and air condition- from both converter and machine. From the other side low ing (HVAC). These applications require only low dynamic u fl x makes motor more sensitive to load disturbances and performance, andinmostcases only voltagesourceinverter degrades dynamic performances [3]. is inserted between grid and induction motor as cheapest Drive loss model is used for optimal drive control in solution. eTh classical way to control these drives is constant loss model control (LMC) [3–7]. These algorithms are fast V/f ratio, and simple methods for efficiency optimization because the optimal control is calculated directly from the can be applied [1]. From the other side there are many loss model. But power loss modeling and calculation of the applications where, like electrical vehicles, electric energy has optimal control can be very complex. Often the loss model is to be consumed in the best possible way and use of induction not accurate enough. motors. es Th e applications require an energy optimized Search strategy methods have an important advantage control strategy [2]. compared to other strategies [8–11]. It is completely insen- One interesting algorithm which can be applied in a drive sitive to parameter changes, while effects of the parameter controller is algorithm for efficiency optimization. variations caused by temperature and saturation are very In a conventional setting, the efi ld excitation is kept expressed in two other strategies. eTh online efficiency constant at rated value throughout its entire load range. If optimization control on the basis of search, where the u fl x is machine is underloaded, this would result in overexcitation decremented in steps until the measured input power settles and unnecessary copper losses. us Th in cases where a motor down to the lowest value, is very attractive. Algorithm is drive has to operate in wider load range, the minimization applicable universally to any motor. Besides all good charac- of losses has great significance. It is known that efficiency teristics of search strategy methods, there is an outstanding 2 Advances in Power Electronics problem in its use. For many applications ux fl convergence to magnetizing ux fl and not specifically taken into account. itsoptimal valueistoo slowly.Also, ufl xisnever reachedits Only conductive losses in the inverter are dependent on the optimal value then in small steps oscillates around it. magnetizing ux, fl and these can be presented in the next form: For electrical drives that work in periodic cycles, it is 2 2 2 𝑃 =𝑅 𝑖 =𝑅 (𝑖 +𝑖 ). (3) INV INV 𝑠 INV 𝑠𝑑 𝑠𝑞 possible to calculate the optimal trajectory of magnetization u fl x, using optimal control theory, so that power losses in Based on the previous considerations, the losses in the one working cycle are minimal [12]. eTh se methods give good induction motor drive, dependent on the magnetizing ux, fl results if the working conditions do not change. can be expressed as follows: Hybrid method combines good characteristics of two 2 2 𝑃 =(𝑅 +𝑅 )𝑖 +(𝑅 +𝑅 +𝑅 )𝑖 optimization strategies SC and LMC [3, 13–15]. It was 𝛾 INV 𝑠 INV 𝑠 𝑟 𝑠𝑑 𝑠𝑞 enhanced attention as interesting solution for efficiency (4) 2 2 2 +𝑐 𝜔 𝜓 +𝑐 𝜔 𝜓 . optimization of controlled electrical drives. During tran- eddy hys 𝑠 𝑠 𝑠𝑑 𝑠𝑑 sient process LMC is used, so fast u fl x changes and good Take into account expression for output power: dynamic performances are kept. Search control is used for efficiency optimization in a steady state of drive. Loss 𝑃 =𝑑𝜓𝜔 𝑖 , (5) out 𝑠𝑑 𝑠𝑞 model of IM in d-q rotational system and procedure for where 𝑃 is output power and 𝑑 is constant which depends out parameter identification in a loss model based on Moore- on the characteristics of Park’s rotating transformation (in Penrose pseudoinversion is given in Section 2.New hybrid this case it is 1.5), and the relation model is presented in Section 3. Qualitative analyses of this method with simulation and experimental results are given 𝑃 =𝑃 +𝑃 (6) in 𝛾 out in Section 4. At the end, obtained results are presented in expression for input power can be written in the next form: Conclusion. 2 2 2 2 2 𝑃 =𝑎𝑖 +𝑏𝑖 +𝑐 𝜔 𝜓 +𝑐 𝜔 𝜓 +𝑑𝜓𝜔 𝑖 , (7) in 𝑠𝑑 𝑠𝑞 1 𝑠 𝑠𝑑 1 𝑠 𝑠𝑑 𝑠𝑑 𝑠𝑞 2. Power Loss Modeling where 𝑎=𝑅 +𝑅 , 𝑏=𝑅 +𝑅 +𝑅 , 𝑐 =𝑐 , 𝑐 =𝑐 , 𝑠 INV 𝑠 INV 𝑟 1 eddy 2 hys and 𝑑 is positive constant. eTh process of energy conversion within motor drive con- Two typical cases are differed: verter andmotor leadstothe powerlossesinthe motor windings and magnetic circuit as well as conduction and (1) linear dependence of magnetizing ux fl from the mag- commutation losses in the inverter [6]. netizing current, The losses in the motor consist of hysteresis losses and (2) nonlinear dependence of magnetizing ux fl from the eddy current losses in a magnetic circuit (iron losses), losses magnetizing current. in the stator and rotor windings (copper loss), and stray In the algorithms for loss minimization, magnetizing flux losses. In nominal operating conditions the iron losses are is less than or equaltothe nominalvalue,soitisusedinthe typically 2-3 times smaller than the copper losses, but at linear part of magnetization characteristics. low loads, these losses are dominant. These losses consist Starting from the expressions (4) and taking into account of hysteresis and eddy current losses. Eddy current losses expression (5), the power losses can be expressed as a function are proportional to the square of supply frequency, and of 𝑖 , 𝑇 ,and 𝜔 as follows: hysteresis losses are proportional to supply frequency. Both 𝑠𝑑 em 𝑠 components of iron losses are dependent of stator ux fl level, 2 2 2 2 2 em so next expression is suitable to represent these losses: 𝑃 (𝑖 ,𝑇 ,𝜔 )=(𝑎 + 𝑐 𝐿 𝜔 +𝑐 𝐿 𝜔 )𝑖 + . 𝛾 𝑠𝑑 em 𝑠 1 2 𝑠 𝑚 𝑠 𝑚 𝑑 2 (𝑑𝐿 𝑖 ) 𝑚 𝑠𝑑 2 2 2 𝑃 =𝑐 𝜓 𝜔 +𝑐 𝜓 𝜔 , (1) (8) 𝛾 Fe eddy 𝑠𝑑 𝑠 hys 𝑠𝑑 𝑠 Slip angular speed can be defined as follows: where 𝑐 is eddy current and 𝑐 is hysteresis loss coeffi- eddy hys cients. 𝑖 𝑠𝑞 (9) 𝜔 =𝜔 −𝜔 ≈ , Copper losses areappearedasaresult of thepassing the 𝑠𝑙 𝑠 𝑇 𝑖 𝑟 𝑠𝑑 electric current through the stator and rotor windings. eTh se where 𝑇 is time rotor constant. losses are proportional to the square of current through stator Based on expression (8) power losses can be given as and rotor windings, and they are given by function of magnetizing current 𝑖 and operating conditions 𝑠𝑑 2 2 (𝜔, 𝑇 ): 𝑝 =𝑅 𝑖 +𝑅 𝑖 . (2) em 𝛾 Cu 𝑠 𝑠 𝑟 𝑠𝑞 2 2 2 2 𝑃 (𝑖 ,𝑇 ,𝜔) = (𝑎 + 𝑐 𝐿 𝜔 +𝑐 𝐿 𝜔) 𝑖 𝛾 𝑠𝑑 em 1 𝑚 2 𝑚 𝑠𝑑 The total additional losses typically do not exceed 5% when thedrive workswithlight loads. Thiscaseisthe most (2𝜔𝐿 +𝑐 𝐿 )𝑇 𝑚 2 𝑚 em important for the power loss minimization algorithms, so + (10) 𝑑𝑇 stray losses are not considered as a separate loss component. Losses in the drive converter consist of the losses in 𝑏 𝑐 1 em 1 the rectiefi r and the conductive and switching losses in the + ( + ) . 2 2 2 2 𝑑 𝐿 𝑇 𝑖 𝑚 𝑟 inverter. eTh losses in the rectifier are independent of the 𝑠𝑑 𝑏𝑇 Advances in Power Electronics 3 2 2 2 2 2 2 𝑇 Putting 𝑘 =𝑎 + 𝑐 𝐿 𝜔 +𝑐 𝐿 𝜔 , 𝑘 =(𝑇 /𝑑 )(𝑏/𝐿 + 𝑊=[𝑎 𝑏 𝑐 𝑐 𝑑] , input signal and the input power are 1 1 𝑚 2 𝑚 2 em 𝑚 1 2 averaged in the period 𝑇=𝑄𝑇 : 𝑐 /𝑇 ),and 𝑘 =(2𝐿𝜔 +𝑐 𝐿 )𝑇 /𝑑𝑇 (10)can be written 1 𝑟 3 𝑚 2 𝑚 em 𝑟 as follows: (𝑛+1)𝑇 (𝑛+1)𝑇 (𝑛+1)𝑇 2 2 ∫ 𝑃 (𝑡 ) = 𝑎 ∫ 𝑖 (𝑡 ) + 𝑏 ∫ 𝑖 (𝑡 ) in 𝑑 𝑞 2 𝑛𝑇 𝑛𝑇 𝑛𝑇 𝑃 (𝑖 ,𝑇 ,𝜔) = 𝑘 𝑖 + +𝑘 . (11) 𝛾 𝑑 em 1 𝑠𝑑 3 (𝑛+1)𝑇 𝑠𝑑 2 2 +𝑐 ∫ [𝜓 (𝑡 ) 𝜔 (𝑡 ) 𝑑𝑡] 𝑑 𝑠 𝑛𝑇 Parameter 𝑘 is a function of 𝑇 which is time variant 3 𝑟 (𝑛+1)𝑇 especially duetotemperature changes. Time rotorconstant +𝑐 ∫ [𝜓 𝑡 𝜔 𝑡 𝑑𝑡] ( ) ( ) is continuously updated in the algorithm for parameter 2 𝑑 𝑠 𝑛𝑇 identification, so the parameter 𝑘 too. (𝑛+1)𝑇 First and second derivations of 𝑃 in a function of 𝑖 are 𝛾 𝑠𝑑 +𝑑 ∫ [𝜔 (𝑡 ) 𝑖 (𝑡 ) 𝜓 (𝑡 ) 𝑑𝑡]⇒ 󳨐 𝑞 𝑠𝑑 𝑛𝑇 𝛾 𝑘 𝑌 =𝑎𝐴 +𝑏𝐵 +𝑐 𝐶 +𝑐 𝐶 +𝑑𝐷 . 𝑁 𝑁 𝑁 1 𝑁1 2 𝑁2 𝑁 =2𝑘 𝑖 −2 , 1 𝑠𝑑 𝜕𝑖 (15) 𝑠𝑑 2 2 (12) Values 𝐴 ,𝐵 ,𝐶 ,𝐶 ,and 𝐷 , 𝑁 = 1, ...,𝑀 suc- 𝜕 𝑃 𝜕 𝑃 𝑁 𝑁 𝑁1 𝑁2 𝑁 𝛾 𝑘 𝛾 =2𝑘 +6 ,𝑘 >0, 𝑘 >0, >0, cessively form the columns 𝑃(:, 1), 𝑃(:, 2), 𝑃(:, 3), 𝑃(:, 4) ,and 1 1 2 2 4 2 𝜕 𝑖 𝑖 𝜕 𝑖 𝑠𝑑 𝑠𝑑 𝑠𝑑 𝑃(:, 5) of matrix 𝑃 . 𝑀×5 for 𝑖 ≤𝑖 ≤𝑖 . 𝑠𝑑 min 𝑠𝑑 𝑠𝑑 max Vector 𝑌 is formed from 𝑀 averaged values of input power 𝑌 , 𝑁 = 1, ...,𝑀 .Vector 𝑊 is calculated by applying 𝑁 𝑔 Value 𝑖 is chosen to be 𝐼 ,and 𝑖 is determined Moore-Penrose pseudoinversion (Figure 1) as follows: 𝑠𝑑 max 𝑑𝑛 𝑠𝑑 min based on characteristics of drive and requirements for elec- 𝑇 −1 tromagnetic torque reserve. In this case 𝑖 = 0.5𝐼 ,where 𝑎 𝑏 𝑐 𝑐 𝑑 (16) 𝑠𝑑 min 𝑑𝑛 𝑊 = [ ] = (𝑃 𝑃 ) .𝑃𝑌 𝑔 𝑔 𝑔1 𝑔2 𝑔 𝐼 is nominal value of 𝑖 current. On the basis of expressions 𝑑𝑛 𝑠𝑑 in (12), it can be concluded that in the steady state of drive and That is 𝑊 is approximate solution of the matrix equations known operating conditions exists accurate value of 𝑖 which 𝑃𝑊 = 𝑌 ,which givesaminimumvalue ‖𝑃𝑊 − 𝑌‖ or 𝑠𝑑 gives minimal losses as follows: minimum mean-square error. eTh choice of 𝑄 is of great importance for the process of parameters identification (see ( 15)) because the input power ∗ 4 2 𝑖 = √ . (13) u fl ctuations should be sufficient in the period 𝑇=𝑄𝑇 . 𝑠𝑑 LMC 𝑆 Otherwise 𝑃 𝑃 matrix will be singular or aspire singularity, that is, det (𝑃 𝑃 ) will be close to 0. The process of determining Basedonthe speciefi d optimalvalue of 𝑑 component stator the parameters in the loss model is repeated during the currentvectorand commandofelectromagnetic torque, 𝑞 operation of electric drive. component of the stator current is determined as follows: 3. Hybrid Model for Efficiency Optimization ∗ em 𝑖 = . (14) 𝑠𝑞 LMC 𝑠𝑑 LMC Electrical drive with block for efficiency optimization is shown in Figure 2. Electric drive is supplied from the primary 2.1. Parameter Identica fi tion in a Loss Model. This proce- power network 3×380 V. This voltage is rectied fi , and the volt- dure of parameter identification is a mainly based on the age and current in DC link are measured. eTh drive inverter procedures described in [6, 7]. In order to determine the is current regulated (CR) voltage three-phase inverter. Refer- parameters in the model losses, 𝑎, 𝑏, 𝑐 ,and 𝑐 ,itisnecessary ence and measured 𝑑 and 𝑞 components of stator current are 1 2 to measurethe inputpower andknowthe exact valueofthe kept in the current controllers. eTh se controllers are realized output power. eTh exact value of the output power is needed in rotational 𝑑, 𝑞 coordinate system as a linear PI controller. to determine correct information of the losses in the drive Outputs of controller are 𝑑 and 𝑞 componentofstatorvoltage. andtoavoid coupling betweenloadpulsation andworkof These voltages are transformed ( B-transformation) in three- ∗ ∗ ∗ optimization controller. Also, the samples of the values that phase reference voltages V , V ,and V .Thesevoltagesare 𝑎 𝑏 𝑐 define input powers V , 𝑖 (𝑃 = V 𝑖 )are available scaled and lead to PWM modulator, where control signals DC DC in DC DC in the controller, and these values are used for protect and of inverter switches are generated. This drive works as speed control functions (dynamic braking, the so-s ft tart operation, controlled drive. Speed reference and measured speed are PWM compensation, etc.). led into speed controller. Speed controller is realized as PI The proposed procedure of parameter identification is controller in incremental form, with proportional coefficient shown in Figure 1. eTh samples that exist in the expres- in a feedback local branch. eTh output of speed controller sion (7) are memorized at each period. Usually the 𝑇 is reference value of electromagnetic torque. Reference value is 100–200 𝜇 s. Due to high-frequency components that do of stator current 𝑑 component is determined in a block for not contribute to identicfi ation of the relevant parameters efficiency optimization and 𝑞 componentofstatorcurrent 𝑑𝐿 𝜕𝑃 𝑑𝑡 𝑑𝑡 𝑑𝑡 4 Advances in Power Electronics 𝑗=𝑄 (:, 𝑃 1) = 𝑢 𝑢 (𝑛𝑇 + 𝑗)𝜏 (:, 𝑃 1) 2 1 1 ∑ 𝑇 𝑠𝑑 [𝐴 ···𝐴 ] 𝑛0 𝑛0+𝑀 𝑗=1 𝑗=𝑄 (:, 𝑃 2) = 𝑢 (𝑛𝑇 + 𝑗)𝜏 𝐵 𝑢 (:, 𝑃 2) 2 2 𝑛 𝑇 𝑇 0.25 𝑠𝑞 [𝐵 ···𝐵 ] ∣det(𝑃 𝑃)∣ 𝑗=1 𝑛0 𝑛0+𝑀 𝑗=𝑄 𝑃 (:, 𝑃 3) = 𝑢 𝑢 (𝑛𝑇 + 𝑗)𝜏 𝐶 3 (:, 𝑃 3) 2 2 3 𝑛1 𝜓 𝜔 ∑ 𝑠𝑑 𝑠 𝑄 [𝐶 ···𝐶 ] 𝑗=1 𝑛0 𝑛0+𝑀 𝑊 =[𝑎 𝑏 𝑐 𝑐 𝑑 ] [𝑎 𝑏 𝑐 𝑐 𝑑 ] = 𝑔 𝑔 1𝑔 2𝑔 𝑔 𝑔 𝑔 1𝑔 2𝑔 𝑔 𝑔 𝑗=𝑄 𝑢 (𝑛𝑇 + 𝑗)𝜏 (:, 𝑃 3) = 𝑇 −1 𝑇 𝑢 4 (:, 𝑃 4) 2 𝑛2 4 (𝑃 𝑃) 𝑃 𝑌 𝜓 𝜔 𝑠 𝑇 𝑠𝑑 𝑗=1 [𝐶 ···𝐶 ] 𝑛20 𝑛20+𝑀 𝑗=𝑄 𝑢 𝑢 (𝑛𝑇 + 𝑗)𝜏 𝐷 (:, 𝑃 4) = (:, 𝑃 5) 5 5 𝑖 𝜓 𝜔 𝑠𝑞 𝑠𝑑 ∑ [𝐷 ...𝐷 ] 𝑄 𝑛0 𝑛0+𝑀 𝑗=1 𝑗=𝑄 𝑢 (𝑛𝑇 + 𝑗)𝜏 𝑌= 𝑢 𝑛 𝑃 (DC) 𝑇 in [𝑌 ···𝑌 ] 𝑗=1 𝑛0 𝑛0+𝑀 Figure 1: A method for determining the parameters 𝑎, 𝑏, 𝑐 ,𝑐 and, 𝑑 from the input signal. 1 2 vector on the basis of 𝑑 stator current vector component and 3.2. Search Controller. Search algorithmisusedinsteady electromagnetic torque reference (see (14)). Position of rotor state, which is detected in the SSC block. Error that exists ufl xvectorisdeterminedinindirectvectorcontrol block between the current reference 𝑖 that is generatedinthe LMC (IVC). model and in the search model appears as a consequence of Hybrid model for efficiency optimization consists from inverter and stray losses which are not included in the model. 3blocks, LMC, SC, and steady state control (SSC) block. The applied search algorithm is simple. Since the current 𝑖 𝑠𝑑 LMC is used during transient states caused of external speed is very close to the value which gives minimal losses, small ∗ ∗ or torque demand [3]. Optimal control (𝑖 ,𝑖 )is step of magnetization current Δ𝑖 = 0.01𝐼 is chosen. 𝑠𝑑 𝑑𝑛 𝑠𝑑 LMC 𝑠𝑞 LMC For two successive values of the 𝑖 current, power losses calculated directly from loss model for a given operational 𝑠𝑑 are determined. Sign of Δ𝑖 is maintained if power losses are conditions what obtains power loss optimization and good 𝑠𝑑 reduced. Otherwise, the sign of Δ𝑖 is opposite in the next dynamic performances. SC is used in a steady state for a 𝑠𝑑 step: constant output power. On the basis of speed reference and measured speed, SSC 𝑖 (𝑛 ) =𝑖 (𝑛−1 ) − sgn (Δ𝑃 (𝑛−1 ))Δ𝑖 . (17) blockdenfi esits output andcontrolsswitches( Figure 2). If 𝑠𝑑 𝑠𝑑 𝛾 𝑠𝑑 transient states is detected, LMC is active, and its outputs are When the two values of magnetization current 𝑖 and 𝑠𝑑1 forwarded to indirect vector control (IVC) block and current 𝑖 were found, so the sign of power loss is changed between 𝑠𝑑2 regulators. When steady state is detected in SSC block, last these values, and new reference of 𝑖 current is specified as: 𝑠𝑑 value of magnetizing current during transient state is used as starting point for search algorithm. 𝑖 +𝑖 ∗ 𝑠𝑑1 𝑠𝑑2 (18) 𝑖 = . 𝑠𝑑 SC In this way, there are no oscillations of 𝑖 current, air gap 3.1. Loss Model Controller. Optimal control calculation in 𝑠𝑑 u fl x, and electromagnetic torque, which are characteristics of LMC for a given operational conditions is described in the search algorithm. Section 2. Expressions for 𝑑 and 𝑞 component of stator current are defined by ( 8)and (10). 4. Simulation and Experimental Results This method is sensitive to parameter changes due to temperature changes and magnetic circuit saturation, what 4.1. Simulation Results. Hybrid method for efficiency opti- consequently leads to error in a current references calcu- mization of IMD has been studied through computer sim- lation. So, algorithm for parameter identicfi ation is always ulation in MATLAB-Simulink. active, and parameters in the loss model are continuously Speed reference and load torque are shown in Figure 3. updated (Figure 2). eTh steep change of load torque appears with the aim MATRICA (𝑀×5) Advances in Power Electronics 5 𝑠𝑞𝑆𝐶 in 𝑃 =𝜔 ∗ 𝑇 ∗ out em 𝑆𝐶 𝑖 𝑠𝑑𝑆𝐶 𝑠𝑑 1/𝑧 𝑑 PI current controller ∗ SW3 SW1 Steady state control 𝐶𝑠𝑑𝑀𝐿 𝑖 ∗ 𝑠𝑞 𝑞 PI current controller 𝐶𝑠𝑞𝑀𝐿 SW2 𝑐 𝑐 𝑎𝑏 1 2 𝑑 Loss model parameter em + Δ𝜔 identification 𝜃 Speed Torque 𝑠 PI speed 𝐼 𝑉 𝐶 3 reference estimator controller em 𝜓 𝑖 𝑖 𝜔 𝜔 𝑃 𝑠𝑑 𝑠𝑞 𝑠 𝑠𝑑 in 𝑠𝑑 3Φ 2Φ 𝑠𝑞 ∗ ∗ 𝑣 𝑣 1 ∗ ∗ 𝑞 2Φ 3Φ 2 𝑖 𝑖 𝑖 ∗ 𝑎 𝑏 𝑐 −1 𝜃 𝑣 𝑠 𝐵 Power supply Incremental CRPWM 𝑖 𝑣 3 × 230 V Rectifier encoder DC DC 50 Hz VSI interface Encoder Power calculation in Figure 2: Overall proposed block diagram of efficiency optimization controller in IMD. of testing the drive behavior in the dynamic mode and its robustness for a sudden load perturbations. Graphs of magnetization current (𝑖 )and active component(𝑖 )of 𝑠𝑑 𝑠𝑞 stator current vector for a given operating conditions and 0.8 appliedhybridmethodare shownin Figure 4. Graphs of power loss for nominal u fl x and hybrid method Speed reference p.u. 0.6 are given in Figure 5. It is obvious that the use of hybrid methodsgives signicfi antly less powerlossesthanwhenthe flux is maintained at nominal value for a light load of drive. 0.4 Load torque p.u. 4.2. Experimental Results. The experimental tests have been 0.2 performed on the setup which consists of the following: (i) induction motor (3 phases, Δ380 V/𝑌220 V, 3.7/2.12 A, cos 𝜙 = 0.71 ,1410r/min,50Hz), 0 2 4 6 8 10 12 (ii) incremental encoder connected with the motor shaft, Time (s) (iii) three-phase drive converter (DC/AC converter and Figure 3: Speed reference and load torque [p.u.]. DC link), (iv) PC and dSPACE1102 controller board with TMS320C31 floating point processor and peripherals, (v) interface between controller board and drive con- Parameters of used induction motor are given in the verter. appendix of the paper. 𝐴𝑀 𝐿𝑀 6 Advances in Power Electronics 1.4 1.2 0.8 𝑞 0.6 𝑑 0.4 0.2 02468 10 12 Time (0.5 s/div) 0 2 4 6 8 10 12 Figure 6: Power losses for nominal magnetization ux fl and opera- Time (s) tional conditions shown in Figure 3. Current 𝑖 p.u. Current 𝑖 p.u. Figure 4: Graphs of 𝑑 and 𝑞 component of stator current for a given operating conditions. Nominal flux 02468 10 12 Time (0.5 s/div) Hybrid method Figure 7: Power losses when the hybrid method is applied and operational conditions shown in Figure 3. 0 2 4 6 8 10 12 Time (s) Based on graph in Figure 6,itcan be concludedthat Figure 5: Graph of power loss for nominal flux and applied hybrid method. the speed drop for a step change of load is small and speed response is strictly aperiodic. 5. Conclusion The algorithm observed in this paper used the MATLAB- Simulink software, dSPACE real-time interface, and C lan- Algorithms for efficiency optimization of induction motor guage. Handling real-time applications is done in ControlD- drive are briefly described. Detailed theoretical analysis of esk. power losses in induction motor is presented. Algorithm for All experimental tests and simulations have been done parameter identification in the loss model based on Moore- in the same operating conditions of the drive, and some Penrose pseudoinversion is presented. Also, hybrid algorithm comparisons between algorithms for efficiency optimization for efficiency optimization has been applied. According to the are made through the experimental tests. Graphs of power theoretical analysis, performed simulations, and experimen- losses for nominal u fl x and when the hybrid method is tal tests we have arrived to the following conclusions. applied are shown in Figures 6 and 7,respectively. Graphs of If load torque has a value close to nominal or higher, magnetization current for a given operational conditions are magnetizing ux fl is also nominal regardless of whether an shown in Figure 8, and speed response is shown in Figure 9. algorithm for efficiency optimization is applied or not. Power losses (W) and stator currents Power losses (10 W/div) Power losses (10 W/div) Advances in Power Electronics 7 2.5 0.75 kW (nominal mechanical power) cos 𝜙 = 0, 71 (power factor) 2 1410 r/min (nominal mechanical speed) 𝑅 = 10.4 Ω (stator resistance) 1.5 𝑅 = 11.6 Ω (rotor resistance) 𝐿 =22 mH (stator leakage inductance) 𝛾𝑠 𝐿 =22 mH (stator leakage inductance) 𝛾𝑟 𝐿 = 0, 557 H (magnetization inductance) 𝑚𝑛 𝐽 = 0, 0072 kgm (inertia moment) 0.5 𝐼 = 1.501A(nominalvalue of 𝑖 current) 𝑑𝑛 𝑠𝑑 𝐼 = 2.093A(nominalvalue of 𝑖 current). 0 𝑞𝑛 𝑠𝑞 02468 10 12 Time (0.5 s/div) Nomenclature Figure 8: Magnetization current 𝑖 and active current when the 𝑅 ,𝑅 : Resistance of stator and rotor winding hybrid method is applied and operational conditions shown in 𝑠 𝑟 𝐿 ,𝐿 : Self-inductance of stator and rotor Figure 3. 𝑠 𝑟 𝐿 :Magnetizinginductance 𝜎:Leakagefactor 𝐿 : Stator transient inductance 𝑃:Numberofpolepairs 𝜗 ,𝜔 : Rotor flux angle and angular speed 𝑠 𝑠 𝜗, 𝜔 : Rotor angle and angular speed 𝜔 : slip speed 𝑇 : Elektromagnetic torque em 𝜓 :Magnetizingufl x 𝑠𝑑 𝑖 ,𝑖 : 𝑑 and 𝑞 components of stator current vector. 𝑠𝑑 𝑠𝑞 References 02468 10 12 [1] F. Abrahamsen,F.Blaabjerg,J.K.Pedersen, P. Z. Grabowski, and P. gTh ersen, “On the energy optimized control of standard Time (0.5 s/div) and high-efficiency induction motors in CT and HVAC appli- Figure 9: Speed response when the hybrid method is applied and cations,” IEEE Transactions on Industry Applications,vol.34, no. operational conditions shown in Figure 3. 4, pp. 822–831, 1998. [2] M. Chis, S. Jayaram, and K. Rajashekara, “Neural network- based efficiency optimization of EV drive,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering (CCECE ’97), pp. 454–457, May 1997. For a light load, hybrid method for efficiency optimiza- [3] E.S.Sergaki andG.S.Stavrakakis,“Online search basedfuzzy tion gives significant power loss reduction (Figures 5, 6,and optimum efficiency operation in steady and transient states 7). for DC and AC vector controlled motors,” in Proceedings of There is no oscillation of magnetization u fl x which is the International Conference on Electrical Machines (ICEM ’08), characteristic of the search algorithms (Figures 4 and 8). Vilamoura, Portugal, September 2008. Also, this hybrid method shows good dynamic perfor- [4] F. Abrahamsen, J. K. Pedersen, and F. Blaabjerg, “State-of-Art of mances and no sensitivity to parameter changes (Figure 9). optimal efficiency control of low cost induction motor drives,” Implementation of presented algorithm is simple, and it in Proceedings of Conference on Fuzzy Systems (PESC ’96),pp. can be universally applied to any electrical motor. Changes 920–924, 1996. are only related to different models of power losses. [5] M. N. Uddin and S. W. Nam, “Development of a nonlinear and model-based online loss minimization control of an IM drive,” Appendix IEEE Transactions on Energy Conversion,vol.23, no.4,pp. 1015– 1024, 2008. Parameters of used induction motor [6] B.Blanusa,P.Matic, ´ Z. Ivanovic, and S. N. Vukosavic, “An improved loss model based algorithm for efficiency optimiza- 3phase Δ220/Y380 V (supply voltage) tion of the induction motor drive,” Electronics,vol.10, no.1,pp. 3,7/2,12 A (nominal stator current) 49–52, 2006. Speed (rad/s) Currents , (0.1 A/div) 8 Advances in Power Electronics [7] S. N. Vukosavic and E. Levi, “Robust DSP-based efficiency optimization of a variable speed induction motor drive,” IEEE Transactions on Industrial Electronics,vol.50, no.3,pp. 560– 570, 2003. [8] G.C.D.Sousa,B.K.Bose, andJ.G.Cleland,“Fuzzy logic based on-line efficiency optimization control of an indirect vector-controlled induction motor drive,” IEEE Transactions on Industrial Electronics, vol. 42, no. 2, pp. 192–198, 1995. [9] D. de Almeida Souza, W. C. P. de Aragao Filho, and G. C. D. Sousa, “Adaptive fuzzy controller for efficiency optimization of induction motors,” IEEE Transactions on Industrial Electronics, vol. 54, no. 4, pp. 2157–2164, 2007. [10] S. Ghozzi, K. Jelassi, and X. Roboam, “Energy optimization of induction motor drives,” in Proceedings of the IEEE International Conference on Industrial Technology (ICIT ’04),pp. 602–610, December 2004. [11] Z. Liwei, L. Jun, W. Xuhui, and T. Q. Zheng, “Systematic design of fuzzy logic based hybrid on-line minimum input power search control strategy for efficiency optimization of IM,” in Proceedings of the CES/IEEE 5th International Power Electronics and Motion Control Conference (IPEMC ’06),pp. 1012–1016, August 2006. [12] B. Blanusa and S. N. Vukosavic, “Efficiency optimized control for closed-cycle operations of high performance induction motor drive,” Journal of Electrical Engineering,vol.8,pp. 81–88, [13] C. Chakraborty and Y. Hori, “Fast efficiency optimization techniques for the indirect vector-controlled induction motor drives,” IEEE Transactions on Industry Applications,vol.39, no. 4, pp. 1070–1076, 2003. [14] B. Blanuˇsa, P. Matic, ´ and B. Dokic, ´ “New hybrid model for efficiency optimization of induction motor drives,” in Proceed- ings of 52nd International Symposium ELMAR-2010, pp. 313–317, [15] P. Was, Electrical Machines and Drives, Oxford University Press, 1992. 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