Electric Vehicles Modelling and Simulations Part 13 pdf

Minimization of the Copper Losses in Electrical Vehicle Using Doubly Fed Induction Motor Vector Controlled 349          * rs m r L s L PM e C (4) The copper losses are giving as: 2 r i. r R 2 s i. s R cl P  (5) The motion equation is: dt d Jd e C   (6) In DFIM operations, the stator and rotor mmf’s (magneto motive forces) rotations are directly imposed by the two external voltage source frequencies. Hence, the rotor speed becomes depending toward the linear combination of theses frequencies, and it will be constant if they are too constants for any load torque, given of course in the machine stability domain. In DFIM modes, the synchronization between both mmf’s is mainly required in order to guarantee machine stability. This is the similar situation of the synchronous machine stability problem where without the recourse to the strict control of the DFIM mmf’s relative position, the machine instability risk or brake down mode become imminent. 3. Nonlinear vector control strategy 3.1 Double flux orientation It consists in orienting, at the same time, stator flux and rotor flux. Thus, it results the constraints given below by (7). Rotor flux is oriented on the d-axis, and the stator flux is oriented on the q-axis. Conventionally, the d-axis remains reserved to magnetizing axis and q-axis to torque axis, so we can write (Drid et al., 2005a, 2005b)         0 rq sd r rd ssq (7) Using (7), the developed torque given by (4) can be rewritten as follows: . rsc k e C    (8) where, r L s L PM c k   s  Appears as the input command of the active power or simply of the developed torque, while r  appears as the input command of the reactive power or simply the main magnetizing machine system acting. Electric Vehicles – Modelling and Simulations 350 3.2 Vector control by Lyapunov feedback linearization Separating the real and the imaginary part of (3), we can write:                      rq u 4 f dt rq d rd u 3 f dt rd d sq u 2 f dt sq d sd u 1 f dt sd d (9) Where f 1 , f 2 , f 3 and f 4 are done as follows :              rd rrq4sq34 f rqr rd 4 sd 33 f sd srq2sq12 f sqs rd 2 sd 11 f (10) With: s T 1 1   ; r L s T M 2   ; s L r T M 3   ; r T 1 4   Tacking into account of the constraints given by (7), one can formulate the Lyapunov function as follows 0 2 ) r rd ( 2 1 2 ) ssq ( 2 1 2 rq 2 1 2 sd 2 1 V  (11) From (11), the first and second quadrate terms concern the fluxes orientation process defined in (7) with the third and fourth terms characterizing the fluxes feedback control. Where its derivative function becomes ) r rd )( r rd ( ) ssq )( ssq ( rqrq sdsd V     (12) Substituting (9) in (12), it results ) r rd u 3 f() r rd ( ) ssq u 2 f() ssq ( ) rq u 4 f( rq ) sd u 1 f( sd V       (13) Let us define the following law control as (Khalil, 1996): Minimization of the Copper Losses in Electrical Vehicle Using Doubly Fed Induction Motor Vector Controlled 351                 ) r rd ( 4 K r3 f rd u ) ssq ( 3 K s2 f sq u rq2 K 4 f rq u sd 1 K 1 f sd u   (14) Hence (14) replaced in (13) gives: 0 2 ) r rd ( 4 K 2 ) ssq ( 3 K 2 rq2 K 2 sd 1 KV    (15) The function (15) is negative one. Furthermore, (14) introduced into (9) leads to a stable convergence process if the gains K i (i=1, 2,3, 4) are evidently all positive, otherwise:                        0 t ) * ssq lim( 0 t ) * r rd lim( 0 t rq lim 0 t sd lim (16) In (16), the first and second equations concern the double flux orientation constraints applied for DFIM-model which are define above by (7), while the third and fourth equations define the errors after the feedback fluxes control. This latter offers the possibility to control the main machine magnetizing on the d-axis by  rd and the developed torque on the q-axis by  sq . 3.3 Robust feedback Lyapunov linearization control In practice, the nonlinear functions fi involved in the state space model (9) are strongly affected by the conventional effect of induction motor (IM) such as temperature, saturation and skin effect in addition of the different nonlinearities related to harmonic pollution due to the supplying converters and to the noise measurements. Since the control law developed in the precedent section is based on the exact knowledge of these functions fi, one can expect that in real situation the control law (14) can fail to ensure flux orientation. In this section, our objective is to determine a new vector control law making it possible to maintain double flux orientation in presence of physical parameter variations and measurement noises. Globally we can write: i f i f ˆ i f  (17) On, i f ˆ : True nonlinear feedback function (NLFF) i f : Effective NLFF i f : NLFF variation around i f . Where: i = 1, 2, 3 and 4. Electric Vehicles – Modelling and Simulations 352 The ∆f i can be generated from the whole parameters and variables variations as indicated above. We assume that all the ∆f i are bounded as follows: |∆f i | <  i ; where are known bounds. The knowledge of  i is not difficult since, one can use sufficiently large number to satisfy the constraint|∆f i | <  i . The ∆f i can be generated from the whole parameters and variables variations as indicated above. Replacing (17) in (9), we obtain                      rq u 4 f 4 f ˆ dt rq d rd u 3 f 3 f ˆ dt rd d sq u 2 f 2 f ˆ dt sq d sd u 1 f 1 f ˆ dt sd d (18) The following result can be stated. Proposition: Consider the realistic all fluxes state model (18). Then, the double fluxes orientation constraints (7) are fulfilled provided that the following control laws are used                ) r rd sgn( 44 K) r rd ( 4 K r3 f ˆ rd u ) ssq sgn( 33 K) ssq ( 3 K s2 f ˆ sq u ) rq sgn( 22 K rq2 K 4 f ˆ rq u ) sd sgn( 11 K sd 1 K 1 f ˆ sd u   (19) where K ii   i and K ii > 0 for i=1; 4. Proof. Let the Lyapunov function related to the fluxes dynamics (18) defined by 0 2 ) r rd ( 2 1 2 ) ssq ( 2 1 2 rq 2 1 2 sd 2 1 1 V  (20) One has      0V) rd sgn( 44 K 4 f) r rd () sq sgn( 33 K 3 f) ssq ( ) rq sgn( 22 K 2 f rq ) sd sgn( 11 K 1 f sd 1 V     (21) where V  is given by (15). Hence the i f variations can be absorbed if we take: Minimization of the Copper Losses in Electrical Vehicle Using Doubly Fed Induction Motor Vector Controlled 353 4 f 44 K 3 f 33 K 2 f 22 K 1 f 11 K     4 f 44 K 3 f 33 K 2 f 22 K 1 f 11 K     (22) The latter inequalities are satisfied since i K >0 and ii K ii f  Finally, we can write: 0V 1 V   (23) Hence, using the Lyapunov theorem (Khalil, 1996), on conclude that                        0 t ) * ssq lim( 0 t ) * r rd lim( 0 t rq lim 0 t sd lim (24) The design of these robust controllers, resulting from (19), is given in the followed figure 2 The indices w can be : sd, sq, rd and rq, (i = 1,2,3 and 4 ) 4. Energy optimization strategy In this section we will explain why and what is the optimization strategy used in this work. Fig. 1 illustrates the problem which occurs in the proposed DFIM vector control system when the machine magnetizing excitation is maintained at a constant level. 4.1 Why the energy optimization strategy? Considering an iso-torque-curve (hyperbole form), drawn from (8) for a constant torque in the ),( rs  plan and lower load machine ( Fig.1), on which we define two points A and B, respectively, corresponding to the two machine magnetizing extreme levels. Theses points concern respectively an excited machine ( ConstWb1 r    ) and an under excited machine ( ConstWb1.0 r  ). Both points define the steady state operation machine or equilibrium points. The machine rotates to satisfy the required reference speed acted by a given slope speed acceleration Const dt d    . So, the machine in both magnetizing cases must develop a transient torque such as: Electric Vehicles – Modelling and Simulations 354 0 1 2 3 4 5 6 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1  s (wb)  r (wb) Transient torque curve: ro C dt d J   Steady state torque curve: ro C A A’ BB’ Fig. 1. Illustration of the posed problem in the DFIM control system with constant excitation.    J ro C dt d J 0r C eT C (25) On the same graph, we define a second iso-torque-curve C eT =Const in the ),( rs   plan. This curve is a transient one on which we place two transient points A’ and B’. Here we distinguish the first transitions A–A’ and B–B’ due to the acceleration set, respectively for each magnetizing case. Both transitions are rapidly occurring in respect to the adopted control. Once the machine speed reaches its reference, the inertial torque is cancelled ( = 0), then the developed torque must return immediately to the initial load torque C ro , characterized by the second transitions A’–A and B’–B towards the preceding equilibrium points A and B. One can notice that during the transition B–B’, corresponding to the under excited machine, the stator flux can attain very high values greater than the tolerable limit ( maxs  ), and can tend to infinite values if the load torque C ro tends to zero. So the armature currents expressed by the following formula deduced from (2) and (7) are strongly increased and can certainly destruct the machine and their supplied converters. s .j r . r i s .j r . s i   (26) Where, r L. 1 ; s L. 1 ; r L. s L. M       In the other hand, for the case A (excited machine), if the A–A’ transition remains tolerable, the armature currents can present prohibitory magnitude in the steady state operation due to the orthogonal contribution of stator and rotor fluxes at the moment that the machine is sufficiently excited. The steady state armature currents can be calculated by (26), where we can note the amplification effect of the coefficients ,  and . Minimization of the Copper Losses in Electrical Vehicle Using Doubly Fed Induction Motor Vector Controlled 355 4.2 Torque optimization factor (TOF) design In the previous sub-section, the problem is in the transient torque, especially when the machine is low loaded. So it becomes very important to minimize the torque transition such as (Drid, 2005b): 0 dt e dC  (27) where, r d r e C s d s e C e dC        (28) This condition should be realized respecting the stator flux constraint given by maxss  (29) In this way the rotor and stator fluxes, though orthogonal, their modulus will be related by the so-called TOF strategy which will be designed from the resolution of the differential equations (27-28) with constraint (29) as follows:        maxss 0 srrs  (30) from (29) we can write maxsrsrrs   (31) thus, r r maxs s         (32) the resolution of (32) leads to r lnC maxs s     (33) where C is an arbitrary integration constant, therefore )C( e r maxs s     (34) Since, the main torque input-command in motoring DFIM operation is related to the stator flux, it becomes dependent on the speed rotor sign and thus we can write       0if s 0if s )sgn( ssq (35) Electric Vehicles – Modelling and Simulations 356 with (35), (34), the rotor flux may be rewritten as follows )C( e r maxs sq     (36) The resolution of (32) gives place to the arbitrary integration constant C from which the TOF-relationship (36) can be easily tuned. This one can be adjusted by a judicious choice of the integration constant, while figure 2 presents TOF effect on armature DFIM currents with C-tuning. Note that this method offers the possibility to reduce substantially the magnitude of the armature currents into the machine and we can notice an increase in energy saving. Hence using TOF strategy, we can avoid the saturation effect and reduce the magnitude of machine currents from which the DFIM efficiency could be clearly enhanced. -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 0 50 100 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 0 50 100  s (wb) I s (A) I r (A) C = 2.3 C = 2.8 C = 1.8 C = 1.3 C = 2.8 C = 1.3 C = 1.8 C = 2.3 Fig. 2. TOF effect on armature DFIM currents 4.3 Torque-copper losses optimization (TCLO) design In many applications, it is required to optimize a given parameter and the derivative plays a key role in the solution of such problems. Suppose the quantity to be minimized is given by the function )x(f , and x is our control parameter. We want to know how to choose x to make )x(f as small as possible. Let’s pick some x 0 as the starting point in our search for the best x. The goal is to find the relation between fluxes which can optimize the compromise between torque and copper losses in steady state as well as in transient state, (i.e. for all {C e } find ( s , r ) let min{P cl }) (Drid, 2008). From (5), (8) and (26), the torque and copper losses can be to written as:        2 s2 a 2 r1 a cl P s . r . c k e C (37) Minimization of the Copper Losses in Electrical Vehicle Using Doubly Fed Induction Motor Vector Controlled 357 with : ) 2 ) s L.( s R 2 ) s L. r L.( 2 M r R ( 2 a ) 2 ) s L. r L.( 2 M s R 2 ) r L.( r R ( 1 a         The figure 3 represents the layout of (37) for a constant level of torque and copper losses in the ( s ,  r ) plan. These curves present respectively a hyperbole for the iso-torque and ellipse for iso-copper-losses. From (37) we can write: 0 2 el C 2 a cl P 2 r 2 c k 4 r 2 c k 1 a  (38) To obtain a real and thus optimal solution, we must have: 0 2 el C 2 a 2 c k 1 a4 4 cl P 4 c k  (39) The equation (39) represents the energy balance in the DFIM for one working DFIM point as shown in fig.3. Then, one can write: 2 c k 2 el C 2 a 1 a4 cl P  (40) This equation shows the optimal relation between the torque and the copper losses. -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8   0  = 0 r (wb) s (wb) iso-torque iso-copper-losses Optimal solution Fig. 3. The iso–torque curves and the iso–losses curves in the plan ( s ,  r ) Electric Vehicles – Modelling and Simulations 358 4.4 Finding minimum Copper-losses values The Rolle’s Theorem is the key result behind applications of the derivative to optimization problems. The second derivative test is used to finding minimum point. We can rewrite (37) as:               2 r . 2 c k 2 e C 2 a 4 r 2 c k 1 a 2 r . 2 c k 2 e C 2 a 2 r1 a cl P r . c k e C s (41) The computations of the first and second derivatives show that the critical point is given by: 4 1 2 c k 1 a 2 a 2 e C rc          (42) For which: 0 1 a8 4 rc . 2 c k 2 e C 2 a6 4 rc 2 c k 1 a2 2 r d ) rc ( cl P 2 d       (43) We can see that the second derivative is positive and conclude that the critical point is a relative minimum. 5. Simulation Figure 4 illustrates a general block diagram of the suggested DFIM control scheme. Here, we can note the placement of optimization block, the first estimator-block which evaluates torque and the second estimator-block which evaluates firstly the modulus and position fluxes, respectively  s ,  r ,  s and  r , from the measured currents using (2) and secondly the feedback functions f 1 , f 2 , f 3 , f 4 given by (10). Optimization process allows adapting the main flux magnetizing defined by rotor flux to the applied load torque characterized by the stator flux. With the analogical switch we can select the type of the reference rotor flux. The switch position 1, 2 gives respectively TCLO and TOF for optimized operation and the position 3 for a magnetizing constant level. The Figure 5 shows the speed response versus time according to its desired profile drawn on the same figure. Figure 6 illustrate the fluxes trajectory of the closed–loop system. It moves along manifold toward the equilibrium point. We can notice the stability of the system. Figures 7 and 8 show respectively the stator and the rotor input control voltages versus time during the test. Figure 9 present the copper losses according to the stator flux variations in steady state operation and we can see the contribution of the TCLO compared to the TOF. Finally figure 10 present the dissipated energy versus time from which we can observe clearly the influence of the three switch positions on the copper losses in transient state. We can conclude that the TCLO is the best optimization. [...]... optimisation and field oriented control without position sensor, IEE proceedings Electric power applications, Vol 145 No 4, (July 1998), pp 360-368, ISSN 135 0-2352 364 Electric Vehicles – Modelling and Simulations Hopfensperger, B et al., (1999) Stator flux oriented control of a cascaded doubly fed induction machine, IEE proceedings Electric power applications, Vol 146 No 6, (November 1999), pp 597-605, ISSN 135 0-2352... charging power and operating temperature Figure 4 depicts a typical EV charging efficiency operated at room temperature and utilizing an AC/DC onboard charger with a maximum output power of 3500 W Fig 3 Electric Vehicle Model Fig 4 EV Charging Energy Flow and Efficiency Diagram 370 Electric Vehicles – Modelling and Simulations 2.3.2 Operational efficiency Generally the efficiency of the EV Electrical Motor... based on power plant types and efficiency The claim of EV technology proponents that this type of propulsion technology will offer a potential to reduce a long- 368 Electric Vehicles – Modelling and Simulations term GHG emission can be verified with the implementation of the Well-To-Wheel (WTW) emission model to analyze the GHG emission of the electrical energy source Fig 2 Electrical Energy Source 2.2... (DFC): To provide the driver feedback relative to drive style including speed, acceleration, and deceleration Fig 8 PIBMS Architecture 374 Electric Vehicles – Modelling and Simulations 3.2.1 Design realization The system design is to offer the user the ability to follow advised upon route model, trip model and electrical accessory model to optimize the following queries: 1 Energy consumption 2 Emission... RSU In order to reduce bandwidth utilization for communication between RSU and PIBMS, repeating traffic data will be communicated to PIBMS only in case of traffic condition change thus eliminating message overhead 378 Electric Vehicles – Modelling and Simulations 4 Simulation environment To evaluate the performance of the PIBMS a simulation tool integrating traffic, vehicle and network models shall... ISBN 0 -13- 067389-7, USA 16 Predictive Intelligent Battery Management System to Enhance the Performance of Electric Vehicle Mohamad Abdul-Hak, Nizar Al-Holou and Utayba Mohammad Electrical & Computer Engineering Department, University Of Detroit Mercy, Detroit, USA 1 Introduction The Electric Vehicle (EV) is emerging as state-of-the-art technology vehicle addressing the continually pressing energy and. .. torque, vehicle route and u (i) is the control vector of the vehicle such as the recommended vehicle speed, the recommenced acceleration, the recommended deceleration, the recommended route and the recommended charge point The optimization problem becomes the search for the control vector u (i) 376 Fig 10 PIBMS Operational Flow chart Diagram Electric Vehicles – Modelling and Simulations Predictive... continues to be the primary challenge in order to achieve the proper balance in the EV design as illustrated in Figure 1 and described below 366 Electric Vehicles – Modelling and Simulations Fig 1 EV Design Parameters  Battery Capacity: EV battery capacity is predetermined by the battery design and cell chemistry Lithium polymer batteries are the target implementation for EV due mainly to their high power-to-weight... Figure 3 and listed below: 1 High voltage electric battery rather than a fuel tank to store and supply the required operational energy 2 Electric motor rather than an internal combustion engine to propel the vehicle 3 Gear box rather than a transmission to couple the power from the electric motor to the drive shaft 4 On Board or Off Board Charger to allow for recharging of the high voltage electric. .. and environment concerns The benefits of EV emerge from these vehicles capability of sustaining their energy demands through electric grid rather than fossil fuel consumption Well- to-Wheel studies have shown that electric drive (E-drive) offers the highest fuel efficiency and consequently the lowest emission of green house gases Grid electricity in the United States of America has been shown to be . variation around i f . Where: i = 1, 2, 3 and 4. Electric Vehicles – Modelling and Simulations 352 The ∆f i can be generated from the whole parameters and variables variations as indicated. position sensor, IEE proceedings Electric power applications, Vol. 145. No. 4, (July 1998), pp. 360-368, ISSN 135 0-2352 Electric Vehicles – Modelling and Simulations 364 Hopfensperger,. 1 and described below. Electric Vehicles – Modelling and Simulations 366 Fig. 1. EV Design Parameters  Battery Capacity: EV battery capacity is predetermined by the battery design and