Assignment 5 1-4
5 Machine characteristics The goal of the fifth assignment is to extend your modelling experience towards estimation of machine characteristics. Firstly, the effect of permanent magnet synchronous machine parameters on field-weakening performance is studied. Secondly, FEM analysis is performed where the machine parameters are estimated. This assignment is a continuation from the previous design task, which is defined by you as an outcome of EMK_task_3. In this assignment the rotor of the initial design is modified in FEMM in order to influence the machine parameters and to compare the modified machine to the initial machine. Your task is to perform introductory study on normalized machine parameters and thereafter continue analysing your own machine design. From this assignment you should be able to become familiar on ― Circle diagram and torque speed characteristics ― Maximum torque per ampere (MTPA) line and constant power speed range (CPSR) as an outcome of machine parameter tuning for field-weakening (FW) performance. Also maximum torque per flux (MTPF) line as remaining operation points at voltage but not current limited operation at high speed. ― Calculation of machine parameters from FEMM
5.1 Machine equations Torque-speed and power-speed characteristics are one of the most explicit information of the mechanical outcome and operation range that an electrical machine can provide. These kinds of characteristics are derived from machine equations, where the field flux linkage is divided between magnetising direction x and perpendicular to that in y direction on a rotating rotor reference frame. These equations include the main machine parameters as an ideal connection in electro mechanics in presence of electromagnetism. The machine equations are described as flux (5.1) and torque (5.2) equations that are limited by the voltage (5.3) and current (5.4).
xs j iLiL yyyxxmxy (5.1)
iiLLiiiLiiLiiiT yxyxymxyyyxxymxyyx (5.2)
max uu s xyx uiLujuu yyy iL xxm (5.3)
22 max iii yx (5.4) For sake of idealization, there is not only resistance that is excluded from the voltage equation, but also the inductances are assumed to be linear and the magnetic core is loss-less. Therefore the compact form of voltage equation includes only the induced voltages due to the magnetisation speed ω. The magnetisation speed differs from the actual rotating speed as well as the electric torque differs from the mechanic torque when the number of pole pairs p is larger than 1. N T p poles mech (5.5) 2 mech T Concerning to the power balance between the electric terminal, machine air-gap and shaft, which is a mechanical terminal, the n-phase voltages, currents and fluxes are represented as “rms” vectors or power invariant quantities that facilitates the calculation of torque and power. The electric torque, which is pole-pair times lower than mechanical torque, consists of excitation torque and reluctance torque. The excitation torque is outcome of excitation flux m and the
EIEN20 Design of Electrical Machines, IEA, 2020 Assignment 5 2-4 stator currents placed in perpendicular to this flux. The reluctance torque is present due to rotor saliency and stator currents that are oriented so that x and y currents both are equal. Therefore the fluxes and currents are shown as two components representing the saliency ξ of the rotor (5.5), when Lx differs from Ly, and the load angle β of the current (5.6).
LLLL xnxy (5.6)
nx cos iiii ny sin (5.7) 1 iT cos i 2 2sin1 (5.8) nm 2 n The torque of electrical machine is expressed two of independent parameters. Concerning to flux weakening operation at the short-circuit point the magnetising flux is balanced by demagnetization current.
nxm 0 LLiL nx 1 (5.9) Based on permanent magnet excited machines with no rotor saliency the nominal stator flux is expressed as
2 2 n nym LLiL ny 1 (5.10) Instead of actual values for current, flux linkage and inductance normalized values are used. Nominal flux linkage 1 gives nominal 1 (vector) voltage 1 at magnetisation speed 1. At the same time the same flux linkage 1 at (vector) current 1 gives torque 1. The magnetizing flux is also normalised and with the presence of coil and current the magnetizing flux is below 1 to produce torque.
5.2 Normalized characteristics of PMSM The assignment, which is formulated in EMK_task_5.m, consist of two parts: assignmenttask=1 is used to generate circle diagram of a permanent magnet synchronous machine (PMSM) and use this diagram to estimate the torque-speed and power-speed characteristics for the machine. This assignment can be even used to visualize the interior or inset permanent magnet machines, where the rotor includes magnetic saliencies and Lx differs from Ly. Initially, the assignment file provides circle diagram and torque speed characteristics (Figure 5.1) of the PMSM that normalized magnetizing flux linkage psim=0.9 and magnetic saliency for rotor results stator inductance ratio to ksii=1.
1 1 1 . 1 2 0.8.2 0.8 1 1 0 Lsx*=0.44 Lsy*=0.44 Psim*=0.90 0 1 . . 8 . 6 2 0.6 0.6 0.5 0.4 0.4 0.8
1
1
1
0.2 0.2.
2 1 0.8 0.6 0.6 0 1 0 0
-0.2 -0.2 0.4 -0.4 -0.4 1
-0.5 1 2
.
1 1-0.6 -0.6 0.2 6 8 . . 2 0 . 0 1 1 -0.8.2 -0.8 -1 1 0 -1 -0.5 0 0.5 1 0 0.5 1 1.5 2 2.5 3 3.5 4 Figure 5.1 Circle diagram (left) with centred (yellow) current circle, offset voltage circles (generally ellipses) and iso-torque (red) lines. The path of operation points from 0 to 4 times of nominal speed is both shown on circle diagram and torque and power-speed characteristic (right).
EIEN20 Design of Electrical Machines, IEA, 2020 Assignment 5 3-4
Your task is to change machine parameters psim and ksii and study the outcome of the diagrams and characteristics
1. normalized magnetization flux linkage ψmn=0.999, 0.99, 0.9, 0.8, 0.7, 0.6, 0.5, …
2 2 0.5 2. normalized stator inductance Ln=( ψn - ψmn ) /In where ψn=1 and In=1
3. inductance ratio due to saliency ξ=Ly/Lx={0.5 1 2} or even wider Please consider that the saliency is not considered in the inductance calculation and this results that torque and voltage become larger than 1 when ξ>1 and smaller than 1 when ξ<1. During your model based experiments try to distinguish 1. current-limited region – speed range from 0 to rated speed and maximum torque per current (MTPA) line 2. current-and-voltage-limited region – constant power speed range (CPSR). Here the drive is operated at rated current with a load angle that gives the rated voltage. 3. voltage limited region – the operation points is selected as maximum torque with a limited voltage along maximum torque per flux (MTPF) line. The speed w is rather magnetization speed than rotation speed and the normalized base speed value is 1. The torque-speed and power-speed characteristics are recorded as vectors that consist of 41 nodes where the time step is defined by dw. Therefore speed step of dw=0.05 brings the maximum speed up to 2w, dw=0.1 to 4w and dw=0.2 to 8w, respectively. The selection of the speed step helps to focus either on rated speed or maximum speed.
5.3 Machine parameters from FE-model The second part of the assignment is the calculation of machine parameters from FE-model and replacement of Imax, psim, Ln and ksii in the previous estimation model for machine characteristics. The second part of the assignment, assignmenttask=2, opens the FE-model 'tmp_magn_ini.fem', which is the outcome of EMK_task_3.m. The post-processing routine does the following: 1. Opens the initial model just for obtaining the value for the rated stator current 2. Applies Isy=In, Isx=0; and calculates machine output for two rotor positions at 0 and 30 electrical degrees 3. Applies Isy=0, Isx=0; and calculates machine output for two rotor positions at 0 and 30 electrical degrees 4. Applies Isy=0, Isx=-Isn; and calculates machine output for two rotor positions at 0 and 30 electrical degrees The calculation output is recorded as 3-phase currents and flux linkages in matrices cur and flu respectively. Vector quantities are calculated also Clarke and Park transformation are used to obtain different components of interest. Your task is to become familiar with the equations and the calculated values (whether they are amplitude or power invariant).
EIEN20 Design of Electrical Machines, IEA, 2020 Assignment 5 4-4
Obtain the average values of fluxes over the rotor positions 0 and 30 degrees and calculate the machine parameters as following:
1. Obtain magnetising flux m from no load points
2. Calculate static Lsx=sx/Isx between no load points and operation points when Isx is applied
3. Calculate static Lsy=sy/Isy between no load points and operation points when Isy is applied Include a new data input: pp, Imax, psim, Ln and ksii in the first part of the assignment and obtain machine characteristics. The continuation of the assignment is the repetition of the parameter extraction and characteristic estimation, but at this time the calculation supposes to be done for modified rotor. Include new 30 degree arcs between outer corners of the magnets and remove old ones. Assign these new arcs into group 2. Now you have created a rotor wit inset magnets like in Figure 5.2.
Figure 5.2 Initial design with modified rotor layout where the surface mounted magnets are inset into rotor core by rotor saliencies between the magnets. After the modification save the new FE-model as 'tmp_magn_mod.fem', and call it from the analysis file by femodelname in the beginning of code. Repeat the previous task: obtain machine parameters and characteristics.
EIEN20 Design of Electrical Machines, IEA, 2020