CC BY
340
UDC 621.313:681.3
doi: 10.20998/2074-272X.2016.1.05
V.I. Milykh, N.V. Polyakova
DETERMINATION OF ELECTROMAGNETIC PARAMETERS AND PHASE RELATIONS IN TURBO-GENERATORS BY THE AUTOMATED CALCULATION OF THE MAGNETIC FIELD IN THE SOFTWARE ENVIRONMENT FEMM
The theoretical bases of calculation of electromagnetic quantities and time-phase relationship are presented for the turbogenerators. This is done by numerical calculations of the magnetic field in the software environment package FEMM (Finite Element Method Magnetics). A program which controls calculations and organizes the issuance of the results to a text file is created on the algorithmic language Lua. The program is universal in terms of a turbo-generator models, as well as steady-state modes of their work with a minimum of input data. The exciting current of the rotor and the phase currents of three-phase stator winding in accordance with their initial phase are given for the calculation of the magnetic field. The key function for the analysis of electromagnetic parameters is the calculated angular function of the magnetic flux phase stator winding. The expansion in the harmonic series is carried out and amplitude and initial phase are received for this function. Next, the phase EMF and voltage, phase shifts between all values, active power, electromagnetic torque, the magnetic flux in the gap and other parameters are determined. The presented Lua script is a prototype for a similar calculation software of electric machines of other types. References 9, figures 6.
Key words: Finite Element Method Magnetics, program FEMM, turbo-generator, electromagnetic parameters, phase relationships, automated calculations, Lua script.
Представлены теоретические основы расчета электромагнитных величин и их фазовых соотношений для турбогенераторов. Это реализуется путем численных расчетов магнитного поля в программном пакете FEMM. Расчеты автоматизированы посредством созданной программы на алгоритмическом языке Lua. Она управляет расчетами и организует выдачу результатов в текстовый файл. Представленный скрипт Lua универсален и может послужить прототипом аналогичного программного обеспечения для других типов электрических машин. Библ. 9, рис. 6.
Ключевые слова: программа FEMM, турбогенератор, электромагнитные параметры, фазовые соотношения, автоматизированные расчеты, Lua скрипт.
Introduction. Widely known software FEMM [1] is effective for the calculation of three-dimensional magnetic fields (MF) of electrical machines (EM), classic design with almost in-plane plane MF within their active part. For example, this applies to the turbo-generators (TG) [2]. This program is freed calculators from the development of implemented mathematical models and programming and has a fairly user-friendly interface.
An additional means of facilitating the work of users of the program FEMM are scripts in the algorithmic language Lua, integrated into it. For example, in [3] our program is described, which automated construction of simulation models of TG, in [4] the program of automated calculations of their electromagnetic processes is given. Efficiency of Lua script is that programs are written once, and used countless times, and by any number of users.
This paper continues the series of works started in [3, 4]. And its purpose is to present the script Lua, automating the preparation of a series of electromagnetic parameters and phase relations in EM by the numerical MP calculations in the software environment FEMM. It is made on the example of TG - one of the largest and responsible of their representatives [5].
Object of investigations. For illustration here, as in [3, 4], we have TG 340 MW. Its parameters are further presented in the file of initial data.
Electromagnetic system of the TG shown in Fig. 1 by its cross-section. Highlighted phase zones of a two-layer shortened three-phase stator winding А-А', В-В and С-С. Shown used rectangular (x, y) and polar (r, a)
coordinate system, the longitudinal d transverse q axis of the rotor.
The basis of the developed Lua script is prepared in advance for the environment FEMM computational model of the electromagnetic system of the TG. We do this through a script Lua, presented in [3], and in the absence of such - in «manual» mode, in accordance with the instructions of the software FEMM.
Fig. 1. Model of the electromagnetic system of the TG
© V.I. Milykh, N.V. Polyakova
26
ISSN 2074-272X. Electrical Engineering & Electromechanics. 2016. no.1
in its cross-section
View on the computer screen in the environment FEMM (file type - Femme Document) of the calculation model of the TG presented as a whole in Fig. 2, and in Fig. 3 its fragment is presented. Visible marks of physical properties of the blocks - limited regions of the calculation area. Marks Fe1, Fe2 and Fe3 set the magnetization curves of ferromagnetic materials, m0 -permeability, m0 - magnetic permeability р0=4-л-10-7 H/m, marks iA, iB, iC - phase currents, Ir - rotor current. Addition of + or - to the mark of current indicates its direction: if the current at this time is positive, then at this point it is taken with the appropriate sign. The number after the colon indicates the number of effective conductors in this block. Circles around marks indicate the maximum size of the triangles in the structure of the finite elements formed by program FEMM.
The fragment in Fig. 3 is taken from the right half of a complete model from Fig. 2, the rest of all similarly formed in accordance with and model in Fig. 1. In particular, the left half of the signs of currents is opposite to that seen in Fig. 3.
Fig. 2. Initial physico-geometrical model of the TG
Fig. 3. Fragment of the physico-geometrical model of the TG
Mentioned blocks in the FEMM-model are combined in groups to operate with them as units of the calculation area. From the designated group number [3] is here used: 2, 3, 4, 5, 6, 7 - the phase zones А, В, С, А', В, Сof the stator winding, 9 - entire rotor (see Fig. 1).
Theoretical basics. The steady-state MF calculation by the program FEMM is carried out on the base of the numerical solution of the differential equation:
=kJz, (1)
where Az, Jz are the axial components of the magnetic vector potential (MVP) and current density; p is the absolute magnetic permeability; k is the ort.
On the external boundary of the calculation area for the MVP the know Dirichlet condition Az = 0 is accepted.
In the model TG (Fig. 2) for calculating of the the instantaneous distribution of MP of the particular steady state mode it is necessary to have the corresponding currents. In generalizing load mode (LM) [9] is given a constant rotor current Ir and the instantaneous values of the symmetrical system of stator phase currents: iA=Imcos(P); iB=Imcos(P-2л/3); iC=Imcos(P+2:rc/3), where
im=42 is is their amplitude and Is is the effective value; P is its initial phase [6-9] specifies the shift of the stator winding MMF Fs from rotor winding MMF Ff (Fig. 1). Here conditional resultant for the MMF at LM is given
Fi = Ff + Fs. (2)
At no-load (NL) conditions only the rotor current is given, at steady mode of short circuit - only the stator currents. Directions of currents (Fig. 1) are regulated according to the system adopted in [7].
For TG the result is a distribution of MF in its crosssection as a function Az(x,y). Picture of MF in the calculation area is represented by a structure of field lines -lines of equal MVP Az=const. An example of this for the TG at the mode to its rated load (RL) is shown in Fig. 1.
One of the key quantities in the analysis of electromagnetic parameters of the TG is the magnetic flux linkage (MFL) [2] and it is determined by the distribution of MVP. For example, for any of the six phase areas (Fig. 1) MFL is determined based on
k
^ = Nk JAzdS * X Az,av, j*Sj , (3)
йф S \ j=1
°(p J
where S is the section square by current-carrying elements of the phase zone; K is the number of elements of its discretization; Az,av,j is the average MVP value in the j-th element.
In the formula (3) the active length of the TG la and the number of turns of the phase stator winding Ns are taken into account, and to determine S and integral in Lua script there are appropriate procedures [1].
The initial basis for identifying the phase relations in any of the design modes is a temporary phase or direction of the vector MFL of the phase winding А-А'. MMF of this base winding in Figure 1 is oriented along the longitudinal axis of the rotor d.
The direction of the vector MFL of the phase
rot
-rot
(k Az)
1
M-
ISSN 2074-272X. Electrical Engineering & Electromechanics. 2016. no.1
27
winding A-А 'is determined by the structure of a particular MF of the actual calculated mode. So, in Fig. 1 this direction is becomes apparent by orientation of field lines of the MP and generally corresponds to the direction of the vector MMF Fj (2). But as long as the vector is constructed a priori, taking into account the results that will be obtained even further based on the methodology, which was published in [4-6]. Here, it shall be presented briefly to understand the meaning of the developed and submitted further the Lua script.
The mentioned techniques will be described with reference to the NL conditions, and then it will be effective for any other mode. Specifically, we assume that the MF at the NL conditions is calculated by the program FEMM. The structure of this field is shown in Fig. 4.
Fig. 4. Displacement of the phase zone of the stator winding against a background of the calculated MF to select the MFL values
In the initial angle position a1 of the phase zone A in Fig. 4,a on the basis of formula (3) the MFL T1 is determined. Now move this zone conditionally on the tooth division to the position a2 (Fig. 4,b) and find the corresponding value of the MFL T1. The same repeat a3 at position a3 (Fig. 4,c), etc. - until the position a30 (Fig. 4,d). In general, the number of positions equals to the number of stator slots Qs. A phase shift of each phase zone is made on angle Aa=360/Qs (in degrees).
As a result we will have a discrete angular function of the MFL of one phase zone at its period T, i.e.
Vk(ak); ak = (k-1) -Aa; k = 1,2,3,... Qs, (4)
where k are number of angular positions of this zone.
For each position of the phase zone between 1 and Qs/2 there is a diametrically opposite position between Qs/2+1 to Qs. They mutually create a conditionally movable phase winding A-A', for which the angular
function of the MFL at its half-period:
VA,k = Vk -Vk+Qs/2; k = 1,2,3,...Qs/2. (5)
By obtaining results, taking into account the periodicity of values in the TG type T(a + T /2) = -T(a)we supplement the half-period of the MFL (5) to full period:
VA,k+Qs/2 =-VA,k; k = 1,2,3,..Q/2. (6)
The number series of the MFL (5) is illustrated in Fig. 5 by set of highlighted points on the curve of the NL in the range of k from 1 to 15. On the basis of (6) the curve is extended to a full period (points 16 to 30) and point 31 repeated the first point (point 1) through a period T.
Similar actions were carried out and after calculating the MF at the RL mode, and the results are presented by the RL curve in the same Fig. 5. To display the initial phases of functions of the MFL the curves are continued to the left.
Fig. 5. Angular dependences of the MFL of the TG phase winding
Obtained numerical full angular function V4,k(ak), k = 1,2,3,...Qs, can be presented as harmonic
series expansion [6, 7]. Because of typical for the TG periodic condition V(a + T /2) =-V(a) in this series there is no constant component and even harmonics. Assumed in [6] cosine series for the MFL is the following
У A = ZTm,v cos (va + Yv) , (7)
v=1,3,5,...
There amplitudes and arguments (initial phases)
Vm,v = -/sV+c2; Yv = -arctg ^ (8)
cv
Are obtained by sinus-cosine coefficients:
2 Qs 2 Qs
sv = Q ZVA,k sin(vak ) ; cv = Q ZVA,k cos(vak ) .
Qs k=1 Qs k=1
In (8) arctangent function arctg(sv/cv) should be extended to give a value in the range of -180° до +180° depending on the signs cv and sv. In Lua there is a corresponding function atan2(sv,cv).
In EM including TG analysis of the phase relationships is carried out for the first harmonics. For the first cosine harmonic of the MFL (7) at the NL the amplitude and initial phase Tmf=51.97 Wb and Yf =0, at
28
ISSN 2074-272X. Electrical Engineering & Electromechanics. 2016. no.1
the RL - *¥„,1 =53.89 Wb and ji = -35.75° are obtained (in the notation we do not show the harmonic number). The remaining harmonic, in principle, were negligible.
Illustration of angles jf and ji is presented in Fig. 5, where we see that the amplitude and hence the vector of the MFL at the RL mode are shifted toward negative value of the angle a relatively to the MFL at the NL mode.
The shift angle © = jf - ji is a load angle of the TG (in this case, it has a positive value). The vectors Fl and Ff in Fig. 1 have a similar shift.
Taking into account that in the TG the rotation angle is connected with time, i.e. a=Q-t, where Q is the angular velocity, it is possible to go to the common temporal vector diagrams (VD) to illustrate and other phase relationships and the definition of other parameters. Such a VD is shown in Fig. 6, where as the origin of the angles vertically disposed longitudinal axis of the rotor d, as well as the angles in Fig. 1 is taken.
Fig. 6. Vector diagram corresponding the load mode of the TG
Phase current vector Is is produced relatively the d-axis with respect to the previously caused p angle (in this case, it equals to -160.43°). The vector of the MFL ¥a phase windings, caused by the MF of the armature reaction corresponding to the vector Fs has the same direction. Vectors of the MFL from the rotor winding and the resulting MFL ¥l are carried out under already determined angles jf and jl.
Actually, selection of ¥a и from the MFL ¥l is conditional at the LM, and here the value is completely different compared to the NL mode. Parts of the MFL are determined by the procedure adopted here.
Namely, we adopt a base already defined MFL ¥l and from the end of its vector draw a line parallel to the vector ¥a to the intersection with a line oriented as at an angle jf. This intersection in the point a and identifies specific length of vectors ¥a and and their values in the scale of the vector ¥l.
Based on the known theory [2] by the amplitude of
the MFL at frequency f we have root-mean-square value of the first harmonic of the phase EMF, including and at the LM:
E =42n fs ¥„,i. (10)
The vector of this EMF, as it is known, behind the vector of its MFL ¥l at -90 °. Vectors of the EMF Ea and Ef from the MFL ¥a and are defined and constructed similarly.
It turns out that the triangle of the EMF Ei, Ea and Ef is similar to the triangle of the MFL ¥l, ¥a and Tf.Therefore, between the vectors Et and Ef will be the same angle of the load ©.
In order to determine phase voltage Us, it is necessary to take into account the voltage drop UR=RsIs at the active resistance Rs and EMF Ev= -jXv £ from the flux of the phase winding end leakage, where Xv is the corresponding inductive reactance.
Obviously, the vector UR is parallel to the vector Is, and the vector Ev - perpendicular (in the direction of lag). So they are attached to the end of the vector Ei and give as a result the vector of the phase voltage Us = U = Ei + Ev - Ur.
It is known that in the TG the UR value is negligible compared with El и Us, but here they appear to demonstrate the full-factor approach.
From the geometric relationships on the VD, a fragment of which in the rotated form is shown in detail below on the right (without observing proportions), the active and reactive components of the voltage Us, its root-mean-square value and the phase shift from the vector of current Is'.
Us,a = El cos Фі - UR; Us,r = El sinФі - Ev; (11)
Us =-\jUla + Ulr ; Фs = arctg(Us,r / Us,a) , (12)
Where by the VD he angle between Is and Ei equals to
Фі = -p - 90 + ji.
As a result, by the field calculation a lot of already considered electromagnetic parameters as well as active electric power of the TG are determined:
Pa = msUshcosФs. (13)
Besides, it is possible to determine the electromagnetic torque of the TG which is made by the tensor of magnetic tension [2] in the correspondence with the formula
2n rs
Mem =------a----- f f r ■ Br ■ Bar ■ dr ■ da, (14)
em M 0(r - r ) J J r a H-0vs ’r) 0 r
where rr and rs are radii of circles limiting the gap from the sides of rotor and stator; Br и Ba are radial and angular components of the magnetic flux density.
The magnetic flux through a surface bounded by the contour i, has the expression [2]:
Ф = (41 - AZ2)• ia , (15)
where Az1, Az2 are the MVP values at the points 1 and 2 in a plane of calculation, through which in the axial direction lateral sides of the mentioned circuit i pass.
To automate all conditioned calculations, the presented further Lua script according to the purpose of
ISSN 2074-272X. Electrical Engineering & Electromechanics. 2016. no.1
29
this work is intended.
File of initial data of the TG for the Lua script.
Requirements to create the program, as in [3, 4] are its flexibility in terms of the geometry and dimensions of the TG, as well as steady-state modes of operation - with a minimum of input data.
The values of various parameters of the TG and serving local constants and variables can be defined directly in the Lua script, or input from a pre-prepared text files. In this work, all the parameters that characterize this problem and perhaps changing for different variants of the TG, entered from a separate file.
Text files of Lua-scripts and data files are written in the editor Notepad.
Here is a data file that may have any name with the extension txt. Data have a form of numbers or text strings in quotation marks " " and accompanied by
commentaries. To mark the beginning of comments the colon been have chosen.
Text of the file of initial data.
"FemC_TG340" : name_fem - name of the model in FEMM
"RezC_TG340" : name_rez - name of the file of results 3 : ms - number of stator winding phases 1 : p - number of pairs of poles 50 : fs - frequency, Hz
-160.47 : beta - initial phase of the stator currents, degree
3151.4 : Ir - rotor excitation current, А
11547 : Is - stator phase current, А
0.8 : bs - relative stub of the stator winding
0.00266 : Rs - active resistance of the stator winding, Q
0.063 : Xv - inductive reactance of the end part of the
stator winding, Q
0.0 : gf - initial phase of the MFL at the NL mode, degree
30 : Qs - number of rotor slots
10 : Ns - number of series turns in the stator phase
1 : as - number of parallel branches of the stator winding
5.308 : la - turbo-generator active length, m
637.5 : rsi - radius of the stator core bore, mm
699 : rv - average radius of the upper layer of the stator
winding, mm
778 : rn - average radius of the lower layer of the stator winding, mm
General characteristics of Lua language.
Language Lua, as well as other programming languages, can create loops, conditional statements, procedures, perform calculations on mathematical formulas for standard and created their own functions. There are functions: sqrt - square root; sin, cos, atan2 - sine, cosine, arctangent, and others. There is built-in n number - Pi. Trigonometric functions operate with radians, but when dealing with geometric objects Lua uses degrees, rectangular coordinates are measured in millimeters, which are predetermined in the formulation of the problem in FEMM menu Problem, what has been done in [3].
The Lua script commands that begin with mo_ or mi_ are its procedures. Their description can be found via the Help button in the working window of FEMM, then
entered the section Lua Scripting [1].
Strings of the program or the right side, starting with a double hyphen - - are comments and do not affect its work.
External data file name Lua script asks after its launch by the operator with a "tip":
File 1ап=ргошр1("Введите имя файла")
This name is entered from the keyboard and entered by press Enter. Script opens the file for reading ("г") and assign it internal name f_d, i.e. f_d = openfile(File_dan .. ".txt","r")
Reading operator read(f_d, "*n", "*l") from the next line reads valus of numeric and string data, how many times in it the option "* n" appears, and the option "* l" will make a transfer to a new line, i.e. remaining in the string any text is ignored and used by the user as a comment (we separate by symbol :).
In operators write to write to the results file the option "\ r \ n" gives a pass to new line, and the use of symbols such as % 6.3f is the format (format) of printing, i.e. in this case 6 position are reserved for the number, including 3 - for a fractional part.
Further a program is presented that after its call in the environment FEMM organizes input of the initial information and the calculation of the MF, forms an angular function of the MFL of the phase winding, determines its amplitude and the initial phase, as well as a number of electromagnetic parameters and phase relationships of different values in the TG.
Lua script.
--Definition of the file of initial --data
File dan=prompt("Input the file name")
--Opening of the data file
f_d = openfile(File_dan .. ".txt","r")
--INITIAL DATA from the text file
name_fem=read(f_d,"*n","*l")
--nameFEMM
--File name for the results writing
name_rez=read(f_d,"*n","*l")
ms=read(f_d,"*n","*l")
—number of phases p=read(f_d,"*n","*l") --pole pairs fs=read(f_d, "*n", "*l") --frequency
By the same way all data from the above-mentioned file are read till rn, i.e.: rn=read(f_d,"*n","*l")
— average radius of the lower layer --of the stator winding
closefile(f d) —closing the data file --Organization of the file of results writeto(name rez) —name rez file name --Name of geometrical —model of TG-type fem name fem=name fem .. ".fem" mi saveas(name fem) —to store model “-ADDITIONAL" DATA FOR CALCULATION: gr=Pi/180 —multiplier degree=>radian beta=beta*gr --value of angle beta, rad Ur=Rs*Is —voltage drop on Rs Ev=Xv*Is —voltage drop on Xv ts=360/Qs —angle of stator tooth step tp=Qs/(2*p) —pole step in
30
ISSN 2074-272X. Electrical Engineering & Electromechanics. 2016. no.1
—tooth division
qsp=tp/ms —slot number per pole and --phase
qsn=0.5*(qsp-tp*(1-bs)) —slot number
-- of the lower layer of the stator
-- winding under q-axis
qsv=qsp-qsn -- slot number
-- of the upper layer of the stator
-- winding under q-axis
--Angle of the first lower bar of the
-- phase A
an1=180-(qsn-0.5)*ts
--Angle of the first upper bar of the
-- phase A
av1=180-(qsv-0.5)*ts
Im=Is*2A0.5/as —amplitude of the phase -- current in the parallel branch --Writing of some TG parameters write("TG exciting data","\r\n") write(format(" Is= %5.0f",Is), format(" Ir= %5.0f",Ir), format(" beta=%7.2f",beta/gr),"\r\n")
F = {} —massive creation to store -- MFL values of phase winding --Phase currents of the stator winding c=2*Pi/3 Ia=Im*cos(beta) Ib=Im*cos(beta-c) Ic=Im*cos(beta+c) --Definition of currents of phases and -- rotor in FEMM mi modifycircprop("iA+",1,Ia) mi modifycircprop("iA-",1,-Ia) mi modifycircprop("iB+",1,Ib) mi modifycircprop("iB-",1,-Ib) mi modifycircprop("iC+",1,Ic) mi modifycircprop("iC-",1,-Ic) mi modifycircprop("Ir+",1, Ir) mi modifycircprop("Ir-",1,- Ir)
--In FEMM-model there are names of --marks of currents
--MF calculation in FEMM and path to --demonstration and extraction of --calculation results mi analyze(1) mi loadsolution()
--Cycle of conditional displacement of --the phase zone A with slot step ts for k=1,Qs,1 do ak=(k-1)*ts --angle --Cycle of calculation of conductors --angles of phase A for i=1,qsp,1 do ai=ak+(i-1)*ts --Calculation of coordinates of --conductors of lower layer and their --extraction
ani=(an1+ai)*gr x=rn*cos(ani) y=rn*sin(ani) mo selectblock(x,y)
--Calculation of coordinates of --conductors of upper layer and their --extraction
avi=(av1+ai)*gr x=rv*cos(avi) y=rv*sin(avi) mo selectblock(x,y) end --end of the cycle by i
--Reading of allocated blocks square S = mo blockintegral(5)
--MVP integral's value by square S A = mo blockintegral(1) mo clearblock() -allocation emptying --MFL of the phase zone of winding А
F[k] = Ns*A/S
end -end of slot steps by k --MFL of phase winding obtaining by --MFL of phase zone and prolongation --on period
q2=Qs/2 —a half of phase zone -- positions
for i=1,q2,1 do F[i]=F[i]-F[i+q2] F[i+q2]=-F[i] end --Amplitude and phase shift -- calculation
--MFL first harmonic by Fourier series Fsin=0 Fcos=0 --storages nulling for k=1,Qs,1 do —cycle by MFL array ak=ts*(k-1)*gr —angular position --Aplitudes of sin and cos components Fsin=Fsin+2*F[k]*sin(ak)/Qs Fcos=Fcos+2*F[k]*cos(ak)/Qs end --sweep of k array elements Fm1=sqrt(FsinA2+FcosA2) —amplitude gl=atan2(Fsin,Fcos) -initial phase
--Electromagnetic parameters of TG --RMS value of the phase EMF El=Pi*2A0.5*fs*Fm1
--phase shift EMF El from current Is fil=-(beta+Pi/2-gl)
--active and reactive components of --phase voltage
Usa=El*cos(fil)-Ur Usr=El*sin(fil)-Ev --RMS value of phase voltage Us=sqrt(UsaA2+UsrA2)
--phase shft between Us and Is --TG power ratio
fis=atan(Usr/Usa) cosfi=cos(fis) teta=gf*gr-gl --TG load angle Pa=ms*Us*Is*cosfi —active power --Results writing to file write(" MFL, phase shifts, EMF, voltage and active power","\r\n")
--Angles recalculation (radians to -- degrees)
gl=gl/gr fil=fil/gr fis=fis/gr teta=teta/gr beta=beta/gr write(format(" Fm1=%5.2f",Fm1), format(" gl=%7.2f",gl),"\r\n") write(format(" El=%5.0f",El), format(" fil=%7.2f",fil),"\r\n") write(format(" gf=%4.1f",gf), format(" teta=%6.2f",teta), format(" Us=%5.0f",Us),"\r\n") write(format(" fis=%7.2f",fis), format(" cosfi=%4.2f",cosfi), format(" Pa=%6.1f",Pa*1e-6),"\r\n") write("Electromagnetic torque and power","\r\n")
--Rotor block groups allocation mo groupselectblock(9)
--Electromagnetic torque reading Mem=mo blockintegral(22) Mem=Mem*1e-3 mo clearblock()—allocation emptying --Electromagnetic power Pem=Mem*2*Pi*fs*1e-3
write(format("Mem=%5.0f",Mem)," KN*m", format("Pem=%6.1f",Pem)," MW","\r\n") --Magnetic flux per pole --in gap on the stator bore
ISSN 2074-272X. Electrical Engineering & Electromechanics. 2016. no.1
31
--Cycle of angular steps in da degrees for i=1,180,1 do da=1 --Coordinates of two neighbor points ai=da*(i-0.5)*gr ai0=da*(i+0.5)*gr
x=-rsi*sin(ai) y=rsi*cos(ai) x0=-rsi*sin(ai0) y0=rsi*cos(ai0)
--MVP reading in two points A=mo getpointvalues(x,y)
A0=mo getpointvalues(x0,y0)
--MVP maximum search on the circle if A0<A then Pot=2*A*la i=181 end end —sweep of I points by the circle write("Magnetic flux per pole, Wb", format(" Pot=%5.3f",Pot),"\r\n") writeto()—Results file closing mi close()—Closing of documents of --magnetism preprocessor
Indications on the program utilization.
To use the script of the field calculation of parameters and phase relationships of the TG it is necessary:
1. The script file with the extension *.lua and file with initial data with the extension *.txt should be in the same folder on the computer disk.
2. Run the program FEMM - the TG model. Editor Lua is called from the working window in FEMM by the «key» Open Lua Script in menu File, and then in the window that opens, the desired file lua is started.
3. At the request of the program in the opened window we enter the data file name and press the button Enter. Further action the program executes itself.
4. The calculation results are in a text file with a name given in the data file with name RezC_TG340 and are read by the editor Notepad.
Content of the file of results.
The data presented correspond to the NL mode and are already illustrated in Fig. 5 and Fig. 6. For convenience of representation in the format of this paper the text of the file of results is partially reformatted.
TG excitation data
Is=11547 beta=-160.43 Ir=3153
MFL, phase shifts, EMF, voltage and
active power
Fm1= 53.89 gl= -35.75
El=11971 fil= 34.68
gf= 0.0 teta= 35.75 Us=11547
fis= 31.79 cosfi=0.85 Pa=340.0
Electromagnetic torque and power
Mems=-1086 KN*m; Pems=-341.2 MW
Magnetic flux per the stator pole, Wb
Pot=6.608
In the full version of the Lua script other results are calculated in inputted to the text file, too.
Conclusion. The presented theoretical basics and Lua scripts provide wide opportunities for users of the
program FEMM for automated obtaining of electromagnetic parameters and phase relations of the TG on the basis of the calculation of the magnetic field. This script is universal in terms of the structure of the electromagnetic system of the TG within their widespread structure, and steady-state modes of their operation. Designed Lua script may be a prototype for similar software for calculations of EM of other types.
REFERENCES
1. Meeker D. Finite Element Method Magnetics. FEMM 4.2 32 bit 11 Oct 2010 Self-Installing Executable. Available at: www.femm.info/wiki/OldVersions (accessed 10 March 2014).
2. Milykh V.I., Polyakova N.V. Numerically-field calculations of the electromagnetic parameters of turbogenerators. Visnyk NTU «KhPI» - Bulletin of NTU «KhPI», 2014, no.38(1081), pp. 3-18. (Rus).
3. Milykh V.I., Polyakova N.V. Automated formation of calculation models of turbogenerators for software environment FEMM. Elektrotekhnika і elektromekhanika - Electrical engineering & electromechanics, 2015, no.4, pp. 7-14. (Rus).
4. Milykh V.I., Polyakova N.V. Automated calculations of the
dynamics of turbogenerator electromagnetic processes in software environment FEMM. Elektrotekhnika і
elektromekhanika - Electrical engineering & electromechanics, 2015, no.6, pp. 24-30. (Rus).
5. Titov V.V., Hutoreckij G.M., Zagorodnaja G.A., Vartan'jan G.P., Zaslavskij D.I., Smotrov I.A. Turbogeneratory [Turbogenerators]. Leningrad, Energiia Publ., 1967. 895 p. (Rus).
6. Milykh V.I., Polyakova N.V. Analysis of phase relationships of electromagnetic parameters in a turbogenerator on the basis of numerical calculation of magnetic fields. Elektrotekhnika і elektromekhanika - Electrical engineering & electromechanics, 2003, no.4, pp. 59-64. (Rus).
7. Milykh V.I., Polyakova N.V. A system of directions and phase relationships for electromagnetic parameters at numerical calculations of magnetic fields in a turbogenerator. Elektrotekhnika i elektromekhanika - Electrical engineering & electromechanics, 2011, no.5, pp. 33-38. (Rus).
8. Milykh V.I., Polyakova N.V. Bases of numerical analysis of phase correlations of electromagnetic sizes are in a turbogenerator. Elektrika - Electrician, 2012, no.3, pp. 31-33. (Rus).
9. Milykh V.I., Polyakova N.V. Organization of numerical calculation of turbogenerator magnetic field under load with specified output parameters control. Elektrotekhnika i elektromekhanika - Electrical engineering & electromechanics, 2012, no.1, pp. 36-41. (Rus).
Received 22.07.2015
V.I. Milykh1, Doctor of Technical Science, Professor,
N.V. Polyakova1, Engineer,
1 National Technical University «Kharkiv Polytechnic Institute»,
21, Frunze Str., Kharkiv, 61002, Ukraine.
тел/phone +38 057 7076514, e-mail: [email protected]
How to cite this article:
Milykh V.I., Polyakova N.V. Determination of electromagnetic parameters and phase relations in turbo-generators by the automated calculation of the magnetic field in the software environment FEMM. Electrical engineering & electromechanics, 2016, no.1, pp. 26-32. doi: 10.20998/2074-272X.2016.1.05.
32
ISSN 2074-272X. Electrical Engineering & Electromechanics. 2016. no.1
