A step capacitor controlled 1 phase a.c. autonomous [624082]

A step capacitor controlled 1 phase a.c. autonomous
PM generator, with experiments

Ion Boldea 1, 2 , Lucian – Nicolae Tutelea 2 , Dan Hulea 2 , N icolae Muntean 2
1 R o manian Academy – Timisoara Branch, 2 Politehnica University of Timisoara , Romania
[anonimizat] , [anonimizat] , [anonimizat], [anonimizat]

Abstract – This paper introduces a high performance (90%
efficiency) 3kW, 3000/3600rpm, 50/60Hz 1 phase autonomous
PM generator with (8+2)kg total weight and simplified control
(switched capacitor) control for max ± 7 % voltage regulation
from pure resistive to resistive inductive (0.8 power factor,
lagging) loads. Topology, design principles, FEM based
characterization are accomplished by modeling for steady state
and controlled transients. Finally full size experiments are used
to validate the prop osed power device so useful in various
standalone applications .

I. I NTRODUCTION
One phase a.c. generators with regulated voltage at rather
constant frequency (speed) are used in the kW range as
standby or auxiliary power source domain driven by an
internal combustion engine or by a micro – hydraulic turbine,
etc.
There are a few solutions proposed (and some commercial)
for the scope.
The single phase synchronous generator [1] with dc excitation
controlled output voltage at constant frequency (speed) is
shown i n Fig.1. The efficiency 80% is insufficient and the
system is bulky. Brushless versions should look as in Fig. 2
[2].
The constant frequency (prime mower speed has to
increase slightly with loa d) two phase induction generator is
presented in Fig.3. The control phase is connected to a fix
capacitor while the load phase has a series capacitor (fix or

Fig. 1. Single phase d c excited synchronous generator .

Fig. 2. Brushless1 – SG.

Fig. 3. Single phase IG with auxiliary distributed winding connected to a
capacitor C e and main phase winding in series with a variable (controlled)
capacitor.

Fig. 4 . Dc and single phase ac stator doubly saliency generator [5]
Brushl ess1 – SG. 978-1-5090-4489-4/17/$31.00 ©2017 IEEE 253

partially controlled (short – circuited) for voltage regulation
control, Fig. 3 [3, 4]. Again the ef ficiency (80%) is
insufficient and the fabrication cost with distributed winding is
rather costly.
Dc. plus ac stator winding double saliency generators
have also being p roposed for the scope [5,6] but the waveform
of voltage is far from sinusoidal and the voltage regulation
limitation is difficult as the machine inductance is large.

II. P ROPOSED CONFIGURATIO N AND D ESIGN PRINCIPLES
To increase the efficiency (up to 90%, at 3kW, 3000rpm)
with decreased weight (8+2) kg, with 7% voltage regulation
up to 0.8 lagging power factor an 1 phase ac PM generator
with no rotor cage [8] and with switched capacitor voltage
control (to lower control costs) was proposed , Fig. 5.
A good saliency ratio X d <X q <1pu produced here by
magnetic saturation is required to reduce the capacitor voltage
control ratings. Ideally the steady state circuit equation of a 1
phase generator is:

(1)

With the phasor diagram in Fig. 6.
It is plausible to expect about the same no load and full
load voltage for resistive load with X d <X q <1pu. Let us assume
that the generator is designed to produce 3000W at a power
angle θ n =45 0 for E 1 =1.05V sn (rated voltage V sn ). The equation
(2) is derived from the phasor diagram, Fig. 6.
(2)

Finally we get:

(3)

The active power balance (with zero mechanical and core
losses) is:

(4)

The reactive power is (for active load) zero.

(5)

In reality conditions 3 are approximate and thus, even for
power resistive load, parallel capacitor is needed to make
condition (5) practical, with the preliminary design and FEM
characterization developed in [8] Table I. Here we will insist
on voltage control with the machine inductance L( θ r )
approximated by (Table II):

(6)
TABLE I. G EOMETRIC D IMENSIONS
Nr. Dimensions Values Units
1 Stator inner diameter 74 mm
2 Stator outer diameter 160 mm
3 Core length 65 mm
4 Permanent magnet height 6 mm
5 Airgap height 2 mm
6 Turns per phase 272
7 Conductor cros section 2 mm 2
Weights: copper:1. 527 kg; iron :
4.17+1.14 (rotor) kg ; PM . : 0.513kg ;
aluminum frame: 2..37kg; total: 10.25kg Note: capacitor
control system has
to be added
separately as cost;;
also the machine
frame. 9 Active materials costs
(copper:10USD/kg, laminations:
1.7USD/kg, PM: 80USD/kg): 66.3USD

Fig. 5. Single phase d c excited synchronous generator .

Fig. 6. Phase diagram of 1 phase IPM generator at unity internal power
factor .
254

The FEM phase inductance (at rated current) with rotor
position (due to magnetic saturation, mainly) is illustrated in
Fig. 7 a, b, c. It is evident that both X q (maximum) and X d (minimum) reactance’s in p.u. are smaller than unity (the
analytic al value of end coil connections leakage inductance is
included in Fig. 7c. It could be notice (Fig. 7d) that the 4 th and
the 6 th harmonic have the same level.

TABLE II. M AIN C IRCUIT P ARAMETERS
Nr. Dimensions Values Units
1 Stator resistance at 105 0 C 0.92 Ω
2 PM linkage flux 0.948 Wb
3 L0 (at 12.5A/16A rms current) 21.9 mH
4 L1 (at 12.5A/16A rms current) 12.6/141.6 mH/deg
5 L2 (at 12.5A/16A rms current) 4.6//165 mH
5 L3 (16A rms current) 2.2/ – 92.88 mH

The FEM calculated cogging and full torque waveforms
versus rotor position are shown in Fig. 8 for sinusoidal current
and unity power factor. The inevitable torque pulsations are
visible but so is an average 10Nm torque required for full
power (3kW at 3000 rpm) delivered

III. V OLTAGE C ONTROL
Two simplified (controlled capacitor) voltage control
options have been compared:
 SCR short – circuiting of a rectified parallel capacitor
(only in digital simulations)
 Step – capacitor voltage control with triac switches (in
digital simulation) and on the prototype
(experim ental).
Now we use the voltage equation valid for transients in
stator coordinate (core loss neglected):

(7)
A. Continuously variable capacitor control with digital simulation
results
A PI controller on voltage is added (k p =8 ∙ 10 – 5 , k i =0.12) –
Fig. 9a, so t he block diagram of the system (eqs (7)) – Fig. 9b.
A dead zone was added to the P component of voltage
regulator (to avoid a strong voltage flicker) which is active for
load voltage errors ( ± 20V band). Key step 0.8 lagging power
factor 20%, 100% load tran sients (Fig. 10) show that the
generator should fit the specifications. The equivalent values
of the capacitor (obtained by PWM short – circuiting capacitor
diode rectified voltage) for 0.8 lagging power factor are
visible in Fig. 10.
Sudden short – circuited simulated in Fig. 11 shows a rms
value of current is about 2 p.u. fitting the protection
requirements though it should be smaller in practice as the
machine desaturates notably during short – circuit.
a)
b)
20 40 60 80 100 120 140 160 180 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Reactance versus position
Rotor Position (deg.) p.u.

FEM
1st approx.
2nd approx.
3hd approx. 1
2 3 FEM
c)
0 2 4 6 8 10 12 14 16 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Inductance harmonics magnitude Inductance (p.u.)
Harmonics order d)
Fig. 7. 2D FEM results: a) PM field in d axis, b) PM and rated current in q
axis, c) machine reactance (in p.u) versus rotor position at generator rated
sinusoidal current(end coil leakage contribution is not included here in FEM
calculations), d) inductance harmonics. 255

B. Step capacitor control with digital simulation results

The step capacitor control scheme with 4 fix capacitors
in 7 combinations is based again on a voltage regulator that
rather smoothly switches the capacitor in and out through 3
triacs (Fig. 12). Finally the control was implemented on a low
cost PLC.
Sample digital simulation results, at 0.8 lagging power
factor 20% to full power transients, (Fig. 13) show rather
acceptable performance in terms of voltage regulation. It also
shows the step capacitor variation when loads are stepped up
to 100% from 20% (at t=1s) and back (at t=2s) .
Note: It may be argued that a parallel off the shelf
power filter could be used to control the output ac voltage
amplitude and reduce the voltage and current harmonics in the
load according to requirements. This evident path was not
considered here because of cost limitations . As figure 13 show
the step capa citor control wit h triac switches can be used
instead an d deliver acceptable performance at notably less
(30 – 40%) initial cost.

0 20 40 60 80 100 120 140 160 180 -20 -15 -10 -5 0 5 Torque versus position
Rotor Position (deg.) (Nm)

Cogging
Total Current interaction
Average

Fig. 8. Torque pulsation around rated power (2.5kW electromechanical
power) .

a)

b)

Fig. 9. Dynamic simulation: a) variable capacitor control, b) block diagram.

Fig. 10 . From 20% to 100% to 20% load step resp onse at 50Hz (0.8 lagging
power factor).

Fig. 11. Short circuit from full load (0.8 power factor RL, 50Hz).

Fig. 12 . The step capacitor voltage control scheme. 256

IV. E XPERIMENTAL WORK
A prototype as close as possible to the design data (Table
1), Fig. 14, has been built and tested though t he no load
voltage is smaller (Fig. 15) due to lower quantity SmCo PMs
and axial PM flux leakage (it should have been 220V (RMS
value) but it is only 186V (rsm)).
The now load voltage waveform at 3000rpm is shown in
fig. 15.a. A permanent connected capacitor (25μF) is used at
3000 rpm to produce the required voltage even at no – load . The output voltage with permanent compensation capacitor is also
presented in fig. 15a while the capacitor current with its large
3 rd harmonic in fig 15.b.
Typical waveform of load current and voltage for resistive
load (Fig. 16) shows that a current in the load is rather
sinusoidal though the curre nt in the generator is not. The
capacitor not only controls the voltage but does some useful
current filtering. For small loads the voltage tends to be non –
sinusoidal, Fig. 15, and, consequently, a third harmonic filter
is required.
The no load voltage ver sus frequency (speed), Fig. 18a, is
rather linear, with PM flux linkage visible as constant above
20 Hz (Fig. 18b). This confirms that the eddy currents in the
PMs influence is actually small (each magnet pole is made of
4×4 pieces).
The voltage – current ch aracteristic without and with step
capacitor voltage control, for pure resistive and 0.8 lagging
power factor control are shown in Fig. 17.
Fig. 13. Step capacit or control – digital simulation : generator current, active
power , voltage and pharalel capacitor versus time durind a step resistive load
variation.
a)
b)
Fig. 14. The prototype: a) generator stator, b) Control development. -0.01 0 0.01 0.02 0.03 0.04 0.05 -400 -300 -200 -100 0 100 200 300 400
time (s) Voltage (V)C=0 C=25uF

a)
-0.01 0 0.01 0.02 0.03 0.04 0.05 -3 -2 -1 0 1 2 3 Capacitor current
time (s) Current (A)

b)
Fig. 15. No load regime at 3000rpm a) voltage waveform, b) compensation
capacitor current (from measurements). 257

The short circuit current is arou nd rated current and does
not depend on speed around at working speed, Fig.19. This is
notably different from simulated short circuited current mainly
because of PM flux reduction and leakage inductance increase,
both due to axial flux fringing not conside red in the
simulations and possible due to under estimation of the end
connection leakage inductance .
The efficiency versus load, Fig. 20, was computed based
on measured output power current and voltage. The input
power was computed considering the copper losses based on
cold stator m easured resistance R s =0.68 Ω, the iron loses
estimated from design P fe60 =33.8W, additional power losses
P ad60 =30W, mechanical losses P mec60 =30W at 60Hz frequency,
respectively, P fe50 =23.5W, P ad50 =20.8W, P mec =25W at 50Hz.
The copper losses were computed cons idering the load current
and compensation capacitor current. At 60Hz the efficiency is
larger than the targeted 90%, but it is smaller at 50Hz due to
smaller PM back voltage and larger copper losses produced by
capacitive current required to keep the volta ge level. -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 -300 -200 -100 0 100 200 300
time (s) Voltage (V)

a)
-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 -30 -20 -10 0 10 20 30
time (s) Current (A)I L o a d I G

b)
Fig. 16. Voltage, a), and current waveforms b) (from measurements). 0 2 4 6 8 10 12 14 180 185 190 195 200 205 210 215 220 225 230
Load current (A) Voltage (V)

50
60
a)
0 2 4 6 8 10 12 14 180 185 190 195 200 205 210 215 220 225 230
Load current (A) Voltage (V)

50
60
b)
Fig. 17. Resistive load test: a) Voltage current characteristic, b) Parallel
capacitor versus load current (from measurements).
0 10 20 30 40 50 60 70 0 50 100 150 200 250
f0 (Hz) V0(V)
a)
0 10 20 30 40 50 60 70 0.545 0.55 0.555 0.56 0.565 0.57 0.575 0.58 0.585 0.59
f0 (Hz) V0/w0 (Vs/rad – rms value)
b)
Fig. 18. No load voltage a) and PM flux b) versus speed (from
measurements). 258

V. D ISCUSSION
The notably difference between experimental tests and
FEM 2D computed no load voltage could be explained by
frontal PM flux leakage. In order to correct the FEM 2D
linkage flux, an additionally axial 2D FEM simulation is
proposed, Fi g. 21a, where half of the magnetic shaft, PM, coil
end connection and stator pole shoe are presented in axial
sections along d axis plane. To account for heavy saturation,
based on magnetic permeance balances in Fig. 21a the stator
core is artificially pro longed axially in two steps. Airgap flux
density distribution in axial direction along stator pole shoe,
presented in Fig 21.b reflects a part of the frontal flux leakage.
A part of the PM flux lines that reaches the stator pole shoe are going back to the rotor without passing the stator coil
using an axial path, fig. 21.a, especially when the stator yoke
is heavy saturated.
The PM flux reduction factor, k af , due to the axial fringing
could be computed as the ratio between average values of
magnetic vector potential, A c , across on the coil area to the
ideal airgap flux per unity length that considers the airgap flux
density in the central section’s, B 0 , (maximum value from
fig.20.b).

(8)

The percent PM flux reduction is:

(9)

The no load voltage relative error between FEM
computation and test results at 3000rpm is:

(10)

If the 2D FEM computed voltage is corrected by
multiplying it with the axial fringing factor k af , a small error
(around 2.72%) still remain between test results and computed
voltage.
The axial fringing factor is sensitive to the st ator core
saturation, and could be increased by reducing the stator core
saturation. Increasing the rotor PM length in comparison with
the stator core length will increase the PM flux reduction
factor (more fringing). If for technological reasons the PMs
a re buried in the solid magnetic core the PM flux reduction
factor is decreasing (more fringing).
The axial flux produced by the armature current is also
increasing the leakage inductance and finally the voltage drop
on the synchronous inductance is larger.

VI. C ONCLUSION
Step capacitor voltage control has been shown feasible for
the scope, both via digital simulations and experimentally
(with resistive load).
Total cost of generator (active materials + framing + step
capacitor control) is 66.3USD for active ma terials for the 3
kW, 3000rpm, 1 phase generator with around 0.9 efficiency
and ± 7% voltage regulation up to 0.8 lagging power factor full
load. The efficiency based on the experimental results is
slightly smaller than computed because a large capacitive
c urrent is necessary to maintain the voltage within desired
tolerance limits.
The axial PM fringing flux is important and should be
considered during the design process in order to preserve the
no load voltage.

a)
b)
Fig. 21. Axial fringing: a) FEM simulation, b) airgap flux density distribution
along axial direction. 259

Optimal design is required for a better compro mise
between contradictory requirements as low cost, low weight
versus low voltage regulation and high efficiency.
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