TRANSACTIONS ON ELECTRICAL ENGINEERINGtransoneleng.org/2015/20154.pdf · · 2015-12-22MATLAB and OrCAD software. A. LCTLC Topology LCLCL converters ... Basic diagram of the LCTLC

TRANSACTIONS

ON ELECTRICAL ENGINEERING

ERGO NOMEN

CONTENTS

Koscelnik, J., Mazgut, R., Kascak, S., Prazenica, M.: Review of Selected Multi-Element Resonant Topologies . . . . . . . . . . . 86 – 90

Rau, D., Rodina, J., Palkovič, L., Hubinský, P.: Sensorless Field Oriented Control of BLDC Motors for MAVs . . . . . . . . . . 91 – 96

Liška, M., Beláň, A., Cerman, A., Janík, M.: Control System of Battery Storage to Eliminate the Power Variation According to the Electricity Prediction . . . . . . . . . . . . . . . . . . . . . . 97 – 101

Polcar, P., Český, J.: Conceptual Design of Electromechanical Systems Using Ferrofluids . . . . . . . . . . . . . . . . . . . . . 102 – 107

Kascak, S., Mazgut, R.: Sensorless Control of Two-Phase Induction Machine using MRAS Techniques . . . . . . . . . . . 108 – 111

Vol. 4 (2015) No. 4 pp. 86 – 111

TRANSACTIONS ON ELECTRICAL ENGINEERING

Publisher: ERGO NOMEN, o.p.s., K13114 FEE CTU in Prague,

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BAUER Jan

HAVLICEK Radek

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ZDENEK Jiri

Periodicity: Quarterly

Language: English

Scope: International scientific journal of electrical engineering

On-line version: www.transoneleng.org

ISSN 1805-3386

Each paper in the journal is evaluated by two reviewers under the supervision of the International

Editorial Board.

International Editorial Board

Editor in Chief:

Prof. LETTL Jiri, Czech Technical University in Prague, Czech Republic

Members:

Prof. BAUER Palo, Delft University of Technology, Netherlands

Prof. BRANDSTETTER Pavel, VSB-Technical University of Ostrava, Czech Republic

Prof. DOLEZEL Ivo, The Academy of Sciences of the Czech Republic, Czech Republic

Prof. DUDRIK Jaroslav, Technical University of Kosice, Slovakia

Prof. NAGY Istvan, Budapest University of Technology, Hungary

Prof. NOVAK Jaroslav, University of Pardubice, Czech Republic

Prof. ORLOWSKA-KOWALSKA Teresa, Wroclaw University of Technology, Poland

Prof. PEROUTKA Zdenek, University of West Bohemia, Czech Republic

Prof. PONICK Bernd, Leibniz University of Hannover, Germany

Prof. RICHTER Ales, Technical University of Liberec, Czech Republic

Prof. RYVKIN Sergey, Russian Academy of Sciences, Russia

Prof. SKALICKY Jiri, Brno University of Technology, Czech Republic

Prof. VITTEK Jan, University of Zilina, Slovakia

Prof. WEISS Helmut, University of Leoben, Austria

Responsibility for the contents of all the published papers and technical notes is upon the authors.

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Copyright: ©2015 ERGO NOMEN, o.p.s. All right reserved.

mailto:[email protected]

Transactions on Electrical Engineering, Vol. 4 (2015), No. 4 86

TELEN2015016

Review of Selected Multi-Element

Resonant Topologies

Juraj Koscelnik 1), Roman Mazgut 1), Slavomir Kascak 1) and Michal Prazenica 1)

1) Department of Mechatronics and Electronics, Zilina, Slovakia, e-mail: [email protected]

Abstract — The paper deals with an analysis and

comparison of multi-element resonant topologies. The

superior performance of the investigated converters

provides inherent current protection and very low

circulating energy. The converter consists of two resonant

tanks and HF transformer in case of the LCTLC topology.

The paper shows the design of the resonant elements. The

converters can achieve zero current switching (ZCS) and

zero voltage switching (ZVS) conditions for the primary and

secondary-side of the device respectively. The converters

achieve high values of power density and efficiency up to

96 % at the full load. The paper includes the basic

equations, analysis and simulation of the chosen topologies

(LCTLC, LCLCL, LCL2C2).

Keywords — Multi-element resonant converter, review of the

resonant converters, switching conditions, LCTLC, LCLCL,

LCL2C2.

I. INTRODUCTION

The progress in the development of semiconductor devices has resulted in formation of a new field of science generally called power electronics (Fig. 1). The newer and higher quality parts affect design of the resonant converter and therefore it is necessary to use sophisticated control algorithms.

In some involvement inverters with high frequency transformers the number of the semiconductor devices in converter may be reduced and this results in price of the product [1]–[3]. Increasing functionality requires more power consumption and higher density requires less size of the power supplies. Therefore, the power supplies for computing, consumer electronics and lighting applications are required to provide more power with small size and low cost.

The most effective way to achieve high power density in converters is to increase the switching frequency so that the size of the passive components, such as the capacitor and inductor, as well as the transformer can be reduced, as they occupy a large portion of the overall size [1].

Fig. 1. Course of the power density development.

II. RESONANT CONVERTERS

The group of resonant and quasi-resonant converters consists of series, parallel and series-parallel resonant circuits. By combining the basic resonant circuits modified multi-element resonant circuits arise. Resonant converters use two kinds of the switching technique: Zero voltage switching (ZVS) and Zero current switching (ZCS) [3]. Those techniques are known as soft switching. The converter can operate in ZVS and/or ZCS. The basic diagram of the resonant converter is in Fig. 2.

SWITCHING

NETWORK

RESONANT

FILTER

MULTIFUNCTION

OUTPUTLOAD

+

-

Fig. 2. Diagram of the resonant converter.

The diagram describes basic connection of the resonant converter composed of the DC source; switching network; resonant filter and multifunction output connected to a load.

A. Multi-resonant Converters

The essence of the multi-resonant switch concept is to combine the desirable characteristics of both quasi-resonant switches in one device. This can he achieved using the multi-resonant switch. In this configuration of the resonant switch, resonant capacitances are placed in parallel with both the switch and the diode, resulting in desirable zero-voltage switching of both devices Zero-Voltage-Switched Multi-Resonant Converters (ZVS-MRCs) generated from PWM topologies by replacing the PWM switch by the multi-resonant switch [2]. The multi-resonant network absorbs all major parasitic components, including the transistor output capacitance, diode junction capacitance and transformer leakage inductances into the resonant circuit. This allows the multi-resonant converters to operate at high frequencies with the most favourable (zero-voltage) switching condition for all semiconductor devices [4], [5].The base of every multi-element resonant converter is that it is usually composed of five resonant components in series or parallel circuit connection. This connection forms the resonant tank.

Using a similar concept, a family of multi-element resonant converters is proposed. Some of the five-element resonant tanks are shown in Fig. 3. Due to space limitations, the formation of all five-element resonant converters cannot be exhibited completely in this work.


TELEN2015016

Fig. 3. Possibilities of the multi-element connections of the resonant

converters.

III. COMPARISON OF SELECTED MULTI-ELEMENT

TOPOLOGIES

As it is described in the previous chapter the multi-element resonant converter is composed of five accumulation elements. There are many possibilities of circuit connections. For this chapter three topologies were chosen: CTLC, LCLCL and LCL2C2. For the review it was done the simulation analysis provided by the MATLAB and OrCAD software.

A. LCTLC Topology

LCLCL converters (Fig. 4) are one of the novel types of converters based on the LLC resonant circuit, and LCTLC inverter consisting of the DC/DC buck converter LCLC resonant filter and HF transformer. The HF transformer can also be connected behind the LCLC filter, if necessary and it can also be used to the DC/DC boost converter types. The inverter (LCTLC) is usually used as a power supply for either HV rectifiers or HF cycloconverters or matrix converters for 2-phase motor applications respectively [6], [7].

Fig. 4. Basic diagram of the LCTLC inverter.

The resonant converter is composed of one series resonant tank (L1, C1), HF transformer (T) and parallel resonant tank (L2, C2). The converter is fed by a DC source and the shape of the input voltage is switched by two switches (S1, S2) in half-bridge connections [7]. In this case the output of the filter is the HF harmonic waveform of the voltage (and current) – direct AC output mode with THD not more than 5 %.

For the analysis, an equivalent LCTLC circuit can be created. The equivalent parameters of the HF transformer (Lσ, Rσ, Lm, RFe) and inter-winding capacitance Ciw and inter-turn capacitance Cit are included into the resulting component parameters. More about the equivalent circuit is given in the paper [7]. On the basis of it the state-space equations for the equivalent circuit with the R-L load will be [6]:

𝑑𝑖𝐿1

𝑑𝑡=

1

𝐿1𝑢(𝑡) −

𝑅1

𝐿1𝑖𝐿1 −

1

𝐿1𝑢𝐶1 −

1

𝐿1𝑢𝐶2 (1)

𝑑𝑖𝐿2

𝑑𝑡=

1

𝐿2𝑢𝐶2 (2)

𝑑𝑢𝐶1

𝑑𝑡=

1

𝐶1𝑖𝐿1 (3)

𝑑𝑢𝐶2

𝑑𝑡=

1

𝐶1𝑖𝐿1 −

1

𝐶2𝑖𝐿2 −

1

𝐶2.𝑅2𝑢𝐶2 −

1

𝐶2𝑖𝐿𝑙 (4)

𝑑𝑖𝐿𝑙

𝑑𝑡=

1

𝐿𝑙𝑜𝑎𝑑𝑢𝐶2 −

𝑅𝑙𝑜𝑎𝑑

𝐿𝑙𝑜𝑎𝑑𝑖𝐿𝑙 (5)

where iL1, iL2 are currents in the inductors L1and L2, respectively; iLL is current in the load R2, L2; uC1,uC2 are capacitor voltages of C1 and C2, respectively, u(t) is the output voltage of the converter (filter input voltage). When the input voltage UDC is varying than the RMS value of the fundamental harmonic will also vary. To be constant an asymmetric control of the duty cycle for the switches S1, S2 has to be provided [7], [8].

Fig. 5. Switching waveforms of the transistor (current ID – red line,

voltage UDS – green line).

Fig. 5 shows voltage and current of the MOSFET transistor. It is also visible that the transistor is turning on in the zero voltage, the conditions preferred for the MOSFET transistors. The output voltage and current of the resonant converters is quasi harmonic. Simulation results of the LCTLC converter confirm the theoretical assumptions. Following figure shows the output waveforms of the proposed resonant converter.

Fig. 6. Output waveforms of the LCTLC resonant converter (current IL – red line, voltage UL – green line).

Fig. 6 shows the output voltage and current in the steady state. The phase shift was 0 °el. due to purely resistant load. The simulated THD value of the output voltage was 4.9 % what met converter requirements.

VDC

L1 C1

L2 C2

Lload

Udc

S1

S2

T

Rload

Time

4.01200ms 4.01600ms 4.02000ms 4.02400ms 4.02800ms 4.03200ms 4.03600ms 4.04000ms4.00904ms1 V(R19:2,E1:4) 2 I(M1:D)

0V

50V

100V

135V1

0.50A

1.00A

1.50A

-0.15A

2

>>

Time

3.9450ms 3.9500ms 3.9550ms 3.9600ms 3.9650ms 3.9700ms 3.9750ms 3.9800ms 3.9850ms 3.9900ms 3.9950ms3.9401ms

1 V(R14:2) 2 -I(R15)

-10V

0V

10V1

-1.0A

0A

1.0A

-1.5A

1.5A2

>>


TELEN2015016

Fig. 7. Voltage transfer function U2/U1 of the LCTLC filter (Bode

diagram).

The voltage transfer function shows that if switching frequency is equal to the resonant frequency the voltage gain is equal 1. Also, in this point the LCTLC converter is not depending on the load magnitude (Fig. 7).

B. LCLCL Topology

The proposed multi-element resonant converter is implemented and illustrated in Fig. 8. The LCLCL resonant tank is selected as the core of this converter. The half-bridge topology is adopted as the primary-side structure. It is easy to extend it to other types of input structures, including full-bridge, stacked half-bridge, and three-level structures. The centre type structure with synchronous rectifiers (SR) is chosen for use on the secondary side. Similarly, it is easy to use other types of output structures, such as the full-bridge, voltage-doubler and current-doubler structures. The secondary side with the SR is better for the low-voltage output applications. The secondary-side devices can be replaced by diodes for high-voltage applications. Thus, complicated SR driving circuits can be avoided. For the front-end converters, the SR output is applied to increase the efficiency [9].

+

-

nLr

Lm

R

Uin

Lp

Cr

Fig. 8. Diagram of the LCLCL resonant converter with the SR.

This topology is well known and well described in the scientific literature. The resonant circuit is composed of series-parallel LLC circuit and one parallel circuit. With one additional resonant element, a second band pass filter is created. A novel LCLCL resonant tank is proposed as an example. The basic resonant tank cell is shown in Fig. 8. The structure is similar to the previously proposed four element resonant tank, but an extra resonant inductor is inserted.

The voltage gain of the proposed LCLCL resonant tank is illustrated in Fig. 9. The curves in Fig. 9 are dependent on the load (10–100 % load).

Fig. 9. Voltage transfer function U2/U1 of the LCLCL filter.

Conceptually, Lr, Cr and Lp contribute to the first band pass filter at low frequencies. The second band pass filter consists of Lr, Cr and Cp, which dominate at high frequencies. The first band pass filter can help to deliver the fundamental component to the load. It functions as the traditional resonant converters. The second band pass filter enhances the power delivery with utilization of higher harmonics. Consequently, with the injection of higher-order harmonics, the reactive power of the resonant tank can be reduced and lower RMS current and lower conduction loss can be achieved.

𝑓01 =≈1

2𝜋√(𝐿𝑟 + 𝐿𝑝)𝐶𝑟 (6)

𝑓02 =1

2𝜋

1

√𝐿𝑝𝐶𝑝 (7)

𝑓03 =≈1

2𝜋√𝐿𝑟

𝐶𝑟𝐶𝑝

𝐶𝑟+𝐶𝑝 (8)

𝑓04 =1

2𝜋

1

√𝐶𝑟(𝐿𝑟+𝐿𝑚+𝐿𝑝) (9)

𝑍0 = 𝐿𝑟2𝜋𝑓01 (10)

For the MOSFETs, the ZVS operation is preferred. As a result, the LCLCL resonant converter can perform boost or buck functioning, according to what is required. For the front-end converters, higher voltage gain is necessary during the holdup time. Therefore, the ZVS Region II is favorable during the holdup time operation. For overload, startup and short output conditions, the ZVS Region I is preferred to limit the current [7].

At the nominal condition, the LCLCL resonant converter operates at the resonant frequency f01, where nearly ZV-ZCS condition can be achieved for the primary-side devices. The current of the secondary-side rectifiers naturally falls to zero, and the reverse recovery issue is eliminated [1], [4]. The topology works with 3th harmonic as well and uses its injection to the output voltage to increase its RMS value (0.9 Um) [7].

C. LCL2C2 Topology

In case of demand of a harmonic sinusoidal voltage for the critical load, it is necessary to use some of the resonant filter types. The resonant components are tuned to the basic harmonic. The LCL2C2 filter can be supplied by

10-1

100

101

10-2

10-1

100

101

102

log(/res

) [p.u.]

Uo

ut/U

in

no load

load 33%

load 66%

load 100%

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

1

2

3

4

5

6

7

/r

|G|


TELEN2015016

either single-phase voltage inverter in the full- or half- bridge connection. A diagram of the resonant converter is shown in Fig. 10.

L1a C1a

L1b C1b

L2b

L2a

C2b

C2a

RL Load

Ubat

S1

S2

Fig. 10. Diagram of the LCL2C2 converter.

The converter in Fig. 10 can be classified as the DC/AC converter with the resonant filter. On the contrary, the following analysis is oriented on the design analysis of the LCLC components, investigation of the transfer- and transient properties and on influence of non-linearity of the inductors [10].

The state space model equations of the LCL2C2 converter are:

d𝑖𝐿1𝑎,𝑏

d𝑡= −

𝑟1

𝐿1𝑖𝐿1 −

1

𝐿1𝑢𝐶2𝑎 −

1

𝐿1𝑢𝐶2𝑏 +

1

𝐿1𝑢(𝑡) (11)

d𝑢𝐶1𝑎,𝑏

d𝑡=

1

𝐶1𝑖𝐿1 (12)

d𝑢𝐶2𝑎

d𝑡=

1

𝐶2𝑎𝑖𝐿1 −

1

𝐶2𝑎𝑖𝐿2𝑎 − (

1

𝑟𝑎+

1

𝑅𝑎)

1

𝐶2𝑎𝑢𝐶2𝑎 (13)

d𝑢𝐶2𝑏

d𝑡=

1

𝐶2𝑏𝑖𝐿1 −

1

𝐶2𝑏𝑖𝐿2𝑏 − (

1

𝑟𝑎+

1

𝑅𝑎)

1

𝐶2𝑏𝑢𝐶2𝑏 (14)

d𝑖𝐿2𝑎

d𝑡=

1

𝐿2𝑎𝑢𝐶2𝑎 (15)

d𝑖𝐿2𝑏

d𝑡=

1

𝐿2𝑏𝑢𝐶2𝑏 (16)

Fig. 11. Simulated waveforms of the LCL2C2 inverter (p.u.).

Fig. 11 shows simulated waveforms of the proposed resonant converter. The output current and voltage have a quasi-harmonic shape with the THD up to 5 %. The input voltage has a value from zero up to maximum value of the voltage what is due to the half-bridge connection of the switching network.

Fig. 12. Switching curves of the voltage and current of the MOSFET

transistor.

The OrCAD analysis in Fig. 12 shows the waveform of the transistor. As it can be seen, the LCL2C2 converter works in the ZVS region. This region is preferred for the MOSFET transistors. The resonant frequency is set higher than switching frequency to operate in the ZVS region [11], [12].

Fig. 13. Output voltage and current of the LCL2C2.

The output voltage and current have quasi harmonic shape (Fig. 13). The phase shift is equal 0 °el. due to purely resistive load. To achieve it in reality it is almost impossible due to parasitic components. The analysis confirms the theoretical assumptions for the LCL2C2 resonant converter. Using the FFT, measured THD of the output voltage of the proposed converter was 4.589 %. It is also clear that only the fundamental harmonic is at the output and a small value of the 3th and all other harmonics are suppressed [8], [9].

IV. EXPERIMENTAL VERIFICATION

The experimental measurements have been done on the physical sample (Fig. 14)

Fig. 14. Experimental set-up for the LCL2C2 converter.

The resonant converter was designed to operate in the ZVS region. This confirms the switching waveforms of

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5

-8

-6

-4

-2

time[p.u.]

Y[p

.u.]

Uin

iin

Uout

iout


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the semiconductor transistor given in Fig. 15. The ZVS is in the required operation area for the MOSFET transistor in order to reduce losses.

Fig. 15. Switching waveforms of the transistor.

The waveforms in Fig. 16 are showing the output voltage and voltage on both branches with a symmetric output of the LCL2C2 circuit. The load voltage (also voltage on the branches) has harmonic shape with low THD value in both legs.

Fig. 16. Measured symmetrical output of the LCL2C2 circuit.

Parameters:

Uin = 100 V, fsw =100 kHz, MOSFETs = IRF5N50C, L1a, L1b = 66 uH, L2a, L2b = 66 uH, C1a, C1b= 39 nF, C2a, C2b = 39 nF, load: R1,2, L1,2 − 42 Ohm, 20 nH of parasitic inductance.

V. CONCLUSION

In the paper it is presented the review of the multi-element resonant converters. Chapter III describes selected topologies and simulation analysis. For the simulation the MATLAB and OrCAD software was used.

The LCTLC belongs to new multi-element topologies. The connection reaches high values of the power density, efficiency up to 94 % and THD < 5 % which meets requirements for an equipment. Voltage transfer functions show that in the point where value of the switching frequency is equal to the resonant frequency the voltage gain is equal 1. Under these conditions the converter does not depend on the magnitude of the load.

The LCLCL is generally known topology. In the area of the resonant frequency No. 3 (f03) where the voltage gain is equal to zero the converter short-circuit is proof. The topology works with 3th harmonic and uses its injection to the output voltage to increase its RMS value (0.9 Um).

The LCL2C2 is new and still not deeply investigated topology. The connection brings possibility of multifunctional output – DC, AC with HF or LF. Essences of the topology are two parallel resonant circuits which can replace center tapped transformers. Therefore, it is possible as a 2nd stage of the converter utilized half-bridge circuit connection, what decreases the number of the semiconductor devices. The LCL2C2 topology is short-circuiting proof as well. Therefore, the LCL2C2 was connected without transformer and the converter can reach efficiency up to 97 %. The THD value is above 4.5 % and power density up to 93 W/in3.

ACKNOWLEDGMENT

The authors wish to thank for the financial support to the APVV 0314/12 and R&D operational program Centre of excellence of power electronics systems and materials for their components No. OPVaV-2008/2.1/01-SORO, ITMS 26220120046 funded by the European regional development fund (ERDF).

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[2] D. Fu: Topology Investigation and System Optimization of Resonant Converters, PhD. thesis, February 4, 2010, Blacksburg :

Virginia

[3] M. Frivaldsky, P. Drgona, P. Spanik: Experimental Analysis and Optimization of Key Parameters of ZVS Mode and its Application

in the Proposed LLC Converter Designed for Distributed Power

System Application, Intern. J. of Electrical Power & Energy Systems, vol. 47, pp. 448-456, May 2013

[4] J. Dudrik, N. D. Trip, Soft-Switching PS-PWM DC-DC Converter

for Full-load Range Applications, IEEE Transactions on Industrial

Electronics, vol. 57, No. 8, 2010, pp. 2807-2814m, ISSN 0278-

0046.

[5] S. Kascak, J. Sedlak, Synthesis of LCLC Type Power Resonant Filter with Integrated Transformer, University of Zilina : Faculty

of Electrical Engineering, 2010

[6] Luo, F.L., Ye. H.: Energy Factor and Mathematical Modeling for Power DC/DC Converters, IEE Proc. on Electrical Power

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[7] B. Dobrucky, M. Benova, S. Kascak, Transient Analysis and Modelling of 2nd- and 4th-Order LCLC Filter under Non-

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TELEN 2015018

Sensorless Field Oriented Control of BLDC

Motors for MAVs

Dávid Rau 1), Jozef Rodina 2), Lukáš Palkovič 3) and Peter Hubinský 4)

1) Institute of Robotics and Cybernetics, Bratislava, Slovakia, e-mail: [email protected] 2) Institute of Robotics and Cybernetics, Bratislava, Slovakia, e-mail: [email protected]

3) Institute of Robotics and Cybernetics, Bratislava, Slovakia, e-mail: [email protected] 4) Institute of Robotics and Cybernetics, Bratislava, Slovakia, e-mail: [email protected]

Abstract — To achieve longer flight duration of the micro

aerial vehicles (MAVs) it is needed to optimize their

propulsion system. A typical propulsion system of VTOL

(vertical take-off and landing) MAV consist of the propeller

BLDC (brushless DC) motor, motor controller and battery

(typically Lithium based chemistry). All these parts of the

propulsion system can be optimized in a specific way. In the

case of the propeller, this can be done by the optimization of

static and dynamic thrust performance. The motor

construction can be optimized by using lighter materials or

stronger rotor magnets. As for the battery - alternative

power sources like solar panels, hydrogen fuel cells etc. may

be used. We are focusing on the optimization of the motor

control part. In this paper, we are presenting synthesis of

the BLDC controller using the field oriented control

strategy which promises better performance in the

dynamical response of the propulsion system, lower power

consumption and generally higher efficiency in comparison

with the traditional six step commutation techniques.

Keywords — MAV, BLDC, FOC, vector control, observer.

I. INTRODUCTION

Growth of the micro aerial vehicle market brings a new application which requires more sophisticated and advanced MAVs. The most often named requirement for such type of vehicle is longer flight duration. There are several solutions/studies how to increase the flight duration, for instance by using hydrogen fuel cells [1], by using solar cells [2] etc. Most of these projects are concentrating on the usage of alternate power sources instead of classical Lithium chemistry based batteries. But there is also another way of how to increase the flight length and it is by optimizing the propulsion system itself. In the case of copter type MAVs we can optimize the used propeller, motor and motor controller. Mostly used motor types are the BLDC which are controlled using six step commutation strategy with the BEMF zero crossing detection [3]. The pros of this technique are cheap HW and FW and also the fact that there is no real need to have motor parameters like stator inductance, nor resistance to be able to start the rotation with motor. The cons of this approach are not an ideal dynamical behaviour when higher dynamical response of the motor control is needed and also that the efficiency of this approach is far from ideal. On the other side, a more advanced approach for controlling the three phase PMSM/BLDC motors is the field-oriented control (FOC) technique which can bring higher efficiency, higher dynamical response of the motor control and overall a better performance than the six step

commutation. However, this approach means also higher HW and FW costs. Nevertheless, even if the costs of HW and FW are higher, the usage of the FOC may lead to cost saves in professional applications of MAVs due to better performance. In this paper, we are presenting the FOC controller design for the BLDC motors in the Matlab SimPowerSystems.

II. MODEL OF MOTOR

A. Sim Power System Model

The simulation model of the brushless direct current (BLDC) motor is based on simulation blocks of the SimPowerSystems Toolbox in Simulink. For our purpose a simulation block called Permanent Magnet Synchronous Machine is used. This machine block based on a three-phase system can be applied like motor operating mode, as well as generator operating mode. The motor operating mode in our research is achieved by zero or positive values of the load torque brought to the model. In order to create a nonlinear model corresponding with to the real BLDC motor, it is necessary to set the outcome of the back electromotive force to a trapezoidal output. The output shape of the BEMF is caused by the salient motor structure. The electrical part of the motor model from the toolbox is defined at [1] by the following equations:

𝑑

𝑑𝑡𝑖𝑎 =

1

3𝐿𝑠(2𝑣𝑎𝑏 + 𝑣𝑏𝑐 − 3𝑅𝑠𝑖𝑎 + 𝜆𝑝𝜔𝑚(−2𝜙′

𝑎+

𝜙′𝑏+ 𝜙′

𝑐)) (1)

𝑑

𝑑𝑡𝑖𝑎 =

1

3𝐿𝑠(2𝑣𝑎𝑏 + 𝑣𝑏𝑐 − 3𝑅𝑠𝑖𝑎 + 𝜆𝑝𝜔𝑚(−2𝜙′

𝑎+

𝜙′𝑏+ 𝜙′

𝑐)) (2)

𝑑

𝑑𝑡𝑖𝑐 = −(

𝑑

𝑑𝑡𝑖𝑎 +

𝑑

𝑑𝑡𝑖𝑏) (3)

𝑇𝑒 = 𝑝𝜆(𝜙′𝑎

∙ 𝑖𝑎 + 𝜙′𝑏∙ 𝑖𝑏 + 𝜙′

𝑐∙ 𝑖𝑐) (4)

where ix is the phase current, Φ’x is the electromotive force, vxy is the phase to phase voltage, Ls is the stator inductance, Rs is the stator resistance, λ is the flux of a permanent magnet, p represents the number of pole pairs, ωm represents the angular velocity of the rotor and Te the electromagnetic torque.

B. Simplified Model

The previous model is applicable for the verification of the motor behaviour, however, for the purpose of the control design it is necessary to simplify it. In this case,


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the previous model has to be reduced to a linear model. The control design is based on the assumption that the control will be applied at a higher speed. In this case, the shape of the BEMF approaches a sinewave. By the means of the above mentioned simplification, it is possible to transform the BEMF into a DC value and therefore we can use a DC model shown in the following figure instead.

Fig. 1. Simplified model of the motor.

This model of the motor is described by transfer function M(s) as follows

𝑀(𝑠) =𝑈(𝑠)

𝐼(𝑠)=

1

𝑅𝑠

(1+𝐿𝑠𝑅𝑠

𝑠) (5)

In this case, the BEMF does not figure in the transfer function at (5) since it behaves as a constant with regards to the current and it does not influence the transient effect of the motor.

III. CONTROL

In order to control the entire drive, we applied the FOC of the BLDC motor using a simplified model of the motor from the previous chapter. For the FOC, the Clarke transformation was used in order to adjust the motor into a two-phase system and the Park transformation to change the stator reference frame into a rotor reference frame. By the above mentioned transformations, we have achieved the transformation of AC values to DC values of quantities, representing a prerequisite for the design of the control. These DC quantities allow designing a two level control – cascade control. The cascade control is necessary in order to apply the Maximum Torque per Ampere (MTPA) control described in [10]. The basic condition of the MTPA control is the achievement of an angle equal to ninety degrees between the rotor flux vector and the stator current vector. Since it is only the current that we can control, we need to use a cascade control with a current loop.

A. Current Loop

The low level control represents the current controllers. At this level, we control the amplitude and the angle of the current vector. The current vector is divided into the direct (Id) and the quadrature (Iq) components of the current. These components of the current have to be regulated by maintaining the angle between the rotor flux and flow. We reached the angle of ninety degrees when the quadrature component reached the desired value – zero. In this case, the direct component affects only the size of torque.

The control loop comprises a PI controller and the above mentioned simplified model of the motor in (5). Closing this loop, we will get the G(s) transfer function illustrated in (6) where Ka represents the proportional gain of the controller and Kb is the integral gain.

𝐺(𝑠) =(1+

𝑠

𝐾𝑏)

(𝐿𝑠

𝐾𝑎𝐾𝑏)𝑠2+(

𝑅𝑠𝐾𝑎𝐾𝑏

+1

𝐾𝑎)𝑠+1

(6)

The given transfer function contains two poles and one zero. Therefore, it is necessary to eliminate the zero from the numerator. Now we proceeded in accordance with [4]. We have split the denominator into two roots, focusing on the linear coefficient of the polynomial.

𝐺(𝑠) =(1+

𝑠

𝐾𝑏)

(1+𝑅𝑠

𝐾𝑎𝐾𝑏𝑠)(1+

𝑠

𝐾𝑏) (7)

By this arrangement in (7), we can eliminate the zero. Nevertheless, we have to fulfill all conditions – this means that the quadratic coefficient of the polynomial must be the product of roots. As a result of the fulfillment of the conditions, we have obtained one of the controller parameters.

𝐾𝑏 =𝑅𝑠

𝐿𝑠 (8)

In order to get the second parameter, it is necessary to substitute (8) into (7). By the above mentioned substitution we have obtained the transfer function of first order from [4] which depends on the bandwidth of the motor.

𝐺(𝑠) =1

𝐿𝑠𝐾𝑎

𝑠+1⇒ 𝐾𝑎 = 𝐿𝑠 ∙ 𝐵𝑎𝑛𝑑𝑤𝑖𝑑𝑡ℎ(𝑟𝑎𝑑/𝑠) (9)

By analysis, we obtained the parameters of the controller which are identical for both the direct and the quadrature components of the current.

B. Speed Loop

The higher level of the control represents the speed controller. The output of the controller is the desired torque which has to be transformed via the motor constant to the desired current in (10).

𝑀𝑡𝑟(𝑠) =3

2

𝑃

2𝜆𝑟 (10)

This desired current is considered as an input of the quadrature current controller. Since we want to transform the entire current vector to torque, the set value of the direct current controller has to be zero. Based on these assumptions, we have created a closed speed loop as follows

𝐺𝐻(𝑠) =

(𝐾𝑐𝐾𝑑(1+

𝑠

𝐾𝑑)

𝑠)(

1𝐿𝑠𝐾𝑎

𝑠+1) (

3

4𝑃𝜆𝑟) (

1

𝑘𝑣(𝐽

𝑘𝑣𝑠+1)

) (1

𝜏𝑠+1) (11)

where Kc represents the proportional gain of the controller, Kd is the integral gain of the controller, J is the moment of inertia and kv is the viscous damping. We also applied a first order filter as a sensor of speed with time constant τ. In order to obtain the parameters of the speed controller, the method published in [5] and [6] was applied in the above mentioned transfer function as follows

𝐾𝑐 =1

𝛿𝐾𝜏 (12)

𝐾𝑑 =1

𝛿2𝜏 (13)

where δ is the damping factor and K is the motor constant divided by the moment of inertia.


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We are aware that the publication of the proposition management is not optimal. However, we decided to apply the solution because it comes from the successful application of the real product. Subsequent identification of motors is problematic and inaccurate. Therefore, we will surely find a place later the usage of adaptive control.

IV. OBSERVER

For the need of the sensorless BLDC motor control, it is necessary to create an observer of the feedback quantities. In our case, it is also necessary to know the angle of the rotor for the Clark transformation and the angular speed of the rotor for speed control.

A. Our Estimation

For the estimation of quantities, a system consisting of the BEMF observer and an element for estimate phase of the BEMF which is equal to the rotor angle was applied. Operates either in the stator reference frame, therefore the angle can be obtained as a result of a trigonometry function.

B. BEMF Observer

The BEMF observer can be designed using the simplified model of the motor. The actual measured current is considered as the disturbance which is compared with the current from the model. This error represents the input of the PI controller, the output of which is our desired BEMF as it is depicted in Fig. 2.

Fig. 2. BEMF observer based on the simplified model.

The second option is to use a state model of the motor where currents are compared as in the previous observer but difference of currents is multiplied by only the matrix L (P controller). In this case, the BEMF is not the output of the diagram but it is an internal variable. This process is shown in Fig. 3.

Fig. 3. State-space model of the BEMF observer [7].

Then the states x, output y, input u and matrices A, B, C may be written in accordance with [7] as follows

𝑥 = [

𝑖𝛼𝑖𝛽𝑒𝛼

𝑒𝛽

] 𝑦 = [𝑖𝛼𝑖𝛽

] 𝑢 = [𝑣𝛼

𝑣𝛽] (14)

𝐴 =

[ −

𝑅𝑠

𝐿𝑠0 −

1

𝐿𝑠0

0 −𝑅𝑠

𝐿𝑠0 −

1

𝐿𝑠

0 0 0 −𝜔0 0 𝜔 0 ]

(15)

𝐵 =

[

1

𝐿𝑠0

01

𝐿𝑠

0 00 0]

(16)

𝐶 = [1 0 0 00 1 0 0

] (17)

where ix is the phase current in a two phase machine, vx represents the phase to the neutral voltage in a two phase machine and ex is the BEMF in a two phase machine. From (14), (15), (16) and (17), we applied state model in (18).

𝑑𝑡𝑥 = 𝐴𝑥 + 𝐵𝑢 𝑦 = 𝐶𝑥 (18)

C. Angle/Speed of the Observer

The calculation of the phase can be done very simply through the trigonometric function atan2. The function is fed by two components of the BEMF that mean αβ parts in the stator reference frame. Function atan2 has handled the dangerous states in comparison to ordinary atan. Trigonometric function is problem for estimation of the speed because periodicity. Another problem of using this solution is the noise created when measuring the outputs from the BEMF observer. Complex filtering structures of the output are time-consuming. The timing is insignificant in non-real-time simulations but in real-time the feedback calculation becomes time critical.

For the estimation of speed it is better to use a phase locked loop (PLL). The PLL is a control system which generates the phase between the input signals. The PLL uses the PI controller in the same way as the BEMF observer, due to its gained error between the phases. The influence of noise of the BEMF signal in the angle and speed is reduced solely by the integrator in the PLL. PLL is illustrated in [8]. The principle is shown in Fig. 4.

Fig. 4. Phase locked loop for the BEMF [8].


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V. SIMULATION

The proposed techniques were simulated in the Matlab/Simulink as mentioned above. The two level control of the BLDC motor with the angle observer was simulated in accordance with the following diagram

Fig. 5. Simulation diagram of the FOC with estimators.

The diagram contains several elements where the motor, inverter and the generator of the space vector modulation (SVM) are parts of the SimPowerSystems Toolbox. We used the BLDC motor with parameters as follows: Rs = 18.7 Ω, Ls = 1.365 mH, λ = 0.1717 Vs, 1 pole pair and J = 2.26e-5 kgm2. The inverter was built as a 3-phase universal bridge with the MOSFET technology. Other elements are the currents and the speed controller where we worked with a motor the bandwidth of which was equal to 8000 rad/s (including the inverter). The damping factor was 3.5 and the low-phase filter τ 1.9894e-5 s.

A. Unit Step with Sensor

The first simulation presents the FOC with sensors for the mechanical speed and the mechanical position of the rotor. We applied a load torque 3 Nm in time 0.1s. The input of the system was fed by speed value 3000 rpm. The following graph shows the view of the speed, position, current and torque of this measurement.

Fig. 6. Rotor speed with applied the unit step.

In the beginning, we gained a significant overshoot but later the speed stabilized. The controller handled the load without any problems. This can be seen zoomed in Fig. 7.

Fig. 7. Zoomed curve of the rotor speed with applied load.

B. Ramp with Sensor

We did not provide additional quantities to the input step but took a closer look at the speed when the motor starts along a ramp. The ramp slope had the value of 300 000. This means that the motor reached revolutions of 3000 rpm in 0.01 s time duration.

The motor was able to follow smoothly the desired ramp as shown in Fig. 8. It also confirms the progress of the position where it is satisfied with the S curve of the position in Fig. 9. Now we will look at the progress of the electromagnetic torque with the connected load.

Fig. 8. Rotor speed with the applied ramp.

Fig. 9. Rotor position with the applied ramp.


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Fig. 10. Electromagnetic torque with the applied load from 0.1 s.

At the time moment of 0.1 second we can see the connected load, which increased the torque by 3 Nm.

C. Full Sensorless Control

In this section we measured the behaviour of the motor with the estimated rotor speed and position. For the estimation, the BEMF observer of the simplified model and the phase locked loop were used. In this case, we observed the shape of the diagrams of the rotor speed with and without load shown in Fig. 11.

Fig. 11. The rotor speed with the sensorless control.

In the sensorless mode, the motor is capable of holding the level of the desired speed and is also capable of handling the disturbance of the load.

D. Comparation of Estimators

We continued with the full sensorless control from the previous section C. We compared the estimated speed (in only one case) and the rotor position with the measured values. Different types of estimators were compared.

The first estimator in order was the BEMF observer of the simplified model where we compared speed and position. It is shown in Fig. 12 and Fig. 13 that this estimator was the best of all our tested estimators, as it approximates the speed and the position of the rotor the most.

Fig. 12. Comparison of the rotor angle for the first estimator.

Fig. 13. Comparison of the rotor speed for the first estimator.

The second type of the estimator contains the previous type of the BEMF observer, however it contains trigonometric function atan2 for the phase elaboration.

Fig. 14. Comparison of the rotor angle for the second estimator.

Regarding this estimator, we observed a ripple of the rotor angle. The angle was not integrated during the calculation but had a periodic cycle between <-2π, 2π > rad. It was caused by the above mentioned periodicity of the trigonometric function. This shape of the rotor angle represents a problem for the speed estimation.

The third estimator with the state-space model with atan2 had the same problem as the second one. In addition, it had a phase shift with the real rotor angle as we can see in Fig. 15.


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Fig. 15. Comparison of the rotor angle for the third estimator.

E. FOC and Six Step Commutation Differences

We take to the comparison FOC control and six-step commutation. From the Fig. 16 follows on that FOC control has a better behaviour of the dynamics when desired value of speed is following almost identical by FOC control value of speed.

Six-step commutation has a problem to keep the pace with the rapid increase of speed. This problem is associated with higher consumption of six-step commutation. The cause of lower efficacy in six-step control is hidden in principle of six-step control. It has not implementation of MTPA. Torque is not more stable during the operation than with FOC control but is crimped. The next reason of lower efficacy is hardware’s format. It is several times the amount of transistor switching compared with FOC control.

Fig. 16. The speed ramp with FOC and six-step.

VI. CONCLUSION

The aim of our study was to create a sensorless vector FOC of the BLDC motor. Our control contained current and speed loops which we could apply through the Park and Clark transformations. Thus, we gained a simulation model suitable for testing control through the Simulink Toolbox SimPowerSystems. After setting the control, we were looking for suitable candidates for the estimation of the position and speed of the rotor. The BEMF observer simplified motor model with PLL seemed to be appropriate, since sufficient precision at high speed provided the speed and the position of the rotor. We have understood that we have sufficiently applied the whole control on the simulation model of the motor and we can now proceed to its application to a real motor.

REFERENCES

[1] Horizon Unmanned Systems (1.7.2015). Hycopter [online]. Available: http://www.hus.sg/

[2] Atlantiksolar (1.7.2015). First fully-solar powered day/night flight achieved: In-air 28 hours without fuel! [onbratisla, vabrafaceline]. Available: http://www.atlantiksolar.ethz.ch/

[3] Renesas (1.4.2010). Six Step Trapezoidal Control of a BLDC Motor Using Back-EMF [online]. Available: http://documentation. renesas.com/doc/products/mpumcu/apn/reu05b0073_r8cap.pdf

[4] MathWorks (1.7.2015). Permanent Magnet Synchronous Machine [online]. Available: http://www.mathworks.com/help/physmod/sps/ powersys/ref/permanentmagnetsynchronousmachine.html

[5] Dave Wilson (4.3.2013). Teaching Your PI Controller to Behave (Part II) [online]. Available: http://e2e.ti.com/blogs_/b/ motordrivecontrol/archive/2013/03/04/teaching-your-pi-controller-to-behave-part-ii

[6] Dave Wilson (9.3.2013). Teaching Your PI Controller to Behave (Part III) [online]. Available: http://e2e.ti.com/blogs_/b/ motordrivecontrol/archive/2013/03/09/teaching-your-pi-controller-to-behave-part-iii

[7] Dave Wilson (14.3.2013). Teaching Your PI Controller to Behave (Part IV) [online]. Available: http://e2e.ti.com/blogs_/b/ motordrivecontrol/archive/2013/03/14/teaching-your-pi-controller-to-behave-part-iv

[8] James Robert Mevey, Sensorless field oriented control of brushless permanent magnet synchronous motors. Kansas State University, Kansas. 2009.

[9] C. Olivieri, M. Tursini, A novel PLL scheme for a sensorless PMSM drive overcoming common speed reversal problems. University of L’Aquila, Italy, 2012.

[10] H. R. Mosaddegh, H. A. Zarchi, Maximum Torque per Ampere Control of Brushless Doubly Fed Induction Machine using Variable Structure Approach. Ferdowsi University of Mashhad, Iran, 2014.

[11] Renesas (10.11.2015). InstaSPIN-FOC and InstaSPIN-MOTION. User’s Guide. [online]. Available: http://www.ti.com/lit/ug/ spruhj1f/spruhj1f.pdf

http://www.hus.sg/

http://www.atlantiksolar.ethz.ch/


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Control System of Battery Storage to Eliminate

the Power Variation According to the Electricity

Prediction

Martin Liška 1), Anton Beláň 2), Anton Cerman 3) and Matej Janík 4)

1) Slovak Technical University of Bratislava/Institute of Power and Applied Electrical Engineering, Bratislava,

Slovakia, e-mail: [email protected] 2) Slovak Technical University of Bratislava/Institute of Power and Applied Electrical Engineering, Bratislava,



Slovakia, e-mail: [email protected]

Abstract — Rapid variations of the output power from

photovoltaic power plants can have some significant side

effects on the quality of electricity, such as the voltage

variation, switching of tap changers, etc. In the other case,

these variations also make the difference between the

prediction and real electricity production. Generally, the

goal of the accumulation of electricity is to charge the

storage element in surplus of electricity and discharge when

the energy is insufficient. In this paper, the accumulation of

electricity in a photovoltaic power plant is not used for this

purpose, but to charge and discharge the storage element

with respect to the prediction of electricity.

Keywords — Photovoltaic power plant, power variation,

battery controller, electricity prediction.

I. INTRODUCTION

The renewable energy sources integration has been extensively increased in the electric power distribution system. To exploit the renewable energy sources more effectively, grid connection of renewable energy sources should be done in the way to eliminate negative local impacts on distribution grids [1], [2]. The output power of the photovoltaic or wind power plants is very depended on the actual atmospheric condition. This strong dependence usually results to the rapid output power variation many times in quite huge range. There is a common approach to use the storage elements in a power system. This approach is to use the accumulated energy in the time periods, when the electricity demand in the power system is required and vice versa. This case of accumulation is more adequate for such systems installed in low voltage distribution systems like transformer substations. Distributed generation especially built in photovoltaic and wind power plants can be beneficial if it meets at least the basic requirements of the system operating philosophy, feeder design and advanced control systems [3]. This paper describes a new approach to utilize the energy storage systems for elimination the unpredictable power variations from the photovoltaic power plant. The control system of the battery is designed and demonstrated on the voltage network simulation model. The main usage of this controller of the storage element is to hold the output

power in the photovoltaic power plant at the predicted value.

II. DISTRIBUTION NETWORK MODEL – IEEE 37 NODE

TEST FEEDER

For the simulation of a storage element controller, the IEEE37 test feeder model was used. It is a part of 4.8 kV distribution network feed from the transformer 230/4.8 kV, 2500 kVA. Some of the properties of this model were changed due to the simulation needs. In the node number 725, the load was replaced by the photovoltaic power plant including the battery as a storage element. The voltage regulator at the feeder transformer was eliminated. The network topology with the place of the photovoltaic power plant is displayed in Fig. 1.

799

701

742

705 702

720

704713

707

722

703744729

728

727

706

725

718

714

730

731709

708732

775733

736

734710

735

737 738 711 741

740

724

712

Fig. 1. IEEE 37 Test feeder with the photovoltaic power plant.

Due to the simplification of load types, all the nodal loads have the same load shape multiplication factor. Using the same multiplication factor, the same power and the same shape of all loads is achieved. The multiplication factor can be than expressed as the load shape curve, which defines the variation loads in p.u. during the weekly simulation. The load shape curve is displayed in Fig. 2.


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Fig. 2. Weekly load shape curve in p.u.

III. PREDICTION OF ELECTRICITY PRODUCTION IN

PHOTOVOLTAIC POWER PLANT

The prediction in the photovoltaic power plant is based on the real photovoltaic power plant (PtP) parameters. The long time prediction is calculated using the program PVGIS (Photovoltaic Geographical Information System) with the database of the meteorological condition typical for that place, where the PtP operates [4]. The parameters of the PtP are listed in the following table.

TABLE I. PHOTOVOLTAIC POWER PLANT PARAMETERS

Parameter Value

Installed power 950 kWp

PV Technology crystalline silicon

Type of construction stationary system

Module inclination 36 º (optimal)

Module orientation –1 º (optimal)

Estimated losses due to temperature 7.2 %

Estimated loss due to angular

reflectance effects 2.8 %

Other losses (cables, inverter etc.) 14.0 %

Combined PV system losses 24.0 %

Prediction of the electricity production in the PtP is calculated for the cloudy sky and clear sky. This is due to demonstrate, how the precision of the electricity prediction can affect the designing of the accumulation system. The output power of the photovoltaic power plants depends on two main factors. The main factor determining the output power is the solar irradiation on the place, where the power plant operates. The second factor is the air temperature. The dependence of the output power and air temperature is in relation, that if more solar irradiation and lower air temperature, than more output power is achieved and vice versa. The output power, respectively production is also affected by the type of construction (stationary or tracking systems), and the losses of the entire system (wires, inverters). In case of the 2-axís tracking systems, the solar panels are moving during the day to get the best position for the solar irradiation flow. The panels move to by oriented directly to the sun position. This results to better efficiency of the

solar irradiation use. Such systems are more sophisticated and more costly due to the tracking control system.

In our study case, the PtP is located at the south part of Slovakia. The following Fig. 3 shows the place, where the PtP operates. It can be seen, that the PtP operates in area with the yearly global irradiation of 1100 kWh/m2.

Fig. 3. The place of the photovoltaic power plant operation.

IV. STORAGE CONTROLLER OPERATION

The battery operation within the photovoltaic power plant is demonstrated on the weekly simulation. To control the dispatch mode of the battery, the controller communicates with the open program OpenDSS (Open distribution system simulator) and PVGIS software. The OpenDSS is a comprehensive electrical system simulation tool for electric utility distribution systems. The algorithm of the battery controller was developed in the Matlab software. The load flow calculation for each time step is executed by the OpenDSS software. This program supports all rms steady-state (i.e., frequency domain) analyses commonly performed for utility distribution systems. In addition, it supports many new types of analyses that are designed to meet future needs; many of them are being dictated by the deregulation of the US utilities and formation of distribution companies worldwide [5]. In our controller system, the OpenDSS also includes the network topology, loads, PtP, properties of power devices, etc. The concept of communication between the Matlab, OpenDSS and PVGIS software is shown in the following Fig. 4.

Fig. 4. Concept of the controller communication.

The battery controller ensures the charging and discharging commands for the battery with respect to the prediction values obtained from the PVGIS and data recorded from real production. The controller evaluates also the required amount of power for dispatch. Dispatch commands and the required power of the battery for both states (charge and discharge state) are calculated by the algorithm shown in Fig. 5.


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Fig. 5. The algorithm of the storage controller.

The value marked as kWhreserve contains the storage capacity to be held in the reserve for normal operation. (Minimum energy discharge level unless there is an emergency). The controller calculates the required output power and sends the commands to charge and discharge the battery to keep the output power of the PtP for each period at or near to the predicted value. The battery executes the discharge command, until the present amount of the stored energy is greater than the kWhreserve value. The battery will take charge only when the present amount of the stored energy is less than the rated storage capacity (kWhRated). The basic concept of the battery as storage element is shown in the following Fig. 6 [6].

Fig. 6. Basic concept of the battery storage system.

The storage element is essentially a generator that can be dispatched to either produce power (discharge) or consume power (charge) within its power rating and its stored energy capacity. The model is used in a Snapshot power flow mode to compute simply the power flow for a selected state of the storage element flow control. In this case, we set simply the state to one of idling or charging or discharging and then solve the steady state. A storage element can either act independently or be controlled by a build in storage controller element. In our case, we designed a new storage controller to control the battery independently.

V. SIMULATION RESULTS OF CONTROLLER OPERATION

The controller operation was simulated in both conditions with respect to the prediction for cloudy and clear sky. The following set of figures (Fig. 7, Fig. 8, Fig. 9, and Fig. 10) shows the weekly simulation results. The real production in the PtP measured at its output terminal is displayed as the blue curve; prediction is represented by the red curve. The green curve displays the output power from the photovoltaic power plant with the controller system dispatching the battery of 350 kWh capacity. The value kWhreserve was set to the value equal to 1 %. The charge and discharge cycles of the battery and the kWh stored value are also displayed to show the present lack of stored energy in the battery. The Figs. 7 and 8 show the simulation results considering the conditions in a cloudy sky. The Figs. 9 and 10 show the simulation results considering the clear sky.


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Fig. 7. Simulation results of the storage controller operation with

cloudy sky.

Fig. 8. Battery cycles with cloudy sky.

Fig. 9. Simulation results of the storage controller operation with clear sky.

Fig. 10. Battery cycles with clear sky.

The next Fig. 11 shows detailed power curves for selected one day to understand the controller algorithm and to see the differences between the particular curves. During the first part of the day, the battery was able to keep the output power of the PtP on the predicted value.

Fig.11. Simulation results for selected day.

It can be seen, that if the stored energy is insufficient, or the battery is fully charged, the battery switch to idling state and the blue and green curves have the same shape. If the lack of the stored energy allows to charge and discharge the battery, the real power supplied to the network from the PtP is equal to prediction. Next Fig. 12 shows the total absolute value of the deviation after one week. This deviation is calculated as a sum of the absolute values between the real production with the battery and the prediction after one week. This deviation is evaluated for several different capacities of the battery from 50kWh

up to 1000kWh. The simulation of deviation was performed also for such scenario, when the battery was disconnected. This is illustrated as the battery with zero capacity.

Fig.12. Total deviation of energy with several capacities of the battery.

If the controller dispatches the battery with respect to the prediction calculated for cloudy sky, the total deviation is much better. Deviation dependence on storage capacity is not linear. It can be seen, that increasing the stored capacity from 400 kWh to 1000 kWh doesn’t change significantly the total deviation.

VI. CONCLUSION

Accumulation systems are becoming an important part of power systems at last mile level, especially in the area of smart grid solutions and services. The described approach using the storage systems to minimize the deviations between the prediction and real electricity


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production in the photovoltaic power plant is suitable more for the stand alone power plants with higher powers, usually above 1 MW. Such power plants are built to be connected directly to high voltage networks and produce the electricity to the network. In these types of plants, there is no load (except of auxiliary systems), where the produced electricity could be primary consumed. All the produced electricity flows to the distribution network. For this reasons, it is reasonable to use the storage system together with the controller to keep the predicted electricity. These simulation experiments were based on the long term prediction. This is the reason, why the accumulation system has not eliminated the deviation enough to acceptable limits. Nowadays, there are many of systems providing short term predictions for solar power plants. It is recommend to use short term prediction for solar plants, which will increase the optimization of storage system operation. Many of the battery controllers, so called smart energy routers are widely used in households equipped with a small photovoltaic system and storage systems. The smart energy routers are programmed to direct the energy primary to electrical equipments in consumer premises and ensure that, the most of the produced energy is consumed within the consumer premises. Thus the proposed controller concept is not suitable for small household photovoltaic systems. The controller operation based on the proposed algorithm ensures that the battery sustains the daily diagram of production at or near to the predicted values. In this paper, the controller operation was simulated with one photovoltaic power plant during one week. The model can be extended and used for assessment and development of accumulation systems in more complicated systems, such controlling the accumulation within the smart grids, yearly simulations with several photovoltaic power plants including the synergy effect in decentralized production and more.

ACKNOWLEDGMENT

This contribution/publication is the result of the project

International centre of excellence for research on intelligent and secure information and communications technologies and systems, ITMS 26240120039 supported by the Research & Development Operational Programme funded by the ERDF.

This paper was supported by the agency VEGA MŠVVaŠ SR under Grant No. 1/1100/12.

REFERENCES

[1] Bhavna J., Shailendra J., R. K. Nema: Power Quality Improvement in Wind Energy Conversion System of Grid Interfacing Inverter Using Hysteresis Band Current Controller. In: WSEAS Transactions on Power Systems, ISSN / E-ISSN: 1790-5060 / 2224-350X, Volume 10, 2015, Art. #3, pp. 20-26

[2] Li-Jun Qin, Wan-Tao Yang: Micro-Grid Droop Control Strategy and Isolated Island Operation System Stability Analysis. In: WSEAS Transactions on Power Systems, ISSN / E-ISSN: 1790-5060 / 2224-350X, Volume 10, 2015, Art. #16, pp. 145-156

[3] A.F.Abdul Kadir, A. Mohamed. H. Sahreef: Harmonic Impact of different distributed generation units on low voltage distribution systems. In: IEEE International electric machines and drives conference. May, 2011, pp. 1201-1206, ISBN 978-1-4577-0060-6.

[4] Database of Photovoltaic Geographical Information System. Available on the internet [online]: http://re.jrc.ec.europa.eu/pvgis/.

[5] R. Dugan: The Open Distribution System Simulator. Electric Power Research Institute, Inc., March 2012.

[6] OpenDSS storage element and storage controller element (Version 7.4.1 Build 35 and Later, Revised 5 March, 2011). [online] http://sourceforge.net/apps/mediawiki/electricdss/index.php?title=Main_Page

http://sourceforge.net/apps/mediawiki/electricdss/index.php?title=Main_Page

http://sourceforge.net/apps/mediawiki/electricdss/index.php?title=Main_Page


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Conceptual Design of Electromechanical Systems Using Ferrofluids

Petr Polcar and Josef Český

Department of the Theory of Electrical Engineering, Faculty of Electrical Engineering, University of West Bohemia in Pilsen, Czech Republic, e-mail: polcarp, [email protected]

Abstract — This paper presents an overview of a new conceptual design of electromechanical systems using ferromagnetic liquids. Idea of the new concept is explained, advantages and disadvantages of such systems are discussed and three illustrative examples are presented. Numerical simulations and experiments on real devices are employed to study properties of these systems.

Keywords — Air gap, ferrofluid, ferromagnetic liquids, electromechanical systems, magnetic forces, static characteristics, dynamic characteristics, numerical simulation, experimental verification.

I. INTRODUCTION

Ferromagnetic liquids present new intelligent material. Magnetorheological liquids with ferromagnetic particles sized in µm, able to change their viscosity and even state of matter with applied magnetic field, are nowadays more and more often used in technical applications such as controlled dampers, brakes, clutches and seals [see e.g. 1]. Unlike of magnetorheological fluids, ferromagnetic liquids with particles sized in nm, called ferrofluids, present a liquid ferromagnetic material with viscosity not dependant (or with very low, negligible dependence) on magnetic field [2]. Nanotechnologies present rather stable liquid ferromagnetic matter that remains liquid even at high values of magnetic field. This brings us to an idea to fill the air gap of an electromechanical system with magnetically conductive matter that still allows movement. This technology has not been fully investigated yet, very few relevant sources can be found [3, 4].

Fig. 1. Ferrofluid EFH-1 without and with applied magnetic field.

It is necessary to say, that authors of this paper work in the field of the theory of electrical engineering and are not professional designers of electric machines. This paper should not be understood as an instruction how to design electromechanical systems; it just presents an idea of an innovative approach. If this idea will be used in future designs, or not, it remains to be seen and must still be investigated and decided.

II. PHYSICAL PRINCIPLE A simple electromechanical system presented in Fig. 2

will be used to demonstrate the physical principle of the idea.

Fig. 2. Simple electromechanical actuator and its equivalent magnetic circuit; 1 – movable part, 2 – magnetic circuit, 3 – winding, 4 – air gap

between movable and static part.

If the winding is powered, the movable part of the actuator is attracted between the poles of the magnetic circuit. With acceptable simplification (neglecting of leakage magnetic flux), the theory of magnetic circuit can be used to model this device. The total magnetic flux Φ enclosing trough the actuator can be counted as

Gapm mFe mGap Fe

Fe Gap

N I N I N IΦ

lR R R l

S S

, (1)

where Rm stands for magnetic reluctance and µFe, µGap for magnetic permeabilities of the used materials. It is clearly visible that as higher is the magnetic permeability of the material in the air gap, the higher is the generated magnetic flux. Force acting on the movable body can be counted e.g. from the energy of the magnetic field as

d d( )

d d

W ΦImFx x x . (2)

When the air gap of an electromechanical system is filled with ferrofluid, higher magnetic forces are generated using the same powering current. This effect is accompanied with several other phenomena that need a further study.

With the decrease of the total magnetic reluctance, the total inductance of the electromechanical system rises. This is a welcomed effect, however, with a higher induction, the total time response of the electric circuit increases. A time constant of a simple RL transient is given as τ = L/R.


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Cooling properties of the ferrofluids are well known [5]. The presence of the ferrofluid may provide additional cooling for the device, among other decreasing the total resistance and electric circuit time constant. The cooling can be achieved by different means than ferrofluid as well, but this phenomenon is positive.

The ferrofluids are considered to be used as advanced insulation materials, e.g. in power transformers [6]. Presence of the ferrofluid in an electromechanical system may provide additional insulation.

The viscous losses caused by the movement of the device movable body in the liquid are the main problem of the ferrofluid presence in the air gap. These losses depend on viscosity of the used fluid and on the speed of the device. These losses can exceed all gains.

Additional problems are related to the construction requirements on the ferrofluid filled devices. The system must be properly sealed to prevent leakage of the fluid, moreover, the ferrofluids have tendency to slowly degrade when exposed to open air.

Next problem is the high cost of the presently available ferrofluids, in hundreds of Euro per litre. This cost significantly depends on the amount purchased and may be lowered with mass production in future.

III. EXAMPLES OF ELECTROMECHANICAL SYSTEMS WITH

FERROFLUID FILLED GAP

Operation of several electromechanical systems with ferrofluid filled gap was observed at our department using numerical simulations and experimentally in order to familiarize with their behavior and to predict possible applicability of this technology.

Ferrofluid EFH-1 from the Ferrotec company was used in these applications. The relative magnetic permeability in the linear part of the magnetization characteristics of this fluid was determined as µr = 1.789. (Method for determination of magnetic properties of liquids presented by authors in [7] was used.)

A. Electromechanical Actuator with Ferrofluid Filled Gap

A simple electromechanical actuator as possible (Fig. 3) was designed with stress on eliminating as much additional physical phenomena as possible in order to study the ferrofluid effect on the device properties.

Fig. 3. Designed simple electromechanical actuator.

Dimensions of the device can be seen in Fig. 4.

Fig. 4. Dimensions of the designed simple electromechanical actuator and its mathematical model.

Due to its simple construction, the actuator is easy to model in 2D. FEM solver Agros2D [8] was used to simulate the generated static forces in dependence on the permeability of the used ferrofluid. The used mesh can be seen in Fig. 5.

Fig. 5. Used mesh for the 2D simulation of the actuator, Agros2D.

The distribution of the magnetic vector potential in the solved area can be determined from the equation

1

curl curl

A J

. (3)

The magnetic induction can be determined from its definition, the magnetic force Fm acting on the movable body can be determined form the change of the total magnetic energy.

mm m

0

dcurl , ( d )d ,

d

B

xV

WW V

x B A H B F . (4)

Convergence of the solution in dependence on the dimensions of the used model, number of elements of the mesh, polynomial order of elements and used adaptability was observed. Simulated dynamic characteristics as the magnitude of acting magnetic forces in dependence on the


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0

vmag mag g

( ) ( )d ( )

d ( )

( , ) ( ( , ) ) 6d

d

d

d

x y

u t Ri ti t

t L x

kF i x F i x F rv

v r

t m

xv

t

actual position of the movable core can be seen in Fig. 6. The ferrofluid with different magnetic permeabilities was used in the model to observe the influence. Magnetic permeability of the ferrofluid was considered in the model linear, real forces are expected to lie lower due to magnetic saturation of the fluid.

Fig. 6. Example of the simulated static characteristics for different permeabilities of the used ferrofluid, the current density of the winding J = 5·106 A/m2, magnetic induction in the fluid B = 0.6 T, Agros2D.

The precondition of the generated magnetic forces increase depending on the permeability of the medium used in the gap was fulfilled. Nowadays available ferrofluids have quite weak ferromagnetic properties, in the range of µr = 1~5, higher relative permeabilities were considered in the model for a better illustration of the effect.

The dynamics of the device with and without ferrofluid was simulated using the mathematical model based on a set of ordinary differential equations built with the use of the classical Newtonian dynamics. The model was implemented and solved in Matlab.

(5)

A nonlinear coil L(x) was considered in the model, acting forces were determined with the use of FEM

simulation, vk

r represents bearings losses, 6 rv

represents viscous losses in the fluid, where stands for

the fluid viscosity.

Series of dynamic simulations for different physical properties of the used fluid were performed. Results show that the viscosity increase of the used fluid negatively affects the overall dynamics as considered. Moreover, because the viscous losses depend on the speed of the device, when higher forces and then speeds are achieved, these losses grow. This problem should be approached

using optimization techniques in the future. Examples of the simulations can be seen in Fig. 7 and Fig. 8.

Fig. 7. Example of the simulated dynamic characteristics as the position of the movable part of the actuator in time; low viscous ferrofluid.

Fig. 8. Example of the simulated dynamic characteristics as the position of the movable part of the actuator in time; high viscous ferrofluid.

To evaluate results gained by the numerical simulation, static characteristics were measured as the magnitude of forces generated by the device for different fixed positions of its core using a dynamometer.

Fig. 9. Apparatus for measuring the static force characteristics of the actuator.


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5

10

15

20

25

30

1,2 1,4 1,6 1,8 2 2,2

F[N

]

I [A]

F(I) at x = 40 mm

With fluid

Without fluid

Fig. 10. Measured horizontal static forces with and without ferrofluid filled air gap at x = 40 mm position (maximal shift) of the movable body

of the actuator.

5

10

15

20

25

1,2 1,4 1,6 1,8 2 2,2

F[N

]

I [A]

F(I) at x = 26 mm

With fluid

Without fluid

Fig. 11. Measured horizontal static forces with and without ferrofluid filled air gap at x = 26 mm position of the movable body of the actuator.

Finally, dynamics of the device as the position of the movable core in time was measured using high speed camera.

0

0,01

0,02

0,03

0,04

0,05

0 0,05 0,1 0,15 0,2

x[m

]

t [s]

With fluid

Without fluid

Fig. 12. Example of the measured dynamical characteristics of the experimental linear electromechanical actuator; winding powered by

DC I = 1.5A (current in the steady state).

Based on the created models, it was experimentally verified that both static and dynamic characteristics of an electromechanical system can be improved using the ferrofluid in its gap. However, as simulations showed, the success of this improvement is dependent on the material properties of the used ferrofluid and speeds of the electromechanical system.

B. Electrically Controlled Switcher Working in a Ferrofluid Bath

Electrically controlled switcher with classical construction (see Fig. 13) placed in a ferrofluid bath was observed in its operation.

Fig. 13. Used electrically controlled switch.

An oscilloscope was connected to the switcher contacts to measure its time response for different values of the powering voltage and different positions of the switcher movable core. The ferrofluids effect to cool the devices was observed as well.

Fig. 14. Experimental setup: 1 – switcher; 2 – ferrofluid container; 3 – regulation of thickness of air gap; 4 – temperature display;

5 – source for LCD display; 6 – contacts of switcher.

Following graphs and table show the experimental results. To study changes of the static characteristics of the ferrofluid filled switcher, its inductance was measured for different positions of the movable body. Measured results were compared with the FEM simulation of the devices in Agros2D.

0

2

4

6

8

0 2 4 6 8

L(x

) [H

]

x[mm]

measured with fluid

simulated with fluid

measured without fluid

simulated without fluid

Fig. 15. Inductance L of the switch with and without ferrofluid filled gap, comparison of the measured and simulation results, measured with RLC meter with a very low measuring current i → 0, simulated with a

very low current density in the powering coil J = 1 A/m2.

The switcher was then DC powered with different voltage levels, current needed to operate the switcher for different starting positions of the movable body was measured.


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0

50

100

150

200

0 1 2 3 4 5 6

I[m

A]

δ [mm]

With fluid

Without fluid

Fig. 16. Minimum current needed to operate the switch for different positions of the movable body.

Because the coil heats during the operation, the total resistance of the circuit was observed in time to find out the cooling properties of the ferrofluid.

400

420

440

460

480

500

520

0 100 200 300

R[k

ohm

]

t [s]

With fluid

Without

fluid

Fig. 17. Total resistance of the electric circuit of the switch, powered by U = 80 V, in time.

Finally, dynamics of the switcher on the time to operate were measured with oscilloscope.

TABLE I. TIME TO SWITCH CONTACTS WITH AND WITHOUT FERROFLUID

FOR DIFFERENT POWERING VOLTAGES

1st contact

t 1f[ms]

2nd contact

t 2f[ms]

1st contact

t 1 [ms]

2nd contact

t 2[ms]

80 40,26 42,53 46,67 50,66

90 27,26 28,87 27,4 29,27

100 22,87 24,27 22,7 23,6

110 20,13 21,13 19,27 20,4

120 18,47 19,47 17,8 18,6

with ferrofluid time to switch without ferrofluid time to switchpowering

voltage

U [V]

The experimental results show that using the ferrofluid, the induction increases, minimum current needed to operate decreases because of the increase of the generated magnetic forces and the ferrofluid provides additional cooling to the electric circuit. However, the overall time response of the switcher improves only at lower powering voltages. This is caused by increasing viscous losses caused by the movement in the fluid; these losses are dependent on the device speed. Higher velocities are achieved with higher generated forces. Positive effect of the ferrofluid on the time response of the switcher is highlighted by blue and the negative effect by red in Table 1.

C. Ferrofluid Filled Rotating Electric Machine

A universal serial motor CG06 (Fig. 18) was injected with EFH-1 ferrofluid and its operation was observed. During the motor operation, centrifugal forces act on the ferrofluid placed between its rotor and stator. It has been

experimentally verified that the magnetic forces acting on the ferrofluid exceed these forces and the ferrofluid does not spurt out of the air gap. When the motor is off, magnetic forces generated by the residual magnetization of the stator material are strong enough to keep the ferrofluid in its position.

Fig. 18. Used universal serial electric machine CG06 1600W.

Static characteristics of the motor were investigated (Fig. 19). The rotor was fixed in a static position and forces acting on the rotor for different power were measured. As expected, forces are increased because of the improvement of the motor magnetic circuit.

0

10

20

30

40

50

0 0,05 0,1 0,15

M [

Nm

]

P [W]

With fluid

Without fluid

Fig. 19. Influence of the ferrofluid on the motor torque in dependence on supported electric power, measured while fixed rotor.

Speed of the unloaded rotor at different levels of powering voltage was investigated to reflect viscous losses caused by the ferrofluid. Example of such characteristics can be seen in Fig. 20.

0

200

400

600

800

1000

0 20 40 60 80

N [

1/m

in]

t [s]

With fluid

Without fluid

Fig. 20. Influence of the ferrofluid filled gap on speed of the unloaded motor, U = 9 V.

It is clear from the figure, that the ferrofluid affects the speed negatively at higher speed. This was expected because of the increase of the viscous losses depending on the speed of the movable body. Fig. 21 shows the beginning of the characteristics presented in Fig. 20, start of the unloaded motor.


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0

100

200

300

400

0 0,5 1 1,5 2 2,5

N[1

/min

]

t [s]

With fluid

Without fluid

Fig. 21. Influence of the ferrofluid filled gap on the start of the unloaded motor.

Viscous losses are lower at lower speed and the ferrofluid filled gap has positive effect on behaviour of the device. However, this gain is cancelled at higher speed.

To investigate the characteristics of the motor at physically real conditions, the motor was loaded and its start was investigated with and without ferrofluid filled gap (Fig. 22). During the start of the motor, at low speed, the ferrofluid once again has positive effect on the behaviour of the motor. Characteristics of the loaded motor confirm the expectation for this technology to be advantageous in slow running electromechanical devices.

0

100

200

300

400

500

600

0 50 100 150

N[N

m]

t [s]

9V With fluid

9V Without

fluid

9,5V With fluid

9,5V Without

fluid

Fig. 22. Influence of the ferrofluid filled gap on the start of the loaded motor, different powering voltages.

It has been experimentally confirmed that the ferrofluid present in the air gap of the examined rotating electric machine has positive effect on its behaviour at low speed. For experimentally studied electric machine CG06, efficiency increase by 5.9 % was calculated under 300 rpm. At higher speed, viscous losses in the fluid exceed the gain in magnetic forces.

CONCLUSION

The presence of up to date available ferrofluid in the air gap of an electromechanical system is not generally advantageous. It improves the magnetic conductivity of the magnetic circuit, its magnetic induction and generated static forces, it may provide additional insulation or cooling, but at higher velocities, the viscous losses caused by the movement in the fluid exceed gains. Although new types of the ferrofluids with lower viscosities and/or better magnetic properties can be expected to be manufactured in a near future due to the intensive boom in the field of nanotechnologies nowadays, this technology does not seem to be generally applicable in electromechanical systems. It may find its use in special, low velocity applications, or in devices that work in a start-stop regime.

Moreover, higher construction requirements to seal up the liquid and high costs of the nanofluids present additional problems to introduce investigated technology in practice.

However, according to our opinion, any technology able to improve the efficiency of an electromechanical system is worth of further research.

ACKNOWLEDGMENT

The financial support of University of West Bohemia, namely research project SGS-2015-035, is gratefully acknowledged.

REFERENCES

[1] M. Kubík, I. Mazůrek, J. Roupec, J., Z. Strecker, O. Macháček, "Design of Semi-active Magnetorheological Valve with Non-magnetic Bypass," Transactions on Electrical Engineering, no. 1, 2015. ISSN 1805-3386. [Online]. Available: http://www. transoneleng.org, [Accessed: 30. Sep. 2015].

[2] S. Odenbach. "Magnetoviscous effects in ferrofluids," Berlin: Springer, 2002, 151 s. Lecture notes in physics. Monographs. ISBN 3-540-43068-7; ISSN 0940-7677.

[3] S. Engelmann, A. Nethe, T. Scholtz , H. Stahlmann, 2004. "Experiments with a ferrofluid-supported linear electric motor," Applied Organo metallic Chemistry, 18(10), pp. 529-531.

[4] A. Judge, "Air gap elimination in permanent magnet machines." Disertation Thesis, 2012, Worcester Polytechnic Institute. 157 p.

[5] S. Odenbach. "Ferrofluids—magnetically controlled suspensions," Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2003, 217.1, pp. 171-178.

[6] P. Kopčanský, L. Tomčo, K. Marton, M. Koneracká, M. Timko, I. Potočová. "The DC dielectric breakdown strength of magnetic fluids based on transformer oil," Journal of Magnetism and Magnetic Materials. 2005, č. 289, s. 415-418. ISSN 0304-8853.

[7] D. Mayer, P. Polcar. "A novel approach to measurement of permeability of magnetic fluids," Przeglad Elektrotechniczny, 88(7 B), 2012, pp. 229-231. ISSN 0033-2097.

[8] P. Karban, F. Mach, P. Kůs, D. Pánek, I. Doležel, I.: "Numerical solution of coupled problems using code Agros2D," Computing, 2013, Volume 95, Issue 1 Supplement, pp 381-408, DOI 10.1007/s00607-013-0294-4.


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Sensorless Control of Two-Phase Induction

Machine using MRAS Techniques

Slavomir Kascak1) and Roman Mazgut1)

1) Department of Mechatronics and Electronics, Zilina, Slovakia, e-mail: [email protected]

Abstract — The paper presents most commonly used

control techniques based on the Model Reference Adaptive

System (MRAS) for the Two-Phase Induction Machine

(TPIM). The theoretical and experimental results are

obtained using the Rotor Flux, Back EMF, and Reactive

power estimators. The main characteristic of this research is

their performance during start-up and reverse conditions.

The experimental results were obtained at the no load

operation. The estimated values of the angular speed are

compared with the data from the incremental encoder. The

Matlab/Simulink simulation software was utilized to

perform the simulation results. The control techniques

implementation and data acquisition were done by the

technical computing device Dspace DS1103.

Keywords — Model Reference Adaptive System, Two-Phase

Induction Machine, Speed estimation.

I. INTRODUCTION

The TPIMs are widely used in industrial, commercial and domestic applications. Their benefits are simple, rugged, low-cost and easy to maintain. The TPIM achieves well control performances as the precise and quick torque and flux response, and the maximum starting torque is its big advantage in comparison with three-phase machine. The wide speed range and the drive control system with the transformation of stator currents into two components (flux and torque producing components) are necessary to provide with the vector control strategy.

In the recent years, the development of sensorless vector-controlled induction motor drives has been receiving much attention due to its low drive cost, high reliability and easy maintenance. The speed estimation is the main parameter which is required in the sensorless techniques for establishing the outer speed loop feedback. A different speed estimation method have been proposed such as Observers (Luenberger, Kalman filter), model reference adaptive system (MRAS) [1], [2], [3], [4], [5].

The MRAS based speed estimator is commonly used in AC speed control systems and also in estimating of the motor parameters such as the stator resistance or mutual inductance due to its easy implementation and good performance.

Firstly, we have to model the two-phase induction motor in order to design the MRAS based sensorless speed control which is considered as a reference model [6]. In the adaptive model, the speed is the adaptive parameter. The purpose of this paper is to examine the operation of the TPIM under different MRAS methods.

II. INDUCTION MOTOR MODEL

Eqs. (1) to (9) present the well-known mathematical model of the TPIM. The dynamic model of the two-phase

induction machine was implemented considering the dq stationary reference frame, since quantities such as voltages and currents are measured on the stator terminals.

dt

diRV sdsdsdsd

(1)

dt

diRV

sqsqsqsq

(2)

rqrd

rdrddt

diR

0 (3)

rqrq

rqrqdt

diR

0 (4)

The stator and rotor flux linkage components are given by:

rdsrdsdsdsd iMiL (5)

rqsrqsqsqsq iMiL (6)

sdsrdrdrdrd iMiL (7)

sqsrqrqrqrq iMiL (8)

The electromagnetic torque of the two-phase induction machine in the stator reference frame is given by:

)( rqsdsrdrdsqsrqpe iiMiiMnT , (9)

where

Tsqsds VVV ],[ is the stator voltage vector,

Tsqsds iii ],[ is the stator current vector,

Trqrdr iii ],[ is the rotor current vector,

Rsd, Rsq and Rrd, Rrq are stator and rotor resistances, respectively; Lsd, Lsq,Lrd, Lrq and Msrd, Msrq are stator, rotor and mutual inductances, respectively and ω is the rotor speed.

These dynamic equations are combined in order to achieve speed estimators based on the rotor flux, Back electromotive force and reactive power.

III. MRAS TECHNIQUES

The basic idea of the MRAS techniques are two independent models: reference model, where the estimated variable is not present; and adjustable model, where the estimated quantity is adjusted by means of an adaptive mechanism until the error between these models are equal


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to zero. The adaptation mechanism can be a PI controller or any other tool as the neural network, Kalman filters or other options.

Fig.1 shows the basic scheme of the MRAS technique applied in this paper in order to estimate the rotor speed of the TPIM. The outputs of the reference and adaptive models can be rotor fluxes, Back EMFs and reactive powers based on the different equations.

Reference model

Adjustable model

Adaptation

mechanism

Vs

is

X

X

Fig. 1. MRAS scheme for speed estimation.

A. Rotor Flux Estimator

Rewriting of Eqs. (1) to (8) to form (10), (11) and (12), (13) yields the reference and adjustable models based on the rotor flux observer, respectively. The reference rotor flux components obtained from the reference model are given by

))(( sdsdsdsdr

srdrd isLRV

L

Ms (10)

))(( sqsqsqsqr

srqrq isLRV

L

Ms (11)

The rotor flux components obtained from the adaptive model are given by

rqrdr

sdr

srdrd

Ti

T

Ms ˆˆ1ˆ (12)

rdrqr

sqr

srqrq

Ti

T

Ms ˆˆ1ˆ (13)

The adaptation mechanism (14), (15) is designed to generate the value of the estimated speed by means of minimizing the error between the reference and estimated fluxes using the PI controller [7].

rqrdrdrq ˆˆ (14)

)(ˆs

KK i

p (15)

B. Back EMF Estimator

The equations for the reference model expressed in (16) and (17) were developed in order to eliminate the need for integration in the reference model of the rotor flux observer, defining em as the Back EMF [8].

sdsdsdsdmd isLRVe )( (16)

))( sqsqsqsqmq isLRVe (17)

The adjustable model is derived from the equation for the

magnetizing current vector rLM

m sir

2 , where

M’= M2/Lr is the equivalent mutual inductance.

)11

('ˆsd

rmd

rmqmd i

Ti

TiMe (18)

)11

('ˆsq

rmq

rmdmq i

Ti

TiMe (19)

The rotor speed adaptation mechanism is done similarly to the previous method and it is:

)ˆˆ)((ˆmqmdmdmq

ip eeee

s

KK (20)

The inductance M’ can be conveniently incorporated into the adaptation gain constants Kp and Ki. The inductance M’ has no influence on the estimation if the gains are high enough.

C. Reactive Power Estimator

In [9], the reference model (21) calculates the instantaneous reactive power and it is independent on the slip speed ωsl. The adjustable model calculates the steady state reactive power and depends on ωsl. The instantaneous reactive power is given as:

sqsdsdsqref iViVQ (21)

The adjustable model (22) can be derived also from the equations of the mathematical model (1) to (8) and it is as follows:

)()( 22sdrdsqrq

rssqsdssad ii

L

MiiLQ (22)

The two-phase induction machine is driven by the indirect rotor field oriented control (IRFOC) [10], Fig. 2.

Therefore, substituting the condition sdrd Mi and

0rq , the more simplified equation (23) of Qad is

2

222 )( sd

rssqsdssad i

L

MiiLQ , (23)

where ωs = ωr+ ωsl.

The adaptation mechanism is:

))((ˆadref

ip QQ

s

KK . (24)

The diagram of the IRFOC (Fig. 2) consists of the TPIM, PWM half/bridge inverters, indirect field orientation algorithm and MRAS techniques.


TELEN2015021

TPIM2 phase

inverterDC BUS

MRAS

Vsd Vsqisd isq

IRFOC

Vsd* Vsq

*

Fig. 2. Diagram of the IRFOC control strategy.

IV. SIMULATION RESULTS

The parameters of the TPIM obtained through the locked rotor and no load tests are used during the simulation and experimental implementation.

TABLE I. TPIM PARAMETERS

Stator resistance in d axis Rsd 58.85 Ω Stator resistance in q axis Rsd 66.11 Ω Rotor resistance Rr 87.3 Ω Stator inductance in d axis Lsd 1.5 H Stator inductance in d axis Lsq 1.68 H Rotor inductance Lr 1,56 H Mutual Inductance Msrd 1.41 H Mutual Inductance Msrq 1.6 H Moment of inertia 4.888x10-4 kgm2 Number of pole-pairs 1 Rated voltage 230 V Frequency 50 Hz

Figs. 3 to 5 represent simulation results of the indirect vector controlled TPIM during the start-up and describe the estimated rotor angular speed using the Rotor Flux observer, Back EMF observer and Reactive Power observer, respectively. In this test, the reference speed was always set to 100 rad/s and the drive was operated at no load.

0 0.5 1 1.5 2 2.5

0

20

40

60

80

100

120

Time [s]

An

gu

lar

spee

d [

rad

/s]

ref

rf

Fig. 3. Simulation of the angular speed ωrf using the Rotor Flux based

MRAS observer.

0 0.5 1 1.5 2 2.5

0

20

40

60

80

100

120

Time [s]

An

gu

lar

spee

d [

rad

/s]

ref

BEMF

Fig. 4. Simulation of the angular speed ωBEMF using the Back EMF based MRAS observer.

0 0.5 1 1.5 2 2.5

0

50

100

120

Time [s]

An

gu

lar

spee

d [

rad

/s]

ref

rp

Fig. 5. Simulation of the angular speed ωrp using the Reactive Power based MRAS observer.

From the simulation results (Fig. 3) we can see the visible transients during the start-up of the rotor flux estimated angular speed and some oscillation remains also in the steady-state operation. Fig. 4 shows the lower ripple of the estimated angular speed using the Back EMF observer and the angular speed in Fig. 5 exhibit the lowest ripple using the Reactive Power observer. The dynamic response on the reference angular speed is very similar and the worst behaviour of the TPIM at the low speed operation is under the rotor flux estimation technique.

V. EXPERIMENTAL RESULTS

To confirm the use of the proposed procedure for two-phase induction motor, the simulation results have to be compared with those given by experimental tests. Experimental measurements were verified using the control device dSpace DS1103, squirrel cage motor, incremental encoder and full-bridge inverters for each phase. The advantage of using two full bridge inverters is that each phase of the machine is connected and controlled independently, so the d component of the stator current is controlled by one full-bridge inverter and the q component of the stator current by the other one. The incremental encoder was used to compare the estimated and real angular speeds. The applied software was the Matlab/Simulink and Control Desk. Functions of the particular library give a direct access from the MATLAB model to the variables of the application program running on the dSpace board.


TELEN2015021

Same as in the simulation the experimental measurement confirm the transients during the start-up using the Rotor Flux observer (Fig. 6) and also the ripple of the angular speed in the steady-state operation. Fig. 7 shows a better response during the start-up and smaller ripple of the angular speed, that is the same result as in the simulation (Fig. 4). The Reactive power based MRAS observer exhibits different behaviour during measurement test (Fig. 8). The ripple of the angular speed in the steady-state is bigger, but the response on the desired angular speed is faster.

0 0.5 1 1.5 2 2.5

0

20

40

60

80

100

120

Time[s]

An

gu

lar

spee

d [

rad

/s]

ref

rf

Fig. 6. Measurement of the angular speed ωrf using the Rotor Flux

based MRAS observer.

0 0.5 1 1.5 2 2.50

20

40

60

80

100

120

Time [s]

An

gu

lar

spee

d [

rad

/s]

ref

BEMF

Fig. 7. Measurement of the angular speed ωBEMF using the Back EMF


0 0.5 1 1.5 2 2.50

50

100

120

Time [s]

An

gu

lar

spee

d [

rad

/s]

ref

rp

Fig. 8. Measurement of the angular speed ωrp using the Reactive Power


The difference between simulation and measurement, where the Reactive power observer was used, can be in motor parameter changes.

VI. CONCLUSION

In the paper we have validated the MRAS based rotor flux, Back EMF and Reactive power observers under the IRFOC control strategy.

The validity of the proposed Sensorless Speed Control for the TPIM was also proven by simulation and experiment results that confirm effectiveness and good dynamic performances of the shown method.

In the future work we want to do some experiments at the load condition. Because of the difference in the test experiments also the parameter estimation of the TPIM will be done.

ACKNOWLEDGMENT

The author s wish to thank for the financial support to the

following project: VEGA 1/0928/15 – Research on

electronic control of power transmission and motion of

road vehicles with ICE, hybrid vehicles HEV and electric

vehicles EV.

REFERENCES

[1] Y. Zhang, Z. Zhao, T. Lu, L. Yuan, W. Xu. J. Zhu, “A comparative study of Luenberger observer, sliding mode observer and extended Kalman filter for sensorless vector control of induction motor drives,”IEEE Energy Conversion Congress and Exposition ECCE 2009, pp. 2466-2473, 20-24 September 2009.

[2] K. Negadi, A. Mansouri, R. Kourek, ”Hardware implementation of vector control of induction motor drive without speed encoder using an adaptive Luenberger based MRAS observer,”Leonardo Electronic Journal of Practices and Technologies, Issue 20, pp.99-114, January-June 2012.

[3] R. Gunabalan, V. Subbiah, B.R. Reddy, ”AdvanSensorless control of induction motor with extended Kalman filter on TMS320F2812 Processor,” International Journal of Recent Trends in Engineering, Vol. 2, No. 5, pp. 14-19, November 2009.

[4] A.V. Leite, R.E. Araujo, D. Freitas, ”Full and reduced order extended Kalman filter for speed estimation in induction motor drives: a comparative study,” 35th Annual IEEE Power Electronics Specialists Conference,pp. 2293-2299, Aachen, Germany, 2004.

[5] Ch. Yang, J.W. Finch,”A comparison of induction motor speed estimation using conventional MRAS and AI-based MRAS parallel system, “Advances in Electrical Engineering and Computational Science, Chapter 7, Vol. 39, pp. 75-85, 2009.

[6] N. Zablodskiy, V. Pliugin, V. Skryl, J. Lettl, “Mathematical model of induction motor with Ferromagnetic rotor,“ Transaction on Electrical Engineering, Vol. 3, No. 2, pp. 51-55, 2014.

[7] S.H. Chadalavada, R.L. Narasimaham, “Rotor flux-MRAS based speed estimation technique for direct torque controlled induction motor,“ International Journal of Engineering Research and Technology (IJERT), Vol. 1, Issue 8, pp. 1-6, Octoer2012.

[8] M. Rashed, A.F. Stronach, “A stable back-EMF MRAS-based sensorless low-speed induction motor drive insensitive to stator resistance variation,“ IEEE Proc.-Electr. Power Appl., Vol. 151, No.6, pp. 685-693, November 2004.

[9] M.N. Gayathri, S. Himavathi, R. Sankaran, “Comparison of rotor flux and reactive power based MRAS rotor resistance estimators for vector controlled induction motor drive,“ IEEE International Conference on Advances in Engineering, Science and Management, pp. 183-189, March 2012.

[10] S. Kascak, M. Prazenica, M. Valco, P. Cubon, M. Klasovity, “Vector control of two-phase IM using dSpace,“ IEEE ELEKTRO Conference, pp.141-144, May 2012.

Transactions on Electrical Engineering, Vol. 4 (2015), No. 4

_____________________________________________________________________________________________

TRANSACTIONS ON ELECTRICAL ENGINEERING VOL. 4, NO. 4 WAS PUBLISHED ON 31ST OF DECEMBER 2015

Koscelnik, J., Mazgut, R., Kascak, S., Prazenica, M.: Review of Selected Multi-Element Resonant Topologies

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The converter consists of two resonant tanks and HF transformer in case of the LCTLC topology. The paper

shows the design of the resonant elements. The converters can achieve zero current switching (ZCS) and zero

voltage switching (ZVS) conditions for the primary and secondary-side of the device respectively. The

converters achieve high values of power density and efficiency up to 96 % at the full load. The paper includes

the basic equations, analysis and simulation of the chosen topologies (LCTLC, LCLCL, LCL2C2).

Rau, D., Rodina, J., Palkovič, L., Hubinský, P.: Sensorless Field Oriented Control of BLDC Motors for

MAVs To achieve longer flight duration of the micro aerial vehicles (MAVs) it is needed to optimize their propulsion

system. A typical propulsion system of VTOL (vertical take-off and landing) MAV consist of the propeller

BLDC (brushless DC) motor, motor controller and battery (typically Lithium based chemistry). All these parts of

the propulsion system can be optimized in a specific way. In the case of the propeller, this can be done by the

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materials or stronger rotor magnets. As for the battery - alternative power sources like solar panels, hydrogen

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Liška, M., Beláň, A., Cerman, A., Janík,M.: Control System of Battery Storage to Eliminate the Power

Variation According to the Electricity Prediction Rapid variations of the output power from photovoltaic power plants can have some significant side effects on

the quality of electricity, such as the voltage variation, switching of tap changers, etc. In the other case, these

variations also make the difference between the prediction and real electricity production. Generally, the goal of

the accumulation of electricity is to charge the storage element in surplus of electricity and discharge when the

energy is insufficient. In this paper, the accumulation of electricity in a photovoltaic power plant is not used for

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Polcar, P., Český, J.: Conceptual Design of Electromechanical Systems Using Ferrofluids This paper presents an overview of a new conceptual design of electromechanical systems using ferromagnetic

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three illustrative examples are presented. Numerical simulations and experiments on real devices are employed

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Kascak, S., Mazgut, R.: Sensorless Control of Two-Phase Induction Machine using MRAS Techniques

The paper presents most commonly used control techniques based on the Model Reference Adaptive System

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using the Rotor Flux, Back EMF, and Reactive power estimators. The main characteristic of this research is their

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