Modelling and basic properties of three-phase hybrid ... - IEEE Xplore

XI International School on Nonsinusoidal Currents and compensation, ISNCC 2013, Zielona Gora, Poland

Modelling and basic properties of three-phase hybrid transformer with unsynchronized active load J. Kaniewski, Z. Fedyczak, P. Szcześniak University of Zielona Góra, Institute of Electrical Engineering, Zielona Góra, Poland, [email protected], [email protected], [email protected] Abstract — This paper deals with three-phase power system with hybrid transformer (HT). The HT contains conventional transformer with electromagnetic coupling and PWM AC line chopper integrated with secondary windings with electric coupling. The HT is located between distribution system and Local Balancing Area (LBA) with small power local energy sources. After description of the three-phase power system with hybrid transformer (HT) and unsynchronized active load, the mathematical and circuit models of the AC source with HT is presented. These models are verified by means of the simulation and experimental test results obtained for HT of about 3 kVA. Keywords — Power system, Hybrid transformer, matrix chopper

I.

INTRODUCTION

Dynamic states in AC power system such as faults, fast load changes, switching effects, and atmospheric discharge, generate undesirable effects on consumer side, such as voltage sags, interrupt and swell [1], [2]. In the case of the supply AC voltage changes, both downward and upward, there is a high risk of damage to devices, which are sensitive to voltage changes, for example: computers, transceivers devices, medical systems [3]-[6]. In the case of big plants and factories, voltage sags and swells may cause very large financial damage. The application of an AC-AC converter using Pulse Width Modulation (PWM) control strategy to build secondary supply sources (voltage sag and swell compensators and voltage regulators) mitigate the unwanted effects of supply [7]–[11]. Some type of AC voltage controller to compensate deep and fast voltage sags and overvoltages is hybrid transformer (HT) described in [12]-[17]. Simplify schematic diagram of HT connected to the AC power system is shown in Fig. 1. In this case HT unit is working with passive load as AC voltage controller.

In the case of modern AC power system (smart grid) there are possibilities to connected small power renewable energy sources (photo voltaic panels – PV, wind generators) to low voltage AC system. The renewable energy sources are connected to the grid by power electronic interfaces [7], [8]. The voltage fluctuations in low voltage AC power system can be caused by turn-on and turn-off renewable energy sources connected to the grid, dependently on condition of primary energy (wind, sun, water flow, etc.). The local AC systems (subsystems) such as residential houses, school, academic campus, etc. with small power energy sources connected to the local AC subsystem is called as “Local Balancing Area” (LBA). In LBA with small power local energy sources, during operation of this subsystem there is a risk of change (fluctuation) of voltage amplitude in LBA. It is caused by operation condition (turn-on and turn-off) of energy sources connected to LBA. In the case of connected HT in power system with LBA (Fig.2), the HT in fact is loaded by active load. From this reason is necessary to obtain bidirectional power follow in HT circuit.

Fig. 2. Hybrid transformer installed in modern power system with active load.

This paper presents a modelling and analysis of three phase hybrid transformer using matrix chopper described in [14] with active load (two-sided supply). The next

chapter described topology and operation of the presented HT. Follow this are chapters about the simulation and experimental test results and conclusions.

Fig. 1. Hybrid transformer installed in power system such as voltage controller with passive load.

XI International School on Nonsinusoidal Currents and compensation, ISNCC 2013, Zielona Gora, Poland II. ANALYSED CIRCUIT DESCRIPTION

b2, b3) are connected in series with the required phase output connectors of MC. The voltages of the transformer secondary windings a1, a2, a3 and b1, b2, b3 are form with ratio pa = 4/3 and pb = 2/3 respectively [14], [15]. Output voltages of HT (uL1, uL2, uL3) are the sum of secondary voltages (pbuS1, pbuS2, pbuS3) and phase output voltages of the MC. The output voltages of HT (uL1-uL3) are controlled by means of the control circuit. The voltages u01, u02, u03 there are voltages of power system II (LBA) with active load (Fig. 3).

The schematic diagram of the considered HT with active load is shown in Fig. 3. The circuit of the TH contains two main units. The first one is a three-phase conventional transformer (TR), with two secondary windings in each phase. The second one is a three-phase matrix chopper (MC). Primary windings are in Yconnections. The main secondary windings (a1, a2, a3) of TR also have Y configurations and, by input filter, are connected with the MC. Secondary phase windings (b1, Power system I (distribution system) b1

uS1

Power system II (Local Balancing Area) u01 Z

HT

01

uS1nb

uS1

uZ01 Z02

uL1

b2

uL2 b3

N uS2

LF1 uS1na

uS3

LL1 S1

uCF1

LL2

uS2na

uCL3

S4

S5 uCF3

CF2

uCL2

LL3

uS3na

CF1

Active Load

S3

uCF2

LF3

a3

uL3

uCL1

LF2

a2

N’

uZ02

uS3nb a1

uS3

i02 u02

uZ02 u03 Z03 i 02

uS2nb

uS2

i01

S2

S6

CF3

CL1

CL3 CL2

N’

S1(t) – S6(t)

Control unit

Fig. 3. Three-phase hybrid transformer using matrix chopper with active load.

Exemplary idealized voltage time waveforms illustrating operation of presented circuit for various value of pulse duty factor D, in condition uS=u0 and switching frequency fS=500Hz are shown in Figs. 4 and 5.

For illustrating operation, the load has a resistance character.

Fig. 5. Idealized voltage and current time waveforms for D=0.95 and fS=500Hz illustrating operation of analyzed HT Fig. 4. Idealized voltage and current time waveforms for D=0.05 and fS=500Hz illustrating operation of analyzed HT

Idealized voltage transmittance of considered HT is

XI International School on Nonsinusoidal Currents and compensation, ISNCC 2013, Zielona Gora, Poland described as (1) and shown in Fig. 6 as a function of pulse duty factor D defined as (2) [14].

H UHT ≅ D=

U L naU S D + nbU S = = na D + nb , US US

(1)

t on , TS

(2)

The parameters of transformer TR after converting to a secondary side are collected in table I [18], [19], [21]. TABLE I PARAMETERS OF SUBSTITUTE CIRCUIT OF TRANSFORMER TR CONVERTED TO A SECONDARY SIDE OF TR

Parameter

name

value

unit

na

Voltage ratio

4/3

-

nb

Voltage ratio

2/3

-

1.12

Ω

0.92

Ω

7605

Ω

0.28

Ω

0.163

Ω

1901

Ω

where TS – switching period, ton – turn-on time of switches S1, S3, S5 [14]. 2

R’1

HU [V/V]

R2 1.6

R’Fea

1.2

R’4

0.8 nb

R5

0.66

Resistance of primary windings Resistance of secondary windings b

R’Feb

0.4 0

Resistance of primary windings Resistance of secondary windings a

0.2

0.4

D

0.6

0.8

X’L1

Leakage reactance

0.48

Ω

XL2

Leakage reactance

0.28

Ω

6112

Ω

1

Fig. 6. Idealized characteristic of voltage transmittances of presented HT as a function of the pulse duty factor D

The output voltage of HT uL is depended on pulse duty factor D (Fig. 6) and for considered circuit is controlled from 0.66uS to 2uS [14], [15]. As is visible in Figs. 4 and 5 the phase of the load current i0 in HT circuit is depend on value of pulse duty factor D. If output voltage of HT (UL) is greater than active load voltage (U0) (Fig. 5) then current i0 is in phase with output voltage of HT. This means that energy is transferred from source US to load (from power system I to power system II). In the case when output voltage of HT is less than active load voltage (US < U0) (Fig. 4) then current i0 is in opposite phase in relation to output voltage of HT. This means that energy is transferred from active load to voltage source US (from power system II to power system I).

X’µa X’L4

Leakage reactance

0.036

Ω

XL5

Leakage reactance

0.081

Ω

1528

Ω

X,µb US

Supply voltage

230/400

V

U1

Secondary voltage

nbUS

V

U2

Secondary voltage

naUS

V

S

Apparent power

10

kVA

On the based Thevenin’s method, and according to Fig.7 we can easily obtain the simplify substitute circuit of analyzed HT with substitute source (Fig. 8).

III. THEORETICAL ANALYSIS With assumption symmetrical and balanced circuit of HT and symmetrical three-phase supply sources and active load sources, we can show circuit from Fig. 3 as a single phase circuit [14]. Taking into account substitute scheme of transformer [18], [20] and averaged circuit model of matrix chopper [20], the single-phase schematic diagram of considered HT after converting all parameters of TR to a secondary side, is shown in Fig. 7. Fig. 8. Simplify substitute circuit model of considered HT with active load

The substitute source and substitute impedance of analysed HT from Fig. 9 in complex form are defined as (3) and (4).

Z HT = Fig. 7. Single phase circuit model of HT with active load

(106.6 − j 244.8) + (0.44 − j 317.3) D 2 , (−132.75 − j111.84) + D 2

(3)

XI International School on Nonsinusoidal Currents and compensation, ISNCC 2013, Zielona Gora, Poland

E HT = (0.99 + j 0.00016)U 1 −

(49.5 + j133.3)U 2 (−48.47 − j133.15) + D 2

,(4)

where U1 and U2 there are voltages converting to a secondary side of transformer TR (Fig. 7, Table I). The static characteristics of (3) and (4) and phase of magnitude of EHT as a function of pulse duty factor D are shown in Figs 9 and 10.

IV. SIMULATION AND EXPERIMENTAL TEST RESULTS A.

Simulation Results

The parameters of simulation circuit of analysed HT with active load are collected in table II. The presented simulation results was obtained in dedicated simulation program PSim. TABLE II PARAMETERS OF SIMULATION CIRCUIT

|ZHT| [Ω]

3 2.5 2 1.5 1 0.5 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

D

name

value

unit

na

Voltage ratio

4/3

-

nb

Voltage ratio

2/3

-

US

Source voltage

230/400

V

50

Hz

1

mH

10

μF

1

mH

10

μF

10

Ω

230/400

V

5

kHz

10

kVA

f LF1 = LF2 = LF3

Fig. 9. The magnitude of impedance of HT as a function of D

|EHT| [V]

600

Parameter

CF1 = CF1 = CF3 LL1 = LL2 = LL3 CL1 = CL2 = CL3

500

2

400

1

│Z01│=│Z02│=│Z03│

3

300

U0

200

fS

100 0

0.2

0.4

D

0.6

0.8

1

S

Supplying frequency Input filter inductance Input filter capacitance Output filter inductance Output filter capacitance Load impedance Load source voltage Switching frequency Apparent power

Fig. 10. The magnitude of output voltage of HT as a function of D for various value of source voltage US: 1- 100% of US, 2 - 115% of US, 3 - 85% of US,

arg |EHT| [rad]

0 -0.02 -0.04 -0.06 -0.08 -0.1

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Fig. 12. Simulation time waveforms of voltage, current and power for pulse duty factor D=0.1

D Fig. 11. The phase of output voltage as a function of D

As is visible in Fig 9 the magnitude of impedance of HT is depending on pulse duty factor D and is changing at range 0.6–2.5 Ω. Assuming supply RMS line voltage 3x230V, the range of change of output voltage is from 153 V–460 V (according to voltage transmittance of HT (1) and Fig 6). In Fig. 10 we can see the static characteristics of substitute source EHT as a function of pulse duty factor D. Characteristic 1: for 100% of US, 2: for 115% of US, and 3: for 85% of US.

Fig. 13. Simulation time waveforms of voltage, current and power for pulse duty factor D=0.9

XI International School on Nonsinusoidal Currents and compensation, ISNCC 2013, Zielona Gora, Poland As is visible in Figs. 12, 13, the output voltage of HT (UL) is depending on pulse duty factor D. In the case when output voltage UL is less then active load voltage U0 the current in HT circuit is in opposite phase in relation to source voltage. From this reason the instantaneous power has negative value (Fig. 12). It means that energy is transferred from source voltage U0. If UL>U0 (Fig 14), then instantaneous power is positive. It means that energy is transferred from source voltage US.

bidirectional switches are implemented with two IRG4PHUD IGBTs connected in emitter to emitter configuration. Because of safety the AC input rated voltage was 50 VRMS. The voltages, currents and instantaneous power time waveforms for various value of pulse duty factor D and for US=U0 are shown in Figs. 15– 17. uL1

i01 100 V/div 2 A/div

uL2

i02 100 V/div 2 A/div

pL1 100 W/div

Fig. 14. Simulation time waveforms of voltages, currents and instantaneous power for D=0.25

Fig. 15. Experymental time waveforms of voltages, currents and power for duty pulse factor D=0.1

In the case when source voltage UL is equal load voltage US (Fig. 14) the current I0 ≈ 0 and the averaged value of power P=0. It means that energy is not transferred at these conditions B.

Experimental Results

A three-phase, 1-kVA prototype has been built and tested in a open-loop control condition. The parameters of experimental model are shown in Table III. TABLE III PARAMETERS OF EXPERIMENTAL CIRCUIT

Parameter

name

value

unit

na

Voltage ratio

4/3

-

nb

Voltage ratio

2/3

-

3x50

V

50

Hz

1

mH

10

μF

1

mH

10

μF

fS

Source voltage (RMS) Supplying frequency Input filter inductance Input filter capacitance Output filter inductance Output filter capacitance Load impedance Load source voltage Switching frequency

IGBT

Transistors

S

Apparent power

US f LF1 = LF2 = LF3 CF1 = CF1 = CF3 LL1 = LL2 = LL3 CL1 = CL2 = CL3 │Z01│=│Z02│=│Z03│ U0

30

Ω

3x50

V

5

kHz

IRG4PH UD 10

kVA

-

The matrix chopper is controlled via a PWM control strategy. The switching frequency is set to 5 kHz, and the “dead time” for commutation is set at 0.7 μs. The

Fig. 16. Experymental time waveforms of voltages, currents and power for duty pulse factor D=0.25

Fig. 17. Experymental time waveforms of voltages, currents and power for duty pulse factor D=0.9

As is visible in Figs. 15-17, the instantaneous power could be with positive (Fig. 17) and negative (Fig. 15) sign. If averaged value of instantaneous power p (active

XI International School on Nonsinusoidal Currents and compensation, ISNCC 2013, Zielona Gora, Poland power) has positive value then energy is transfered from source voltage US to load voltage UL, and oposite when p has negative value. The acquired experimental results validate theoretical and simulation analysis. V. CONCLUSION In this paper a three phase hybrid transformer using matrix chopper with unsynchronized active load has been presented. The circuit and operation have been described, and the main characteristics and time waveforms have been shown. This prototype was operated using a control strategy based on the PWM modulation of the IGBTs. The described solution gives possibility to bidirectional energy flow in power system with active load. The acquired experimental results validate theoretical and simulation analysis. Future research will be focused on the analysis of the HT with active load and closed-control loop and possibility to energy transfer control in low voltage power system under source and load voltage fluctuation. ACKNOWLEDGEMENT The project has been funded by the National Science Centre granted on the basis of decisions number DEC2011/03/B/ST8/06214 REFERENCES [1]

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