2014
International Symposium on Power Electronics,
Electrical Drives, Automation and Motion
Szcze ś niak Pawe ł
University of Zielona Góra,
Institute of Electrical Engineering,
Zielona Góra, Poland,
P.Szczesniak@iee.uz.zgora.pl
Abstract — Advanced power electronic converters can provide the means to control power flow and ensure proper and secure operation of future smart-grid networks. The three-phase, direct matrix converter is an alternative solution to the conventional
AC-DC-AC converter for interfacing two AC systems at different voltages and/or frequencies. This paper presents a control analysis of a three-phase matrix converter employed as power interfaces of future electrical grids. The proposed system has typically occupy from 30% to 50% of the total volume of the converter for power levels greater than a few kW.
Furthermore, the application of electrolytic capacitors is a major cause of reduced converter lifetime.
PV
Fuel
PV
Cell Battery been successfully tested for bidirectional power flow operation with different grid operating conditions, such as, frequency and voltage variation.
DC/AC DC/AC DC/AC
Keywords—Matrix converter; AC systems; smart-grid Local network, f
1
Local network, f
2
I.
Traditional electricity networks were built to transport electrical energy from a relatively small number of large, centralized power generation units to a very large number of distributed loads. Power flows are essentially in one direction
-from centralized generator to distributed loads. The smartgrid concept hinges on making energy use more efficient by utilizing the integration of advanced technologies such as information, communication technologies and power electronics technologies, aimed at more effective power delivery and providing increased reliability to the bulk power system [1]. In the adoption of renewable energy, improvement of energy quality and control of power flow there are a number of problems to solve in novel power systems. Power electronic based devices can provide the means of solving problems met in the tasks that are required in this type of power grid [2]-[4]. Fig. 1a illustrates the most important areas of use of power converters in the power network [2]. In the majority of cases the solutions in AC-AC systems use power electronic converters with a two-stage electric energy conversion AC-DC-AC (Fig. 1b). AC-DC or DC-AC and DC-
DC converters are used in the connection of an AC system with DC parts (DC energy storage, DC-sources), as shown in
Fig. 1. Thus it seems obvious that DC circuits cannot be eliminated from electric systems. In some cases, a converter with a DC energy storage element is recommended.
The DC energy storage in the conventional indirect frequency converter is a bulky component [3]. In the solution with a voltage source inverter (VSI) the DC-link capacitors are relatively large compared to the size of the rectifier and inverter semiconductor components. Electrolytic capacitors
AC/AC LINK
AC/DC/AC
DC/AC
SMES
SG
DVR/SAPF
DC/AC
Diesel
STATCOM
DC/AC
UPFC
AC/DC/AC
(a)
Local network, f
2
SG
DFG
SG
SG
MT
Flywheel
(b)
Fig. 1. Examples of power converter applications in an electrical power network constituting an infrastructure of a smart-grid with commonly used
AC/DC/AC: a) electrical power network structure, b) circuit of AC/DC/AC converter.
Part of the power conversion in an electric power network is based on AC-AC conversion (wind generators, flywheels energy storage, micro turbines, FACTS, etc.). In these cases, the commonly used AC-DC-AC converters can be substituted by AC-AC converters without DC energy storage element [5].
It is also possible to integrate two systems of different parameters (voltage and frequency) by a power electronic
978-1-4799-4749-2/14/$31.00 ©2014 IEEE
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converter without DC energy storage. The most widely known
AC-AC power converter is the matrix converter (MC) [5]-[7].
Generally, the three-phase matrix converter is a single-stage converter with nine bidirectional power switches, able to connect directly three input phases to a three-phase load [7].
For high performance, the MC should have a source filter which consists of a second order LC resonant circuit. The main purpose of the source LC filter is the minimization of the high frequency components in the input current. The potential application of the MC in a smart-grid is depicted in Fig. 2.
Fuel
PV
PV Cell Battery
Local network, f
2
AC/AC LINK
MC
DC/AC DC/AC DC/AC
DC/AC
SMES
SG Diesel
STATCOM
DC/AC
UPFC
MC
Local network, f
1
Local network, f
2
MC
MC
SG
DFG
MC
SG MT
DVR/SAPF
MC
MC SG
Flywheel
Fig. 2. Examples of power converter applications in an electrical power network constituting an infrastructure of a smart-grid with matrix converter.
The most obvious area for the application of AC-AC converters is in distributed generator systems, in wind installations. Four possible wind solutions with AC-AC converters are presented as follows [2]:
- Squirrel cage induction generator (IG) with self-excitation and an AC–AC converter in the main line,
- Synchronous generator (SG) with an AC-AC converter in the main line and an AC–DC converter in the exciter circuit,
- Permanent magnet synchronous generator (PMSG) and
AC–AC converter in main line,
- double fed wound rotor induction generator (DFIG) with an
AC–AC converter in the rotor circuit.
Usually, a frequency converter with voltage source inverter
(VSI) is used in order to achieve full control of the active and reactive power. An increasing number of scientific publications, e.g., [3], [8], suggests matrix converters as an alternative solution to a system with DC-link. A MC can be used for controlling the active and reactive power independently [6]. Furthermore, a MC is responsible for the quality of the generated power and the grid code requirements.
Other types of AC source fed by a MC are micro-turbine generators (MTG) [9] and flywheel energy storage systems
[3].
A second group of potential applications for an AC-AC converter without DC-link are FACTS devices, e.g., unified power flow controllers (UPFC) [10], dynamic voltage restorer
(DVR) [11], active power filters (APF) and AC powerelectronic network couplers.
A MC can be used for controlling the active and reactive power independently. Different control strategies can be used for the power converter to provide power control requirements
[12]. One such strategy is based on a synchronous Voltage
Oriented Control (VOC) with PI controllers. The analysis of a
MC with VOC for power control is the main aim of the paper.
II.
The basic topology of the three phase MC that interfaces with two AC systems is shown in Fig. 3 [5]-[7]. Generally in three phase systems, the MC is a single-stage converter which has an array of nine bi-directional switches that allow any load phase to be connected to any source phase. For good performance, the MC should have a source filter to minimize the high frequency components in the input currents and reduce the impact of the perturbations from the input grid. The
MC topology is constructed using bi-directional four-quadrant switches, which are capable of conducting currents and blocking voltages of both polarities.
ω
S
ω
L
Source Side
R
LF 1 u
S 1 u
S 2
R
LF 2 u
S 3
R
LF 3
L
F 1
L
F 2
L
F 3
C
F 1
C
F 2
C
F 3
S aA
S bB
S bC
S cA
S cB
S cC
S aB
S aC
S bA
Network Side
R
LL 1
L l 1
R
LL 2
L l 2
R
LL 3
L l 3 u
L 1 u
L 2 u
L 3
Fig. 3. Schematic representation of two AC systems interfaced by a MC.
The MC has several modulation strategies which can be applied [13]. The most frequently used modulation strategy for
MCs is the Space Vector Modulation (SVM) [13]. The SVM modulation for MCs is able to synthesize the reference output voltage vector and it is also able to control the source current displacement angle. The SVM technique is based on the instantaneous space vector representation of load voltages and source currents in the MC. For the SVM of the MC it is convenient to define the following space vectors for each switch configuration [13]: u
OL
=
2 ( u ab
+ a u bc
+ a 2 u ca
)
= u
OL
( ) e j α
OL
( ) , (1)
3 i
S
=
2
3 i
(
A
+ a i
B
+ a 2 i
C
)
= i
S
( ) e j β
I
( ) , (2) where u
OL
is the space-vector representation for the output line-to-line voltage, i
S
is the space-vector representation for a = e − j 2 π / 3 the input phase current and . The space-vectors may be categorized as one of three groups of “zero”, “active” and
“synchronous” vectors. The reference output voltage and source current space-vectors are constructed by selecting four nonzero configurations, applied for suitable time intervals within the switching sequence period T configurations are applied to complete time T
Seq
Seq
.
while zero
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The required modulation duty cycles for the switching configurations I, II, III, IV are given by equations (3)-(6): d
I
= ( − 1 ) S
0
+ S i
+ 1
2
3 q cos( α
0
− π 3 ) cos( cos ϕ i
β i
− π 3 )
, (3) d
II
= ( − 1 ) S
0
+ S i
2
3 q cos( α
0
− π 3 ) cos( β i cos ϕ i
+ π 3 )
, (4) d
IV d
III
=
= ( − 1 ) S
0
+ S i
( − 1 ) S
0
+ S i
+ 1
2
2
3
3 q q cos(
0 cos( α
0
+
+ π
3 ) cos(
i cos
i
3 ) cos( β i cos ϕ i
−
+ π
3 )
3 )
, (5)
, (6) where φ i
is the input phase displacement angle, α
O
and β i
are the angles of the output voltage and input current vectors measured from the bisecting line of the corresponding sectors, and are limited as follows:
− π 6 < α
0
< π 6 , − π 6 < β i
< π 6 . (7)
III.
The classical AC/DC/AC converter (Fig. 1b) have the limitation connected with a minimum DC-link voltage [3], [4].
For proper operation of the rectifier, a minimum DC ‐ link voltage is needed to obtain undistorted current waveforms and operate with a unity power factor (in both direction of energy flow). Theoretically for diode rectifier, the maximum DC output voltage is the peak value of line ‐ to ‐ line voltage (Fig. 4):
U
DC min
= 2 3 U
S
= 2 U
S l − l
(8)
This limitation is introduced by freewheeling diodes in voltage source rectifier (VSR) which operate as a diode rectifier, when all of IGBTs are turn-off. In practical case the DC ‐ link voltage is about 15 ‐ 20% more than U (Fig. 4). For small level of
DC min the generated voltages (from distributed sources) there is a need to increase the DC-link voltage, by using additional
DC/DC converter.
In solution with MC there is no need to increase the generated voltage, because MC have not a DC-link and freewheeling diodes. The energy fed back to the grid with unity power factor, in system as shown in Fig. 3, is possible even at low levels of the generated voltages [7]. Theoretically the generated voltage should be higher than the voltage drop in the power electronic components (transistors and diodes) and passive elements. This is a main advantages of power electronics interfaces solution with matrix converter compared to two stage AC/DC/AC converter.
Fig. 4. DC ‐ link voltage condition in AC/DC/AC converter
IV.
A MC can be used for controlling the active and reactive power independently. Furthermore, a MC is responsible for the quality of the generated power and the grid code requirements. Different control strategies can be used for the power converter to provide these specified requirements [12].
One of them is based on synchronous Voltage Oriented
Control (VOC) with PI controllers. A simplify block diagram of the VOC control with PI controllers and MC is shown in
Fig. 5. This control strategy is based on the coordinate transformation between the stationary α β and the synchronous d-q reference frames. It provides fast transient response and high static performance due to the internal current control loops.
In voltage oriented d-q coordinates, the AC line current vector i
L
is split into two rectangular components
The component i
Lq i
Ld
and i
determinates reactive power, whereas i
Lq
Ld decides on active power flow. Thus, the reactive and the active power can be controlled independently. As current controller,
. the PI-type can be used. The output signals from PI controllers after dq/ αβ transformation are used for switching signal generation by a Space Vector Modulator [13].
Fig. 5. Control block diagram for a matrix converter interface of two three-phase AC systems.
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80
60
40
20
V.
To validate the accuracy of the developed MC controls, the study of the system in Fig. 5 is considered. Fig. 5 shows schematic representation of a matrix converter that interfaces with two AC systems with nominal frequencies of and f
L f
S
= 60 Hz
=50 Hz [7], [15]. To verify the validity of the proposed scheme, two simulations are carried out in Matlab/Simulink.
In the first one, energy control from the network side to source side is considered; in the second there is a reversal of the energy flow – from source to network side.
[A]
I i
Ld i
Ld ref
100
0
0
[A]
I
0.1
u
L 1
[100 V/div]
0.2
0.3
(a) i
L 1
[100 A/div]
0.4
0.5
t [s]
0.6
100
[A]
-20
-40
-60
-80
-100 i
Ld i
Ld ref
-120
0
[A]
0.1
I u
L 1
[100 V/div]
0.2
I
0.3
(a) i
L 1
[100 A/div]
0.4
100
0
-100
-200
0
[A]
I
0.1
0.2
0.3
(b) u
S 1
[200V/dz] i
S 1
[40A/dz]
40
0.4
0.5
0.6
0.5
t [s]
0.6
0
-100
-200
0
[A]
I
0.1
0.2
0.3
(b) u
S 1
[200V/dz] i
S 1
[40A/dz]
40
0.4
0.5
t [s]
0.6
0
-40
-80
0
[kW]
I I q
S
0.1
20
0.2
0.3
(c)
0.4
0.5
t [s]
0.6
0
10
-40
-80
0
[kW]
0
I
-10
-20
0.1
q
S
0.2
0.3
(c)
0.4
0.5
t [s]
0.6
-30
0 0.1
0.2
0.3
(d)
0.4
0.5
t [s]
0.6
Fig. 6. Energy transfer from network side to source side: a) reference and measurement network side current in direct axis, b) time waveforms of i network side current
S 1
and voltage u i
L 1
and voltage u
L 1
; c) time waveforms of source current
S 1
; d) instantaneous value of input active and reactive power.
0 t [s]
0 0.1
0.2
0.3
(d)
0.4
0.5
0.6
Fig. 7. Energy transfer from source side to network side: a) reference and measurement network side current in direct axis, b) time waveforms of network current and voltage u i
L 1
and voltage u
L 1
; c) time waveforms of source current i
S 1
; d) instantaneous value of input active and reactive power.
S 1
Some studies have been done using the following parameters: source voltage 230 V/ 60 Hz, network voltage
133 V/50 Hz, input filter inductance filter capacitance C
0.05 Ω , switching frequency f
Seq
T p k
P
F
=20 μ F, load inductance L
=10 kHz and simulation step
=1 μ s. The parameters for current PI controllers are:
=17.5, k
I
=0.58 and T s
L
F
=1 mH/0.05 Ω , input
L
=5 mH/
=0.1 ms.
Fig. 6 shows the energy flow from network side to source side. This case is typical for generator mode. The direct-axis reference and measurement network side current are shown in
Fig 6a, whereas, the time waveforms of network current and voltage are indicated in Fig. 6b. In the case of i
Ld ref it was
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subjected to a step change from 15 A to 100 A in time intervals every 0.1 s. The input voltage and current of the matrix converter are shown in Fig. 6c. The phase shift of source current and voltage is almost equal 180°, whereas the network side voltage and current are the same phase shift.
Then only active energy is reversed to the source, as is visible in Fig. 6d. The active power has minus polarity, which means, that the energy is delivered back to the source. The dynamics of the system are very good. The duration time of step response is short, but the overshoot is visible. A detailed analysis of PI regulator parameters is required [14].
Fig. 7 presents energy transfer in the opposite direction with similar waveforms as the latter case. This case is typical for motor mode. The active power has positive polarity, which means that the energy is transferred from the source to network side. The phase shift between network side current and voltage equals 180°. The dynamics of the system also produce very good performance.
Fig. 8 shows the reference voltages u d ref
and u q ref responses for different control gains of the PI controller at the reference current i q ref
step from 30 A to 50 A. As can be seen from Fig. 8, the PI gains k
P
=17.5, k
I
=0.58 are recommended for applications. The detailed analysis of PI parameters requires detailed knowledge of the system transmittance, including MC circuit and passive elements (Fig. 3). Because the parameters of MC depends on used switch modulation strategy [16], [17], the detail mathematical model, taking into account the modulation strategy should be defined.
VI.
Power electronic converters are an integral part of the energy power network in such applications as power interfaces of distributed sources, network couplers, devices for improving energy quality, compensation of non-active power and control power flow in the power system. In the majority of cases of power converters implemented in AC power systems, power electronic converters with a DC energy storage element are used. This element is often the least reliable part in the whole power converter. DC circuits cannot be eliminated from power systems, but in some applications the commonly used converters can be replaced by converters without a DC energy storage element. The AC-AC converter offers many potential benefits to the power converter applications. This converter will not be the best solution for all applications, but it offers significant advantages for some.
The working principle of the MC to interface with two AC system controls has been presented. The system has been tested with the step change in reference to a direct-axis network side current i
Ld ref
. The dynamics of the system have produced very good performance, but a detailed analysis of PI regulator parameters and system parameters is required.
The MC structure can be used of a part of power electronics transformer as was presented in [18]. MC in combination with station power transformer can work as a power flow regulator or voltage sag or swell compensator.
This work presents an initial study, in order to know the MC control possibilities in power systems. Analysis of MC in the configuration of the hybrid transformer [18], as the power flow controller will be the subject of future research.
The project has been funded by the National Science Centre, granted on the basis of the decision number DEC-
2011/03/B/ST8/06214
(a)
(b)
Fig. 8. Compensated the reference voltages a) u d ref
and b) u q ref
responses for different control gains of the PI controller at the reference current i q ref from 30 A to 50 A.
step
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