Power Electronic Transformer application to Grid Connected Photovoltaic Systems G. Brando, A. Dannier, R. Rizzo Department of Electrical Engineering University of Naples, Via Claudio 21 – 80125 Naples (Italy)
Abstract—Grid-connected photovoltaic systems utilize static converters which influence the efficiency of the system. The energy conversion depends on the architecture of the converter, different solutions are available and Hbridge multilevel converters seem to be an optimal solution also for the power quality. In the paper is proposed an architecture that includes a Power Electronic Transformer which is practically an isolated high-frequency link AC/AC converter that substitute a conventional transformer. An MPPT control technique is presented and validated by simulation implemented on a photovoltaic system with H-bridge nlevels converter and Power Electronic Transformer. The simulation results confirm that the control is able to effectively track the Maximum Power Point and to stabilize immediately in the new steady-state condition.
II. INTRODUCTION The implementation of Maximum Power Point Tracking (MPPT) techniques for grid-connected Photovoltaic (PV) arrays requires the utilization of dedicated architectures of the power electronic converters in order to control and optimize power flows. The architecture proposed in this paper includes a multilevel H-bridge as a stage in cascade to the photovoltaic array, the medium frequency transformer, an output n-level H-bridge that supply a dc-link which is connected to the MV feeding grid through another Hbridge converter as represented in Fig. 1. The conventional transformer is substituted by a Power Electronic Transformer (PET) - an isolated highfrequency link AC/AC converter is termed an electronic transformer - that has reduced size, volume and weight, it improves dramatically the efficiency and is better suitable for the optimization of power flows. It may be seen that the literature has extended the application of high-frequency link AC transformation not only for low-level electronic power conversion but also for medium-level distribution power transformers [1, 2]. The major payoff expected is size reduction. The advantages extend to more innovative control possibilities as well [3]. The basic design of PETs couples an HV grid with a MV grid. A frequency converter on each side of the transformer connected directly to the HV resp. MV grid transforms voltages and currents from basic frequency of 50 Hz into a medium frequency MT. Different frequency converter schemes have been presented and discussed in literature relating to realization in distribution grid application with modern power electronic devices such as i.e.: three-phase to three-phase cycloconverter topology, back-to-back connection of voltage source converters, matrix converters [4]. The architecture considered in this paper is a multilevel H-bridge that gives good response also to power quality problems that are more and more significant in the considered application. Currently power quality indexes of distribution networks are strongly influenced by the presence of a high number of loads where power electronics systems are widely used. Therefore a possible solution to overcome or to reduce this problem can be given by multilevel conversion topologies [5]. The advantages in the introduction of a PET in PV Grid-connected system is further explored, first the
Index Terms—Power Electronic Transformer, H-bridge, Multi-level Converter, MPPT Maximum Power Point Tracking.
I. NOMENCLATURE i p , j , v p, j current,
voltage
of
transformer-phase is , j , vs , j current, voltage of
the the
primary
j-th
secondary
j-th
transformer-phase iL, j , vL, j current, voltage of the j-th line-phase vdc, pj
total dc-link voltage of the j-th H-Bridge phase
vdc, sj
on the primary side total dc-link voltage of the j-th H-Bridge phase
L, R LT , RT
on the secondary side line-phase inductance, resistance transformer-phase inductance, resistance
T
sampling interval for the PET converters
idc
dc-link current generated by PV modules
si
current slope
sv
voltage slope
si , p
positive slope current
si , n
negative slope current
si ,0
start-up slope current
R. Rizzo is corresponding author. e-mail:
[email protected]
978-1-4244-2544-0/08/$20.00 ©2009 IEEE
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electronic transformer principle of operation and topology is presented and than the MPPT is implemented
on the proposed architecture reporting the results to evidence the advantages obtained by utilizing the PET.
LV Inverter
MV Rectifier-Inverter MF Transformer
vdc, p1,1
v p1 PV
H-Bridge Module 1st
vs1
i p1
is1
PV vdc, p1,2
GRID
H-Bridge Module 10th
vdc, p2,1
H-Bridge Module 1st
i p2
vp2
vs 2 is 2
PV
iL1 R L vL1 iL 2 vL 2 vL 3 iL 3
O
PV vdc, p2,2 H-Bridge Module 10th
vdc, p3,1
H-Bridge Module 1st
i p3 v p 3
vs 3 is 3
PV
PV vdc, p3,2
H-Bridge Module 10th
Fig. 1. A multi-stage DC/AC converter with intermediate three-phase MF transformer (PET)
idc = i0 + si t
III. THE MPPT CONTROL STRATEGY
where si is the current slope. Increasing the current idc, if si > 0 , vdc decreases with a slope sv assumed to be sv < 0 . The slope sv depends on si and on the working point of the cells. In particular, assuming si constant, sv increases strongly, in absolute value, when the cells are working in the stable part of the characteristic. This condition is taken in consideration to determine the MPP. If a positive slope si,p is considered for the current, for each value of si , p is possible to determine a specific
The MPPT is determined by means of an hysteresis control which modulates the variation (slope of variation) of the current that the dc-link absorbs from the cells in function of the variation of the dc-link voltage. The control technique can be described referring to the simple scheme that is shown in Fig. 2. idc
L
(1)
R
+
PV
value − sv* , where sv* > 0 , that identify the operation in the unstable part of the characteristic. Obviously imposing in (1) si = si , p when sv < − sv* the current idc is
-
Fig. 2. Equivalent circuit with current generator
higher than the maximum current idc , M which correspond
The current generator represents in this scheme the converter. The PV arrays current idc is assumed to be:
to the optimal operation. To guarantee that the system works closed to the MPP it is sufficient to invert the slope
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of the current assuming in (1) si = si , n with si , n < 0 .
MF Transformer
vdc,p,j
After inverting the slope, the system will work again at the optimal condition. When sv > sv* , it will be sufficient
i1p,j
LV inverter
vp,j
vs,j
to invert again the current slope assuming si = si , p .
Shifting selection
It is possible to contain the oscillation of the current idc just around the maximum point and contemporarily track the MPP against variations of irradiation. The oscillation of the current will decrease when decreasing si , p , while the time response of the control - when the
TΔ*
i1p,j
Predictive computation
vdc,p,j i1p,j vdc,p,j
MPPT
Equation n. 2
irradiation varies - will decrease when increases si , n .
Control system
vdc,s,j
vdc,s,j
Pj*
This control technique can be realized by means of an hysteresis controller which imposes the value of si as
(
vdc,s,j
HV rectifier
Fig. 3. Control scheme of PET
)
In the first step, the control computes the reference current as a function of the reference power. With reference to the equivalent circuit of fig. 4, which synthesises one phase of the power circuit of PET (where RT and LT are the resistance and inductance of the transformer and of possible additional components), the following simple equation can be stated: d i pj v pj − vsj = RT i pj + LT dt Assuming that in steady-state operating conditions the voltages vpj, vsj have a square waveform, with magnitude vdc,pj, vdc,sj and a period 2T with T si , p . The considered sensorless control, proposed by authors [5] is set up to deliver the maximum power to the grid in presence of variations of incident irradiation on the photovoltaic arrays. IV. PET PRINCIPLE OF OPERATION AND TOPOLOGY
∼
i pj =
The power electronic transformers (PET) considered configuration has dc-links either in high-voltage or in low-voltage stages. Both primary and secondary windings of the ferrite-core transformer are supplied by a voltage-source-inverter (VSI, on low-voltage side) and by a voltage-source-rectifier (VSR, on high-voltage side) which impose square-wave voltages. The proposed topology employs a static converter on the primary side of the MF-transformer for voltage step up application as shown in fig. 1. A multilevel converter must be employed in the secondary side, where the voltage is higher than ratings of available devices. The number of input/output multilevel stages can be increased to allow higher voltages. This configuration can be applied when the secondary side voltage is much higher than the primary side voltage. The power generated by the PV modules is injected in the power grid by a V.S.I. multilevel cascaded H-bridge converter that is able to keep constant and balanced the voltages on the different dc-link capacitors on the high voltage side of the converter. On the other hand, the dclink voltages of the low voltage side of the converter are strongly variable, since they are influenced by the operating conditions of the PV cells. This topology allows to fully decouple the dc-link voltages on the primary and secondary side without additional dc/dc converters. The schematic representation of the control structure is shown in the fig. 3. The control operates in two steps.
Pj T ⎛ ⎜ vdc , sj − vdc, pj 1 − 2 LT ⎜ Pmax, j ⎝
⎞ ⎟ ⎟ ⎠
(2)
where: Pj =
vdc , pj ⋅ vdc , sj T LT
TΔ ⋅ (T − TΔ )
is the power generated on phase j by the PV cells and Pmax,j is the maximum value of Pj given by: Pmax, j = Pj
T TΔ = 2
=
vdc , pj ⋅ vdc , sj 4 LT
T
In equation (2), i ∼pj is the value of the current ipj at the end of the shifting interval i ∼pj between the two square voltages vpj and vsj applied at the transformer sides. With equation (2) the reference current i*pj can be easily evaluated as a function of the reference power Pj* : it is enough to set: i*pj = i ∼pj
Pj = P*j
The required current i*pj can be obtained by properly defining the shifting angle TΔj between primary and secondary voltages. This angle can be evaluated using a predictive procedure, employed in the control step two.
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We denote with tn, tn+1, tn+2 three arbitrary consequent sampling instants, with tn+1= tn+Ts and tn+2= tn+1+Ts .The sampling interval Ts is assumed equal to the half-period T of the square wave voltages vpj, vsj. On the basis of the different detected actual values and of the computed
of the circuit) we can obtain a dynamic response very close to the fastest one.
LT
RT
ipj
reference current i*pj at the instant tn, the equation i
⎛ TΔj , n ⎞ ⎛ RT TΔj , n ⎞ = ⎜ i pj , n ⎜1 − ⎟⋅ ⎟ + ( vdc , pj + vdc.sj ) ⎜ L LT ⎟⎠ T ⎝ ⎠ ⎝ T − TΔj , n ⎞ vdc , pj − vdc , sj ⎛ ⋅ ⎜ 1 − RT (T − TΔj ,n ) ⎟+ LT ⎠ LT ⎝
vpj
pj , n +1
Fig. 4. Equivalent circuit of the PET
allows to “predict” the state of the system at the instant tn+1, if we assume constant the dc-link voltages vdc,pj and vdc,sj in the interval (tn, tn+1). Using the same equation referred to the interval (tn+1, tn+2), we can evaluate the unknown value of TΔ*j , n +1 , which has to be applied at the
V. CONTROL OF VSI GRID CONNECTED CONVERTER A mathematical model of multilevel PWM-converter is pointed out and described in [5]. The model formulation is generalized to “m” voltage levels. The mathematical model links currents and voltages of the supplying line to the currents and voltages in the dclink. The control technique, synthesized by the scheme shown in fig. 5, carries out the following tasks: • to force the line currents to be sinusoidal and in phase with the fundamental harmonic of the positive linevoltage sequence; • to keep constant the total dc-link voltages vo i ; In some cases the first two tasks could not be satisfied simultaneously: this occurs when the link load is unbalanced and/or when the three-phase grid voltages are unsymmetrical. A priority is needed in the selection of the task to be satisfied.
instant tn+1 in order to obtain at the instant tn+2 a current equal to the reference value at the instant tn, i.e.: i
pj , n + 2
vsj
= i*pj , n
The strategy used by the control technique is the following: one voltage is kept as a reference and the other one is shifted of the optimum time-delay TΔ*j ; the block “shifting selection” in fig.3 selects what voltage has to be fixed and what has to be shifted of TΔ*j , depending on the versus of the energy flux. If the value of the sampling frequency is properly chosen (taking into account the effective time-constants
Phase 1
L
VL,j
R
1, 2,3 → α , β
Active V.S.I.
iL,j
iL vL
Phase 3
C1,1
C3,1
C1,10
C3,10
s j,k
1, 2,3 → α , β
Phase 2
∑
PREDICTIVE CONTROL AND MODULATION
∑ vdc ,1
∑ vdc ,2
vdc ,3
* − * * − vdc − vdc vdc ,1 ,2 ,3 + + +
i*L Reference current computation
vL
PLL
Iˆ n e - jω t
I p e jω t
V p e jω t ˆ e - jω t V n
PL,1
REFERENCE CURRENT PL,2 SEQUENCES PL,3 COMPUTATION
Fig. 5. Block diagram of VSI grid connected converter
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PI PI PI
The input quantities of the block “predictive control and modulation” are: • α and β components in the stationary frame of the actual line voltages and currents symmetrical components; • actual dc-link voltages vo i ; • neutral voltages vni (reference value for these voltages is vn* = 0 ); • the reference current i *s . The input quantities of the block “predictive control and modulation” are: • α and β components in the stationary frame of the actual line voltages and currents symmetrical components; • actual dc-link voltages vo i ; • neutral voltages vni (reference value for these voltages is vn* = 0 ); • the reference current i *s . The reference current i *s is obtained by processing the powers PL,j, computed by the PI controllers of the dc-link voltages, as described in details in the following. In the 1st step, the powers PL,j are transformed in a current positive sequence with magnitude I sp* and a current negative sequence with magnitude I sn* and phase φn* by means of the equation
(
three phase cascaded H-bridge, 5-level, 1 MVA. Each Hbridge module is fed by 22 arrays of 48 series-connected photovoltaic modules. Each module has a maximum power of 175 W at irradiation of 1000 W/m2 and temperature of 25°C. On the high voltage side of the transformer, it was considered a three phase cascaded H-bridge, 21-levels. The control sampling frequency is fp= 2 kHz and determines a square voltage waveform with a frequency equal to 1 kHz. The grid connected converter is controlled with a sampling frequency equal to 10 kHz: this allows the currents injected in the grid power systems to be practically sinusoidal. In Fig. 6 can be easily seen that the control quickly tracks and holds the MPP with an oscillation
