XIX International Conference on Electrical Machines - ICEM 2010, Rome
A High Performance Control Technique of Power Electronic Transformers in Medium Voltage Grid-Connected PV Plants G. Brando, A. Dannier, A. Del Pizzo, R. Rizzo
Φ Abstract -- With reference to medium-voltage gridconnection of large photovoltaic (PV) plants, the paper proposes and analyses a high performance solution based on a power electronic transformer (PET). It Includes dc-links and multilevel converters either in low-voltage or in high-voltage side, and a medium-frequency (MF) transformer. Together with the very reduced sizes of the whole conversion apparatus, an important feature of the proposed topology is the permitted presence of unbalanced voltages on the different dc-links corresponding to the partitions of the PV plant. This is enabled by the multilevel cascaded H-bridge configuration of the lowvoltage side converter, in order to take into account the nonuniform distribution either of temperature or (mainly) of solar radiation on the different cells arrays, together with eventual different kind or age of used cells. another advantageous feature is the good level of power quality indexes on grid quantities, ensured by a multilevel NPC front-end: mainly low values of either harmonic distortion, or voltage and current dissymmetry. this occurs even if the commutation frequency of the switching devices of this converter is not high (1÷2 kHz). However, the paper is mainly focused on the control technique of the multilevel converters connected to the primary and secondary windings of the MF transformer, imposing multistep- or square-wave voltages. Some simple control algorithms are presented in order to maximize the power generated by every partition of the plant (also in unbalanced operations) together with the minimization of the joule losses of the central conversion unit in quasi-stationary operating conditions.
I
I.
INTRODUCTION
N the last years Distributed Generation (DG) is a more and more growing approach for providing electric energy in power systems, preferably using renewable sources. As it is known, a well established and widely used technology is based on photovoltaic (PV) electric energy generation. The grid-connection of PV plants (in low or in medium voltage) is always made by means of static converters, whose architecture and control influence performance and efficiency of energy conversion. Among the different available solutions, the ones based on power electronic transformers (PET) appear particularly interesting, especially in case of large power plants, which need to be connected to medium voltage (MV) grid. Practically PET is an isolated medium-frequency (MF) link ac/ac converter, that substitutes a conventional transformer and is able to perform some power quality functions, using power electronics on primary and secondary sides of the MF transformer. Really, conventional transformers are highly reliable, relatively inexpensive and rather efficient; however, they have some disadvantages which are becoming increasingly
Α
G. Brando, A. Dannier, A. Del Pizzo, R. Rizzo are with the Department of Electrical Engineering, University of Naples Federico II, Naples, Italy (email:
[email protected]).
978-1-4244-4175-4/10/$25.00 ©2010 IEEE
important in power distribution systems. Among them we can underline heavy weight and large sizes, voltage drop under load, need of protection against either short-circuits or overloads or over-voltages, sensitivity to harmonics, low performance under load unbalance or in presence of dcoffset, environmental concerns regarding mineral oil. [1,2] Moreover modern grids need the presence of components (like active filters or FACTs) to improve quality of the distributed energy. PET can overcome many of these drawbacks and is better suitable for the optimization of power flows, by means of addition to the MF transformer of proper multilevel converters in multistage configuration. In the technical literature we can find several conversion topologies using PET, together with different control strategies. [3] However, they can not be immediately and suitably applied in the field of large PV plants. In fact, in this case, the presence of PV modules having different characteristics, the deviation of the main parameters from the nominal values, the different ageing (decay) curves of the used modules, the different exposure of the arrays to the sun irradiation, the eventual damaging of some modules or arrays can cause unbalanced power flow among groups of arrays in the plant. In order to maintain the operating point of every cells-array around the correspondent maximum power point it is necessary to activate several independent MPPT (maximum power point tracking) controls and to ensure separate different dc-link voltages; this can be efficaciously made using a dc/ac multilevel converter, with cascaded H-bridge topology. It allows us to obtain an ideal parallel of several circuits without a physical parallel connection of them. Moreover, intrinsic fault-tolerant characteristics of cascaded H-bridge converters can be profitably exploited in order to ensure the service dependability, also in case of faults in the power devices. On the other hand, good values of some grid power indexes can be obtained using multilevel converters, e.g. in neutral point clamped (NPC) configuration, for the grid-connection (active front-end) in medium voltage (20 kV) Obviously, an important role is played by the interlaced control strategy of both converters (the one interfaced to PV arrays on lowvoltage side, and the one interfaced to the grid) which are connected to primary and secondary windings of the MF transformer. Simplicity, effectiveness and high-resolution of the control are important aspects which can strongly improve performance of PET and, consequently of the energy conversion. These features are the main objective of the innovative high-performance control technique presented in the paper. The proposed control technique is based on algebraic equations derived from a properly simplified mathematical model of the considered system and has the aim to define the optimised delay between primary and secondary voltages (which have different time-waveforms) in order to obtain the instantaneous demanded power,
ensuring fast dynamic response and maximization of the power/current ratio. II.
PET CONFIGURATIONS
We refer to a large PV plant that is partitioned in some sections (N) in order to take into account possible different solar exposures and temperatures. If the plant total power requires a grid-connection in MV, a PET with appropriate converter topology either in low (LV) or in high voltage (MV) side could be conveniently taken into consideration. Possible configurations could be the ones in fig.1, which use a cascaded H-Bridge multilevel dc-ac converter on LV side with a separate dc-link for each section of the PV plant. The MF transformer configuration is three-phase in fig.1a and single-phase in fig.1b. These architectures allow different voltages on the dc-links; thus, implementation of separate MPPT control algorithms can be carried out for the different PV sections. The high-voltage windings of MF transformer are interfaced to the MV grid by means of a multilevel converter composed by a rectifier (three-phase in fig.1a, single-phase in fig.1b) and a three-phase inverter. Cascaded H-bridge or NPC topology could be considered for this converter; the
number of voltage levels is selected according to the rated grid-voltage and to the characteristics of the used switching devices. In the paper a configuration like the one of fig.1b is preferred, due to a greater simplicity and also considering that the solution of fig.1 could be really applied only when the number of sections N is equal to 3 or a multiple. In addition fig.2 shows a PET configuration similar to the one in fig.1b; the converter on MV side is composed by a NPC single-phase rectifier and a NPC inverter. The needed number of voltage-levels is the same of the one in fig.1b; only due to simplicity reasons, the converter represented in fig.2 is a 3-level NPC. III. MATHEMATICAL MODEL We consider the converter architecture of fig.3, which represents the same power electronic circuit of fig.2 as a block-diagram. A dc-ac converter on LV-side is considered with N singlephase H-Bridge inverters, each one corresponding to a sector of the PV-plant. The quantities vdc,h (with h=1, 2, .., N) are the voltages of the different dc-links, while the quantities vp,h are the corresponding output voltages. MV Rectifier-Inverter
MV Rectifier-Inverter H-Bridge - 1stmodule
is1
LV Inverter
H-Bridge – 1st module
(a)
(b)
vdc ,1 i p1
PV
LV Inverter
v p1
vdc,1
vs1
MF
Transformer H-Bridge - 10th module
vdc,2
H-Bridge -10th module
PV
H-Bridge - 1st module
H-Bridge - 1st module
ip2 v p 2
iL1 RL
vdc,3 i p3 v p 3
LL vL1
iL 2
vL 2
iL 3
vL 3
iL1 RL LL vL1
vdc,2 O
vs
vp
PV
vs 3
iL 2
vL 2
iL 3
vL 3
O
vdc,3
PV H-Bridge - 10th module
H-Bridge - 10th module
PV
H-Bridge - 1st module
MF Transformers
GRID
GRID
vs 2 is 2
PV
H-Bridge – 1st module
is 3
H-Bridge - 10th module
H-Bridge – 10th module
Fig. 1. Two possible PET configurations for connecting large PV plants to MV grid with a three-phase (case a) or a single-phase (case b) MF transformer.
LV Inverter
MF Transformer
MV Rectifier-Inverter
LV Inverter
PV GRID
Ca
iL1 iL 2 iL 3
PV
RL LL v L1 vL 2 vL 3
PV
vdc,1
H-B1
MF Transformer
vp,1
MV Rectifier
ip
MV Inverter
O
vp
Cb
vs
GRID
iL1 RL
C1
NPC
NPC
singlephase
threephase
LL
vL1
iL 2
vL 2
iL 3
vL 3
O
CNs PV
PV
vdc,N
H-BN
vp,N
Fig. 2. PET configuration for PV plants with NPC rectifier+inverter on MV side (three voltage-levels only for design simplicity).
Fig. 3. Schematic representation of a PET with a N-level inverter on LV side (cascaded H-bridge) and a N’-level NPC converter on MV side.
Referring to a digital control with Ts sampling interval, the N H-bridge inverters are controlled in order to obtain the time-behaviours vp,k in fig.4: i.e., in the duty-cycle having width 2δk the voltage is assumed constant and equal to ±Vp,k , strictly dependent on the corresponding dc-link voltage. In the following, the different voltages vp,k are ordered from 1 to N for descending δk values, as shown in fig.4. The resulting primary voltage of MF transformer is expressed by:
The Δv values in the different subintervals of Ts are synthesized in Tab. I. vp,j Vp,2
Vp,3
∑
0
γ
where τ=Ts/2 is half sampling period, and 2δ1 is the largest dutycycle. One can demonstrate that (3) is a necessary condition to be satisfied in order to obtain optimized performance. vp,1 2δ1 t vp,2 Vp,2
2δ2
0
t
Ts
t
2δN Ts
vs
t
-Vs
a1 a3
a5
a4 a2
a0
Ts
Fig. 5. Primary and secondary voltages of the MF transformer in a sampling period. Sample case : N=3 TABLE I VALUES OF Δv VOLTAGES AND OF ip CURRENTS IN DIFFERENT SUBINTERVALS Subinterval
Δv
γ
Vs
λ
- Vs
αh
w
∑ V p,k
with: h=0,1, …, 2N-1
k =1
ip i0 + i0 +
iλ f +
− Vs
Vs t L
Vs (2γ − t ) L
N 1 ⎧⎪ N h ⎨ ∑ V p,k δ k + (−1) ∑ V p,k δ k + L ⎪k =1 k = q +1 ⎩
w ⎫⎪ − τ ∑ V p,k + [1 + (−1)h ]Vqδ q + Δv ⋅ t ⎬ ⎪⎭ k =1
By integrating (2), expressions of primary current ip are obtained for the different subintervals of Ts and are listed in the right column of Tab. I, with the following positions: iλ , f = i0 +
Vs ( 2γ − τ + δ1 ) ; L
q=
2h + 3 + (−1)h ; w = h +1− q 4
The power generated by the jth dc-link of the primary circuit has expression: 1 Pj = Ts
Ts
∫ v p, j i p d t = 0
V p, j Ts
τ +δ j
∫
ip d t =
τ −δ j
(4) N ⎧⎪ ⎫⎪ V p, j δ j Vs 1 V p,k δ k ⎬ = ⎨i0 + ( 2γ − τ ) + L L k =1 ⎩⎪ ⎭⎪ τ The steady-state value of Pj can be easily derived from (4) by imposing: ip
Vs
γ 0
-Vs
0
∑
vp,N Vp,N 0
t
Vs
v p,k
Moreover, the secondary voltage referred to the primary winding is vs; it has a rectangular time-behaviour in an interval 2Ts (see the lowest diagram of fig.4), considering that the voltage on the dc-link of the MV-side NPC-inverter can be assumed constant in short intervals. By referring all the quantities to the primary winding, the operations of the MF transformer are described by the simple differential equation: d ip (1) v p − vs = R i p + L dt if the magnetizing current and iron losses are neglected. In (1) R and L are the internal resistance and inductance of the transformer and ip the primary current. If we neglect the resistance R (to simplify the solutions), (1) can be rewritten as: d ip (2) Δv = v p − vs L dt This equation can be easily solved dividing the sampling interval Ts in (2N+2) subintervals where Δv is constant, as schematically shown in fig.5 in a simple case with N=3. If γ denotes the time-delay of the secondary voltage with respect to the primary one (see fig.5), we can assume: γ ≤ τ − δ1 (3)
0
Ts
τ =Ts/2 vs
k =1
Vp,1
2δ2 2δ3
λ
N
vp =
2δ1
Vp,1
t
T=2Ts
Fig. 4. Waveform -in one period T- of the primary voltages vp,j (j=1,...,N) and of the secondary voltage vs of the MF transformer.
t =Ts
= − ip t =0
→ i p,0 (Ts ) = − i0
(5)
On the basis of the expression of ip,h (with h=0) in tab.I, (5) allows the evaluation of i0: N ⎫⎪ 1 ⎧⎪ i0 = ⎨Vs (τ − 2γ ) − ∑ V p , j δ j ⎬ ; (6) L ⎪ ⎪⎭ j =1 ⎩ consequently, the jth steady-state power has expression:
Vs V p, j γ δ j π with: ω = and j = 1,...., N Ts ω L Ts τ
Pj = π
(7)
From the set of eq.s (7) the duty-cycles δ j can be evaluated as a function of the power Pj and of the delay-angle γ.
δj =
2 Pj
Ptot V p , j
⎛ ⎞ y ⎡⎣Vs (τ − 2γ ) − L i0 ⎤⎦ ⎜1 + ⎟ ⎜ 1 + 2 y +1 ⎟ ⎝ ⎠
(8)
where: y=
2τ L Ptot
N
Ptot = ∑ Pk .
;
[Vs (τ − 2γ ) − L i0 ]2
(8’)
k =1
The system (8) is composed of N equations with N+1 unknown quantities (δ1, …,δN, γ). Thus, an additional condition is needed in order to solve the system (8). We can exploit the presence of a freedom degree by imposing an optimizing criterion, like the minimization of rms value of the primary current ip, in order to efficaciously transfer the expected power from primary to secondary windings of the PET in fig.3. The minimization of ip,rms can be found by solving the equation:
d i p ,rms
=0
dγ
(9)
from which, the optimizing γ value is given by:
γ opt = τ − δ1
(10)
The analytical expression of ip,rms as a function of γ and of other parameters can be found with reference to subintervals where the resultant applied voltage is constant; however, for sake of simplicity, it is not shown here. Comparing (10) to fig.5, we deduce that the optimizing condition corresponds to λ=0. Substituting (10) in (8) with j=1, the duty-cycle δ1 can be evaluated and, in sequence, the quantities γ and δj (with j>1). IV. PET CONTROL TECHNIQUE On the basis of the considerations of the previous section, the control diagram of the PET in fig.3 can be the one represented in fig.6. The different vdc,j voltages (j=1,…N) of the H-bridge dcMF Transformer
vdc,j
LV Inverter
ip
vp
vs
MV Rectifier
Vs
αj H-Bridge Modulation
vdc,j
δj
ip
PET Control
Duty-cycles Computation
ip vdc,1
Vs
γ , δ1
Pj* MPPT Algorithm
NPC Modulation
Control Strategy
Vs
* 1
P
Fig. 6. Control diagram of the PET in fig.3
γ
Vs
links are detected and processed by the MPPT algorithm separately applied to each PV field. This MPPT block [8] evaluates the power reference values Pj* in order to operate at the maximum power of the PV fields. Such Pj* are obtained in the power circuit thanks to the action of the “PET control” which is mainly composed by two cascaded parts: “control strategy block” and “duty-cycles computation block”. On the basis of the dc-voltage (vdc,1) and the reference power ( P1* ) of the H-bridge having the largest δk value (with subscript “1” as previously described), by means of rel.s (8’)&(10) the “control strategy” block computes the δ1 dutycycle of LV inverter together with the delay angle γ between primary and secondary square voltages of the MF transformer. The “control strategy” block needs also the knowledge of the primary current ip and of the total dc-link secondary voltage Vs of the MV rectifier, which must be measured. The previously computed δ1 and γ values are the input of the block “duty-cycle computation” which is able to evaluate the remaining δj duty-cycles (with j=2,.., N) using eq.(8). As shown in fig.6, the “duty-cycle computation” block needs also the knowledge of ip, Vs, vdc,j and Pj* (with j=2, …, N). As final steps of the control, the block “H-bridge modulation” generates the command signals αj for the LV inverter on the basis of the duty-cycles values δj (with j=1, .., N). Separately, the block “NPC modulation” generates the commands for the MV rectifier. V.
NUMERICAL ANALYSIS
A numerical analysis has been carried out with reference to a PV-plant of 1 MW, that is divided in 10 fields, each one having a different irradiated power. The reference power and control circuits are the ones in fig.3 and 6. According to fig.3 a 10-level cascaded H-bridge inverter (N=10) is considered on low-voltage side, whose rated voltage is 800 V (10 x 80V). The a.c. grid is three-phase at 50 Hz, with a rated voltage of 20 kV. The operating frequency f=1/T of the MF transformer is assumed equal to 1 kHz; consequently, the control sampling interval is Ts=500 μs (from fig.4 we have T=2Ts). The numerical analysis has the aim to show the behaviour of the main electrical quantities of the PET in fig.3 either in balanced or in unbalanced operations. The results are shown in fig.s 7, 8 and 9. Initially (at the instant t=0) all the PV fields are assumed uniformly irradiated by a 1000 W/m2 power. The used MPPT algorithm is able to stabilize the different PV modules around the maximum power value in about 18 s. At the instant t=20 s we assume that the irradiating power starts to vary for two of the PV fields; in particular we suppose that the irradiating power of the two considered fields decreases linearly with a slope of -20W/m2s-1. For the first field (k=1) the irradiating power reaches the value 0.8 Pmax; for the second field (k=2) the value 0.6 Pmax (this situation corresponds to a reduction of 20% and of 40% of the irradiating power on the two considered PV fields). Fig.7A shows the behaviour of the
total power Ptot generated by the N fields which become unbalanced starting from t=20s, as previously described. Fig.7B shows the corresponding behaviour of the rms value of the resulting primary current ip. In both diagrams the quantities plotted are in p.u. values referred to the corresponding rated values in balanced operations. Diagrams in fig.8 show the time-behaviour of: - the p.u. power (fig.8A1) and the dc-link voltage (fig.8B1) of the generic PV field which works in rated operating conditions; - the p.u. power (fig.8A2 and A3) and the dc-link voltage (fig.8B2 and B3) of the fields operating in unbalanced conditions, respectively with -20% and -40% of the rated power. (A)
Ptot [p.u.]
1
ip,rms [p.u.]
(B)
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0 0
10
20
t [s]
30
40
50
0 0
10
20
t [s]
30
40
50
Fig. 7. Time-behaviour of the p.u total power generated by the PV fields (A) and of the p.u. rms value of the primary current (B).
Starting from the instant t=20s, from fig.s8A we observe a transient interval of about 10 s for the first field (k=1) and of about 20 s for the second field (k=2). Since the variation of the generated power is linear like the assumed variation of the irradiated power, we can deduce that the MPPT is able to ensure the maximum power also during transient conditions. From fig.8B2 and B3, we deduce that the dc-link voltages of the unbalanced PV fields reach values different from the rated ones, according to either the corresponding generated power or the irradiated power. With reference to steady-state operations, Fig.9 shows some time-behaviours of the primary current and of primary and secondary voltages. In particular reference is made either to balanced conditions (18
