Generalized Direct Power Control for Grid Connected ... - IEEE Xplore

Generalized Direct Power Control for Grid Connected Multilevel Converters Sebastián Rivera1 , Samir Kouro2 , Patricio Cortés1 , Salvador Alepuz3 , Mariusz Malinowski4 , Bin Wu2 and José Rodríguez1 1 Dep.

of Electronics Engineering, Universidad Técnica Federico Santa María, Valparaiso, Chile, [email protected]

2 Dep.

of Electrical and Computer Engineering, Ryerson University, Toronto, Ontario, Canada, [email protected]

Abstract—This paper presents a generalized direct power control (DPC) scheme for grid connected multilevel converters. The proposed method extends the original DPC operating principle by considering only for selection the closest vectors to the present switching state. This approach requires the power derivatives for feedback, which can present numerical implementation problems in real time. Therefore a grid virtual flux based observer is proposed to overcome this issue. The proposed method is applicable to any multilevel converter topology of any number of levels. In this paper simulations results are presented for a 9 level cascaded H-bridge converter. The proposed solution enables DPC for multilevel converters used in medium voltage applications while improving overall power quality and efficiency of the system. Index Terms—Direct power control, multilevel converters, grid connection.

I. I NTRODUCTION Currently, there is an increasing need for higher power levels for grid side connected converters. One of the reasons is that renewable energy power conversion systems are reaching higher power levels into the multi-megawatt range [1]. In addition, new grid codes for large wind power systems are demanding the power plant to contribute to support the power network, which together with the increase of the size of the wind turbine has set variable speed wind turbines with fully rated converter and synchronous generators as of the most suitable topologies [1], [2]. Since a fully rated converter is needed for this application, which in current commercial turbines reaches up to 3.5MW, the classic two level voltage source converter is at its limits of keeping up with the power level, the power quality, and maximum switching frequency. The latter is very important since power converters in the megawatt range cannot afford average switching frequencies above 1kHz to keep efficiency and heat dissipation at an acceptable level. The reduction in the switching frequency in two level converters will introduce necessarily lower order harmonics which affect the power quality and grid code compliance requirements [3]. A similar trend is starting in photovoltaic (PV) power conversion systems, where mainly due to the reduction in cost of PV modules among other factors has triggered several large PV based powerplants over 10MW [4], [5]. For PV system topologies, such as the centralized and multi-string, which concentrate all the connections into a single grid connected

978-1-4244-5697-0/10/$25.00 ©2010 IEEE

3

Dep. of Electronic Engineering, Technical University of Catalonia, Barcelona, Spain, [email protected]

4

Institute of Control and Industrial Electronics, Warsaw University of Technology, Warsaw, Poland [email protected]

inverter [6], these power plant will face the same challenges in terms of converter requirements as the wind power case. Not only renewable energy power conversion systems require high power rates at the grid side. Several high performance adjustable speed drive applications with regenerative operating conditions, such as train traction and downhill conveyors, require fully rated high power active front end rectifiers at the grid side, to enable an energy path back to the grid during regenerative braking [7]. The challenge to settle a trade-off between the high power rate, power quality and reduced switching frequency has been addressed in load side converters (mainly motor drives) with the use of multilevel converters [7], [8]. This is why there is an increasing interest to speed up the maturation process for the grid connection of multilevel converter topologies. However this imposes challenges (and opportunities) on the control scheme, since the extra degrees of freedom provided by these converters need to be taken into account. Traditionally voltage oriented control (VOC) [9], direct power control (DPC) [10], DPC with space vector modulation DPC-SVM [11], and Virtual Flux based DPC (VF-DPC) [12], [13], have been the main control schemes proposed to interface converters to the grid. Both, VOC and DPC-SVM can be easily extended for multilevel converters since the only difference is the modulation stage, which is changed to a multilevel modulation suitable for the topology and applications [7]. For DPC and VF-DPC the extension is not straightforward, since it is based on hysteresis controllers for active and reactive power whose outputs are directly linked to a specific voltage vector or switching state of the two level converter. Since the multilevel converter voltage vector number increases over-proportional to the number of levels, this approach cannot be applied. In [14] an extension has been done for a 3-level NPC multilevel converter. In this paper a multilevel DPC (ML-DPC) method is presented. It retains the attractive features of classic DPC: fast hysteresis active and reactive power controllers, and no need of power linear PI controllers and converter modulation stage. It also overcomes some of the main drawbacks of two level DPC: large power ripple due to the hysteresis controller. More important since it is based on the space vectors generated by the inverter, it can be applied to any multilevel converter topology with any number of levels. The motivation of the

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proposed method has been to find the analogy between direct torque control (DTC) and DPC (motor side and grid side respectively), of the multilevel DTC method developed in [15]. In order to test and analyze the performance of the method a 9-level cascaded H-bridge inverter (CHB) has been considered. CHBs have promising application field in active filters, FACTS and in large PV systems [16]– [18], since they do not require the complicated zig-zag transformer that they need for motor applications, and can operate with reduced switching frequency and reach higher voltages. The CHB could also be useful for multi-pole multi-winding wind turbines [2]. Nevertheless, the back to back NPC configuration for a variable speed wind turbine, or down-hill conveyor, or a train traction system [7], could be also considered and used with the proposed ML-DPC scheme. II. C LASSIC V IRTUAL F LUX D IRECT P OWER C ONTROL As in the Direct Torque Control (DTC) of an induction machine fed by a voltage source inverter, in which the torque and stator flux can be controlled by using a switching table, it is possible to obtain a similar Direct Power Control (DPC) scheme, to control the active and reactive power at the input of a grid connected voltage source converter [10]. Also the use of a virtual flux concept can be used to improve performance and eliminate grid voltage sensors [19], originating the Virtual Flux DPC (VF-DPC) [12]. To find the analogy, consider the three-phase vector equivalent circuit of the multilevel converter connected to the grid via the filter inductance Ls shown in Fig. 1. The grid can be seen as a virtual AC machine, whose line to line voltages are induced by a virtual air gap, i. e. that the integration of the supply voltage vector leads to a virtual flux vector Ψs . In the same way the integration of the converter voltage leads to a converter virtual flux vector Ψc , given by Ψs =

vs (t)dt

and

Ψc =

vc (t)dt,

(1)

where vs and vc , are the grid and converter voltage space vector respectively. On the other hand, the expression to obtain the active power is given by 3 ∗ (2) Re vs is . 2 By writing the supply voltage in terms of its virtual flux, by neglecting the voltage drop in the resistor Rs and replacing c , and using a dq reference frame the grid current by ΨsL−Ψ s orientated with Ψs , the active power can be expressed in terms of the virtual fluxes by P

P =

=

3ωs 3ωs Re jΨs (Ψs − Ψc )∗ = − ψsd ψcq . 2Ls 2Ls

(3)

In the same way, the reactive power can be expressed by

Fig. 1. Space vector equivalent circuit of grid connected multilevel converter.

Q=

3ωs 3ωs Im jΨs (Ψs − Ψc )∗ = ψsd (ψsd − ψcd ). (4) 2Ls 2Ls

Note that in (3) and (4) the quantities ψ are the scalar dq components of the vector Ψ, and ωs the grid frequency. Assuming that the virtual grid flux magnitude is kept constant (which is the case in an ideal voltage supply), from (3) and (4) it can be observed that the changes in both active and reactive powers are proportional to each one of the synchronous components of Ψc , hence ΔP ∝ −Δψcq

and

ΔQ ∝ −Δψcd .

(5)

Furthermore, by discretizing (1) via Euler with sample period Ts , the converter flux is related to the converter voltage by = Ψkc + vck Ts Ψk+1 c

⇒

ΔΨk+1 = vck Ts . c

(6)

By joining (5) and (6) it is clear that P and Q can be controlled generating the appropriate voltage vector in the converter. To find out how a specific voltage vector affects P and Q, the stationary αβ frame is divided into 12 sectors as can be observed in Fig. 2. The dq synchronous reference frame is aligned with the grid virtual flux Ψs , whose angular position in the αβ frame given by θs determines the sector in which the system is operating at a given time. As with DTC it is possible to define using (5) and (6) the influence of each voltage vector generated by the converter over P and Q for a specific sector. Figure 2 shows an example for sector 5. If voltage vector v3 is applied, according to (6), the component of the converter virtual flux ψcd would be larger, and ψcq would be negatively smaller, which according to (5) would reduce Q and P respectively. Hence if hP and hQ are the outputs of hysteresis comparators used to control P and Q respectively, the choice of v3 would be adequate for hP = 0 and hQ = 0. This example is listed together with all the other possibilities for all the other sectors in Table. I. Note that vectors v0 = v7 = 0 are also considered, since both lag the converter flux respect the grid flux. The later keeps rotating at ωs along with the synchronous frame, and therefore both zero vectors do affect P and Q. Since both vectors are equal in terms of voltage output, they are alternated to distribute evenly the usage of the switches of the converter.

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Finally Fig. 3 shows the classic DPC diagram for a 2-level VSC [10]. A proportional-integral linear controller (P I) is used to control the dc-link voltage vdc of the converter. The output of the controller is the active power reference P ∗ . For unity power factor reactive power reference is set to zero Q∗ = 0. Both powers are estimated from measurements for feedback, and the errors are controlled with hysteresis comparators. The outputs hP and hQ are used to access the voltage vector lookup table, along with the corresponding sector. The table has as outputs the gating signals that generate the corresponding TABLE I VOLTAGE VECTOR SELECTION TABLE FOR CLASSIC DPC. hP

hQ

1

2

3

4

5

0 0 1 1

0 1 0 1

v1 v2 v5 v0

v1 v2 v6 v0

v2 v3 v6 v7

v2 v3 v1 v7

v3 v4 v1 v0

Sector 6 7 v3 v4 v2 v0

v4 v5 v2 v7

8

9

10

11

12

v4 v5 v3 v7

v5 v6 v3 v0

v5 v6 v4 v0

v6 v1 v4 v7

v6 v1 v5 v7

6 7

5

8 4

30°

9

3

dQ 3ω dψcd =− . (7) ψsd dt 2Ls dt This means that the changes in P˙ and Q˙ are proportional to the changes in ψ˙ cq and ψ˙ cd respectively, i. e.

2

ΔP˙ ∝ −Δψ˙ cq , and

1

12

Fig. 2.

ΔQ˙ ∝ −Δψ˙ cd . vc3

Sectors division of the Stationary Frame for VF-DPC. Ls is

2L-VSC

vdc

DC AC

vdc

III. M ULTILEVEL D IRECT P OWER C ONTROL (ML-DPC) As it was shown in the previous sections, the active and reactive powers can be controlled using the voltage vector generated by the converter. This concept also applies to the vectors generated by a multilevel converter. However, to determine the influence of each one over P and Q for a particular sector and with such a simple controllers as the hysteresis comparator is not feasible. Nevertheless, it is possible to simplify the multilevel vector selection approach by limiting the vector selection to the closest vectors to the one previously applied. This approach not only reduces the complexity of the problem but it also reduces the amplitude of the dv/dts, and the number of commutations to only one per vector change. Figure 4 shows this concept for a generic multilevel converter, where for t = k an arbitrary converter voltage vector vck is shown with the surrounding closest vectors. The difference between the surrounding vectors and vck are the delta (Δ) vectors (Δvc1,...,c6 ). In other words, the control logic will be the same as in classic DPC, with the difference that now the influence of Δvc over P and Q needs to be obtained instead of vc . This can be obtained by differentiating the power expressions (3) and (4), which yields to 3ω dψcq dP =− , and ψsd dt 2Ls dt

10

11

voltage vector. A direct consequence of the operating principle of 2-level DPC, is that in the case of having more voltage vectors it becomes very difficult and even impossible to determine the influence of each vector over P and Q and associate them to the output of an hysteresis or non-linear based controller. Therefore another approach needs to be devised for multilevel converters.

PI

P

Q

hQ

vc1

vck

vk c

vs

hP

Grid

Switching table

vc2

vc4

vL

vc

(8)

vc5

vc6

Gating signals

Sector

Power and virtual flux voltage estimator

Fig. 3.

iabc

Classic 2-level VF-DPC control diagram [12].

vdc

Fig. 4. Space vectors generated by a generic multilevel converter, and the 2-level Δ vectors closest to vck .

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On the other hand, based on (1), the converter flux is related with the applied voltage by the converter by ˙ c = Δvc . ˙ c = vc =⇒ ΔΨ Ψ

(9)

This is an important relation, because it can be seen that the relation between the change in the applied voltage vector (Δvc ) and the slopes of the active and reactive power (P˙ and Q˙ respectively) is equivalent to the relation observed between vc and the power signals P and Q. For this reason, the same operating principle of classic DPC can be applied to multilevel converters, taking into account the influence of Δvc over P˙ ˙ This yields to the Δ vector selection look-up table and Q. given in Table II. It is worth mentioning that it is not possible to use the delta zero voltage vectors Δvc0 or Δvc7 in the proposed multilevel DPC algorithm. The reason for this lies in the fact that, in classic DPC, when the table selects a zero voltage vector (v0 or = Ψkc . v7 ), it means that vc = 0 and, according to (6), Ψk+1 c In other words, this selection lags the converter flux respect the source flux. This has a direct impact in the power signals because the source flux keeps rotating at ωs along with the synchronous d − q frame, reducing both components of the converter flux Ψc , thus increasing both active and reactive powers. Instead, in the proposed multilevel DPC method, the selection of a delta zero voltage vector does not necessarily means that vc = 0 and, according to = Ψkc + vck−1 Ts + Δvck Ts ,

Ψk+1 c

(10)

the converter flux maintains its previous rate of change and generally in the next sample period Ψk+1 = Ψkc . This is c the reason why the two delta zero vectors were replaced by delta active vectors that reduce both converter flux d and q components in each one of the 12 sectors, explaining the difference in the last line of Tables I and II where the analogy of classic DPC and multilevel DPC does not hold. Note that the table selects only the voltage vector variation (Δvck ) for a given time k. Hence, in order to compute the total vector vck that will be generated, the following relation has to be considered vck = vck−1 + Δvck .

(11)

In addition, the fact the we are now controlling P˙ and Q˙ (and P and Q are continuous variables in steady state), makes the use of hysteresis controllers not the best choice. Instead,

simple comparators can be used to see if the slopes need to be increased or decreased. The proposed ML-DPC scheme is illustrated in Fig. 5. The active power reference P ∗ comes from he dc-link voltage control loop. This loop will depend on the type of multilevel converter used (NPC, CHB or Flying capacitor) and has no direct relation with the proposed ML-DPC and therefore has been omitted in the control scheme of Fig. 5. The reactive power reference Q∗ is usually set to zero to achieve unity power factor, although it can be set to any value in case needed (for example to meet low voltage ride through requirements of wind power conversion [3]). Then the slopes P˙ ∗ and Q˙ ∗ are computed using a simple euler approach. The feedback for these variables are obtained from an observer that will be explained later in this paper. The errors are compared to zero with a simple comparator and the outputs are used to access the vector variation look-up table II. The selected Δ vector is then used to compute the vector to be applied according to (11). This vector is then generated by the multilevel converter. The grid current measurements and the applied vector are used to estimate the grid virtual flux vector. A PLL extracts the angle θs of the virtual flux, to access the look-up table with the proper sector. The grid and converter virtual fluxes together with the grid current are used to estimate the power slopes necessary for feedback with an observer. IV. P˙ , Q˙ AND Ψs OBSERVERS . The biggest technical challenge in changing from 2-level to multilevel DPC, is that there are power derivatives involved. Derivatives have a high-pass nature and would greatly amplify the current measurement noise up to a point it is not feasible in practical implementation. This problem can be solved by estimating P˙ and Q˙ with observers. From the equivalent vectorial circuit of Fig. 1, the following voltage equation holds dis . (12) dt Using the synchronous dq reference frame, oriented with Ψs , the current derivatives can be expressed by vs

= vc + Rs is + Ls

1 disd − vcd − Rs isd + ωs Ls isq , (13) = dt Ls disq 1 = vsq − vcq − Rs isq − ωs Ls isd . (14) dt Ls Under the assumption that the grid voltage is sinusoidal, the active and reactive power are proportional to each one of the

TABLE II Δ VOLTAGE VECTOR SELECTION FOR THE PROPOSED ML-DPC Sector hP

hQ

1

2

3

4

5

6

7

8

9

10

11

12

0 0 1 1

0 1 0 1

Δvc1 Δvc2 Δvc5 Δvc4












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Switching Table Grid

PLL

Power and derivatives observer

Fig. 5.

Control scheme of the proposed virtual flux based ML-DPC.

components of the grid current is . This idea can be extended and used to estimate the power derivatives dP dt dQ dt

= =

Virtual flux observer

3vsq vsq − vcq − Rs isq − ωs Ls isd , 2Ls 3vsq − vcd − Rs isd + ωs Ls isq . 2Ls

(15) (16)

With these observers the harmonic distortion possibly present in source voltages has a lower effect in the control system signals, improving overall performance. In addition, there are no derivative implementation problems and since it is estimated using only the voltage generated by the converter and the measurement of the line currents, there is no need of extra grid voltage sensors.

This way of obtaining P˙ and Q˙ is feasible in practice, since no real derivations are performed. It is important to mention the fact that this method of estimating the slopes of active and reactive power is very sensitive to disturbances in the supply voltage (mainly harmonics), because of the simplifications assumed. A solution to this problem is to use a PLL to retrieve only the fundamental component of this voltage or make the estimation in terms of the virtual fluxes. Due to the low pass nature of the integrator used to observe this fluxes, the disturbances are attenuated. Performing the same steps from (12) to (16) but considering the grid virtual flux in dq reference frame yields to

V. DC- LINK VOLTAGE CONTROL

As mentioned before the dc-link voltage control loop is responsible of providing the active power reference P ∗ . Since the different multilevel converter topologies have different dc-link configurations, this external control loop will vary depending on which converter is used. Since this external control loop has no direct relation with the ML-DPC scheme presented in this work, they will not be addressed in full detail in this paper. The easiest to control is the NPC multilevel converter. The total dc-link voltage is measured and fed-back to control with a single PI controller. The control of the neutral point (or dc-link voltage balance) can be performed easily with one of the many voltage balancing algorithms available in literature dψsq 3ωs dP = + ωs (ψsd − Ls isd ) − Rs isq − vcq (17) [7]. Most of them are based in selecting one of the redundant ψsd dt 2Ls dt voltage vectors to adjust the dc-link voltage unbalance. dψsd 3ωs dQ = + ωs (Ls isq − ψsq ) − Rs isd − vcd (18) ψsd A very similar approach can be used for the flying capacitor dt 2Ls dt multilevel converter. A central controller for the main dcThe terms in (17) and (18) related to Rs can be neglected link capacitor, and then a sub-algorithm based on vector due to its small value. In the same way the terms dψsq /dt redundancies to control each flying capacitor voltage to the and dψsd /dt, can also be neglected, since the grid flux in dq desired level. coordinates is constant even in presence of harmonics in the The cascaded H-bridge (CHB) is the most difficult to grid voltage, due the integral action (low pass nature) of the control, since all the H-bridges are connected to a separate grid virtual flux estimator. dc-link capacitor. Moreover the grid current flows trough all Note that the power and derivatives observer block in the the cells, since they are connected in series complicating even control scheme of Fig. 5 is composed by (3) and (4) to more the control method. Nevertheless, it is possible to control estimate P and Q, and by (17) and (18) to estimate P˙ and an overall dc-link voltage (sum of all the cells) with a unique Q˙ respectively. The virtual flux observer block of Fig. 5 is active power reference P ∗ and then perform the power sharing obtained by the integral of (12). according to a rotation in the use of the cells depending on

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PI

Gate signals

Dc-link voltage control loop for CHB multilevel converter of m

Symbol

Value

vˆs fs Ls Rs C vdc ∗ 4vdc ∗ R Ts

150 V 50 Hz 15 mH 0.1 mΩ 4700 µF 50 V 200 V 10 Ω 100 µs

7500

P P* Q

Power [W]

5000 2500 0

-2500 -5000 0.65 40

0.7

0.75

0.8

Current [A]

0.85

is(abc) vsa

20

1

0

0 -20 -40 0.65

-1 0.7

0.75

0.8

0.85

vca

200

VI. S IMULATION R ESULTS

0 -200 0.65 70

Voltage [V]

To study the performance of the proposed ML-DPC, a 9level 4-cell CHB multilevel converter has been considered. The main parameters used for the system are presented in Table III. To evaluate the performance of the virtual flux observer and the power derivatives observers used for feedback, measurement noise has been added to the currents in the simulation. Figure 7 shows the dynamic performance during a 100% load step at t = 0.7s, and an active load connection at t = 0.8s. During the load step the active power increases from 3 to 6kW, which can also be appreciated in the increase of the grid currents amplitude. Note also that the increase in the demand of current during the step has affected the dclink voltages, who have slightly reduced their value before the voltage control loop changes the active power reference and draw them back to 50V. The dc-link voltages have higher ripple at higher load since the current is also higher. The grid currents appear highly sinusoidal, mainly because of the multilevel voltage waveform provided by the converter with low harmonic distortion and reduced dv/dts. In addition the virtual flux and power derivatives observers are immune to the added measurement noise of the currents and even added harmonics to the grid voltages. The reactive power remains constant at zero, even throughout the dynamic behavior of P . This shows that both quantities are well decoupled by the control scheme and can be controlled separately.

Parameter Grid voltage amplitude Grid frequency Input filter inductance Input filter resistance DC-link capacitance DC-link voltage reference per cell Total DC-link voltage per phase Load resistance Sample time

Voltage [pu]

their imbalance. Similar approaches of this idea have been applied in [18], [20]. In Fig. 6 the outer dc-link voltage control loop for a CHB of m cell can be observed. The dc-link reference voltage for each ∗ . Since its a three phase converter and there are m cell is vdc cells it is considered 3m. It has been passed trough the square function to keep linearity with respect power quantities, and facilitate the PI controller design. For feedback each dc-link voltage vji is measured (where j is the phase a, b or c and i the number of the cell), and they are squared and then added. In this way all the dc-link voltages are considered for a unique active power control reference. The way in which this active power is shared among the cells to control possible unbalance between cells is performed after the vector selection by using a simple control logic that rotates the cells in the generation of the voltage vector. Since the cells are connected in series, there is no difference in generating a voltage level with different combinations of cells (voltage level redundancy).

Voltage [V]

Fig. 6. cells.

ML-DPC

TABLE III S IMULATION PARAMETERS

CHB multilevel converter

0.7

0.75

0.8

0.85

vdc* va(1234)

60 50 40 30 0.65

0.7

0.75 Time [s]

0.8

0.85

Fig. 7. ML-DPC dynamic performance for a 100%load step a t = 0.7s and an active load connection at t = 0.8s. a) Active and reactive power, b) grid currents and phase a grid voltage, c) Converter phase voltage and d) Converter dc-link voltages of phase a.

Note that when the active load is applied (for example PV strings or a regenerative drive application), the active power goes from positive to a negative value, injecting power to the grid. This is equivalent to a motor speed reversal in DTC, but now in DPC. The currents change their phase, and are in exact 180 degrees displacement with the grid voltage, achieving unitary power factor as well. They remain highly sinusoidal even during the phase change. Note that the dclink voltages increase their value when the active load is connected. Nevertheless they quickly return to 50V after the transient given by the external PI dc-link voltage controller. In addition all the dc-link voltages remain controlled thanks to

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grid can also be appreciated, and they do not affect the system performance, since they do not appear in the estimated virtual flux.

Voltage [V]

200 100 0 -100

VII. C ONCLUSION

-200

Voltage [V]

0.65 500

0.655

0.66

0.655

0.66

0.665

0.67

0.675

0.665

0.67

0.675

250 0 -250 -500 0.65

Time [s]

Fig. 8. Steady state converter voltages: a) phase voltage, b) line-line voltage. 1

20 0

0 -20 -40 0.65

0.66

0.67

0.68

0.69

Voltage [pu]

Current [A]

40

-1 0.70

Time [s]

Fig. 9. Steady state input current and grid voltage of phase a including added harmonic distortion.

the swapping control logic that shares the power according to the unbalance among them (only dc-link voltages for phase a are shown). Both, active and reactive power show extremely low ripple compared to classic 2-level DPC control schemes. This is due to the reduced dv/dts and consequently low ripple in the current achieved with the multilevel voltage generated by the converter. The phase a converter voltage can be appreciated during the dynamic responce in Fig. 7 and in steady state in Fig. 8. In the later the line-line voltage is also shown. Note that the stepped multilevel waveform is generated without any type of modulators and that it has very low switching frequency. In fact the device average switching frequency is 700Hz, which is suitable for megawatt range applications. This is not achievable with a two level converter, where higher switching frequencies are necessary to obtain similar results (although with higher dv/dts, higher current ripple, and hence power ripple). The closest vector selection operating principle can be appreciated in the converter phase voltage, where all 9 levels are visible, with only one-level transitions, reducing the dv/dts as expected. The grid currents are shown together with phase a grid voltage to show the proper synchronization achieved with the virtual flux approach, even here no grid voltage measurement is performed. This can be seen in the dynamic responce of Fig. 7 and in steady state in Fig. 9. In addition the 5th (5%) and 7th (2.5%) harmonics added to the phase voltage of the

A generalized multilevel DPC method has been proposed. Since it is based on the voltage vectors generated by the converter, it can be applied to any multilevel converter topology. This enables the use of DPC for existing grid connected multilevel applications and those to come. Because of the larger number of vectors available, it is possible to improve the power quality and also reduce the switching frequency of the semiconductor devices. The main reason for this lies in the fact that the multilevel converter represents a much richer actuator than two-level converters and, because of this, the active and reactive power tracking is smoother and its ripples are reduced. The use of the grid virtual flux approach instead of direct grid voltage measurement, improves the results for systems connected to polluted grids. In addition, the use of observers to determine the power derivatives enables practical implementation, even in presence of measurement noise. Since renewable energy power conversion systems, such as state of the art wind-turbines and large photovoltaic farms are now in the megawatt range, the use of multilevel converters and the proposed ML-DPC scheme can introduce power quality and efficiency improvements compared to the existing 2-level VSC solution. ACKNOWLEDGMENT The authors gratefully acknowledge financial support provided by FONDECYT under grant no. 1080582, by Ryerson University, and by Universidad Técnica Federico Santa María. In addition work of M. Malinowski has been supported by the European Union in the framework of European Social Fund through Center for Advanced Studies Warsaw University of Technology.

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R EFERENCES [1] O. Anaya-Lara, N. Jenkins, J. Ekanayake, P. Cartwright, and M. Hughes, Wind Energy Generation: Modelling and Control. Wiley, September 2009. [2] J. Carrasco, L. Franquelo, J. Bialasiewicz, E. Galvan, R. PortilloGuisado, M. Prats, J. Leon, and N. Moreno-Alfonso, “Power-electronic systems for the grid integration of renewable energy sources: A survey,” IEEE Transactions on Industrial Electronics, vol. 53, no. 4, pp. 1002–1016, August 2006. [3] “Grid code - high and extra high voltage,” E.ON Netz Gmbh, April 2006. [4] Renewable Energy Policy Network for the 21st Century, “Renewables global status report–2009 update,” available at http://www.ren21.net/publications, 2009. [5] pvresources.com, “Large-scale photovoltaic power plants: ranking,” available at http://www.pvresources.com/en/top50pv.php. [6] S. B. Kjaer, J. K. Pedersen, and F. Blaabjerg, “A review of single-phase grid-connected inverters for photovoltaic modules,” IEEE Trans. on Industry Applications, vol. 41, no. 5, pp. 1292–1306, September/October 2005. [7] J. Rodriguez, L. G. Franquelo, S. Kouro, J. I. Leon, R. Portillo, M. A. Prats, and M. Perez, “Multilevel converters: an enabling technology for high power applications,” Proceedings of the IEEE, vol. 97, no. 11, pp. 1786–1817, November 2009.

[8] J. Rodríguez, S. Bernet, B. Wu, J. Pontt, and S. Kouro, “Multilevel voltage-source-converter topologies for industrial medium-voltage drives,” IEEE Transactions on Industrial Electronics, vol. 54, no. 6, December 2007. [9] M. Malinowski, M. P. Kazmierkowski, and A. M. Trzynadlowski, “A comparative study of control techniques for pwm rectifiers in ac adjustable speed drives,” IEEE Transactions on Power Electronics, vol. 18, no. 6, pp. 1390–1396, November 2003. [10] T. Noguchi, H. Tomiki, S. Kondo, and I. Takahashi, “Direct power control of PWM converter without power-source voltage sensors,” IEEE Trans. on Ind. Appl., vol. 34, no. 3, pp. 473–479, May/June 1998. [11] M. Malinowski, S. Sty´nski, W. Kolomyjski, and M. P. Kazmierkowski, “Control of three-level pwm converter applied to variable-speed-type turbines,” IEEE Transactions on Industrial Electronics, vol. 56, no. 1, January 2009. [12] M. Malinowski, M. P. Kazmierkowski, S. Hansen, F. Blaabjerg, and G. D. Marques, “Virtual-flux-based direct power control of three-phase pwm rectifiers,” IEEE Transactions on Industry Applications, vol. 37, no. 4, pp. 1019–1025, July/August 2001. [13] D. Zhi, L. Xu, and W. Bary, “Improved direct power control of grid connected dc/ac converters,” IEEE Transactions on Power Electronics, vol. 24, no. 5-6, pp. 1280–1292, 2009. [14] J. Eloy-García, S. Arnaltes, and J. L. Rodríguez-Amenedo, “Extended direct power control for multilevel inverters including dc link middle point voltage control,” IET Electronic Power Applications, vol. 1, no. 4,

pp. 571–580, 2007. [15] J. Rodríguez, J. Pontt, S. Kouro, and P. Correa, “Direct torque control with imposed switching frequency in an 11-level cascaded inverter,” IEEE Trans. Ind. Electron., vol. 51, no. 4, pp. 827–833, August 2004, Special Section on DTC. [16] O. Alonso, P. Sanchis, E. Gubia, and L. Marroyo, “Cascaded h-bridge multilevel converter for grid connected photovoltaic generators with independent maximum power point tracking of each solar array,” in in Proc. 34th Annu. IEEE PESC, vol. 2, June 2003, pp. 731–735. [17] E. Villanueva, P. Correa, J. Rodriguez, and M. Pacas, “Control of a single-phase cascaded h-bridge multilevel inverter for grid-connected photovoltaic systems,” IEEE Transactions on Industrial Electronics, vol. 56, no. 11, pp. 4399–4406, November 2009. [18] S. Kouro, A. Moya, E. Villanueva, P. Correa, B. Wu, and J. Rodriguez, “Control of a cascaded h-bridge multilevel converter for grid connection of photovoltaic systems.” Porto, Portugal: 35th Annual Conference of the IEEE Industrial Electronics Society (IECON09), November, pp. 1–7. [19] M. Weinhold, “A new control scheme for optimal operation of a threephase voltage dc link pwm converter,” June 1991, pp. 371–383. [20] J. I. Leon, S. Vazquez, S. Kouro, L. G. Franquelo, J. M. Carrasco, and J. Rodriguez, “Unidimensional modulation technique for cascaded multilevel converters,” IEEE Transactions on Industrial Electronics, vol. 56, no. 8, pp. 2981–2986, August 2009.

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