Real-time implementation of finite control set model predictive control for matrix converter based solid state transformer

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 2 ( 2 0 1 7 ) 1 7 9 7 6 e1 7 9 8 3

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Real-time implementation of finite control set model predictive control for matrix converter based solid state transformer Yupeng Liu a,b,*, Wencheng Wang a, Yushan Liu b, Sertac Bayhan b,c a

College of Information and Electrical Engineering, China Agriculture University, 100083 Beijing, China Department of Electrical and Computer Engineering, Texas A&M University at Qatar, Qatar Foundation, 23874 Doha, Qatar c Department of Electronics and Automation, Gazi University, Ankara, Turkey b

article info

abstract

Article history:

Solid state transformer formed by back-to-back connection of two three-to-single-phase

Received 14 November 2016

matrix converter, so called MC-SST, owns aceac power conversion in a single stage and

Received in revised form

an absence of the bulky line-frequency transformer when linking ac sources of different

26 April 2017

voltage amplitudes and frequencies. Current modulation methods for this topology include

Accepted 28 April 2017

sophisticated computation of current and voltage vectors besides duty cycle composition.

Available online 1 June 2017

Moreover, extra control design is required to manage the power exchange. In this paper, the easy-to-perform finite control set model predictive control (FCS-MPC) for this type of

Keywords:

MC-SST is implemented in real-time platform and compared with the proportionalein-

Solid state transformer

tegral control strategy. The active power changes, different voltage amplitudes and phases,

Matrix converter

and parameter variations are investigated. Simulation and real-time implementation re-

Grid interfacing

sults demonstrate the simplicity and validity of the MPC approach for power management

Real-time implementation

of the MC-SST system. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction A solid state transformer (SST) replaces the traditional one by using a medium to high frequency transformer that significantly reduces the volume and weight of the magnetic components [1]. Besides the fault isolation and voltage amplitude regulation, the SST also provides bidirectional power flow, voltage frequency conversion, multi-terminal interfacing, and power factor correction that a traditional transformer does not have [1e3]. The SST has attracted considerable interests in applications for traction, renewable energy integration, and

smart grids thanks to the rapid development of power electronic technology in recent decades [4e6]. Numbers of control methods have been developed for the dual-active-bridge (DAB) based SST, including power management among modules, voltage balance under imbalanced loads, integration with renewable energy sources, stability analysis, and frequency control, etc. [2,7]. The DAB-SST comprises a high-voltage side acedc conversion formed by numbers of modules in series, an intermediate highfrequency isolated dcedc conversion, and a low-voltage side dceac conversion. Though the low-voltage dc link is easy to combine dc microgrid/loads, it brings in stability concerns due

* Corresponding author. College of Information and Electrical Engineering, China Agriculture University, 100083 Beijing, China. E-mail address: [email protected] (Y. Liu). http://dx.doi.org/10.1016/j.ijhydene.2017.04.293 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

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and generates a virtual dc link, which passes through the transformer in the form of a chopped HF ac. Then the secondary MC restores the virtual dc by rectifying the HF ac from the primary, and inverts it to match the load grid voltage. The source and load-grid voltages could be of different frequencies, phases, and voltage levels. In the following parts of the paper, we use bolded symbols to express vectors. In Fig. 1, the three-phase source-grid voltages Us, currents Is, and MCSST input voltages Ui represented by vectors are, respectively

to multiple power conversion stages and a number of component counts [8]. The single/three-to-single-phase matrix converter (MC) in back-to-back connection formed SST is capable of removing the energy storage capacitors, due to direct aceac power conversion [9e12]. It brings in more compact volume and higher reliability than the DAB-SST, and has a great potential in lifetime increase, space saving, and efficiency improvement. The three-to-single-phase MC-based SST has less component counts than that of single-to-single-phase MC based one. However, similar to a traditional MC when using the traditional space vector pulsewidth modulation (SVPWM), the much complicated voltage and current vectors computation and duty cycle synthetization may hinder its wide spread applications [13,14], even though the indirect vector control based SVPWM was developed to simplify the vectors computation and duty cycle composition [11,12]. Additional control loops are inevitable for the power management and voltage regulation using the SVPWM [15,16]. A finite control set model predictive control (FCS-MPC) was presented for this SST serving standalone loads or grids [17,18]. The MPC is an efficient method in power management and power electronics control, owing to its fast dynamic responses and accurate tracking ability [18e25]. In this paper, the main contribution is to investigate the FCS-MPC of the MC-SST system in real time and compare it with the traditional proportionaleintegral (PI) control. The paper focuses on following contents: Section “MC-based SST” introduces the mentioned MC-SST system [16e18]; Section “PI control of the MC-SST” addresses the traditional PI control of it [16]; Section “FCS-MPC of MC-SST” details the FCS-MPC of the MC-SST [18]; Section “Simulation and real-time implementation results” illustrates simulation and real-time implementation results; finally, Section “Conclusion” concludes this work.

In (3) and (4), Skj 2 {0, 1} represents the on-off state of power switches; subscript k 2 {a, b, c} represents the primary three phases, or k 2 {A, B, C} represents the secondary three phases; subscript j 2 {1, 2} represents the upper or lower bridge arm of the two three-to-single-phase MCs in Fig. 1.

MC-based SST

PI control of the MC-SST

Fig. 1 displays the discussed three-to-single-phase MC-based single-stage SST system [18]. Two different power grids are connected by an n:1 transformer operating at a high frequency (HF). The primary side three-phase ac source represents the source grid side, and that at the secondary represents the load grid. Firstly, the primary MC draws power from the source grid

The closed-loop PI control of the MC-SST system proposed in [16] is recalled here, as the block diagram of Fig. 2 shows. The control comprises the transformation between the static three-phase abc coordinates and the rotary two-phase dq coordinates, acquisition of grid voltage phase angle by Phase Locked Loop (PLL), and PI controllers.

Sa1

usa i sa

Lf

ua

ia

Sb1

a

Cf

usc T ; Is ¼ ½ isa

usb

isb

T

isc  ; Ui ¼ ½ ua

ub

uc T (1)

Similarly, the output currents Io and voltages Vg in the load grid side are written as Io ¼ ½ ioA

ioB


T ioC  ; Vg ¼ vgA

vgB

vgC

T

(2)

The virtual dc-link voltages and currents of the two MCs to the primary side could be represented as [17] Vdc ¼ ½ Sa1  Sa2 idc ¼ ½ SA1

SB1

Sb1  Sb2

Sc1  Sc2 $Ui ;

(3)

SC1 $Io =n

Then the input current vector and output voltage vector can be acquired from (3) as 2 3 2 3 3 2 3 Sa1  Sa2 SA1  SA2 voA ia Vdc Ii ¼ 4 ib 5 ¼ 4 Sb1  Sb2 5$idc ; Vo ¼ 4 voB 5 ¼ 4 SB1  SB2 5$ n Sc1  Sc2 voC SC1  SC2 ic 2

(4)

Sc1

SA1

+ vp c –

b Source Grid

Us ¼ ½ usa

n:1

SB1

SC1

ioA Lg

+ A voA vs B –

vga

C Load Grid

Sa2

Sb2

Sc2

SA2

Fig. 1 e Topology of discussed MC-SST.

SB2

SC2

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CSR

VSI

n:1 LC filter

3

3

Forward Direction of Active Power

Io 6

SVPWM dq

Iqr=0

dq abc

6

Iqf

PLL θ

abc

PI

+

-+

dq

Vd

Then the PI controller outputs are transformed to the threephase abc frame to perform the SVPWM of the MC-SST [14].

FCS-MPC of MC-SST

abc

Po*

Idr

×

PI

-

Idf

Vg

2/3

3

Load Grid

Lg

÷

Source Grid

The FCS-MPC for the MC-SST includes predicting the state variables by discrete model, defining the cost function, choosing the optimal switching state, and compensating the discrete delay [18].

Discrete predictive model

Idr

As Fig. 1 shows, the input side of the MC-SST contains an inductance-capacitance (LC) filter. Then a state-space model representing the source side with state variables ui and Is is obtained as [18]

Fig. 2 e Block diagram of traditional PI-regulator-based control [16].



The dq transform obtains the direct-axis, quadratic-axis, and zero-sequence components in the rotary two-phase reference frame. Using the transform of grid voltage as an example, there are Vd ¼

     2 2p 2p vga sinðuo tÞ þ vgb sin uo t  þ vgc sin uo t þ 3 3 3 (5)

     2 2p 2p vga cosðuo tÞ þ vgb cos uo t  þ vgc cos uo t þ Vq ¼ 3 3 3 (6) V0 ¼ vga þ vgb þ vgc

(7)

Through this qualitative change, the Vd and Vq represent the Vg in static two-phase coordinates of the positive-sequence component. The transfer function of PI controller can be written as  GðsÞ ¼ Kp þ Ki =s

(8)

In digital implementation in time domain, there is  uðkÞ ¼ Kp þ Ki eðkÞ  Kp eðk  1Þ þ uðk  1Þ

(9)

where u(k  1) and u(k) denote the control variable in the previous and present sampling time, respectively; Kp and Ki denote the proportional and the integral gains, respectively; e(k) denotes the error between the command and measured variable. It is performed in each sampling time Ts. The PLL is used to detect the phase angle of the load grid voltage for the dq-abc transformation. The MC-SST output currents and load grid voltages are transformed to the dq frame. Then the transformed grid-tie currents Io are delivered to the PI controllers in d-axis and q-axis, respectively. The daxis current reference Idr is obtained by the active power reference divided by the d-axis voltage Vd; and the q-axis current reference Iqr is zero to force interfacing at a unity power factor. Therefore, the PI controllers regulate their outputs, in order to minimize errors between the references and feedbacks.

_i U I_ s





    0

1 C

f $ Ui þ 0 1 Lf Rf Lf Is 1 Lf     Ui Us ¼ A$ þ B$ Is Ii ¼

   U 1 Cf $ s 0 Ii (10)

where Rf, Cf, and Lf denote the source grid side internal resistance, capacitance, and filter inductance, respectively. Then by the general forward-difference Euler formula to (10), the discrete state-space model is further derived as [24,25] 

     U ðkÞ U ðkÞ Ui ðk þ 1Þ ¼ F$ i þ G$ s Is ðk þ 1Þ Is ðkÞ Ii ðkÞ

(11)

where F ¼ eATs , G ¼ A1 ðF  I22 ÞB, and Ts denotes the sampling period. Similarly, with the inductor filter at the load grid side, the discrete model of load-grid currents is obtained as

Io ðk þ 1Þ ¼

   Rg Ts Ts
Io ðkÞ Vo ðkÞ  Vg ðkÞ þ 1  Lg Lg

(12)

where Lg and Rg denote the load-grid filter inductance and internal resistance. Note that an LC filter is also applicable to the load grid side, except to establish the model accordingly. In addition, from the operating principle mentioned above, the LC filter design of a conventional matrix converter could be used to this type of MC-SST [26].

Definition of cost function and selection of switching state The aim of the MC-SST which was discussed is to stabilize the active power at load side according to the required frequency and amplitude of the grid voltage. Furthermore, the input side unity power factor is still expected. Then, at the end of the sampling period, a cost function is defined by the prediction of MC-SST output currents Io closest to the references I*o . Additionally, the instantaneous reactive power in the input side of the MC-SST must be minimized [25]. Hence, we define the cost function as gðk þ 1Þ ¼ Di2o ðk þ 1Þ þ lDq2s ðk þ 1Þ

(13)

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Firstly, simulation studies are conducted to a 20-kW MC-SST system by MPC, in cases of active power value and direction changes and different phases between the two grids. Furthermore, MPC of the MC-SST system is implemented in dSPACE1006 real-time implementation platform and compared with the PI control in Fig. 2, which is the final step before testing the prototype benefiting to validating the strategy and protect the hardware. Table 1 lists the system specifications, where the 0.1 U internal resistance includes the filter resistance and the line resistance in distribution network. Figs. 3e5 show simulation results and Figs. 7 and 8 show real-time implementation results.

Simulation results Case I: active power value and direction changes Active power change and bidirectional power flowing of the MC-SST are observed under the designed MPC. Fig. 3 shows the results when P*o changes from 18 kW to 10 kW at t ¼ 0.04 s, i.e., the active power decreases and the power flowing changes from forward to reverse direction. Fig. 3(a) shows source-side grid voltage usa and load-side grid voltage vgA in phase A; Fig. 3(b) shows the active power Po and reactive power Qo at the coupling point of the MC-SST with the loadside grid; Fig. 3(c) shows three-phase grid interfacing currents io{A,B,C}; Fig. 3(d) shows one phase of reference and actual grid interfacing currents (phase B as an example); and Fig. 3(e)

Table 1 e System specifications. Parameters Power rating of load-side grid, Pm Turns ratio of the HF transformer, n RMS voltage of load-side grid RMS voltage of source-side grid Fundamental frequency, f0 Filter inductance of source-side grid, Lf Filter capacitance of source-side grid, Cf Internal resistance of source-side grid, Rf Filter inductance of load-side grid, Lg Internal resistance of load-side grid, Rg

Values 20 kW 2.45 400 V 1.1 kV 50 Hz 5 mH 10 mF 0.1 U 3 mH 0.1 U

Usa & Vg A (V)

vgA 0

0.02

20 10 0 -10 -20

0.04 t (s)

0.06

0.08

Po Qo 0

0.02

0.04 t (s)

0.06

0.08

(b) 40 20 0 -20 -40

40 20 0 -20 -40

ioB

ioA

0

ioB

ioC

ioC

ioA

0.02

0.04 t (s) (c) ( )

0.06

0.08

0.02

0.04 t (s)

0.06

0.08

ioB

ioB*

0

(d) Mag (% of Fundamental)

Simulation and real-time implementation results

usa

(a) ( ) Po ( k W) & Qo ( k VA)

where ioa and iob denote the Io in two-phase ab coordinates in k þ 1 sampling time; i*oa and i*ob denote that of references I*o ; usa, usb and isa, isb are two-phase ab coordinates from source grid voltages Us and currents Is, respectively; l denotes the weighting factor. Therefore, the cost function is calculated for every possible switching state in each sampling period. Then the switching state obtaining the tiny error of (13) is selected and applied to the power devices of the two primary and secondary MCs at the beginning of the next sampling instant.

1000 500 0 -500 -1000

Io (A)

Dqs ðk þ 1Þ ¼ 0  jusa isb  usb isa j

(14)

Io B with Io B* (A)

        Dio ðk þ 1Þ ¼ i*oa  ioa  þ i*ob  iob ;

Fundamental (50Hz) = 20.24 , THD= 2.45%

5 4 3 2 1 0

0

5

10 Harmonic order

15

20

(e)

Fig. 3 e Simulation results of active power changing from 18 kW to ¡10 kW. (a) Source-side grid voltage usa and loadside grid voltage vgA in phase A; (b) active power Po and reactive power Qo supplied to the load-side grid; (c) threephase grid interfacing currents io{A,B,C}; (d) reference i*oB and actual ioB grid interfacing current in phase B; and (e) FFT spectrums of grid interfacing current at ¡10 kW power. shows the Fast Fourier Transform (FFT) spectrums of grid interfacing current after the active power change. Theoretically, the load-side grid will deliver power to the source-side grid and the load-side interfacing currents will reverse after the power flow direction changes. From Fig. 3(b), the active power Po changes from 18 kW to 10 kW after 0.04 s, indicating reverse power flowing and tracking of the power reference. Whereas, the reactive power Qo remains at zero, presenting unity power factor. From Fig. 3(c) and (d), the three-phase actual currents respond to the references rapidly and coincidently. At the active power value decreases and power flow direction reverses, the three-phase grid-tie currents track the references at a fast speed, which is less than one fundamental period. At the steady state (after the transient), the currents are out of phase with the grid voltage and well match the reference.

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Low harmonic distortions are achieved regardless the operating power value or power flow direction. As FFT spectrums of grid-tie current shown in Fig. 3(e), the grid-tie current presents a 2.45% total harmonic distortion (THD) at half of the rated power and reverse power flow.

Case II: different phases between grids

Usa & Vg A (V)

The MC-SST with the proposed MPC is investigated on linking two grids at different phases. The phase angle of source-side grid is used as the reference and a 60 deg phase lead is applied to the load-side grid. In addition, the active power variation from 18 kW to 15 kW is also performed in this case at t ¼ 0.04 s. Related results are shown in Fig. 4. From Fig. 4(a), (c), and (d), it can be seen that even though the two grids have

1000 500

usa

0

vgA

-500

-1000

0

0.02

0.04 t (s)

0.06

0.08

0.04 t (s)

0.06

0.08

Po (k W) & Qo (k VA)

(a) 20 15 10 5 0

Po Qo 0

0.02

Io (A)

(b) 40 20

Case III: parameter variations The effect of parameter variations on the MPC is analyzed through changing the values of grid filter impedance in the MPC algorithm while keeping the same value in the circuit. The system operates at 20 kW full power and ±50% variations are applied to the filter inductance Lg. The THD of grid-tie current and the peak-to-peak ripple of active power versus filter inductance are shown in Fig. 5. It can be seen that the THD varies within 0.5% and the active power ripple varies within 1% when there are ±50% variations of Lg. Especially, no changes appear in the 10% variation of Lg and little bit changes in the 10% variation of Lg. Note that the parameter variations of the system are mainly from the filter inductance and capacitance. They are commonly ±10% in practice, which prove to have little effect on the MPC control objectives [27].

Real-time implementation

0 -20 -40

0

0.02

0.04 t (s)

0.06

0.08

(c) Io B with Io B* (A)

different phases, the MC-SST output currents are in phase with the load-side grid voltage and accurately track the references. Fast dynamic response is also fulfilled when the active power changes. And the grid-tie current presents low harmonic distortions, as the FFT spectrums shown in Fig. 4(e), which indicates 1.52% THD at the 18 kW power. From Figs. 3 and 4, it is noted that for different amplitudes and phases of the two grids, the interfacing currents fulfill rapid responses, accurate tracking, and high-quality waveforms through the proposed MPC according to the discrete models of MC-SST system. There is no requirement of current and voltage vectors computation, duty cycles synthetization, and additional control loop design as those in the SVPWM.

40 ioB 20 0 -20 -40

ioB* 0

0.02

0.04 t (s)

0.06

0.08

Mag (% of Fundamental)

(d) Fundamental (50Hz) = 36.23 , THD= 1.52%

5 4

The proposed MPC for the MC-SST is implemented in the dSPACE1006 real-time platform. Fig. 6 shows block diagram of the implementation procedure. The MC-SST circuit model is built in the MATLAB/Simulink environment, with the same system parameters as Table 1. The DS2004 analogedigital interface is used to return the measured Us(k), Is(k), Ui(k), Io(k), and Vg(k) in the present time instant, to the DS1006 processor, in order to predict Is(k þ 1) and Io(k þ 1) in the next period, based on the established discrete model of (10)e(12). To compensate the discrete delay, one time instant is compensated by predicting the state variables in the (k þ 2)th time instant [28,29]. The defined cost function of (13) is then

3 2 1 0

0

5

10 Harmonic order

15

20

Fig. 4 e Simulation results of different phases between the grids, with active power decrease. (a) Source-side grid voltage usa and load-side grid voltage vgA in phase A; (b) active power Po and reactive power Qo supplied to the loadside grid; (c) three-phase grid interfacing currents io{A,B,C}; (d) reference i*oB and actual ioB grid interfacing current in phase B; and (e) FFT spectrums of grid interfacing current at 18 kW power.

Fig. 5 e Analysis of effect of parameter variations.

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MC-SST Circuit Model in Simulink

DS2004 analog-digital interface Measure Us (k), Is (k), Ui (k), Io (k), Vg (k)

DS4003 digital input-output interface

Select Optimal Switching States

Predict Is (k+1) Io (k+2) Evaluate Cost Function and Io (k+1) I (k+2) s DS1006 Processor Dealing Proposed MPC for the MC-SST

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load grid interfacing currents io{A,B,C}; Fig. 7(d) shows phase-B load grid interfacing current ioB and its reference i*oB . From Fig. 7(a) and (c), it can be seen that though the source grid and load grid have different voltage phases and amplitudes, the load grid interfacing currents track the reference at low harmonics. From Fig. 7(b), it can be seen that when the reference power changes, the active power changes from positive to negative, demonstrating reverse power flowing. The active power value matches the 15 kW before the reference power changes and is 10 kW after the change. Moreover, the reactive power remains at zero, presenting unity power factor operation. From the comparison of grid interfacing current with its reference in Fig. 7(d) and the sharp variation of active power Po in Fig. 7(b), fast responses and accurate traces are achieved for the interfacing currents of the MC-SST system.

Comparison with PI-based control Fig. 6 e Block diagram of the real-time implementation in dSPACE1006.

evaluated from the predictions and the optimal switching states are selected, which are performed to drive the CSR-MC and VSI-MC power devices through DS4003 digital inputeoutput interface.

Results of MPC The active power value and direction changes are performed in the real-time implementation through changing the power reference from 15 kW to 10 kW. The source grid and load grid are with a 60 phase difference. Real-time implementation results are shown in Fig. 7. Fig. 7(a) shows one-phase source grid voltage usc and load grid voltage vgC; Fig. 7(b) shows active power Po and reactive power Qo; Fig. 7(c) shows three-phase

The PI based control strategy with SVPWM for the MC-SST of Fig. 2 is compared with the proposed MPC strategy in real-time implementation platform. Fig. 8 shows the results of the two methods when the reference active power changes from 10 kW to 15 kW. Fig. 8(a) and (c) shows the active power Po and reactive power Qo of the MC-SST by MPC and PI, respectively; Fig. 8(b) and (d) shows three-phase interfacing currents io{A,B,C} of the MC-SST by MPC and PI, respectively. By contrast of Po and Qo in Fig. 8(a) and (c), it can be seen that the MPC brings in much faster response to go into steady state than the PI control. The active and reactive powers under the MPC become stable in less than one fundamental period, whereas when using the PI-SVPWM control, they take almost 0.3 s to stabilize. Similar conclusion can be seen from the three-phase output currents io{A,B,C} of the MC-SST under the two methods in Fig. 8(b) and (d). In addition, the highfrequency ripple of active and reactive powers is higher in the case of PI based control than with the MPC.

Fig. 7 e Real-time implementation results of active power changing from 15 kW to ¡10 kW. (a) One-phase source grid voltage usc and load grid voltage vgC; (b) active power Po and reactive power Qo supplied to the load grid; (c) three-phase load grid interfacing currents io{A,B,C}; and (d) phase-B load grid interfacing current ioB and its reference i*oB .

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Fig. 8 e Comparison results of MC-SST under the PI and MPC. (a) Active power Po and reactive power Qo by MPC; (b) threephase MC-SST output currents io{A,B,C} by MPC; (c) active power Po and reactive power Qo by PI; (d) three-phase MC-SST output currents io{A,B,C} by PI.

Conclusion This paper discussed a real-time implementation for the MPC of MC-SST power system and compared it with the PI control strategy. The MPC is able to adopt the most suitable switching state for the next sampling period, through predicting the circuit variables and evaluating a cost function that defined the error between predictions and references. This goal was achieved in one simple control loop, without complicated vectors computation and duty cycle synthetization as that using the traditional SVPWM. Simulation and real-time investigations were carried out with active power value and direction changes at the two different grids voltages and parameter variations. Comprehensive analysis as well as comparison studies with the PI control strategy was presented. The real-time results showed faster and more accurate tracking ability with the MPC than the traditional PI control, leading to an effective control method to such SST.

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