The extended model predictive-sliding mode control of three-level AC/DC power converters with output voltage and load resistance variations

Figures & data

Figure 1. System general diagram.

Figure 2. Three-level AC/DC converter.

Figure 3. Voltage vectors representation using the Clarke transformation (αβ coordinate system).

Figure 4. The system Block diagram of EMPSMC scheme.

Table

Algorithm Proposed Algorithm based on EMPSMC scheme (shown in Figure 5)

Start t>0

1: Sense three-phase grid voltages and currents

2: Transform the sensed values to the two-phase system using Clarke transformation

3: From Equation (3) and Equation (4), the three-phase input voltage is mapped to the dual-axis with eight voltage vectors using the SVPWM technique

4: The EMPC uses the values from steps 2 and 3 to predict the next sample in discrete time using Equation (6).

5: The predicted sample is used to compute the predicted sample of active and reactive power using Equation (7)

6: The active reference power is computed by SMC using Equations (12), (13), and (14).

7: The values from step 5 and step 6 are used to compute the optimal space vector for the next switching step with a minimal value of cost function by using Equation (8).

8: Repeat from step 1 until the tracking error in Equation (10) satisfy the desired limit

Stop

Figure 5. The system Algorithm of EMPSMC Scheme.

Figure 6. Trajectory Plot like any sliding action into SMC.

Table 1. Parameter of converter.

Parameter	Value
C (Filter capacitor)	6.0000e02
L (Filter inductance)	80e06
RL (Load resistance)	160 ohms
VLL (line-line voltage (RMS))	50 V
F(Frequency)	50 HZ
Vdc (Dc Output voltage)	150
K (sliding coefficients Gain)	< 1
$\lambda$(Proper sliding coefficients)	0.3

Figure 7. The output response of Step Response of EMPSMC schemes.

Table 2. Dynamic performance evaluation of EMPSMC and MMPIC

	Comparison of Table
Controller Characteristics	EMPSMC	(Zhang, Sun, et al., 2013)	MPPIC	(Zhang, Sun, et al., 2013)
Rise Time	0.0873 Sec	0.125 sec	0.1327 sec	–
Overshoot	0.1886%	2.33%	0.8776%	2.65%

Table 3. System dynamic performance evaluation.

	Comparison of Table
Controller Characteristics	EMPSMC	(More et al., 2015)	MPPIC	(More et al., 2015)
Rise Time	0.0873 Sec	0.03 sec	0.1327 sec	–
Overshoot	0.1886%	8.53%	0.8776%	2.45%

Figure 8. The Output response of the system with EMPSMC plus interference (Disturbance).

Figure 9. Output reaction to an unpredicted of dc voltage load demand increase (a) demand load increase (b) demand load decrease.

Figure 10. Output reaction to an unpredicted of dc voltage load demand increase (a) Active power increase (b) Active power decrease.

Figure 11. Output reaction to an unpredicted of dc voltage load demand increase (c) Phase A voltage and current increase (d) Phase A voltage and current decreases under EMPSMC.

Figure 12. The output response of Step Response of MPPIC schemes.

Figure 13. The Output response of the system with MPPIC plus interference (Disturbance).

Figure 14. Comparison of EMPC, MPPIC, and MPC.

Zhang, X., Sun, L., & Zhao, K. (2013). Non-linear speed control for PMSM system using sliding-mode control and disturbance compensation techniques. IEEE Transactions on Power Electronics, 28(3), 1358–1365. https://doi.org/https://doi.org/10.1109/TPEL.2012.2206610

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More, J. J., Puleston, P. F., Kunusch, C., & Fantova, M. A. (2015). Development and implementation of a supervisor strategy and sliding mode control setup for fuel-cell-based hybrid generation systems. IEEE Transactions on Energy Conversion, 30(1), 218–225. https://doi.org/https://doi.org/10.1109/TEC.2014.2354553

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