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Computationally Efficient Model Predictive Control of Delta-Connected CHB-Based Active Power Filter

Zdeněk Kehl

Zdeněk Kehl

University of West Bohemia, RICEPilsen, Czech Republic
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Kehl, Zdeněk
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Tomas Glasberger

Tomas Glasberger

University of West Bohemia, RICEPilsen, Czech Republic
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Glasberger, Tomas
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Zdeněk Peroutka

Zdeněk Peroutka

University of West Bohemia, RICEPilsen, Czech Republic
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Peroutka, Zdeněk
  
Feb 23, 2025
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Article Category: Research paper
Published Online: Feb 23, 2025
Page range: 74 - 95
Received: Jan 03, 2025
Accepted: Jan 20, 2025
DOI: https://doi.org/10.2478/pead-2025-0005
Keywords
© 2025 Zdeněk Kehl et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

Power circuit configuration of investigated APF and designed testbed. APF, active power filters; CHB, cascaded H-bridge.
Power circuit configuration of investigated APF and designed testbed. APF, active power filters; CHB, cascaded H-bridge.

Figure 2.

Proposed two-level control of shunt APF based on CHB converters in delta connection. APF, active power filter; CHB, cascaded H-bridge; LPF, low pass filtration.
Proposed two-level control of shunt APF based on CHB converters in delta connection. APF, active power filter; CHB, cascaded H-bridge; LPF, low pass filtration.

Figure 3.

Model for step 1 of FCS-MPC: Power circuit configuration used for the derivation of the mathematical model describing the interaction between the power grid and CHB converter. CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control.
Model for step 1 of FCS-MPC: Power circuit configuration used for the derivation of the mathematical model describing the interaction between the power grid and CHB converter. CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control.

Figure 4.

Model for step 2 of FCS-MPC: Power circuit used for derivation of the mathematical model describing the behaviour of a general n-level CHB converter. CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control.
Model for step 2 of FCS-MPC: Power circuit used for derivation of the mathematical model describing the behaviour of a general n-level CHB converter. CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control.

Figure 5.

APF start-up: (a) full-state FCS-MPC and (b) proposed two-step FCS-MPC. The power grid is loaded by the 3ph diode rectifier supplying RC load with R = 32 Ω, C = 3.25 mF. Udc_ref = 42.5 V (*Udc_tot = 170 V). Green, purple: CHB converter output voltage u1_CHB, red, blue: CHB converter current i1_CHB. CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control; RC,
APF start-up: (a) full-state FCS-MPC and (b) proposed two-step FCS-MPC. The power grid is loaded by the 3ph diode rectifier supplying RC load with R = 32 Ω, C = 3.25 mF. Udc_ref = 42.5 V (*Udc_tot = 170 V). Green, purple: CHB converter output voltage u1_CHB, red, blue: CHB converter current i1_CHB. CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control; RC,

Figure 6.

APF start-up analysed from the power grid viewpoint: (a) transient conditions, (b) steady-state; the same test scenario as in Figure 5. APF, active power filter.
APF start-up analysed from the power grid viewpoint: (a) transient conditions, (b) steady-state; the same test scenario as in Figure 5. APF, active power filter.

Figure 7.

Comparison of full-state and two-step FCS-MPC during step unloading of the power grid in t = 0.5 s (a) and loading of the power grid in t = 1 s (b). The power grid is loaded by the 3ph diode rectifier supplying RC load with R = 32 Ω, C = 3.25 mF. Udc_ref = 42.5 V (*Udc_tot = 170 V). FCS-MPC, finite control set model predictive control; RC,
Comparison of full-state and two-step FCS-MPC during step unloading of the power grid in t = 0.5 s (a) and loading of the power grid in t = 1 s (b). The power grid is loaded by the 3ph diode rectifier supplying RC load with R = 32 Ω, C = 3.25 mF. Udc_ref = 42.5 V (*Udc_tot = 170 V). FCS-MPC, finite control set model predictive control; RC,

Figure 8.

Detail of compensated grid currents iU in steady-state for both the full-state FC-MPC (red) and the proposed two-step FCS-MPC (blue). FC-MPC, FCS-MPC, finite control set model predictive control.
Detail of compensated grid currents iU in steady-state for both the full-state FC-MPC (red) and the proposed two-step FCS-MPC (blue). FC-MPC, FCS-MPC, finite control set model predictive control.

Figure 9.

Harmonics analysis of compensated grid currents iU: Red: full-state FCS-MPC, blue: two-step FCS-MPC. FCS-MPC, finite control set model predictive control; THD, total harmonic distortion.
Harmonics analysis of compensated grid currents iU: Red: full-state FCS-MPC, blue: two-step FCS-MPC. FCS-MPC, finite control set model predictive control; THD, total harmonic distortion.

Figure 10.

Sensitivity analysis of key model parameters for both mentioned control approaches (full-state FCS-MPC and two-step FCS-MPC). The power grid is symmetrical, and it is loaded by the 3ph diode rectifier supplying RC load with R = 32 Ω, C = 3.25 mF. FCS-MPC, finite control set model predictive control; THD, total harmonic distortion.
Sensitivity analysis of key model parameters for both mentioned control approaches (full-state FCS-MPC and two-step FCS-MPC). The power grid is symmetrical, and it is loaded by the 3ph diode rectifier supplying RC load with R = 32 Ω, C = 3.25 mF. FCS-MPC, finite control set model predictive control; THD, total harmonic distortion.

Figure 11.

Comparison of full-state FCS-MPC and two-step FCS-MPC during start-up of APF with unbalanced initial DC-link voltages in one CHB converter (initial states: U1_dc_A = 42 V, U1_dc_B = 35 V, U1_dc_C = 58 V and U1_dc_D = 42 V). APF, active power filter; CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control.
Comparison of full-state FCS-MPC and two-step FCS-MPC during start-up of APF with unbalanced initial DC-link voltages in one CHB converter (initial states: U1_dc_A = 42 V, U1_dc_B = 35 V, U1_dc_C = 58 V and U1_dc_D = 42 V). APF, active power filter; CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control.

Figure 12.

APF with two-step FCS-MPC control under the unbalanced power grid operation: (a) grid voltages and compensated grid currents and (b) load currents. Voltage drop in phase V of 10%. The power grid is loaded by the 3ph diode rectifier supplying RC load with R = 32 Ω, C = 3.25 mF. APF, active power filter; FCS-MPC, finite control set model predictive control; RC,
APF with two-step FCS-MPC control under the unbalanced power grid operation: (a) grid voltages and compensated grid currents and (b) load currents. Voltage drop in phase V of 10%. The power grid is loaded by the 3ph diode rectifier supplying RC load with R = 32 Ω, C = 3.25 mF. APF, active power filter; FCS-MPC, finite control set model predictive control; RC,

Figure 13.

APF with two-step FCS-MPC control under 10% voltage sag of all the phase voltages in t = 0.5 s. The power grid is loaded by the 3ph diode rectifier supplying an RC load with R = 32 Ω, C = 3.25 mF. Udc_ref = 42.5 V (*Udc_tot = 170 V). APF, active power filter; FCS-MPC, finite control set model predictive control; RC,
APF with two-step FCS-MPC control under 10% voltage sag of all the phase voltages in t = 0.5 s. The power grid is loaded by the 3ph diode rectifier supplying an RC load with R = 32 Ω, C = 3.25 mF. Udc_ref = 42.5 V (*Udc_tot = 170 V). APF, active power filter; FCS-MPC, finite control set model predictive control; RC,

Figure 14.

APF start-up under two-step FCS-MPC control: (a) start-up transient and (b) steady-state after the start-up. Power grid loaded by the 3ph diode rectifier supplying RC load with R = 32 Ω, C = 3.25 mF. Udc_ref = 42.5 V (*Udc_tot = 170 V). Cyan: grid voltage [50V/div], green: grid (compensated) current [10A/div], purple: load current [10A/div], DC-link voltages in one CHB converter [20V/div]. APF, active power filter; CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control; RC,
APF start-up under two-step FCS-MPC control: (a) start-up transient and (b) steady-state after the start-up. Power grid loaded by the 3ph diode rectifier supplying RC load with R = 32 Ω, C = 3.25 mF. Udc_ref = 42.5 V (*Udc_tot = 170 V). Cyan: grid voltage [50V/div], green: grid (compensated) current [10A/div], purple: load current [10A/div], DC-link voltages in one CHB converter [20V/div]. APF, active power filter; CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control; RC,

Figure 15.

Response of APF with two-step FCS-MPC to step changes in the power grid load. Interval I and III—power grid loaded by 3ph diode rectifier supplying RC load with R = 32 Ω, C = 3.25 mF. Interval II—unloaded grid. Udc_ref = 42.5 V (*Udc_tot = 170 V). Cyan: grid voltage [50V/div], green: grid (compensated) current [10A/div], purple: load current [10A/div], DC-link voltages in one CHB converter [20V/div]. APF, active power filter; CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control; RC,
Response of APF with two-step FCS-MPC to step changes in the power grid load. Interval I and III—power grid loaded by 3ph diode rectifier supplying RC load with R = 32 Ω, C = 3.25 mF. Interval II—unloaded grid. Udc_ref = 42.5 V (*Udc_tot = 170 V). Cyan: grid voltage [50V/div], green: grid (compensated) current [10A/div], purple: load current [10A/div], DC-link voltages in one CHB converter [20V/div]. APF, active power filter; CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control; RC,

Figure 16.

Response of APF with two-step FCS-MPC to step changes in the power grid load—detail of Figure 16: (a) unloading of the power grid (transition interval I → II) and (b) step loading of the grid (transition interval II → III). Cyan: grid voltage [50V/div], green: grid (compensated) current [10A/div], purple: load current [10A/div], DC-link voltages in one CHB converter of the active filter [20V/div]. APF, active power filter; CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control.
Response of APF with two-step FCS-MPC to step changes in the power grid load—detail of Figure 16: (a) unloading of the power grid (transition interval I → II) and (b) step loading of the grid (transition interval II → III). Cyan: grid voltage [50V/div], green: grid (compensated) current [10A/div], purple: load current [10A/div], DC-link voltages in one CHB converter of the active filter [20V/div]. APF, active power filter; CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control.

Figure 17.

Balancing of DC-links of CHB converters—steady-state: (a) two-step FCS-MPC with one Udc_tot voltage controller in power grid control (control level 1), (b) two-step FCS-MPC with three separated Udc_tot in the power grid control. Udc_ref = 42.5 V (*Udc_tot = 170 V). All channels: [20V/div]. CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control.
Balancing of DC-links of CHB converters—steady-state: (a) two-step FCS-MPC with one Udc_tot voltage controller in power grid control (control level 1), (b) two-step FCS-MPC with three separated Udc_tot in the power grid control. Udc_ref = 42.5 V (*Udc_tot = 170 V). All channels: [20V/div]. CHB, cascaded H-bridge; FCS-MPC, finite control set model predictive control.

Figure 18.

Balancing of DC-links of CHB converters—fault in DC-link in cell B of CHB converter 1 caused by parallel resistance R = 85 Ω to Cdc in interval II. Interval I and III without fault. Udc_ref = 42.5 V (*Udc_tot = 170 V). All channels: [20V/div]. CHB, cascaded H-bridge.
Balancing of DC-links of CHB converters—fault in DC-link in cell B of CHB converter 1 caused by parallel resistance R = 85 Ω to Cdc in interval II. Interval I and III without fault. Udc_ref = 42.5 V (*Udc_tot = 170 V). All channels: [20V/div]. CHB, cascaded H-bridge.

Figure 19.

Designed laboratory prototype of three-phase APF 60 kW. APF, active power filter; CHB, cascaded H-bridge.
Designed laboratory prototype of three-phase APF 60 kW. APF, active power filter; CHB, cascaded H-bridge.
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Harmonic analysis of currents

Simulations Experiments
Control strategy Full-state FCS-MPC Two-step FCS-MPC Two-step FCS-MPC
THD of load current iLU 54.8474% 54.8475% 41.8789%
THD of compensated grid current iU 9.0095% 9.2130% 9.9983%
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