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

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

Power Electronics and Drives
Volume 10 (2025): Issue 1 (January 2025)
By: Zdeněk Kehl,  Tomas Glasberger and  Zdeněk Peroutka  
Open Access
|Feb 2025

Figures & Tables

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.

Harmonic analysis of currents

SimulationsExperiments
Control strategyFull-state FCS-MPCTwo-step FCS-MPCTwo-step FCS-MPC
THD of load current iLU54.8474%54.8475%41.8789%
THD of compensated grid current iU9.0095%9.2130%9.9983%
DOI: https://doi.org/10.2478/pead-2025-0005 | Journal eISSN: 2543-4292 | Journal ISSN: 2451-0262
Journal RSS Feed
Language: English
Page range: 74 - 95
Submitted on: Jan 3, 2025
|
Accepted on: Jan 20, 2025
|
Published on: Feb 23, 2025
Published by: Wroclaw University of Science and Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
active power filter,
grid tied converters,
FCS-MPC,
CHB converter,
power grid quality
Related subjects:
Computer sciences,
Artificial intelligence,
Engineering,
Electrical engineering,
Electronics

© 2025 Zdeněk Kehl, Tomas Glasberger, Zdeněk Peroutka, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution 4.0 License.

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