## Model predictive control strategies for power electronics converters and ac drives

Research output: Book/Report › Doctoral thesis › Monograph

### Details

Original language | English |
---|---|

Publisher | National Technical University of Athens |

Number of pages | 172 |

Publication status | Published - Jul 2013 |

Externally published | Yes |

Publication type | G4 Doctoral dissertation (monograph) |

### Abstract

This thesis focuses on model predictive control (MPC) strategies for power electronics converters and ac drives. Due to their switching nature, power electronic systems constitute nonlinear systems with multiple inputs and outputs, and subject to constraints (e.g. the duty cycle should be limited between zero and one). Over the years many control strategies have been proposed that are mainly based on the conventional proportional-integral-derivative (PID) controller combined with nonlinear techniques, such as pulse

width modulation (PWM). However, PID controllers are ideally suited to linear, single-input, single-output (SISO), unconstrained control problems. Moreover, controllers of this type are usually tuned to achieve satisfactory performance only in a narrow operating range. Therefore, the problems associated with many power electronics applications and their closed-loop performance still poses theoretical and practical challenges.

A control algorithm that has recently been gaining popularity in the ﬁeld of power electronics is MPC. MPC is a control strategy that was developed as an alternative strategy to the conventional PID control. Its success is based on the fact that it uses a mathematical model of the plant, which allows the controller to predict the impact of its control actions. Furthermore, MPC is capable of handling complex and nonlinear dynamics, while several design criteria (constraints) can be explicitly included in a simple and eﬀective manner. By imposing constraints on the variables of concern the plant is able to operate at its physical limits without violating them. Thus, the most favorable operation

can be obtained, while the operational limits of the plant are fully respected. Hence, thanks to all these advantageous features, MPC has attracted the interest and attention of research and academic communities. Furthermore, the advent of immensely powerful microprocessors with increased computational capabilities enabled its application in the ﬁeld of power electronics with signiﬁcant success.

This thesis is divided into two parts. In the ﬁrst part the key notions behind MPC are presented, including the concepts of optimization, optimal control, and receding horizon policy. In addition, a brief introduction to the modeling of hybrid systems as hybrid automata is included. Finally, the notion of enumeration strategy is introduced. The second part is devoted to applications of MPC in the ﬁeld of power electronics. It consists of three chapters, each of which refers to a diﬀerent application. More speciﬁcally, Chapter 3 is devoted to dc-dc boost converters, Chapter 4 to cascaded H-bridge (CHB) multilevel rectiﬁers, and Chapter 5 to ac drives.

Chapter 3 presents two MPC approaches for dc-dc boost converters. A discrete-time switched nonlinear (hybrid) model of the converter is derived, which captures both the continuous and the discontinuous conduction mode. The controller synthesis is achieved by formulating an objective function that is to be minimized subject to the model dynamics. In the ﬁrst approach, MPC is implemented as a current-mode controller. Two control loops are employed, with the inner loop being designed in the framework of MPC. Two diﬀerent objective functions are formulated and investigated. The control objective, i.e. the regulation of the current to its reference, is achieved by directly manipulating the switch, thus a modulator is not required. The second proposed strategy, utilized as a voltage-mode controller, achieves regulation of the output voltage to its reference, without requiring a subsequent current control loop. Furthermore, for both approaches, a state estimation scheme is implemented that addresses load uncertainties and model mismatches.

In Chapter 4 an MPC strategy is adapted to the CHB multilevel rectiﬁer. The proposed control scheme aims to keep the sinusoidal input current in phase with the supply voltage, and to achieve independent voltage regulation of the H-bridge cells. To do so, the switches are directly manipulated without the need of a modulator. Furthermore, since all the possible switching combinations are taken into account, the controller exhibits favorable performance not only under nominal conditions, but also under asymmetrical voltage potentials and unbalanced loads. Finally, a short horizon is employed in order to ensure robustness; in this way the required computational eﬀort remains reasonable,

making it possible to implement the algorithm in a real-time system.

In Chapter 5 an approach to include a variable switching time point into predictive torque control (PTC) is introduced. In PTC the switching frequency is limited by the sampling frequency; its theoretical maximum value is half the sampling frequency. However, in reality the switching frequency is lower than this value, and thus high current and torque ripples occur compared to modulator-based control methods. In order to overcome this an optimization problem is formulated and solved in real-time. Thereby, apart from the regulation of the torque and the stator ﬂux magnitude to their references, an

additional control objective should be met: the minimization of the torque ripple. To do so, the time point at which the switches of the inverter should change state is calculated. The proposed control scheme, called variable switching point predictive torque control (VSP2 TC), is employed to control both a two-level inverter driving an induction machine (IM), as well as a three-level neutral point clamped (NPC) voltage source inverter driving an IM.

width modulation (PWM). However, PID controllers are ideally suited to linear, single-input, single-output (SISO), unconstrained control problems. Moreover, controllers of this type are usually tuned to achieve satisfactory performance only in a narrow operating range. Therefore, the problems associated with many power electronics applications and their closed-loop performance still poses theoretical and practical challenges.

A control algorithm that has recently been gaining popularity in the ﬁeld of power electronics is MPC. MPC is a control strategy that was developed as an alternative strategy to the conventional PID control. Its success is based on the fact that it uses a mathematical model of the plant, which allows the controller to predict the impact of its control actions. Furthermore, MPC is capable of handling complex and nonlinear dynamics, while several design criteria (constraints) can be explicitly included in a simple and eﬀective manner. By imposing constraints on the variables of concern the plant is able to operate at its physical limits without violating them. Thus, the most favorable operation

can be obtained, while the operational limits of the plant are fully respected. Hence, thanks to all these advantageous features, MPC has attracted the interest and attention of research and academic communities. Furthermore, the advent of immensely powerful microprocessors with increased computational capabilities enabled its application in the ﬁeld of power electronics with signiﬁcant success.

This thesis is divided into two parts. In the ﬁrst part the key notions behind MPC are presented, including the concepts of optimization, optimal control, and receding horizon policy. In addition, a brief introduction to the modeling of hybrid systems as hybrid automata is included. Finally, the notion of enumeration strategy is introduced. The second part is devoted to applications of MPC in the ﬁeld of power electronics. It consists of three chapters, each of which refers to a diﬀerent application. More speciﬁcally, Chapter 3 is devoted to dc-dc boost converters, Chapter 4 to cascaded H-bridge (CHB) multilevel rectiﬁers, and Chapter 5 to ac drives.

Chapter 3 presents two MPC approaches for dc-dc boost converters. A discrete-time switched nonlinear (hybrid) model of the converter is derived, which captures both the continuous and the discontinuous conduction mode. The controller synthesis is achieved by formulating an objective function that is to be minimized subject to the model dynamics. In the ﬁrst approach, MPC is implemented as a current-mode controller. Two control loops are employed, with the inner loop being designed in the framework of MPC. Two diﬀerent objective functions are formulated and investigated. The control objective, i.e. the regulation of the current to its reference, is achieved by directly manipulating the switch, thus a modulator is not required. The second proposed strategy, utilized as a voltage-mode controller, achieves regulation of the output voltage to its reference, without requiring a subsequent current control loop. Furthermore, for both approaches, a state estimation scheme is implemented that addresses load uncertainties and model mismatches.

In Chapter 4 an MPC strategy is adapted to the CHB multilevel rectiﬁer. The proposed control scheme aims to keep the sinusoidal input current in phase with the supply voltage, and to achieve independent voltage regulation of the H-bridge cells. To do so, the switches are directly manipulated without the need of a modulator. Furthermore, since all the possible switching combinations are taken into account, the controller exhibits favorable performance not only under nominal conditions, but also under asymmetrical voltage potentials and unbalanced loads. Finally, a short horizon is employed in order to ensure robustness; in this way the required computational eﬀort remains reasonable,

making it possible to implement the algorithm in a real-time system.

In Chapter 5 an approach to include a variable switching time point into predictive torque control (PTC) is introduced. In PTC the switching frequency is limited by the sampling frequency; its theoretical maximum value is half the sampling frequency. However, in reality the switching frequency is lower than this value, and thus high current and torque ripples occur compared to modulator-based control methods. In order to overcome this an optimization problem is formulated and solved in real-time. Thereby, apart from the regulation of the torque and the stator ﬂux magnitude to their references, an

additional control objective should be met: the minimization of the torque ripple. To do so, the time point at which the switches of the inverter should change state is calculated. The proposed control scheme, called variable switching point predictive torque control (VSP2 TC), is employed to control both a two-level inverter driving an induction machine (IM), as well as a three-level neutral point clamped (NPC) voltage source inverter driving an IM.