Arkadiusz Kaszewski

Particle Swarm Optimization of the Multioscillatory LQR for a Three-Phase Four-Wire Voltage-Source Inverter With an

This paper presents evolutionary optimization of the linear quadratic regulator (LQR) for a voltage-source inverter with an LC output filter. The procedure involves particle-swarm-based search for the best weighting factors in the quadratic cost function. It is common practice that the weights in the cost function are set using the guess-and-check method. However, it becomes quite challenging, and usually very time-consuming, if there are many auxiliary states added to the system. In order to immunize the system against unbalanced and nonlinear loads, oscillatory terms are incorporated into the control scheme, and this significantly increases the number of weights to be guessed. All controller gains are determined altogether in one LQR procedure call, and the originality reported here refers to evolutionary tuning of the weighting matrix. There is only one penalty factor to be set by the designer during the controller synthesis procedure. This coefficient enables shaping the dynamics of the closed-loop system by penalizing the dynamics of control signals instead of selecting individual weighting factors for augmented state vector components. Simulational tuning and experimental verification (the physical converter at the level of 21 kVA) are included.

LC

The paper presents control system synthesis for a true sine wave four-leg inverter with an LC output filter. Our main goal is to ensure high quality voltage waveform for unbalanced and nonlinear loads. An LQR approach was chosen. The LQR design approach has proven effective in many industrial applications. Although weights in a cost function are usually set by guess and check method, the LQR in proposed system gives satisfactory results as far as some general and very intuitive rules are applied, e.g. the penalty coefficient for an integral of control error is a few orders of magnitude away from penalty coefficients related to plant state variables. In order to immunise system against nonlinear loads oscillatory terms are included in the control scheme. They can be tuned for typical harmonics like 5th, 7th, 11th and 13th. A novelty of the proposed solution lies in the fact that all controller gains (including all integral and oscillatory terms) are determined altogether in one LQR procedure call. Controls are calculated in rotating reference frame. Simulation (continuous and discrete) and experimental results (at the level of 10kW) are included. They establish consistent set of tests that validates effectiveness of the design approach.

Output Filter

In this paper we develop a new approach to combined full-state and disturbance feedforward control system synthesis for a three-phase four-leg true sine wave inverter. Proposed scheme is an extension of the augmented state feedback controller with multi-oscillatory terms. Multi-resonant controllers are well-established solution for this kind of converters if high quality output voltage is needed in the presence of nonlinear loads. They take advantage of repetitiveness of the control process under the steady load conditions (this includes nonlinear and unbalanced loads). No presumption on load type entails introduction of oscillatory terms for all three voltage components with resonant frequencies up to available bandwidth dictated by technically justified switching/sampling frequency. This makes the practical implementation challenging. Our idea is to reduce number of needed oscillatory terms by adding disturbance feedforward. In the discussed system the disturbance signal is easily accessible/measurable and hence this feedback can be very effective because of lack of estimation errors. The control system is designed in dq0 reference frame rotating with the fundamental output frequency. Extensive numerical experiments indicate that the number of oscillatory terms can be reduced significantly and high quality of output voltage can be maintained.

Multi-oscillatory LQR for a three-phase four-wire inverter with L 3n C output filter

This paper presents a state-feedback current controller with oscillatory terms for three-phase grid-connected PWM converters. Use of the oscillatory terms allows for shaping the sinusoidal input currents of the converter under distorted grid voltage conditions. Linear-quadratic optimization method is used to calculate the current controller gains. In the converter control structure the state current controller and PI DC-link voltage controller are used. Mathematical analysis and simulation results of the proposed control system are presented and discussed. n symulacyjnych. (Uklad sterowania przeksztaltnikiem sieciowym wykorzystuj ˛ acy regulator stanu ze sprz ˛zeniem od pr ˛ adow i sygnalow z czlonow oscylacyjnych)

An LQ controller with disturbance feedforward for the 3-phase 4-leg true sine wave inverter

In this paper three different implementations of the full-state feedback linear-quadratic (LQ) controller for a 3-phase 4-leg sine wave inverter are compared. The LQ controller is designed in stationary reference frames abc and αβγ as well as in a dq0 reference frame rotating with the fundamental output frequency, and is not cascaded with any inner controller. In the proposed control schemes integral and multi-oscillatory terms are added to the input of the LQ controller to ensure high quality output voltage waveforms for unbalanced and nonlinear loads. All three approaches are tested in an experimental inverter (a physical model at the level 10kVA). The experimental results for linear and nonlinear loads are presented, discussed and some remarks on choosing the best reference frame are then given.

Control system of the grid-connected converter based on a state current regulator with oscillatory terms

This paper presents a control strategy for four-leg grid-connected PWM rectifiers that have an active power filtering function. The four-leg voltage source converter topology gives ability to control an input current in the neutral leg. That is important for the active power filtering function when there is an unbalanced load. The control strategy is based on a voltage oriented method that has a cascaded DC voltage and current controllers designed in a rotating reference frame. The DC voltage controller is a PI-type, whereas the input current is shaped by a full-state feedback controller. The novelty of the proposed solution is the control structure that has modified the DC voltage error signal by adding a discontinuity element and reduction the number of current signals by half. The discontinuity element is needed to provide a constant reference current signal during active power filtering operation. The paper describes in detail the design procedure for the voltage and current controllers. Numerical results for active rectification and active power filtering operations are presented and discussed. Numerical results have been obtained by using a discrete control model.

The LQ controller for the 3-phase 4-leg inverter with an LC output filter — Choosing the right reference frame

This chapter presents the application of a particle swarm optimization (PSO) to a controller tuning in selected power electronic and drive systems. The chapter starts with a relatively simple tuning of a cascaded PI speed and position control system for a BLDC servo drive. This example serves as the background for a discussion on selecting the objective function for the PSO. Then the PSO is used in two challenging controller tuning tasks. This includes optimizing selected learning parameters in the adaptive artificial neural network (ANN) based online trained speed controller for an urban vehicle (3D problem) and selecting penalty factors in the LQR with augmented state (i.e. with oscillatory terms) for a three-phase four-leg sine wave inverter (15D problem). It is demonstrated with the help of these case studies why and where the PSO, or any other similar population based stochastic search algorithm, can be beneficial. Engineers encounter many non-straightforward controller tuning problems in power electronic systems and this chapter illustrates that in some cases it is relatively easy to reduce these tasks into the objective function selection problem. The relevant controller parameters are then determined automatically by the PSO.

State-space current control for four-leg grid-connected PWM rectifiers with active power filtering function

This paper presents a powertrain system for an urban electric vehicle. The powertrain system consists of a hybrid energy source (battery storage and ultracapacitors) and drivetrain system (two in-wheel outer-rotor PMSM motors). Battery performance improvement, has been achieved by supporting it with ultracapacitor energy storage. Power flow control using fuzzy logic controller is presented in detail. An electronic differential algorithms have been implemented and tested.

Advanced Control and Optimization Techniques in AC Drives and DC/AC Sine Wave Voltage Inverters: Selected Problems

This paper presents a scalable and effective discontinuous pulse width modulation algorithm for multileg converters. The method can also be used in three- and four-leg voltage-source converters, though its simplicity in comparison to so called vector modulators shows up clearly in systems with more than three legs. Some similarities between vector and sinusoidal modulations are discussed and issues regarding naming these methods are raised. Numerical simulation test results are presented.

Powertrain system with the ultracapacitor-based auxiliary energy storage for an urban battery electric vehicle

This paper presents the design of a control system of a three-phase three-level pulse-width modulated rectifier operated under unbalanced and distorted grid voltage conditions. The developed scheme is based on a voltage-oriented control method. Instead of proportional-integral current controllers a state-feedback current controller in rotating reference frame is used. In order to achieve a zero steady-state current control error in response to step commands, integral terms are incorporated into the current control scheme. Similarly, to ensure the rejection of the sinusoidal component of current control error caused by unbalance and distortion in the grid voltage, the oscillatory terms are added to the current control system. To calculate the current controller gains, an augmented plant model is developed and linear-quadratic optimization method is applied. The physical experiments indicate that using state-feedback current control with oscillatory terms allows for notable improvement of the shape of the input currents of the converter and increases the power conversion efficiency.