A Neural-Network-Based Model Predictive Control of Three-Phase Inverter With an Output LC Filter

Ihab S. Mohamed; Stefano Rovetta; Ton Duc Do; Tomislav Dragicevic; Ahmed A. Zaki Diab

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A Neural-Network-Based Model Predictive Control of Three-Phase Inverter With an Output LC Filter

Ihab S. Mohamed, Stefano Rovetta, Ton Duc Do, Tomislav Dragicevic, Ahmed A. Zaki Diab

arXiv:1902.09964v3Feb 22, 2019eess.SYcs.LGstat.ML

TL;DR

MPC provides effective three-phase inverter control but requires extensive online optimization. The paper uses MPC to train a feed-forward ANN offline, then deploys the ANN for online voltage control without MPC. Simulations report lower THD and faster settling for the ANN approach across tested load conditions.

Problem
MPC control of three-phase inverters requires solving an optimization problem online, creating a large computational burden.
Method
A feed-forward ANN is trained offline from MPC-generated data and directly outputs one of seven inverter voltage-vector commands during online control.
Results
The ANN-based controller achieves 1.6% output-voltage THD versus 3.95% for MPC in the reported resistive-load simulation.
Takeaways & Limitations
The trained ANN controls the inverter without an online mathematical model, cost-function evaluation, or MPC optimization.

Abstract

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Model predictive control (MPC) has become one of the well-established modern control methods for three-phase inverters with an output LC filter, where a high-quality voltage with low total harmonic distortion (THD) is needed. Although it is an intuitive controller, easy to understand and implement, it has the significant disadvantage of requiring a large number of online calculations for solving the optimization problem. On the other hand, the application of model-free approaches such as those based on artificial neural networks approaches is currently growing rapidly in the area of power electronics and drives. This paper presents a new control scheme for a two-level converter based on combining MPC and feed-forward ANN, with the aim of getting lower THD and improving the steady and dynamic performance of the system for different types of loads. First, MPC is used, as an expert, in the training phase to generate data required for training the proposed neural network. Then, once the neural network is fine-tuned, it can be successfully used online for voltage tracking purpose, without the need of using MPC. The proposed ANN-based control strategy is validated through simulation, using MATLAB/Simulink tools, taking into account different loads conditions. Moreover, the performance of the ANN-based controller is evaluated, on several samples of linear and non-linear loads under various operating conditions, and compared to that of MPC, demonstrating the excellent steady-state and dynamic performance of the proposed ANN-based control strategy.

I. INTRODUCTION

Three-phase inverters with LC filters require control that maintains low-THD voltage despite load variation, nonlinearity, and transient demands. The paper motivates replacing MPC’s online optimization with an ANN trained from MPC-generated data.

Three-phase inverters with output LC filters are used to provide high-quality, low-THD sinusoidal voltage for varied loads.
Controllers must handle load variations, system nonlinearity, stability, and fast transient response.
MPC predicts future behavior and selects switching actions by minimizing a predefined cost function.
MPC is intuitive and flexible but requires substantial online computation to solve its optimization problem.
The proposed feed-forward ANN is trained offline by MPC under full-state observation, then controls inverter voltage online without MPC.
The approach directly generates inverter switching signals without requiring an inverter model or an online cost function.

II. SYSTEM DESCRIPTION AND MODELING

The system is a three-phase voltage-source inverter with complementary switching devices, an output LC filter, and either linear or nonlinear loads. Switching states are transformed into αβ voltage vectors for control.

A. System description via Clarke transformation: The modeled power circuit connects a three-phase voltage-source inverter and output LC filter directly to an unknown linear or nonlinear load.
A. System description via Clarke transformation: Each converter leg uses complementary switches, so the inverter state is represented by binary signals Sa, Sb, and Sc.
A. System description via Clarke transformation: The switching states are transformed into the complex αβ reference frame to obtain inverter voltage vectors.
A. System description via Clarke transformation: The inverter has eight switching combinations but only seven distinct output voltage vectors because v0 = v7.
A. System description via Clarke transformation: The filter current, capacitor voltage, and output current are expressed in vectorial form for the system description.

B. LC filter modeling

The LC filter is represented as a continuous- and discrete-time state-space model that predicts output voltage from candidate inverter voltage vectors while treating load current as a disturbance.

B. LC filter modeling: The LC filter model separates inductance and capacitor dynamics into a continuous-time state-space system.
B. LC filter modeling: The measured filter current and capacitor voltage form the system state, while the output voltage is the modeled system output.
B. LC filter modeling: The continuous-time model is discretized for sampling time Ts to support predictive control.
B. LC filter modeling: MPC predicts output voltage for every candidate input vector using estimated output current, assuming io(k −1) = io(k) for sufficiently small Ts.

III. MODEL PREDICTIVE CONTROL FOR NEURAL NETWORK

MPC is used as the reference controller for both generating offline ANN-training data and comparing ANN and MPC performance under linear and nonlinear loads.

MPC generates the data required to train the neural network offline and provides the comparison baseline for linear and nonlinear loads.

A. Proposed Predictive Controller Strategy

The MPC strategy predicts the inverter’s future output voltage for each possible switching state and selects the state minimizing the voltage-tracking cost. Its inputs are measured filter variables and the voltage reference, and its outputs are the three switching signals.

Predictive control: MPC uses the inverter’s discrete-time model to predict controlled variables for each possible switching state before selecting the optimum state.The controller assumes a finite set of switching states and corresponding output-voltage vectors.
Cost-function evaluation: The cost function compares the reference output-voltage vector with the predicted output-voltage vector in orthogonal coordinates.The reference components are v∗cα and v∗cβ, while vcα and vcβ represent the predicted output voltage at k + 1.
Inputs and outputs: At each sampling instant, MPC receives filter current, output voltage, and reference-voltage measurements and returns switching signals Sa, Sb, and Sc.The variables are expressed in αβ coordinates in the control-cycle description.
Online optimization: The optimization sequentially evaluates seven possible voltage vectors, predicts vc(k + 1), and retains the vector with the lowest cost.The selected switching state is ultimately returned to the converter switches.

B. Discussion

The paper identifies online optimization as MPC’s main computational drawback and proposes replacing online MPC with an offline-trained neural-network approximation of its optimal control law. MPC remains the teacher during training rather than the online controller.

Limitation of MPC: MPC determines the control signal by minimizing a cost function online at every time instant, leading to many online computations.This computational burden motivates the alternative controller proposed in the paper.
Proposed alternative: The proposed feed-forward ANN is trained offline to represent the optimal control law generated by MPC.MPC is used only as a teacher for generating training data.
Online control: The ANN-based approach is presented for a three-phase inverter with an output LC filter and is described as avoiding online cost-function evaluation and optimization.The paper also states that the approach does not require the controlled system’s mathematical model during online control.

IV. IMPLEMENTATION OF ANN-BASED CONTROLLER

The proposed controller uses a feed-forward ANN to map measured inverter variables to switching actions. The implementation uses a shallow fully connected network whose parameters are trained from data generated by MPC.

ANN structure: Feed-forward networks implement memoryless input-to-output mappings through layered computing elements without loops.The ANN structure includes input, hidden, and output layers.
ANN model: The ANN model uses an activation function, input vector, weights, and bias, with training optimizing the weights and bias through a cost function.The activation function may be nonlinear, such as a logistic sigmoid or hyperbolic tangent.
Controller inputs: Each sampling instant, the trained ANN receives measured filter current, output voltage, output current, and reference-voltage variables as inputs.The block diagram describes these measured variables as the controller inputs.
Controller outputs: The ANN explicitly generates the optimum voltage vector, after which switching states Sa, Sb, and Sc are directly applied to the converter switches.This maps the learned control output to the inverter’s switching commands.
Network implementation: The implementation uses a shallow fully connected multilayer perceptron with one hidden layer and 15 hidden units selected by grid-search tuning.Training uses the Scaled Conjugate Gradient method.

B. ANN Training Procedure

The proposed ANN is trained offline from MPC-generated data to map measured inverter and filter variables to the optimal voltage-vector switching choice. After training, it directly controls the inverter online using measured states and the reference voltage.

ANN inputs and outputs: The ANN receives eight αβ-coordinate features derived from filter current, output voltage, output current, and reference voltage measurements.Real and imaginary components are fed separately.
ANN inputs and outputs: Its seven-element one-hot output identifies the optimum voltage vector among the inverter’s seven possible vectors.Only the selected vector index is active at each sampling instant.
Training data: MPC-generated training data covers 70 experimental conditions, including 60 resistive-load cases and 10 diode-bridge rectifier cases with varied parameters.The simulations vary operating and component conditions such as sampling time, filter values, DC-link voltage, and reference voltage.
Training data: The dataset contains 217,510 instances for 60 conditions and 247,820 for 70 conditions, split into 70% training and 30% testing and validation.The 70-condition dataset is larger than the 60-condition dataset.
Online control procedure: After offline fine-tuning, the ANN replaces MPC online and directly generates switching states from measurements and the voltage reference at each sampling interval.The trained ANN produces the optimum vector for the next instant, whose corresponding switching states are applied to the converter.

V. SIMULATION IMPLEMENTATION AND RESULTS

The simulations evaluate ANN-based and MPC controllers for resistive, no-load, inductive, and diode-bridge-rectifier conditions. Across most tested cases, the ANN controller provides lower THD and faster settling, although some cases favor MPC or expose ANN tracking failure.

Simulation setup: The study evaluates both controllers under linear and nonlinear loads, examining steady-state and dynamic performance across varied operating conditions.The simulations use MATLAB/Simulink and compare resistive loads, no-load transients, inductive loads, and diode-bridge-rectifier operation.
Steady-state performance: For a 5 kΩ resistive load, ANN output-voltage THD is 1.6%, compared with 3.95% for MPC.Both output voltages are sinusoidal with low distortion, while LC filtering attenuates high-frequency harmonics in the filter current.
Dynamic performance: Under no-load transients, ANN reaches steady state in less than 5 ms, whereas MPC requires about 20 ms, with voltage THD of 0.72% versus 1.92%.The comparison uses a 50 µF filter capacitor, 3.5 mH filter inductance, and 30 µs sampling time.
Nonlinear and inductive loads: For the inductive load, output-voltage distortion is 2.2% with ANN and 4.86% with MPC.The MPC result could be improved using a smaller sampling time or a larger filter capacitance.
Cross-case comparison: Across 50 unseen test cases, ANN generally outperforms MPC in THD and settling time, with similar performance for 60 and 70 training cases.The test set includes 30 resistive-load cases and additional diode-bridge-rectifier cases.
Observed limitations: MPC performs better in cases S26–S30, while ANN fails to track the reference in S49; higher sampling frequency, larger capacitance, or more varied training data are proposed remedies.A one-delay input step improves ANN performance in several cases, reducing the listed ANN THD values for S26, S27, S28, S29, and S49.

THD (%)

The section frames sinusoidal-voltage generation as a repetitive control task that neural networks can learn, while noting that simulation evidence alone does not establish practical novelty.

ANN rationale: Generating a sinusoidal output voltage is treated as a repetitive task whose action sequences a neural network can learn.This rationale supports applying a feed-forward ANN to inverter voltage control.
Practical scope: Simulation results alone are insufficient to prove the proposed method’s novelty in practical applications.The paper identifies practical validation as a limitation and suggests that the trained network may require fine-tuning for practical use.

VI. CONCLUSIONS AND FUTURE WORK

The paper develops and tests a feed-forward ANN controller for a three-phase inverter with an LC filter, using MPC for training-data generation and comparison. Across 50 unseen simulations, ANN achieves lower THD and faster transient response than MPC, while practical novelty remains unproven from simulation alone.

Contribution: A feed-forward ANN directly controls the inverter output voltage without requiring the inverter’s mathematical model during online control.The controller is tested for different loads and operating conditions.
Method: MPC generates the offline training data and provides the comparison baseline for linear and nonlinear load conditions.The ANN is trained to replace MPC during online voltage tracking.
Results: Across 50 test cases different from the training cases, ANN provides lower THD and faster, safer transient response than MPC.The conclusion characterizes the resulting steady-state and dynamic performance as excellent within the simulation study.
Future work: The method’s practical novelty is not established because the evidence is limited to simulations.The paper identifies practical validation as the main limitation.