AI-Powered Digital Twin for Grid-Forming Inverter   

GFMIs are predesigned based on linear models and accurate time-invariant parameters to operate at a specific operating condition and after commissioning, the operating conditions cannot be guaranteed. This will reduce the performance, reliability, and efficiency [4]. Linear models neglect nonlinearity and the interactions with the RESs and the grid, operating GFMIs under different conditions, for example, low voltage and black start could lead to stability problems [5]. A nonlinear high-fidelity adaptive model for GFMI is needed to capture the dynamics and interactions with the RES and the grid. The nonlinear model can be used to analyze the transient stability and ensure robustness under different grid operating conditions. Furthermore, leveraging both data-driven and physics-based nonlinear modeling provides the required level of accuracy and intelligence for GFMIs to adapt to various grid operating conditions.

 The project will develop a digital twin based on deep neural networks (DNNs) model for GFMI. The nonlinear model will be developed with the aid of Physics-Informed Neural Networks (PINNs) and Explainable AI (XAI) where the coordination between the GFMI and the RES, and the interaction between the GFMI and the grid will be considered. Based on the developed model Lyapunov function will be constructed to derive a transient stability criterion to ensure stability under various grid operating conditions as this is an urgent need to ensure green transition in Denmark. Artificial intelligence-based digital twins could revolutionize our power grid as they can handle nonlinearity and unknown parameters and can learn and adapt to various operating conditions. The AI-powered digital twin will ensure the operation of GFMIs under various operating conditions which enhances stability, efficiency, and reliability and will pave the way to develop an AI-powered digital twin for the future power grid.

2. State of the art

The most widely used modeling approach for GFMIs is based on linear models which neglect the nonlinear dynamics and are not robust against grid impedance variations and system parameter changes [6], more research is needed to investigate large signal stability [7]. The current trend in GFMI focuses on the controller to mimic the synchronous machine, however, no attention is paid to the GFMI model as it does not behave like a synchronous machine. Linear models are not able to analyze transient stability and a nonlinear model is needed [8]. In [9], [10], [11] enhancement of large signal stability is carried out by introducing a current limiting loop to be activated during contingencies. However, in a PECs-dominated grid, the current may not be enough to trigger the current limiter.

Deriving stability conditions for GFMI that guarantee the operation at different complex network topologies remains one of the big challenges. There are few research works dealing with the large signal stability of GFMI, where Lyapunov Krasovskii Passivity (LK-PBC) is used. In [12], passivity theory is used to find the stability region for the voltage source converter, however the converter is represented as a linear model. In [13], a provable Lyapunov-based stability analysis is presented for GFMI, however, a reduced-order model for the network is used. The impact of the delay on stability has only been reported in a few publications, see for example, [14]. The coordination between the RES, for example, the wind turbine, and the GFMI have not been investigated [15]. The interactions between the GFMI and the PECs-dominated grid can also lead to instability, for example, sustained oscillation has been detected in the Xinjiang region in China due to the interactions between a weak AC grid and permanent magnet wind turbine [4]. The nonlinear model of GFMI can address grid interaction, coordination with the RES, transient stability, and seamless operation between grid-following and grid-forming modes.

The project will develop a novel DNNs digital twin for GFMI, based on the developed model a transient stability based on the Lyapunov theory will be derived. Conventional neural networks (NNs) suffer from two handicaps, they are unexplainable black-box models and require heavy computations which make them unsuitable for industrial applications. The project proposes the use of XAI [16] and PINNs [17] which are recent AI models, and they have the potential to rectify the shortcomings of small-signal models and conventional NNs. PINNs are implemented in [18] to reduce the requirement for training data for grid-connected converters. PINNs have been reported in [19] to provide accurate state estimation for power systems with less computation. Bayesian PINNs are implemented for system identification in the inverter-dominated power grid, and they proved superior performance compared to conventional methods [20]. PINNs can provide accurate DNN models with simpler structures [21] and can capture nonlinear dynamics [22] and XAI can explain the DNNs models.

One of the main challenges facing AI-based models is to guarantee stability as the conventional control methods in industry are based on well-established theories. It is still a challenge to guarantee the stability of an NNs-based system [23] due to the complexity and difficulty of explaining the model, for industry applications, the lack of theoretical guarantees on stability will hinder the applications [24]. With the aid of PINNs and XAI an explainable nonlinear model could be derived. In this project, Lyapunov functional will be constructed for the developed model and the problem can be formulated as Linear Matrix inequalities (LMIs) or Bilinear Matrix inequalities (BMIs), in case of robust stability [25]. The GFMI AI-based digital twin will be used to investigate transient stability that will improve GFMI performance which will facilitate the green transition toward a 100% RE scenario. The following problems will be addressed in the project: 1) an AI-powered digital twin for GFMI that is suitable for transient stability that can be integrated into commercial simulation software models 2) to develop stability criteria based on the DNNs model that guarantees the operation of the GFMI at different operating conditions.

3. Competences and infrastructure

The project will be carried out at DTU Engineering Technology where the Power Electronic Systems Lab is equipped with different PECs, Speedgoat real-time simulator, dspace controller, inductions and permanent magnet machines, grid simulator, and all measurement equipment required for the project (see Fig.2). The project will involve a PhD student to be supervised by Associate Professor Ashraf Khalil and co-supervised by Professor Mehdi Savaghebi. Ashraf Khalil has long experience in power electronics modeling, the Lyapunov method, robust control, artificial intelligence, and time delay systems. Mehdi Savaghebi is a professor in power electronic-enabled power systems and has extensive research experience in the control, operation, and grid integration of PECs. The PhD student should have a background in electrical engineering and AI with a preferable master’s degree in power electronics and he will be recruited based on the recruitment procedure at DTU, and it is expected that the recruitment will be finalized before the start of the project. The PhD student will spend three months at RWTH Aachen University with Prof. Antonello Monti who is an expert in digitalization and complex power systems, and he is the leader of ACS lab which is equipped with high-performance real-time simulators and real-power system equipment.

4. Objectives & Methodology

The goal of this project is to develop an AI-powered digital twin for GFMI. The main objectives are: 1) an AI-powered digital Twin for GFMI DNNs based on XAI and PINNs, and 2) to develop a nonlinear stability analysis tool based on Lyapunov theory for investigating the transient stability of GFMIs. The proposed plan is divided into three work packages as shown in Fig. 2. The Gannt chart of the project is shown in Table 1.

WP1: A DNNs model for the GFMI. A DNNs model for the FGMI will be developed based on XAI and PINNs. T1.1: DNNs model for GFMI: The physics laws governing the dynamic of the inverter, the RES (wind turbine with permanent magnet machine), and the grid will be combined in the DNNs model.  Based on real measurements from the inverter, the RES, and the grid, a DNNs model will be developed. XAI will be implemented to explain the model.  T1.2: Validation of the GFMI DNNs model: MATLAB and Speedgoat real-time simulator will be used to accomplish this task. The developed models will be validated under different operating scenarios. In case of not achieving the required accuracy, the modeling procedure will be iterated.

WP2: Optimization and Stability Assessment Tools for GFMI. T2.1. Optimization of the DNNs model: In case the developed model is heavy for computation, the model will be optimized to achieve light computation. T2.2 Lyapunov-based transient stability method for GFMI: Based on the optimized DNNs model, the controller that includes the coordination between the GFMI and machine side will be designed using multi-objective optimization. Lyapunov function will be constructed to develop transient stability assessment tools including the time delay in the digital control loop. The stability assessment will be formulated as BMIs, LMI toolbox in MATLAB will be used. T2.3 Test the stability criteria for GFMI: the developed stability criterion will be tested at various operating conditions.

WP3: Implementation of the AI-Powered Digital twin. T3.1: Building and testing the GFMI test rig: The developed DNNs model and the stability criterion will be tested using an existing test rig in the lab, which consists of an induction machine attached to a permanent synchronous generator to mimic a wind turbine and inverter operating in a grid-forming mode which is connected to grid simulator through LC filter, see Fig. 2. T3.2: Implementation of the DNNs-based control: The DNNs model will be implemented using FPGA built-in Speedgoat real-time simulator to validate the proposed approach. T3.3: Testing the GFMI operation under various operating conditions.

5. Originality, expected outcomes and impacts.

The developed AI-powered digital twin will leverage both artificial intelligence and physics-based modeling which will achieve high-fidelity adaptive models that can be used in operation monitoring and provide a transient stability analysis tool to investigate the operation of the GFMI under severe grid conditions. This will improve the robustness, performance, efficiency, and flexibility of GFMI which will facilitate the green transition. The integration of DNNs and Lyapunov direct method to develop transient stability of the GFMI, the RES and the grid is a novel approach that will be a milestone toward an AI-power digital twin for the future power grid.