Networked System Modeling for Power Grid Analysis

🔄 Power System Dynamic Simulation: Cracking the DAE Code! ⚡ Ever wondered how we simulate faults, switching events, or dynamic responses in power systems? Behind the scenes, it's all about solving Differential-Algebraic Equations (DAEs) — a powerful mathematical framework that blends electrical physics with numerical methods! 🧠⚙️ Here’s a crisp breakdown of the simulation journey ⬇️ 🔧 1: Model the Subsystems We start by modeling each component using physics-based equations: 🔹 Synchronous Generators (in dq0 reference frame) 🔹 Excitation systems 🎛️ 🔹 Turbine-Governor dynamics ⚙️ 🔹 Transmission Network & Loads (static ZIP & dynamic motor) 🔹 Optional: HVDC systems & FACTS devices (like STATCOM, TCSC, etc.) Each of these has its own differential or algebraic equations depending on whether they have dynamic states or steady constraints. 🌀 2: Axis Transformation Since dq axes differ per generator, we align all machine variables to the common network reference frame (R-I). This requires a transformation like: 📐 ER = Ed·sinδ + Eq·cosδ 📐 EI = Eq·sinδ - Ed·cosδ So now, everyone speaks the same "electrical language"! ⚡🗣️ 📚 3: DAE Framework! All those individual models come together into a DAE system: 🔸 Differential equations for dynamic components (like rotor angle, speed, field current):   📌 𝑥̇ = f(x, V) 🔸 Algebraic equations for the network (Kirchhoff’s laws, load flow, constraints):   📌 I = g(x, V) = Y·V Where: 🧮 x = system state vector (machine states, control system states) 🔌 V = bus voltage vector (real & imaginary) ⚡ I = current injections into the network 📊 Y = network admittance matrix Together, these form the full picture of system dynamics and network interactions. ⏱️ 4: Solve It Smartly! Two major solution approaches: 1️⃣ Partitioned Solution with Explicit Integration  • Solve differential & algebraic equations separately but iteratively  • Methods like Runge-Kutta help simulate time steps 2️⃣ Simultaneous Solution with Implicit Integration  • Solve the whole DAE set in one go using methods like Backward Euler  • More stable, especially for stiff systems 💥 At fault inception, voltages may change instantly, but state variables (like δ, ω, Eᶠ) remain continuous — a key assumption in simulations! 🎯 Big Picture When all subsystems are synchronized via the DAE framework, we can simulate: ⚡ Faults 🔁 Transients 🎯 Stability margins 🧪 Control system responses …all from millisecond to minute-level timeframes. Power system dynamic simulation isn't just about solving equations — it's about replicating how the grid thinks, reacts, and stabilizes in real time. As grids become more complex with renewables, HVDC, and FACTS, mastering this integrated DAE approach is essential for building resilient and intelligent power systems of the future. ⚡📈🌍 https://lnkd.in/gqD6ygpC

As power systems transition toward higher shares of Inverter-Based Resources (IBRs), traditional Root Mean Square (RMS) models are no longer sufficient to fully capture the dynamic interactions between converters and the grid. ✓ RMS models provide averaged, simplified representations that are effective for conventional synchronous machines. ✓ However, IBR control dynamics — such as phase-locked loops (PLL), fast inner control loops, and ride-through strategies — can lead to sub-synchronous oscillations, control interactions, or stability issues that RMS models simply cannot detect. This is where Electro-Magnetic Transient (EMT) models become indispensable EMT simulations operate at microsecond-level time steps (10–20 µs) and include detailed switching and control behaviours. They allow engineers to: ▪️Analyze sub-synchronous oscillations and converter-grid interactions. ▪️Validate protection schemes under unbalanced faults. ▪️Accurately assess plant performance during disturbances. ▪️Ensure interoperability between multiple IBR technologies (e.g., hybrid BESS + PV). In essence: ▪️RMS = quick overview. ▪️EMT = high-resolution “slow-motion” insight into system dynamics.

Stability Analysis of Grid-Following and GridForming Converters Based on State-Space Modelling Xian Gao, Student Member, IEEE, Dao Zhou, Senior Member, IEEE, Amjad Anvari-Moghaddam, Senior Member, IEEE, and Frede Blaabjerg, Fellow, IEEE AAU Energy, Aalborg University, Aalborg, Denmark Abstract - This paper conducts a comprehensive analysis and comparison of the control loops of the grid-following and grid-forming voltage source converters connected to the power grid. Eigenvalue trajectories are studied in order to obtain an accurate stability analysis. A timedomain simulation model of a 1.5 kW grid-connected converter is developed by using Matlab/Simulink to investigate the stability of the grid-following and gridforming control under different short-circuit ratios. The stability boundaries of the grid-following control and the grid-forming control are explored and compared with theoretical analysis. The result reveals that the gridfollowing control is better suited for a stiff power grid, while the grid-forming control is more suitable for a weak power grid. Finally, an experimental prototype is established to verify the effectiveness of the theoretical analysis. VIEW ARTICLE : https://lnkd.in/dRRk9Uwq

I’m a power systems modeler and a lot of folks wonder what it is we do all day. I’d like to go over what power systems modeling is and how we do it. Now what is a grid model? It’s a mathematical representation of the grid that can be used in simulations. We take the entire power grid that you see in the field, all those power lines, substations, and generators and convert that into a form that can be used in computer simulations to predict its behavior. As a power systems modeler, we build models of the grid to be used in various simulations. For us a model is a snapshot of the grid at a specific point in time meant to simulate a specific operating state. We are ultimately in the business of collecting data that represents these grid elements, then figuring out how to manage it and store that data before validating it. Then finally we transform the data into different formats for different simulators. Power systems modelers typically have to work in an interdisciplinary manner combining both power systems engineering and software development. You need to know how devices operate at a fundamental level but also how to collect and manage large amounts of data using programming and software development skills. Knowing programming languages like SQL, Python, Java, C#, and more are very useful in this role. You may use software like PSSE, PowerWorld, TARA, PSLF, Aspen Oneliner, CAPE, PSCAD, or EMTP. You may also use the Common Information Model or CIM to convey operational modeling information. On a daily basis the work is very cross-functional. A modeler is typically gathering data from many other stakeholders both internal and external. Then they need to understand their customers needs to deliver the models they need to plan and operate the grid. To do this you’ll have to spend a lot of time communicating with stakeholders. You’ll need to work with engineers who design infrastructure, planners, operators, and more. Ultimately the models we develop can be used in both the operations and planning horizons. These models may include steady state, dynamic, short circuit, electromagnetic transient, geomagnetic disturbance, market models, operations models, and more. At the end of the day we create a model representing the grid as shown in the image below for many different softwares. It’s a constant effort to keep the models up to date as the grid changes. But ultimately our work forms the foundation of reliable power system operations and planning. Without good models every study would be wrong. #powersystems #powersystemsmodeling #engineering

A critical challenge in modern grid stability is that inverter-based resources (IBRs) are often “black boxes” to utilities and system operators. Inverter manufacturers and plant developers understandably hesitate to disclose proprietary control strategies, leaving operators with limited visibility into internal dynamics. The problem is further compounded by the fact that IBRs can switch among multiple control modes, which are typically unknown to operators yet can exhibit dramatically different dynamic behaviors. In the final days of 2025, we were excited to learn that our paper on black-box IBR modeling was accepted by IEEE Transactions on Smart Grid. In this work, we develop a comprehensive data-driven framework that uses only terminal measurements to discover unknown control modes and learn continuous-time models that accurately capture IBR dynamics under each mode. By leveraging physics-inspired deep learning, the proposed approach addresses four major challenges in a unified way: 🚀 High-Order Nonlinear Representation Using only terminal measurements, the framework provides a general learning approach for characterizing arbitrary high-order nonlinear dynamics of IBRs. It is not tied to any specific control paradigm and can cover anything from power/voltage/current control loops to virtual synchronous machines (VSMs) and phase-locked loops (PLLs). 🚀 Continuous-Time Modeling Unlike most data-driven methods built on discrete-time models (e.g., RNNs, LSTMs, Transformers), our approach learns continuous-time state-space models (differential-algebraic equations). This enables seamless integration of the learned IBR models into standard power-system time-domain simulations with arbitrary numerical integration schemes and step sizes. 🚀 Discovery of Unknown Control Modes A physics-inspired deep unsupervised learning mechanism automatically identifies distinct control modes from historical disturbance data and learns separate state-space models that represent the dynamics associated with each mode. 🚀 Robustness to Noise and Uncertainty Inspired by Kalman filtering, the learning architecture explicitly accounts for system uncertainties and measurement noise, both of which are ubiquitous in real-world grid systems and data. It ensures the method’s robust performance in practical settings. The examples in the paper demonstrate how the proposed framework can learn accurate time-domain models of fully black-box IBRs and deliver highly accurate long-horizon predictions of their responses to grid disturbances, e.g., subsynchronous oscillations caused by PLL interactions in weak grids. See details here: https://lnkd.in/eFd5CU4e #PowerSystem #SmartGrid #InverterBasedResources #RenewableEnergy #PowerElectronics #Control #PowerSystemStability #PowerSystemModeling #PowerSystemSimulation #SystemIdentification #DataDriven #MachineLearning #DeepLearning #ArtificialIntelligence #PhysicsInformed #IEEETransactionsOnSmartGrid

⚡ Analysing the stability criteria of a power system containing a large number of voltage source converters (VSCs) can become a complex task due to their non-linear nature and the various time scales different controllers employ. Therefore, it is no surprise that over time, many methods to model such systems arose to analyse under which conditions they became unstable.   💡 Small-signal modelling and stability analysis have a strong theoretical foundation and are widely used due to their relative simplicity and effectiveness. The best-known approach is based on state-space models and then uses either eigenvalue or root locus analysis to derive stability criteria. A similar approach is adopted by the methods, representing the systems as a source with impedance cascading with load impedance. The core advantage of the impedance modelling methods is that they can be used for systems containing several "black boxes", i.e., converters with unknown internal structures and parameters. However, impedance-based approaches face challenges when systems contain multiple VSCs with coupling over a wide frequency range. use numerical simulation with detailed models in the time domain. However, an approach based on Lyapunov’s stability criterion can be employed to prove the asymptotic stability of the nonlinear system. However, the key challenge that this approach faces in many practical applications is finding the Lyapunov function, i.e., the function that captures the dynamics of the system and can be used to prove that the system will eventually dampen the oscillations. A detailed overview of these methods can be found at https://lnkd.in/dKStX6Xs.   🎯 The grid or converter port impedance can be obtained by active injection of current or voltage and pertinent measurement. Hence, the external characteristics of converters and grids can be obtained regardless of the internal information of the system. However, the impedance measurement methods must fulfil several criteria. First, the equipment used during measurement must impose the operating point of interest, i.e., the nominal operating voltage and currents. Second, the disturbance injection must have enough voltage and power to create disturbances that can be distinguished from system noise. Third, the equipment must be able to generate disturbances across a wide frequency range to capture important dynamics. Using EGSTON amplifiers, measuring the impedance of a battery, a converter, or a grid up to 30 kHz is possible. If you would like to know more about EGSTON solutions for impedance measurement, check out https://lnkd.in/dny_ze_x. #smartgrids #stability #renewableenergy #testing #hil

Modeling of Grid Connected BESS: - When modeling a Grid-Connected Battery Energy Storage System (BESS), several factors need to be considered. Here are some key aspects of the modeling process: 1. Battery Model: A battery model that accurately represents the behavior of the battery is crucial. This includes considering parameters such capacity, efficiency, charge/discharge rates, voltage limitations, and any manufacturer specifications. Battery models can include nonlinearities, thermal effects, aging processes, and electrochemical characteristics. 2. Power: The power electronics converter, typically including a DC-DC converter and a DC-AC in, plays a vital role in connecting the battery to the grid. The converter's control algorithms and its dynamic response need to be modeled accurately to ensure proper grid integration, power flow control, and regulation. 3. Grid Interface: The BESS needs to be connected to the grid through appropriate interface equipment such as switchgear, protection devices, and transformers. Modeling these components accurately, including their response to grid disturbances, is essential to ensure safe and reliable operation. 4. Control Strategy The control strategy is a crucial part of the BESS model. It governs how theSS reacts to grid conditions, handles charge/discharge cycles, and interacts with other grid assets. The control strategy typically includes power flow control, frequency regulation, voltage regulation, and active/reactive management. 5. Grid Dynamics: The grid is a highly dynamic and complex system influenced by various such as generation/load fluctuations, system faults, and stability issues. The BESS model should consider these dynamics in terms of grid frequency, voltage fluctuations, and grid disturbances to accurately represent its interactions the grid. 6. System Integration: To accurately model the grid-connected BESS, its integration the overall power system should be taken into account. This includes modeling the interactions with other generation sources, loads, and control systems present in the grid. These modeling aspects can be implemented using various simulation tools, such as power system simulation software like PSS/E, PSCAD, Grid-D, or MATLAB/Simulink. It is important to calibrate and validate the model using actual data, test cases, and field measurements to ensure its accuracy and reliability in representing the of a real-world Grid-Connected BESS. A good document is attached to explore the modeling aspect of BESS in PSCAD. #electricalengineering #BESS #renewableenergy #solarenergy #windpower #powersystems #powersystemexperts #PSCAD #EMTStudies #electricaldesign #electricalengineer

𝐈𝐧𝐯𝐞𝐫𝐭𝐞𝐫 𝐌𝐨𝐝𝐞𝐥𝐢𝐧𝐠 𝐟𝐨𝐫 𝐒𝐭𝐞𝐚𝐝𝐲-𝐒𝐭𝐚𝐭𝐞 𝐚𝐧𝐝 𝐃𝐲𝐧𝐚𝐦𝐢𝐜 𝐒𝐭𝐮𝐝𝐢𝐞𝐬 The modeling of inverters varies significantly based on the type of study being performed—steady-state or dynamic analysis. 𝐈𝐧 𝐬𝐭𝐞𝐚𝐝𝐲-𝐬𝐭𝐚𝐭𝐞 𝐬𝐭𝐮𝐝𝐢𝐞𝐬, detailed control mechanisms of inverters are generally not modeled. Instead, the inverter's output is fixed based on the type of analysis being conducted. 𝐋𝐨𝐚𝐝 𝐅𝐥𝐨𝐰 𝐀𝐧𝐚𝐥𝐲𝐬𝐢𝐬: The inverter is modeled as a source with specified real power (P) and reactive power (Q) outputs. The power injection values are typically based on system operating conditions and inverter ratings. 𝐒��𝐨𝐫𝐭-𝐂𝐢𝐫𝐜𝐮𝐢𝐭 𝐀𝐧𝐚𝐥𝐲𝐬𝐢𝐬: The inverter’s short-circuit contribution is considered for fault current calculations (initial steady state value) 𝐇𝐚𝐫𝐦𝐨𝐧𝐢𝐜 𝐀𝐧𝐚𝐥𝐲𝐬𝐢𝐬: Inverters are modeled as harmonic current sources based on their harmonic spectrum and Thevenin or Norton equivalent In steady-state models, the inverter’s dynamic behavior and its interaction with the grid (voltage and frequency variations) are not represented. 𝐃𝐲𝐧𝐚𝐦𝐢𝐜 𝐬𝐭𝐮𝐝𝐢𝐞𝐬 require a detailed representation of the inverter, including its control system and interaction with the grid. The dynamic model reflects the inverter’s response to grid voltage and frequency fluctuations and its behavior under transient conditions. 𝐃𝐲𝐧𝐚𝐦𝐢𝐜 𝐂𝐨𝐧𝐭𝐫𝐨𝐥 𝐌𝐞𝐜𝐡𝐚𝐧𝐢𝐬𝐦𝐬 The inverter interacts with the Point of Common Coupling (PCC) to ensure proper voltage and frequency regulation. When the grid conditions exceed the inverter’s operational limits, the inverter operates independently, responding dynamically to protect itself and maintain stability. 𝐒𝐨𝐟𝐭𝐰𝐚𝐫𝐞 𝐦𝐨𝐝𝐞𝐥𝐥𝐢𝐧𝐠 𝐜𝐚𝐩𝐚𝐛𝐢𝐥𝐢𝐭𝐲 𝐨𝐟 𝐢𝐧𝐯𝐞𝐫𝐭𝐞𝐫 𝐄𝐓𝐀𝐏: Steady-State: ETAP allows steady-state modeling of inverters, focusing on power flow, short circuit, and harmonic analysis. 𝐃𝐈𝐠𝐒𝐈𝐋𝐄𝐍𝐓 𝐏𝐨𝐰𝐞𝐫𝐅𝐚𝐜𝐭𝐨𝐫𝐲: Steady-State: Inverters can be modeled with fixed steady-state values for load flow and harmonic studies. Dynamic Modeling: For dynamic studies, an inverter’s control behavior can be modeled using user-defined or OEM-provided models. 𝐏𝐒𝐒𝐄: Steady-State: Inverters are modeled as generators with fixed outputs for steady-state analysis. Dynamic Modeling: The generator can be integrated with dyr file of generic or user defined model. 𝐏𝐒𝐂𝐀𝐃: Dynamic Studies: PSCAD is primarily used for transient and dynamic studies, where detailed inverter models provided by the OEM are required. To achieve accurate results, always prefer OEM-provided models for dynamic studies, as they include proprietary control features tailored to the specific inverter design. POWER PROJECTS #powersytem #inverter #solar #powerplant #generator #modelling #OEM #manufacturer #manufacturing