#### GRID-CONNECTED INVERTERS

Welcome to the application example of a grid-connected inverter emulation using Impedyme’s Combined Hardware and Power Hardware-in-the-Loop (CHP) technology. In this discussion, we'll explore the role these inverters play in modern power systems, integrating distributed energy sources with the grid. Join us as we unravel the complexities and shed light on the critical functions that grid-connected inverters perform. Furthermore, we will also emulate the built models in real-time to test these at full power level using Impedyme’s CHP.

Fig 1. Grid-Connected Inverter

In the modern energy systems, the integration of renewable energy sources and storage solutions has become paramount. The 3-phase grid-connected inverters with battery storage, offers a robust solution to enhance grid stability, maximize renewable energy utilization, and ensure reliable power supply.

At the heart of the operation lies the grid interconnection capability of 3-phase inverters. These power electronic systems serve as the interface between energy sources, such as solar or wind power systems, and the electrical grid. By converting the direct current (DC) output from renewable sources into alternating current (AC) compatible with the grid, these inverters facilitate integration of renewable energy into the existing infrastructure.

Beyond grid interconnection, the integration of battery storage systems enhances the functionality of 3-phase inverters. Batteries serve as reservoirs of energy, enabling the capture and storage of surplus electricity generated during peak periods. This stored energy can then be discharged during times of high demand or low renewable energy generation, hence smoothing out fluctuations and enhancing grid stability.

Another crucial aspect of 3-phase grid-connected inverters is their ability to control reactive power. By actively managing reactive power flow, these inverters contribute to voltage regulation, power factor correction, and overall grid stability. This capability is particularly critical in maintaining grid reliability and ensuring optimal performance.

Furthermore, the 3-phase grid-connected inverters with battery storage can provide ancillary grid support functions. These include frequency regulation, voltage support, and black start capabilities, which further enhance the resilience and robustness of the grid. By having advanced control algorithms, these inverters actively participate in grid stabilization efforts, contributing to the transition towards a smarter, more resilient energy infrastructure.

In summary, through their ability to integrate renewable energy sources, store excess energy, and provide grid support functions, these inverters play a role in modern power systems.

A typical circuit diagram for the 3-phase grid-connected inverter is presented in Fig. 2.

Fig 2. Circuit Diagram of 3-Phase Grid-Connected Inverter System

#### SIMULINK MODEL IMPLEMENTATION:

Battery Pack Modeling:

The Simulink model of the battery for the inverter is shown in the figure below. The model relies on the battery current to estimate the state of charge (SoC), and similarly predicts the open circuit voltage dynamically as a function of SoC. This Coulombic counting approach is known for its simplicity and is primarily dependent on the discharge from the battery pack.

Fig 4. Simulink Battery Model

State of Health (SoH) is determined by comparing the measured voltage of a battery pack to its nominal voltage. The SoH expresses the battery's current condition as a percentage, with values below 100% indicating degradation. This calculation helps assess battery health and anticipate performance changes over time. Now, let us look at the inverter modeling.

Inverter Modeling:

Behind their inverter’s operation lies a set of fundamental equations that govern their behavior and performance. Let's delve into the mathematical equations of these inverters.

In a 3-phase system, the relationship between line voltages and phase voltages is crucial. The equation, Vphase=Vline/√3, says that the phase voltage is simply one-third of the line voltage. This relationship ensures balanced power distribution across the three phases.

Likewise, phase currents mirror line currents in balanced 3-phase systems. This means that Iphase=Iline .

The active power output of a 3-phase grid-connected inverter, denoted as P, is a parameter determining its energy conversion efficiency. Expressed as follows:

P=√3 Vphase Iphase cosθ

This equation considers the phase voltage, phase current, and power factor, cos θ. Active power represents the real power transferred to the grid, driving electrical loads, and contributing to overall energy consumption.

On the other hand, reactive power (Q), plays a vital role in maintaining voltage stability and system reliability. Defined by the following equation:

Q=√3 Vphase Iphase sinθ

The above equation captures the reactive power output of the inverter, accounting for the phase angle difference between voltage and current θ. Reactive power flow supports voltage regulation and reactive power compensation, essential for grid stability.

Central to this control framework is the P and Q control method, where adjustments to the inverter's output voltages are made to track desired references for active and reactive power. By continuously monitoring the deviation between actual and desired power levels, the inverter ensures proper energy delivery to the grid.

In parallel, the Phase-Locked Loop (PLL) with ABC-to-DQ transformation serves as a critical component in achieving synchronization with the grid voltage. By accurately tracking the phase and frequency of the grid voltage and transforming it into the DQ coordinate system, the inverter achieves granular control over active and reactive power output. This transformation simplifies the control mechanism by decoupling the control of active and reactive power, thereby enabling independent regulation, and ensuring optimal performance under varying grid conditions. Furthermore, the decoupling system acts as a catalyst for precision control, ensuring seamless coordination between current and voltage references to generate Pulse-Width Modulation (PWM) signals. These signals dictate the switching of inverter components, allowing for meticulous regulation of output voltages and seamless integration with the grid.

In essence, the integration of P and Q control, PLL with ABC-to-DQ transformation, and the decoupling system empowers 3-phase grid-connected inverters with unparalleled precision in controlling active and reactive power output. This intricate control architecture not only ensures efficient operation but also fosters seamless integration with the electrical grid, laying a solid foundation for the widespread adoption of renewable energy sources and paving the way for a sustainable energy future.

Fig 5. Simulink Inverter Model

### Grid Modeling:

Here, we seek to replicate the behavior of various components like generators, loads, and transmission lines. At the core of grid modeling lies the "3-Phase Programmable Voltage Source" block, a Simulink component that allows us to define the characteristics of the voltage source of the grid.

By configuring parameters such as voltage magnitude, frequency, and phase angle, we can emulate diverse grid conditions, ranging from nominal operation to fault scenarios.

Integration of the "3-Phase Programmable Voltage Source" along with series impedances blocks within Simulink provides us a good platform for simulating and analyzing grid behavior. By running simulations with these blocks incorporated into the model, we can explore a wide range of grid scenarios and assess system performance under various conditions.

Fig 6. Simulink Grid Model

#### IMPEDYME’S CHP TECHNOLOGY

Fig 7. Impedyme’s CHP Cabinet

Fig 11. Grid-Connected Inverter testing using Impedyme’s CHP

Let us now see how the system, that is, the battery, the inverter, and the grid, are modeled in Simulink [1].

Fig 3. Simulink Implementation of Grid-Connected Inverter

#### EMULATION PARAMETERS & EXPERIMENT RESULTS

If the inverter hardware is readily available, you can also connect the external hardware to Impedyme’s CHP and test the dynamics of your system.

REFERENCES

[1] A. Bakeer, M. A. Ismeil and M. Orabi, "A Powerful Finite Control Set-Model Predictive Control Algorithm for Quasi Z-Source Inverter," in IEEE Transactions on Industrial Informatics, vol. 12, no. 4, pp. 1371-1379, Aug. 2016, doi: 10.1109/TII.2016.2569527.

All models have now been built, and before proceeding to the tests, let us get introduced to Impedyme’s CHP technology.

The Impedyme’s emulation solutions mimic your MATLAB Simulink models that can be used for high power tests, up to a few Mega Watts scale, for bandwidths up to 20 kHz. Simply connect the optical links to our cabinets and deploy your models to begin the testing. The cabinets have multiple optical links each up to 12.5 giga-bits per second. For simulations with ultra-low step-times, the equipment supports FPGA-based tests, that allows you to have time steps as low as a few nanoseconds. Moreover, the FPGA brings in a better performance for your real-time emulation since the processing speed of an FPGA is much higher than that of a CPU.

Also, for high-speed emulations, the individual FPGAs of the drawers can communicate among them. The testing using Impedyme’s CHP is straightforward as it uses Simulink designs. Our products come with a wide range of pre-designed models, which you can customize the designs according to your needs and requirements. Furthermore, if we were to emulate both the input and the output side of the power systems, we can have a circulating power flow. Since the power is recirculated, we only must feed in power losses from the grid. By having such a technology can reduce the power requirements of your lab for testing large power systems. Moreover, during the real-time emulation of your models, our integrated thermal management utilizes an advanced liquid + air cooling technology that ensures that does not require any additional chiller for cooling. Thus, we use Impedyme’s CHP to emulate the developed powertrain model in real-time.

Now that we have developed the grid-connected inverter models, let us see how the connections are given to kickstart the testing process.

Fig 8. Grid-Connected Inverter Emulation: Impedyme’s CHP Connection Diagram

We allocate the first drawer, that is the top-most drawer, for the battery model and the second drawer for the 3-phase inverter. Likewise, finally, the third drawer is dedicated for the grid. The last two, that is the two bottom-most drawers are dedicated for the Active Front end Converters that provide the DC coupling for the emulation.

Now, let’s see how the connections are made to allocate these drawers. the power connections are given on the backside of the cabinets. The DC supply from the active front end drawer is given to the battery model drawer and the battery voltage is provided to the 3-phase inverter’s input supply. The second drawer emulates the action of an inverter and converts the DC from the battery to 3-phase AC (purple connections), which are subsequently provided to the grid drawer below, and finally the DC coupling is given back to the active front end drawer from the grid model to have a circulating power flow. Since the connections are complete, we are now ready to test.

Fig 9. Transient Response of the Emulation

Fig 10. Emulation Response for Step Power Change

The system parameters for the experiment are as follows.

CHP seamlessly integrates hardware-in-the-loop (HIL) and power hardware-in-the-loop (PHIL) capabilities, offering unparalleled accuracy and efficiency in EV development. With CHP, engineers can simulate real-world scenarios with precision, testing grid-connected inverter systems under dynamic conditions. From battery systems to inverters, CHP empowers manufacturers to optimize performance, enhance reliability, and accelerate time-to-market for your products. The modular design ensures flexibility to adapt to evolving testing needs, while its intuitive Simulink interface streamlines the testing.

Some of Impedyme CHP’s features include: