Models are the core of all model-based techniques for design, control, optimization, simulation, etc. Detailed models are the core of design activities and can be complex and slow to compute. How to create simplified, multi-purpose versions to scale and deploy your usage? The answer is Reduced Order Models *(* ROMs).

ROMs are an efficient way to reduce the complexity of models and expand their range of applications. They are key components for various applications, such as integrating 3D models into 1D models, accelerating simulations, enabling digital twins and real-time applications, creating virtual sensors and protecting IP (Intellectual Property).

Today's application will show you how to scale down electrical power systems using **Simcenter**'s Reduced Order Modeling . The system represented in **Figure 1** represents a transmission system in which the generated power (here represented by the input voltage source) is amplified by the transformer and transmitted to the load (battery) through the transmission line.

Here, the complexity comes from the transmission line model. Basically, to capture transient phenomena well, the transmission line model is discretized in space where each section (here 50 sections per 100 km) is represented by a simple circuit, as shown in Figure **1** . When the number of snippets increases, the model will be more accurate, but the number of state variables will increase. This makes the entire model quite large and consumes a lot of memory.

In this context, the objective behind creating a ROM is:

Reduce the total number of state variables by simplifying the transmission part model (transformer + transmission line)

Faithfully reproduce the transient phenomena resulting from different interconnections

This will be done using **Simcenter**** ****Reduced Order Modeling** .

The tool offers several ways to make ROMs: either from simulation data using, for example, Neural Networks and Response Surface Models (RSM) techniques or models such as state space matrices of a linearized model as in our application here.

Figure 1

The entire process can be summarized in a few steps:

Isolate the transmission part

Use

**Simcenter**Connect the ROM to the rest of the system

Check the accuracy of the results

Let's start.

**Step 1:**

Before making a ROM, the transmission part is disconnected from the rest of the system as shown in Figure 2 and linearized using **Simcenter Amesim**. The input variables are the transformer input voltage as well as the voltages at the end of the transmission line. It was decided to consider the voltages at the connection points as inputs and the currents as outputs. This helps establish a physical connection between the ROM and the rest of the physical model.

Figure 2

Now we are ready to start making a ROM.

**Step 2:**

The second step consists of loading the linearization data (matrices) into **Simcenter Reduced Order Modeling** , computing a reduced model, evaluating it and exporting it. Let's see how this works.

The first step is to open **Simcenter Reduced Order Modeling** and create a state space project as illustrated below.

Then load the linearized model you created before using the **Add Data** button. When selecting the **Simcenter Amesim** model of the transmission part, all computed linearized models are proposed. Let's choose the one calculated in 1 second.

Figure **5** shows the properties of the loaded model.

**Figure 5**

Now, let's go to the model tab and make a ROM. **When you click on the New template** button, different types of templates are proposed. Here we are dealing with a medium-sized model with **104** state variables. In this case, Balanced Truncation is a good candidate.

**When you click the start** button , a ROM is automatically computed and evaluated. A truncation order of **58** is proposed here based on the Hankel singular values of the model. The tool indicates an overall loyalty rate of **86%** . Looking at the frequency response graph, it can be seen that the ROM covers a large frequency bandwidth (up to **2.6** kHz) of the original model, which is good enough for our application.

The next step is to save the computed model using the **Add Model** feature as illustrated below.

The computed model being saved, we go to the Export tab and export it.

**Step 3**

To handle diverse applications, four targets are proposed when exporting state space ROMs. They allow connection to both **Simcenter Amesim** and other simulation tools using, for example, FMUs (Functional Mock-up Units) for co-simulation or binary files.

Here, the computed ROM is exported as a **Simcenter Amesim** submodel .

Back in **Simcenter Amesim**, we will now connect the exported ROM (available in the ROM library specified in the export stage) to the rest of the power system, as illustrated in **Figure 9** . Two first-order phase shifts with a cutoff frequency of 2.5 kHz are added to keep the signals within the frequency range of interest (up to 2.6 kHz). Our reduced power system now has **62** state variables compared to **106** for the full power system depicted in Figure 1. The total size of the original model is then reduced by **41.5** %.

Almost ready! All that remains now is to validate the ROM by comparing the full simulation results ( **Figure 1** ) and the reduced power system models ( **Figure 9** ).

**Figure 9**

**Step 4**

Both power systems depicted in **Figures 1 and 10** are simulated for **2** s with a variable step solver using **Simcenter Amesim**.

Figure **10** shows the battery input voltage as well as its state of charge.

**Figure 10**

The results show a high goodness of fit with fewer state variables ( **62** compared to **106** ). This is reflected in the loyalty metrics ( **86** % overall loyalty) indicated by **Simcenter Reduced Order Modeling** . In terms of usability, the ROM obtained can be used as a digital twin of the transmission part. It can also be shared between different partners working on the same application and possibly using different simulation tools.

**Conclusion**

It was shown here how to reduce electrical power systems using **Simcenter Reduced Order Modeling** . It allows you to easily minimize the number of state variables of a power system by creating a ROM of its transmission part. This has many advantages:

It widens the scope of the model, making it less memory consuming

Allows you to share models with different partners while preserving IP

It enables rapid prototyping and design

For this, **Simcenter Reduced Order Modeling** offers great features to easily create a ROM for a large-scale state space model. The workflow is simple and intuitive, with the ability to easily evaluate ROM fidelity based on different fidelity indicators. The tool also offers different export targets to suit all possible uses, so that the computed ROM can be used in different contexts.

In summary, **Simcenter**** **Reduced Order Modeling offers an effective approach to simplify models in electrical power systems. By following the outlined process, you can achieve computational efficiency and facilitate model sharing, providing the ability for rapid prototyping and design.

Leading this innovation, CAEXPERTS stands out as a company specialized in solving industrial challenges through digitalization and advanced engineering. Its experienced and multidisciplinary team uses cutting-edge technology, such as **Simcenter**** **Reduced Order Modeling, to offer assertive solutions with a high return on investment.

To explore how CAEXPERTS can boost your efficiency and innovation, schedule a meeting with us now!

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