As a follow-up to the April issue, SEL-3555: Synchrophasor Processor, Jeff Otto, SEL automation engineer, details the advantages and interworking of the new SVPplus library for the SEL RTAC family.
The SEL Real-Time Automation Controller (RTAC) has always been a synchrophasor data processor. Initially released with the IEEE C37.118 client, followed by server support in 2014, the RTAC is on a steady trajectory to become SEL’s keystone synchrophasor data concentration and control solution. With the recent introduction of the SEL-3555 platform (RTAC on the SEL-3355 third-generation rugged computing platform), it will truly have the horsepower to shine as a synchrophasor processor. The open development environment and more-than-ample horsepower will enable realization of the most impactful synchrophasor applications.
To provide users a powerful synchrophasor based tool set for the RTAC, we’ve released the new SVPplus library, which includes the same powerful built-in functions found in the SEL-3378 Synchrophasor Vector Processor (SVP) and more! The initial implementation includes modal analysis. The following release will provide a tool for out-of-step prediction.
The SVPplus library is currently included in the acSELerator RTAC SEL-5033 Software library extensions and can be downloaded from SEL-5033 software page. Once installed, adding a library to a project can easily be done via the "IEC 61131-3" dropdown on the "Insert" tab within the acSELerator RTAC Software.
Fig. 1. Selecting the SVPplus Library.
Note that the SVPplus library is a for-pay adder. Look for it on the MOT configuration page for each RTAC platform. Only RTACs with the appropriate MOT option will accept projects that use the SVPplus library.
The first addition to the new SVPplus library is a fully overhauled rendition of the original Modal Analysis function from the SEL-3378 Synchrophasor Vector Processor.
Modal analysis is an algorithmic means of inferring information about the dynamic properties of a signal. It is commonly used to study and predict stability issues on the electrical grid. The algorithm decomposes a measured signal (power, frequency, phase angle difference, or whatever you choose) into individual frequencies or modes. For each mode, approximations are calculated for the relative power, phase, and damping ratio. Equation 1 depicts the Prony decomposition performed by the SVPplus modal analysis function set.
N (t) is a reconstructed version of the original signal, based on the approximated modes,
N is the number of modes approximated,
An is the amplitude of mode n,
an is the damping coefficient of mode n,
fn is the frequency of mode n, and
Θn is the phase angle of mode n.
From the damping coefficient, we can calculate the damping ratio ϛ, which is a dimensionless measure of how system modes decay over time. To calculate the damping ratio, we take the approximated damping coefficient over the critical damping coefficient for that mode frequency, as shown in Equation 2.
The damping ratio is especially important because it can be used to predict an uncontrolled oscillation on the system before it happens. Figure 2 compares the effects of varying damping ratios on a mode with f = A = 1.
Fig. 2. The effects of the damping ratio.
A mode with ϛ = 1 is critically damped (mode oscillation decays immediately), while ϛ = 0 indicates a sustained oscillation and modes with negative ϛ will increase exponentially over time. A threshold of 0.05 is often used for ϛ to indicate a potentially hazardous oscillation. This information is useful for real-time system stability control.
For example, the Guatemalan power utility, Administrador del Mercado Mayorista (AMM) is applying this same technique to protect customers and equipment from damaging oscillations. To learn more about this application, please reference this publication.
Since the calculated signal parameters are just approximations, modal analysis provides a signal-to-noise (SNR) ratio which gives a measure of similarity between the approximated signal N(t) and original signal S(t). The SNR is calculated with Equation 3 where the subscript indicates the "nth" output mode set.
The SNR is calculated on a decibel logarithmic scale. So for an SNR of 40, the original signal is 100 times greater than the error between the original and approximated signals, while an SNR of 80 indicates a signal that is 10,000 times greater. The SNR can be used to validate the integrity of the modal estimation.
Modal analysis processes large blocks of data in order to produce mode parameter estimates. Wide-area oscillations can often be less than 1 hertz. For modal analysis to detect such low-frequency signals, it must buffer a significant amount of data per calculation result (10 – 30 seconds, for example). It wouldn’t be very helpful if we had to wait for 30 seconds of new data to arrive in between modal approximations, so a circular data buffer is commonly employed. A circular buffer, in essence, is a fixed-size data buffer that uses a "first in, first out" update method.
Fig. 3. Circular buffer.
For the purposes of modal analysis, the user specifies a value between 1 and 100 as an overlap percentage of the total buffer size. This parameter is denoted as "N" in this description. Each modal estimate is then calculated based on N% new samples and (100 – N)% old samples. The update rate is effectively limited by the update rate of incoming samples and the specified buffer overlap percentage. Possibly the most noticeable difference between the SVPplus library implementation and the SEL-3378 implementation of modal analysis, in terms of usability, is the minimum mode estimate update rate. We'll cover the differences in the following section.
SEL-3378 users often provide the following feedback: "This modal analysis feature is great, but can it update any faster than once every 10 seconds?"
To aid in regulating the SEL-3378 CPU burden, the SEL-3378 implementation of modal analysis imposes a minimum 600-sample update before calculating the next modal estimate (10 seconds worth for an incoming message rate of 60/second). Note that the SEL-3378 is based on the SEL-3351 System Computing Platform hardware platform.
The new SVPplus modal analysis offers much greater control over how modal estimates are processed and updated. It answers the questions of update rate and CPU burden management by providing user control over both buffer update percent (minimum is 10 percent of the total buffer size) and modal analysis duty cycle (amount of per/task time spent on modal estimation).
As an example, for a sample buffer containing 600 samples (10 seconds worth at 60 messages/sec) modal estimates can be updated as fast as once per second. Achieve even higher update rates by reducing the sample buffer size. Much can be said as to the optimal buffer size for the mode frequencies of interest, but we'll save that conversation for another day.
To give you a sense of the processing required to compute modal analysis, we did some benchmark testing on two different SEL hardware platforms from opposite sides of the hardware capability spectrum. The SEL-3555 is an RTAC embedded in the SEL-3355 rugged computing platform. The SEL-2241 is the RTAC module made for the SEL-2240 Axion.
The stepTime setting used when initiating an instance of the SVPplus library allows us to define the time per task cycle spent on modal analysis. For this test, we assigned 5 ms per task cycle for modal analysis processing. The results below show the number of task cycles required to generate a set of mode estimates for a certain number of modes and sample buffer size.
|Modes and Samples|
Count of 5 ms scans
|4 Modes 500 Samples||2||14|
|8 Modes 500 Samples||7||52|
|16 Modes 500 Samples||26||202|
|4 Modes 600 Samples||2||17|
|4 Modes 5k Samples||10||92|
|8 Modes 5k Samples||28||266|
|16 Modes 5k Samples||93||905|
Table 1. Benchmark test results.
Don’t forget, each RTAC library contains its own set of comprehensive documentation, covering everything from class elements and use cases to benchmark test results and example code.
As you can see, the SEL RTAC now offers an incredibly versatile set of functions for conducting modal analysis. Stay tuned for future additions to the SVPplus library.