James Guest, Ian Commerford, Nilesh Modi, Sheler Saadati, Juan Carlos Alonso, Thisandu Kahingala
IMAGE LICENSED BY INGRAM PUBLISHING
As the penetration of complex software-driven inverter-based resources (IBRs) rapidly increases in power systems around the world, the need for modeling large areas of these systems in a time-domain electromagnetic transient (EMT) environment has also increased. Since 2016, the Australian Energy Market Operator (AEMO) has been developing “large-scale” EMT models of parts of Australia’s interconnected Eastern Australian power system, known as the National Electricity Market (NEM), for use across many of AEMO’s functions as the NEM’s independent system operator. Due to the size and complexity of the models, these simulations have required large computational requirements and were typically very slow, taking more than 24 h for a 30-s simulation in 2016.
This article presents AEMO’s efforts to reduce simulation time and computational requirements for large-scale models with many site-specific IBR models, the majority of which are fully switched. The article examines the reasons for the simulation complexity, proposes methods for improving speed without affecting accuracy or fidelity, discusses the implementation of these methods in a commercial EMT simulation tool, and presents the results of the improvements on simulation speed and a method for converting models to newer software and compiler versions. Finally, it proposes recommendations for future developments.
EMT simulation methods and software have been around for many decades. They allow a user to model and analyze the full dynamics of power system components in a time-domain environment, including high-frequency components and nonlinearities. They can do this by utilizing a very small time step, in the order of a microsecond (1/1,000,000 of a second). The consequence of this level of detail is that the computational requirements are very large. Typical uses of studies have historically included analyzing the effect of lightning surges on transmission lines, analyzing the effect of inrush current and saturation on transformers, coordinating protection systems, filter tuning and harmonic analysis, studying subsynchronous resonance, and designing and controlling power electronic switched devices such as flexible alternating current transmission systems and high-voltage direct current (HVdc).
The use of traditional root-mean-square (RMS) tools is being challenged in recent years as IBRs displace traditional synchronous resources. While the dynamics of synchronous generators are widely understood and are governed by the laws of physics, the dynamics of IBRs are determined by the control systems and software specific to individual plants. This includes systems and behavior that cannot be adequately represented in RMS-type simulations.
One of the first major instances of this for AEMO was in 2015, following a root-cause investigation into a commutation failure of a major HVdc link during weak grid conditions. It was found that a simulation in an RMS environment with site-specific models predicted the link riding through a network event without any issues. However, when the study was replicated with identical conditions in an EMT tool, the simulation identified a commutation failure and trip of the link, matching the observed behavior of the link in real life. This exercise showed that an RMS simulation, even with highly detailed site-specific models, was unable to correctly demonstrate the behavior of IBRs in weak grid conditions.
In December 2019, a system strength gap was declared for a part of the NEM power system in an area straddling two NEM regions, known as the West Murray Zone. This area is known for low fault levels due to the large geographical distance to any source of synchronous generation, but many IBRs, including several large solar farms, were commissioned in the area due to its favorable solar irradiation. Analysis of the area using a large-scale EMT model showed persistent subsynchronous oscillations following a fault. This instability was attributed to control interactions of the IBRs in the area, in particular, high bandwidth control systems such as fast current control and the phase-locked loop. Due to the inherent simplifications, these control systems could not be modeled in an RMS environment, and as a result, the instability could not be replicated. A system test was performed by switching a line out of service and monitoring the response using high-speed data recorders. The test confirmed the result of the EMT simulation. By working closely with IBR manufacturers, AEMO was able to use the large-scale model to tune controller parameters and mitigate the oscillations.
Recent international examples of wide-area modeling include the 2016 study in the Texas Panhandle Region and studies following the 2021 Odessa Disturbance in the Electric Reliability Council of Texas network. As of mid-2022, AEMO has developed an EMT model of the entire mainland section of the NEM, including more than 130 site-specific IBR models and 150 site-specific synchronous generator models, which can run 30 s of simulation on a high-performance machine in under 1.5 h. The size of the case combined with the relatively short runtime has allowed AEMO to perform a wide range of studies and analyses that were not previously possible. The developed model is being used in
AEMO has used the simulation software PSCAD for this work. It should be noted that there are many different EMT simulation software packages available, each with different implementations. This article does not discuss the merits of any specific EMT tool, and findings presented on optimizing simulation speed and managing a case with a large number of site-specific IBR models can be applied to any simulation tool.
The NEM power system is the longest in the world, stretching more than 5,000 km from Port Douglas in far north Queensland to Port Lincoln in South Australia on the mainland and including the island of Tasmania. Developing an effective model in the EMT domain, containing the entire system without compromising the level of detail, required significant research, development, and optimization.
The core of all EMT simulation software is the electrical network solution. Every single electrical component can be represented as an equivalent network of current sources, voltage sources, resistors, capacitors, and inductors. Capacitors and inductors in turn can be represented as an equivalent current source in parallel with a resistance. By doing this, the network can be represented using the equation \[{GV} = {I} \tag{1} \] where G is the admittance matrix of size N × N, and N is the number of nodes in the model.
On every time step, the equation can be solved for voltages given known node current injections. The most common method to do this is to perform a LU decomposition of G and then solve for V using forward and back substitution. This method is computationally slow, on the order of O(N3), where again N is the number of nodes. Sparse matrix methods and solution algorithms can be used to improve the efficiency of the operation; however, solution complexity is still directly related to the number of nodes.
If the admittance matrix G is constant (i.e., independent of time), then the LU decomposition needs to be performed only once, at the beginning of the simulation. On every subsequent time step, the voltage can be solved using forward and back substitution using the already decomposed matrix, which is a much more efficient operation. This is the case with most of the transmission network, which consists of devices such as transmission lines, transformers, loads, and shunts, which all have constant admittance. Even synchronous generators can be represented by a Norton equivalent circuit, which contains only constant admittances, with magnetization and saturation effects provided by a compensating current source.
The process of both LU decomposition and then forward/back substitution is highly linear; in other words, it is not simple to perform in a parallel manner. However, a property of the distributed parameter model of transmission lines to split up the admittance matrix and solve each portion in parallel can be used.
Literature on the modeling of transmission lines typically relies on the method of characteristics (Dommel 1969). This assumes that a transmission line has inductance L and capacitance C evenly distributed along the entire length. The line can then be split up into infinitesimally small segments ${\Delta}{\text{x}}$, with each segment containing a series inductance ${L}\,{\cdot}\,{\Delta}{\text{x}}$ and shunt capacitance ${C}\,{\cdot}\,{\Delta}{\text{x}}$. By integrating across the entire length and solving the resulting differential equations, we end up with the equivalent circuit shown in Figure 1.
Figure 1. (a) and (b) A distributed transmission line equivalent circuit.
In Figure 1, the current sources inject the following values: \begin{align*}{I}_{k} & = {-}\frac{1}{{Z}_{0}}{v}_{m}{\left({t}{-}{\tau}\right)}{-}{i}_{m,k}{\left({t}{-}{\tau}\right)} \tag{2} \\ {I}_{m} & = {-}\frac{1}{{Z}_{0}}{v}_{k}{\left({t}{-}{\tau}\right)}{-}{i}_{k,m}{\left({t}{-}{\tau}\right)}{.} \tag{3} \end{align*}
From these equations, we can see that there is a time delay ${\tau}$ between the sending and receiving ends of the line. This is physically interpreted as an inherent time delay due to the wave propagation between both ends.
If the transmission line parameters are calculated from RMS R, X, and B parameters (known as the Bergeron model), the delay in seconds can be calculated using the following equation: \[{\tau} = \frac{\sqrt{{X}\,{\times}\,{B}}}{{2}{\pi}{f}} \tag{4} \] where X is the pu series impedance of the line, B is the pu shunt capacitance of the line, and $f$ is the base frequency of the system. If the delay is larger than the simulation time step, then the network on either end is decoupled, i.e., their admittance matrices are independent and can be solved independently. Splitting can also be done by utilizing higher order models (such as utilizing geometric line parameters). In this case, the simple equation in (4) does not apply, and the user should rely on the EMT software’s line constants program to calculate the propagation delay.
One can utilize the advantage of multiprocessing on modern CPUs by splitting up the EMT model into independent sections broken by distributed transmission lines and running each smaller section in parallel on a different core. For the computer hardware available to AEMO, trial and error revealed that the optimal number of buses in each project was approximately 200. Suitable split points separated by long transmission lines were identified, and the model was broken up into multiple cases. Each project was connected to its neighbors, utilizing the network splitting technique described previously.
It is worth noting that if a transmission line has a propagation delay smaller than the simulation time step, then the distributed parameter model cannot be used. Instead, a lumped parameter model known as the PI model must be used in which both ends cannot be solved independently. A way to get around this is to reduce the simulation time step so that more transmission lines can utilize the distributed parameter model. However, reducing the time step will also decrease the simulation speed, so a balance must be found. AEMO determined a time step of 25 μs was optimal for the large-scale model.
Any devices that utilize power electronics switches force the LU decomposition to be performed again. This is because switches are modeled by having a very small ON resistance and a very large OFF resistance. When the switch is triggered, the resistance switches between the two, causing the admittance matrix G to change, thus triggering a matrix decomposition. In the case of power electronics devices, this could occur on every time step due to gating on thyristor-based devices or pulsewidth modulation on insulated-gate bipolar transistor-based devices. This includes all power electronic devices, including solar farms, type 3 and 4 wind farms, batteries, static var compensators, static synchronous compensators, line-commutated current-source converter HVdc links, and voltage-source converter HVdc links. It also includes type 2 wind turbines as the rotor resistance is varied continuously, triggering a matrix decomposition on every time step.
To optimize the simulation speed with power electronic devices, it is desirable to keep as few nodes as possible to reduce the computational burden of the LU decomposition. To achieve this, each power electronic device can be moved into its own case using the aforementioned method of case splitting. This allows the number of nodes in the network with the power electronic devices to be kept to a minimum while also allowing the model to run in parallel with other power electronic devices and the network cases on different CPU cores. Synchronous machine, models including synchronous condensers, do not contain fast switching elements and, as such, can be placed directly into the network cases with little impact on simulation speed.
Most inverter-based plants are connected radially to the transmission system through a transmission line. If the transmission line connecting the plant to the system is long enough, then the plant can be split at that point. However, in some cases, the transmission line has a travel time delay less than the simulation time step of the network cases. In this case, to split the plant, the impedance of the line needs to be increased. This can be achieved by removing impedance from the plant transformer and adding it to the transmission line, as seen implemented in an EMT program in Figure 2.
Figure 2. Using transformer impedance to achieve the required time delay. ENI: Electrical Network Interface; POC: Point of Connection.
There are two main issues with this approach.
Therefore, the use of transformer impedance for interfacing should be carefully considered in the context of the system and studies being performed.
Many of the models for switch-based devices received by AEMO are site specific and were designed to operate on a specific time step, usually corresponding to the internal clock of the control system. Most EMT software packages are fixed-step solvers, and there will almost certainly be conflicts between the required time steps of different plants. To overcome this limitation, a “multirate” interface can be used. This allowed the connection of two cases with different time steps by linearly interpolating voltages and currents on either end between time steps.
Figure 3 shows the process of linear interpolation when the receiving end is a larger time step. The receiving end calculates the value utilizing the following equation: \[{V}_{r} = \frac{{\left({V}_{2}{-}{V}_{1}\right)}{\left({t}{-}{t}_{2} + {\Delta}{t}\right)}}{\Delta{t}} + {V}_{1} \tag{5} \]
Figure 3. A linear interpolation example.
where ${V}_{r}$ is the receiving end value at time ${t}$, ${V}_{2}$ and ${V}_{1}$ are the current and previous values on the sending end, ${t}_{2}$ is time on the sending end, and ${\Delta}{t}$ is the time step on the sending end.
Note in Figure 3 that the errors are exaggerated as the oscillation period is close to the time step. This interpolation error in effect acts as a low pass filter, but as the time step for EMT simulations is on the order of microseconds, this impacts only very high-frequency oscillations.
The overall setup of the case is summarized in Figure 4. Each network case is split up into roughly equal portions of approximately 200 buses and contains passive equipment (lines, transformers, shunts, and loads) as well as synchronous generator models. Branching off these network cases are the site-specific IBR models, connected via the multirate interface.
Figure 4. An example large-scale EMT model structure.
Every passive device in the network contains a mapping to an element in a supplementary loadflow case, allowing conditions such as outages and tap changer settings to be transferred. In addition, all synchronous generators and IBR models were set up to receive set points taken from the same loadflow case. This allows for the network and models to initialize correctly and closely match the desired loadflow.
Each case needs to be able to communicate with its connected neighbors and remain synchronized. To do this, some method of interprocess communication (IPC) is required. Prior to 2021, this was done using TCP/IP, which was found to cause a bottleneck for the simulation when there are many interconnected cases. In 2022, all data transfer components were switched to use another method of IPC called shared memory, which resulted in a significant speed gain.
Two deficiencies in the simulation software utilized by AEMO were identified as the size and complexity of the large-scale model increased. This prompted AEMO to complete a transition process from PSCAD Version 4.6 and Intel Visual Fortran (IVF) 2010 to PSCAD Version 5 and IVF 2021. While the motivation for migrating is specific to PSCAD, the methodology for testing and benchmarking applies to any simulation platform.
In PSCAD Version 4.6 and earlier, typically a maximum of 64 cases (or “projects”) per PSCAD instance can be run in parallel. Each project contains either a single generator model or a portion of the transmission system running in parallel on its own CPU core to maximize the speed of the simulation. There are more than 150 transmission-connected inverter-based devices in the NEM, and therefore, a limit of 64 projects is insufficient. There are two ways to get around this limitation. The first is to “double up” with multiple generator models in a single project. This would drastically impact simulation speed with the full mainland model taking up to several days to run and would likely crash due to insufficient memory. The second is to use multiple computers with a shared communications protocol. To run the full NEM mainland model would, however, require three high-performance machines and three individual PSCAD software licenses. Additionally, communication between the computers uses the TCP/IP protocol, which is slow and takes up large amounts of network bandwidth. While this had been the approach AEMO used prior to 2022, it was far from ideal as the case was very difficult to use and took up to 4.5 h to run a 30-s simulation when all operational IBR models were included. This extended to 8 h for planning studies when some recently committed generation was included.
PSCAD requires a Fortran compiler to operate. It works by turning a graphical circuit diagram into Fortran code, which is then compiled into very fast machine code to be executed on the CPU. IVF 12 has been the standard compiler for many years; however, it is no longer supported by Intel. IVF 12 can no longer be purchased or downloaded from Intel, and Australian PSCAD users have been unable to perform studies assessments due to their inability to acquire the legacy version of the compiler.
Manitoba Hydro International (MHI) released PSCAD Version 5 (V5) in early 2021. In addition to bug fixes, new models, and speed improvements, PSCAD V5 has no physical limitation on how many projects can be run on a single computer (instead, limits are license based), provided there is sufficient CPU and RAM. In addition, it is compatible with the latest release of the Intel Fortran compiler—“2021 Classic.”
Due to the potential benefits of PSCAD V5 and the obsolescence of IVF 12, AEMO decided to migrate the NEM mainland EMT model to PSCAD V5. It was decided that the case would be converted to operate in PSCAD V5 and IVF Compiler Classic 2021 in 32 b. It was also decided to take advantage of PSCAD V5 fully and attempt to run the entire mainland model on a single computer. To gain confidence that the model performed as expected in the newer version of PSCAD, a methodology was developed to test and validate the new version.
The first step of the process was to import all IBR and synchronous machine models into PSCAD V5. This was done as a precheck before testing the actual dynamic performance of the plant to make sure the models and library files compiled and started correctly with the new Fortran compiler. PSCAD V5 features an import function for V4 cases, which made this process straightforward.
The main challenge with importing PSCAD V4 cases arose due to the many “blackboxed” models used in the large-scale PSCAD case. The models provided to AEMO are site specific, proprietary, and typically the exact same source code that was running on the inverters out in the field. As a result, the controller portions of these models are provided as obfuscated machine code.
A common issue encountered was models not correctly linking into an executable. This arose as the blackboxed code contained within some static library files was compiled using an older version of Visual Studio and referenced incompatible library files. To correct this, the blackboxed library files were wrapped into a dynamic linked library (DLL) with the required library files from the older version of Visual Studio using Microsoft build tools. The DLL was then linked to the simulation in place of the static library files.
Each migrated IBR model was rerun in PSCAD V5 and IVF 2021 to confirm that they compiled and executed correctly. The vast majority were able to be successfully run in PSCAD V5.
Once all models had been confirmed to compile correctly, the performance of each individual model was assessed and compared with the result from the previous software to gain confidence that any modifications made during import did not inadvertently affect the performance of the model. It was decided that a small subset of tests from AEMO’s Dynamic Model Acceptance Tests (DMATs) would be performed. A single-machine infinite-bus (SMIB) test environment was set up as per the DMAT guidelines in both old and new simulation environments. Figure 5 demonstrates the setup.
Figure 5. A single-machine infinite-bus (SMIB) setup. RLC: resistance, inductance, capacitance.
The impedances ${Z}_{2}$, ${Z}_{1}$, and ${Z}_{f}$ are calculated to produce both the desired fault level at the point of connection during the steady state and the desired voltage dip during fault conditions. Most models tested produced near-identical results. As expected, slight insignificant differences in jitter were apparent in the results; however, this was attributed to the new solution engine and changes to master library components, such as the three-phase transformer model, which received some bug fixes. Figure 6 shows sample results of the comparison.
Figure 6. (a) A wind farm response to a long-duration fault. (b) A wind farm response to a sizable short-term overvoltage (DMAT test 146).
Once the individual models had been validated, the entire large-scale model was run in both the old and new simulation platforms to check the consistency of the results produced by both versions. The model tested contained approximately 130 site-specific IBR models, the majority of which were fully switched; 150 site-specific synchronous generator models; and 3,000 buses. The network and dynamic models were initialized from a loadflow snapshot and were given time for transients to settle before applying a disturbance.
It was critical that this was a “like-for-like” test as any differences in set points, or loadflow would produce results that could not be compared. It was acknowledged that it would be very difficult to match both sets of results identically, particularly in reactive power output, yet the overall behavior should be similar, and any major differences should be explainable.
This part of the validation was the most time-consuming and iterative process. Getting a match between both versions of the case was very difficult to achieve. To produce a close result, all modifications and bug fixes made to individual models in the new case were replicated in the old one. After much effort, an acceptable match was achieved. Figure 7 shows a comparison between both simulation software packages for one set of conditions and for one disturbance. The slight differences are attributed to a large number of site-specific type 2 wind turbine models that initialize unpredictably to slightly different set points as well as bug fixes in standard library models. This process was repeated for one critical fault per region totaling four scenarios.
Figure 7. (a) An interconnector flow following a large transmission line fault including multiple IBR runbacks. (b) An interconnector flow following a fault and trip of a large coal generator.
Due to the development of shared-memory data transfer components and optimizations in PSCAD V5 and Intel Fortran 2021, the V5 case ran 55% faster than the equivalent V4 case. The average simulation time for a 30-s simulation with operational generation only is shown in Figure 8 with the following hardware:
Figure 8. A runtime comparison between PSCAD V4 and V5.
AEMO continues to develop the large-scale EMT model as the NEM power system continues its transition to increasing IBR penetration and continues to investigate methods to improve the speed and accuracy of simulations as well as ease of use. There are many recent developments and areas for future work in EMT simulation. Next are the three critical areas that AEMO is investigating in the short term.
There are many factors that impact the speed of the simulation, and not all can be addressed directly. While much of the complexity of the EMT simulation lies in the electrical network solution, improving the underlying algorithm will help the simulation speed only up to a point. In many cases, the bottleneck is the individual plant models and “blackboxed” control systems, especially fully switched models that run at a very small time step.
Utilizing higher specification hardware should directly improve the simulation speed, with CPUs with more than 64 cores anticipated to be released in the coming years. Requiring models to utilize an “interpolation” algorithm will allow for fully switched IBR models to be simulated accurately at larger time steps. Averaged converter bridge models do not require matrix refactorization and allow the network solution to be solved very quickly, even in real-time and faster than real-time speeds. Finally, there has been research in replacing the traditional resistive switch model with an “LC” switch model; however, further research is required into the suitability for large-scale studies.
Currently, the large-scale model is associated with a single operating point only. Minor modifications to loadflow conditions are possible, such as changes to outages, load and generation dispatch, and tap changer settings through the use of a loadflow program such as PSS®E and then “reimporting” those changes into the large-scale model. A loadflow base case and import tool have been developed internally to provide this functionality. However, as the large-scale model is tightly coupled to the loadflow base case, major changes, such as reconfiguration of the network or applying a completely different loadflow case (such as a historical snapshot from a state estimator), are currently impossible. Further research and development are required if EMT simulations are to be used in online analysis applications.
As encountered during AEMO’s transition to PSCAD V5, the continuity and compatibility of “blackboxed”/“real-code” EMT models and transitioning between different software packages are still major areas for development. There is currently no standard to interface between the “real code” and the simulation platform, and as such, each manufacturer has a different approach, requiring different libraries and dependencies. Some methods used unfortunately tie the model to a specific version of the simulation tool or compiler, so these models cannot be used in newer versions or different software. There are some workarounds that work in limited cases; otherwise, the only resolution in these instances is to request a model from the manufacturer that is compatible with the newer software. In some situations, this is often not easily obtainable—for example, if the manufacturer is no longer trading or is unable to support the model.
A joint CIGRE/IEEE working group B4.82 was approved in February 2019 to explore this very issue with a final report expected to be published in April 2023.
This article outlines methods for improving the simulation speed and efficiency of large-scale EMT simulations with a large proportion of site-specific IBR models. By utilizing distributed transmission line models and optimizing the number of nodes in each case, a large model can be broken down into smaller subsystems and run in parallel on one or multiple computers. Utilizing multirate data transfer components, site-specific IBR models can be run at different time steps, typically corresponding to their clock speed, and by utilizing shared memory to communicate between cases and running the entire simulation on a single machine with a large CPU, a substantial speed improvement can be gained. The process for migrating and testing EMT models between two different simulation platforms was also presented. Apart from a few discrepancies due to static and dynamic library files, the results matched closely, giving confidence about using the new simulation tool. The improvements in the tool and process have reduced the computational time substantially, providing an opportunity for AEMO to use the large-scale EMT model more frequently for system security assessment of an IBR-dominated grid.
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James Guest (james.guest@aemo.com.au) is with the Australian Energy Market Operator, Brisbane, QLD 4000, Australia.
Ian Commerford (ian.commerford@aemo.com.au) is with the Australian Energy Market Operator, Sydney, NSW 2000, Australia.
Nilesh Modi (nilesh.modi@aemo.com.au) is with the Australian Energy Market Operator, Brisbane QLD 4000, Australia.
Sheler Saadati (sheler.saadati@aemo.com.au) is with the Australian Energy Market Operator, Melbourne, VIC 3000, Australia.
Juan Carlos Alonso (jcgzipa@mhi.ca) is with Manitoba Hydro International, Winnepeg, Manitoba R3C 0G8, Canada.
Thisandu Kahingala (thisandu.kahingala@aemo.com.au) is with the Australian Energy Market Operator, Melbourne, VIC 3000, Australia.
Digital Object Identifier 10.1109/MELE.2023.3291270
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