Look-ahead Dynamic Simulation
Power system dynamic simulation aims to determine the time-series trajectory when the system is subject to disturbances such as a short-circuit fault, generator tripping, or line switching. It solves a set of differential-algebraic equations (DAE) that describe the electro-mechanical interaction of generators as well as other dynamic devices and their controllers. Because of computational inefficiency, dynamic simulation, although widely used for off-line studies, has not been used in real-time operation. That limits the ability to operate a much-evolved power system with significant dynamic and stochastic behaviors introduced by the increasing penetration of renewable generation and the deployment of smart grid technologies. The need for performing dynamic simulation in real time or faster than real time for power grid operation becomes apparent. Predictive dynamic simulations can enable many new power grid operation functions such as real-time path rating. To improve the computational efficiency of dynamic simulation requires parallel computing implementations of the solution methods, to utilize today’s multi-core computers.
At Pacific Northwest National Laboratory, we have examined the DAE algorithms and implemented a parallel version of power system dynamic simulation. There are several important elements in our algorithmic design:
- A reduced admittance matrix builder based on Woodbury matrix identity method;
- A parallel linear system solver;
- A selective computing approach;
- A sparse matrix data structure for efficient memory management and fast matrix computation;
- An OpenMP Application Program Interface (API) parallel dynamic simulation implementation on a shared-memory HP Superdome machine.
Figure 1. Speedup of dynamic simulation with respect to the number of processors (cores). Click for a larger image.
Our testing results have shown a significant improvement in computational performance. For the first time, power system dynamic simulation of a large-scale power system with a size equivalent to the Western U.S. power grid achieves a performance of three times faster than real time. The simulation time using different number of cores is shown in Table 1. When 16 processors or more are used, the total solution time of the overall dynamic simulation is faster than real time. With 64 processors, the simulation time is only 9.04 seconds, which is more than 20 seconds ahead of the real time and 13 times faster than today’s commercial tools, which needs 120 seconds after considering the difference between CPU configurations. Figure 1 shows the speedup curves based on the timing results in Table 1. The speedup numbers are calculated by normalizing the execution time using their respective single processor time.
A MPI based parallel dynamic simulation implementation on a clustered machine is also under development. We are implementing the implicit integration method and parallel linear solver in the MPI environment, and will develop a demonstration on a large-scale power system with detailed dynamic models using this parallelization technology.
Table 1. Solution time for 30 second dynamic simulation of an interconnection-scale system using classical model.
Number Of Cores
Reduced Admittance Matrix Computing (Second)
Predictive dynamic simulation can have multiple important applications in improving power grid reliability and efficiency. For example, it can enable real-time path rating to take actual operating conditions into consideration instead of computing transmission path limits based on assumed off-line worst-case conditions. The path rating can be more accurate based on the current operating conditions, and thus improve asset utilization and confidence during operation.
Figure 2. One -line diagram of the 39-bus test system. Click for a larger image.
Figure 3. Calculated total transfer capability. Click for a larger image.
The concept of real-time path rating can be explained and verified by a case study, which was conducted on a 39-bus test system, shown in Figure 2. To calculate the total transfer capability of Path 1, the generation level in Area I is increased and the generation in Area II is decreased progressively while screening contingencies. Comprehensive path rating studies considering N-1 contingencies are conducted using DSA Tools, developed by Powertech Labs. Simulation results, shown in Figure 3, reflect that the total transfer capability can vary significantly in real time. The path rating estimated with the worst-case scenario would be the smallest of all values for 24 operating hours. Any capacity above the smallest number is an additional gain enabled by real-time path rating studies. If the additional transfer capability can be fully utilized, a total amount of 25.74% more energy can be transferred without compromising the current reliability level. This could generate multi-million dollar revenues.
Z. Huang and J. Nieplocha, “Transforming power grid operations via high performance computing,” in Proceeding IEEE Power Energy Society General Meeting, 2008.
Z. Huang, S. Jin, and R. Diao, “Predictive dynamic simulation for large-scale power systems through high-performance computing,” presented at 2nd International Workshop on High Performance Computing, Networking and Analytics Power Grid, 2012.
Z. Huang, N. Zhou, Y. Li, P. Nichols, S. Jin, R. Diao, and Y. Chen, “Dynamic paradigm for future power grid operation,” in Proceeding 8th Power Plants Power System Control Symposium, 2012, pp. 218–223.
R. Singh, R. Diao, N. Cai, Z. Huang, B. Tuck, and X. Guo, “Initial studies toward real-time transmission path rating,” in Proceeding IEEE Power Energy Society Transmission and Distribution Conference and Exposition, May 2012.
S. Jin, Z. Huang, R. Diao, D. Wu, and Y. Chen, “Parallel implementation of power system dynamic simulation,” in Proceeding IEEE Power Energy Society General Meeting, 2013, to appear.