Comparing Different Approaches for Solving Large Scale Power Flow Problems on the CPU and GPU with the Newton-Raphson Method
Sammanfattning: Power system modelling is increasing in importance. It is vital for power system operations and transmission grid expansions, and therefore the future energy transition. The Swedish power system is under fast development to face the progress of more flexible demand, a higher share of distributed renewable sources, and updated capacities. In order to ensure the power system’s secure physical capacities on a real-time basis in the future, the power system models must be able to handle this increased complexity. Hence, more efficient modelling and reduced computational time are necessary in order to secure the efficient daily operation of the Swedish grid. This thesis focuses on using the Newton-Raphson method to solve the power flow problem. The most computationally demanding part of the Newton- Raphson method is solving the linear equations at each iteration. Therefore, this study investigates different approaches to solve the linear equations on both CPU and GPU. Six different approaches were developed and evaluated in this thesis. Two of these run entirely on CPU while other two of these run entirely on GPU. The remaining two are hybrid approaches that run on both CPU and GPU. The main difference between the six approaches is where the linear equations are executed. However, all approaches either use LU or QR factorization to solve the linear equations. Two different hardware platforms were used to conduct the experiments, namely one single NVIDIA Quadro T2000 GPU on a laptop and one single NVIDIA V100 GPU on Kebnekaise system at HPC2N. The results show that the GPU gives better performance compared to the CPU for larger power flow problems. The results also show that the best performing version is a hybrid method where the Jacobian matrix is assembled on GPU; the preprocessing with KLU analysis is preformed on the CPU; and finally the linear equations are solved on the GPU. If the data transfers between the CPU and GPU are not considered, the hybrid version yielded a speedup factor of 46 in comparison with the baseline CPU version using the LU algorithm on the laptop. This speedup was obtained on the largest case with 9241 buses. Furthermore, the execution time of the hybrid version on the Kebnekaise system was approximately 114 times faster than the baseline CPU version on the laptop.
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