# A Review of Parallel Heterogeneous Computing Algorithms in Power Systems
## 3 PHC in Power Systems
### CPU Clusters, Fog and Cloud Computing, and FPGA
#### 3.2.6 Other Applications  
With less than four references per application, PHC technologies have been used in dynamic state estimation [94; 200; 201], power system planning [236; 237], TSCOPF [230; 231], power system reliability [238; 239], electromagnetic transient simulation [91; 92], dynamic models [2; 216], short circuit analysis [235], security constrained economic dispatch [242], probabilistic power flow [224], and hydro thermal scheduling [243]. In ref. [201], a power system is divided into multiple areas, and the state estimation of each area is performed individually in each area processor. Areas exchange border information through the coordinator processor (central processor). The proposed method attempts to define areas with similar sizes to balance the workload of area processors as much as possible. The state estimation is implemented in a cluster of computers. The high-performance portable implementation of MPI (MPICH2) is used to communicate the coordinator and area processors. The researchers in ref. [236] presented the implementation of a parallel genetic algorithm to optimize the integration of different types of generation units during different time intervals. The generation planning method was implemented on a cluster of transporters. The coarse-grain version of the parallel genetic algorithm was implemented, where distributed subpopulations were optimized into several processes, and information was exchanged between subpopulations if required. In ref. [230], the implementation of a parallel Differential Evolution (DE) algorithm to improve TSCOPF computation time was presented. The developed DE algorithm combines the time-domain simulation and the Transient Energy Function (TEF) method. The objective function corresponds to the generating fuel cost of the power system. The algorithm evaluates the power system stability under the specified contingencies where the transient event during a fault condition and an acceptable steady-state operating condition are considered. First, the time-domain simulation calculates the generator rotor angles. Then, the TEF method computes the transient energies to determine the system stability. The DE algorithm is implemented on a Beowulf CPU-cluster with one control node and 30 working nodes connected with the MPI protocol. The initial population is divided into subpopulations. Each working node performs an individual DE algorithm to the corresponding subpopulation where the load flow calculation, fitness evaluation, transient stability assessment, and the selection are executed. The control node oversees the initialization, reproduction, and update of the global best individual. In ref. [238], a parallel metaheuristic TSCOPF was implemented to determine the minimal investment costs to satisfy power system reliability constraints. The authors in [91] analyzed and compared the instantaneous relaxation and direct method solvers for real-time transient stability simulation and variations of nodal and state-space solvers for real-time electromagnetic transient simulations. The tests were performed in multi-core and multi-processor computers and FPGA. In ref. [216], a parallel PSO was implemented to estimate the parameters of a wide variety of photovoltaic models. The parallel PSO was implemented in OpenCL. The evaluation of all particles was performed at the same time in multi-processor devices. In ref. [235], the probability density curves of short-circuit levels were obtained based on running a Monte-Carlo simulation in parallel in multiple virtual machines. Regarding Security Constrained-Economic Dispatch, ref. [242] presented a multithread solution of a power system economic dispatch based on the Multi-Thread Interior Point Barrier algorithm considering the generator limitations, transmission losses, and nonlinear cost functions. The algorithm validates that the optimal dispatch satisfies line flow limits adding line flow constraints as security constraints. The authors in ref.