Closed-form-Power-Flow

This file contain the code related to the paper:

Parikshit Pareek and Hung Nguyen, "A Framework for Analytical Power Flow Solution using Gaussian Process Learning" IEEE Transactions on Sustainable Energy", Sept. 2021. Preprint

Cite As:

@article{pareek2022framework,
  title={A Framework for Analytical Power Flow Solution Using Gaussian Process Learning},
  author={Pareek, Parikshit and Nguyen, Hung D},
  journal={IEEE Transactions on Sustainable Energy},
  volume={13},
  number={1},
  pages={452--463},
  year={2022}
}

In particular, the code can be used to obtain the closed-form power flow expression and performance analysis results as given in table 1 and section V-A of the manuscript.

Details of Files:

• CFPF_multikernel.m : Main file to run the code for obtaining the CFPF Approximation and Performance for different kernels.
• input_dataset_Load.m : Creating load data set for training and testing
• MCS_output.m : Monte-Carlo Simulation to obtain testing data points
• rand_sample_x.m : Generating random samples
• runpf_complete.m : MATPOWER codes combined together to avid downloading
• Sampling_Jaco.m : Cover to 'runpf' for obtaining power flow datasets

Dependencies:

GAUSSIAN PROCESS REGRESSION AND CLASSIFICATION Toolbox version 4.2 for GNU Octave 3.2.x and Matlab 7.x and higher. Copyright (c) by Carl Edward Rasmussen and Hannes Nickisch, 2018-06-11. Link

• Newer GPML toolbox might require matching hyperparameter initialization. To avoid such issues, I have uploaded the GPML Toolbox version I use.

Variables and Code Outputs:

1. Loutkr : Cell array containing structre of results for each kernel

N_train: Number of training samples N_bus : Number of PQ buses N_test: Number of testing samples #Hyper_parameters : Number of hyper-parameters D : Number of random injections

 alphaV: [N_train × N_bus double] : Value of alpha for Voltage Magnitude from equation (4)
    muV: [N_test × N_bus double]  : Mean prediction of Voltage Magnitude from equation (5)
    s2V: [N_test × N_bus double]  : Predicitive variance of Voltage Magnitude from equation (16)
  sf_lV: [#Hyper_parameters × N_bus double] : Hyper-parameters for Voltage Maginitide learning
    ytV: [N_train × N_bus double]: Training samples of Voltage Maginitide

alphaTh: [N_train × N_bus double] : Value of alpha for Voltage Angle from equation (4)
   muTh: [N_test × N_bus double]   : Mean prediction of Voltage Angle from equation (5)
   s2Th: [N_test × N_bus double]   :  Predicitive variance of Voltage Angle from equation (16)
 sf_lTh: [#Hyper_parameters × N_bus double] : Hyper-parameters for Voltage Angle learning
   ytTh: [N_train × N_bus double] :  Training samples of Voltage Angle

2. maeV (maeTh) : Mean Absolute Error Voltage Magnitude (Angle)

3. Mcskr : Cell array for MCS Results

        V     : [N_test × N_bus double]
       erV_par: [N_test × N_bus double]
       erV_L1 : 0.037771 % L_1 Norm Error in |V|
       erV_L2 : 0.024608 % L_2 Norm Error in |V|
       erV_Linf: 0.062861 % L_inf Norm Error in |V|
       Thac: [N_test × N_bus double ]
       erTh_par: [N_test × N_bus double ]
       erTh_L1: 2.6544 % L_1 Norm Error in Voltage Angle 
       erTh_L2: 3.5956 % L_2 Norm Error in Voltage Angle 
       erTh_Linf: 7.7006 % L_inf Norm Error in Voltage Angle 

4. D_learningkr: Learning data cell array, each array has a structre with data

                    xx: [N_train × D double] Training dataset or Design Matrix
                   xs: [N_test × D double]  Testing dataset 

Other variable names are self explaintory

• All the codes are tested on MATLAB R2020b