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constrained_paper.py
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constrained_paper.py
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#! /usr/bin/env/python
from __future__ import division
import sys
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LinearSegmentedColormap
from multiprocessing import Pool
import aurespf.solvers as au
from aurespf.tools import get_q, get_quant_caps
from link_colour_less import track_flows, get_link_direction
from new_linkcolouralgorithm_less import track_link_usage_total
from link_namer import node_namer, link_namer, link_dict
from functions import binMaker, bin_prob, bin_CDF, node_contrib
from europe_plusgrid import *
from EUgrid import EU_Nodes
from figutils import *
"""
Script to investigate the transition of a node's usage of the links as
the transmission is constrained
All ouput files are saved to ./constrained/
Figures are saved to ./figures/constrained/
Call the script using only one of the following command line arguments:
- init: Calculate link capacities from unconstrained flows
- solve: Solve power flows for various constraints
- trace: Run flow tracing and save results.
- usage: Calculate node's usage of links.
- plot: figures of total network usages
- plot area: stacked area figures of network usages
"""
if len(sys.argv) < 2:
raise Exception('Not enough inputs')
else:
task = str(sys.argv[1:])
dataPath = 'ConstrainedFlowData/'
figPath = 'figures/constrained_paper/'
b = np.linspace(0.05, 1.5, 30)
nNodes = 30
lapse = 8766 # 280512
directions = ['import', 'export', 'combined']
schemes = ['minDis', 'lin']
scheme = schemes[0]
cmap = LinearSegmentedColormap('blue', Blues_data, 1000)
def solver(b):
Nodes = europe_plus_Nodes()
N, F = au.solve(Nodes, mode='linear', h0=h0, b=b, lapse=lapse)
N.save_nodes(filename='Europe_aHE_' + str(b) + 'q99_lin', path=dataPath)
np.save(dataPath + 'Europe_aHE_' + str(b) + 'q99_lin_flows', F)
def calc_usage(N, F, lapse, scheme, b):
"""
Calculate powermixes and nodes' usages of links and save results to file.
"""
"""
N2 is a new nodes object containing individual powermixes for import and
export in the variables N2[n].power_mix and N2[n].power_mix_ex respectively.
"""
N2, power_mixes_total = track_flows(N, F, admat=N.pathadmat, lapse=lapse)
"""
track_link_usage_total tracks each nodes usage of all links. The results
are saved to files '..._links_ex_...' and '..._links_im_...'.
"""
boxplot, boxplotlabel = track_link_usage_total(N2, F, mode=scheme, lapse=lapse, constrained=b)
def calc_contribution(b):
"""
Calculate nodes' contribution for a single scheme and save results to file.
"""
F = abs(np.load(dataPath + 'Europe_aHE_' + str(b) + 'q99_lin_flows.npy'))
# Get 99% quantile of link flow
quantiles = [get_q(abs(F[link, :lapse]), .99) for link in xrange(len(F))]
# Do everything below for both import and export usages unless we want the combined case
for direction in directions:
if direction == 'combined':
Usages = np.load('./constrained/linkcolouring/' + scheme + '_link_mix_import_b_' + str(b) + '.npy')
Usages += np.load('./constrained/linkcolouring/' + scheme + '_link_mix_export_b_' + str(b) + '.npy')
Usages /= 2
else:
Usages = np.load('./constrained/linkcolouring/' + scheme + '_link_mix_' + str(direction) + '_b_' + str(b) + '.npy')
print('Loaded ' + scheme + ' usages')
Node_contributions = np.zeros((nNodes, len(F))) # empty array for calculated usages
for node in xrange(nNodes):
for link in xrange(len(F)):
# Stacking and sorting data
F_vert = np.reshape(F[link, :lapse], (len(F[link, :lapse]), 1))
exp_vert = np.reshape(Usages[link, node, :lapse], (len(Usages[link, node, :lapse]), 1))
F_matrix = np.hstack([F_vert, exp_vert]) # [flow, usage]
F_matrix[F_matrix[:, 0].argsort()]
H, bin_edges = binMaker(F_matrix, quantiles[link], lapse)
Node_contributions[node, link] = node_contrib(H, bin_edges)
np.save('./constrained/Node_contrib_' + scheme + '_' + direction + '_b_' + str(b) + '.npy', Node_contributions)
print('Saved Node_contributions to ./constrained/Node_contrib_' + scheme + '_' + direction + '_b_' + str(b) + '.npy')
if direction == 'import':
np.save('./constrained/quantiles_' + scheme + '_b_' + str(b) + '.npy', quantiles)
print('Saved 99% quantiles to ./constrained/quantiles_' + scheme + '_b_' + str(b) + '.npy')
def caller(b):
N = europe_plus_Nodes(load_filename='../' + dataPath + 'Europe_aHE_' + str(b) + 'q99_lin.npz')
F = np.load(dataPath + 'Europe_aHE_' + str(b) + 'q99_lin_flows.npy')
calc_usage(N, F, lapse, scheme, b)
"""
Calculate link capacities from unconstrained flows
"""
if 'init' in task:
print('Mode selected: Calculate link capacities from unconstrained flows')
Nodes = europe_plus_Nodes()
N, F = au.solve(Nodes, mode='linear copper verbose')
N.save_nodes(filename='Europe_aHE_copper_lin', path=dataPath)
np.save(dataPath + 'Europe_aHE_copper_lin_flows', F)
"""
Solve power flows for various constraints
"""
if 'solve' in task:
print('Mode selected: Solve power flows')
# Calculate link capacities from 99% quantile of unconstrained flow
h0 = au.get_quant_caps(filename=dataPath + 'Europe_aHE_copper_lin_flows.npy')
p = Pool(8)
p.map(solver, b)
"""
Calculate powermixes and nodes' usages of links and save results to file.
"""
if 'trace' in task:
print('Mode selected: flow tracing')
p = Pool(8)
p.map(caller, b)
"""
Calculate nodes' contributions and save results to file.
"""
if 'usage' in task:
print('Mode selected: usage calculation')
p = Pool(8)
p.map(calc_contribution, b)
"""
Plotting figures of total network usages
"""
if (('plot' in task) and ('area' not in task)):
print('Plotting total node- and link usages')
# Get or calculate results for plotting
try:
results = np.load('./results/constrained_paper_results.npz')
totalUsagesLin = results['lin']
totalUsagesminDis = results['minDis']
totalUsagesLin = results['lin']
totalUsagesminDis = results['minDis']
except:
N = np.load('./ConstrainedFlowData/Europe_aHE_copper_lin.npz', mmap_mode='r+')
node_mean_load = N['mean']
# Country's usage of all links as function of b
for node in xrange(nNodes):
plt.figure(figsize=(12, 6))
totalUsagesLin = []
scheme = 'lin'
for B in b:
# Load data and results
F = abs(np.load('./ConstrainedFlowData/Europe_aHE_' + str(B) + 'q99_DC_' + scheme + '_flows.npy'))
quantiles = np.load('./constrained/quantiles_' + scheme + '_b_' + str(B) + '.npy')
N_usages = np.load('./constrained/Node_contrib_' + scheme + '_combined_b_' + str(B) + '.npy')
totalUsagesLin.append(np.sum(.5 * N_usages, 1) / node_mean_load)
totalUsagesminDis = []
scheme = 'minDis'
for B in b:
# Load data and results
F = abs(np.load('./ConstrainedFlowData/Europe_aHE_' + str(B) + 'q99_lin_flows.npy'))
quantiles = np.load('./constrained/quantiles_' + scheme + '_b_' + str(B) + '.npy')
N_usages = np.load('./constrained/Node_contrib_' + scheme + '_combined_b_' + str(B) + '.npy')
totalUsagesminDis.append(np.sum(.5 * N_usages, 1) / node_mean_load)
# Figure comparing nodes' total network usage as function of b
totalUsagesLin = np.array(totalUsagesLin).transpose()
totalUsagesLin = totalUsagesLin[node_mean_load.argsort()]
totalUsagesminDis = np.array(totalUsagesminDis).transpose()
totalUsagesminDis = totalUsagesminDis[node_mean_load.argsort()]
np.savez('./results/constrained_paper_results', lin=totalUsagesLin, minDis=totalUsagesminDis)
# Plot figures of total network usage
# Figure comparing nodes' total network usage as function of b
names = loadNames[::-1] # reversed because .argsort above sorts from smallest to largest
plt.figure(figsize=(12, 6))
ax3 = plt.subplot(121)
ax3.set_xticks(np.linspace(0, 30, 16))
ax3.set_xticklabels(np.linspace(0, 1.5, 16), fontsize=8)
ax3.set_yticks(np.linspace(.5, 29.5, 30))
ax3.set_yticklabels(names, ha="right", va="center", fontsize=9)
plt.pcolormesh(totalUsagesLin, cmap=cmap)
cbl3 = plt.colorbar()
cbl3.solids.set_edgecolor('face')
plt.xlabel(r'$\beta$')
plt.title('Total network usage, DC')
ax4 = plt.subplot(122)
ax4.set_xticks(np.linspace(0, 30, 16))
ax4.set_xticklabels(np.linspace(0, 1.5, 16), fontsize=8)
ax4.set_yticks(np.linspace(.5, 29.5, 30))
ax4.set_yticklabels(names, ha="right", va="center", fontsize=9)
plt.pcolormesh(totalUsagesminDis, cmap=cmap)
cbl4 = plt.colorbar()
cbl4.solids.set_edgecolor('face')
plt.xlabel(r'$\beta$')
plt.title('Total network usage, min. diss.')
plt.savefig(figPath + 'total-network-usage.pdf', bbox_inches='tight')
# Figure plotting the same as just above, but viewed from a different angle
betas = np.linspace(0.05, 1.5, 30)
plt.figure(figsize=(12, 6))
ax5 = plt.subplot(121)
for n in xrange(len(names)):
if n in [4, 7, 9, 14, 15]:
col = '#000099'
alph = .7
elif n in [21, 27, 28, 29]:
col = '#990000'
alph = .7
else:
col = '#000000'
alph = .3
plt.plot(betas, totalUsagesLin[n], '-', color=col, lw=1.5, alpha=alph)
ax5.set_xlabel(r'$\beta$')
ax5.set_ylabel(r'Network usage [MW$_T$/MW$_L$]')
plt.axis([0.05, 1.5, 0, np.ceil(np.max(totalUsagesLin))])
plt.title('Total network usage, DC')
ax6 = plt.subplot(122)
for n in xrange(len(names)):
if n in [4, 7, 9, 14, 15]:
col = '#000099'
alph = .7
elif n in [21, 27, 28, 29]:
col = '#990000'
alph = .7
else:
col = '#000000'
alph = .3
plt.plot(betas, totalUsagesminDis[n], '-', color=col, lw=1.5, alpha=alph)
ax6.set_xlabel(r'$\beta$')
plt.axis([0.05, 1.5, 0, np.ceil(np.max(totalUsagesminDis))])
plt.title('Total network usage, min. diss.')
plt.savefig(figPath + 'total-network-usage-lines.pdf', bbox_inches='tight')
# normalisation across betas
normedUsagesLin = totalUsagesLin / np.sum(totalUsagesLin, 0)
normedUsagesminDis = totalUsagesminDis / np.sum(totalUsagesminDis, 0)
plt.figure(figsize=(12, 6))
ax5 = plt.subplot(121)
for n in xrange(len(names)):
if n in [4, 7, 9, 14, 15]:
col = '#000099'
alph = .7
elif n in [21, 27, 28, 29]:
col = '#990000'
alph = .7
else:
col = '#000000'
alph = .3
plt.plot(betas, normedUsagesLin[n], '-', color=col, lw=1.5, alpha=alph)
ax5.set_xlabel(r'$\beta$')
ax5.set_ylabel(r'Network usage [MW$_T$/MW$_L$], normalised across $\beta$')
plt.axis([0.05, 1.5, 0, 1.1 * np.max(normedUsagesLin)])
plt.title('Total network usage, DC')
ax6 = plt.subplot(122)
for n in xrange(len(names)):
if n in [4, 7, 9, 14, 15]:
col = '#000099'
alph = .7
elif n in [21, 27, 28, 29]:
col = '#990000'
alph = .7
else:
col = '#000000'
alph = .3
plt.plot(betas, normedUsagesminDis[n], '-', color=col, lw=1.5, alpha=alph)
ax6.set_xlabel(r'$\beta$')
plt.axis([0.05, 1.5, 0, 1.1 * np.max(normedUsagesminDis)])
plt.title('Total network usage, min. diss.')
plt.savefig(figPath + 'total-network-usage-beta-normed.pdf', bbox_inches='tight')
plt.close('all')
"""
Plotting stacked area figures of network usages
"""
if (('plot' in task) and ('area' in task)):
print('Plotting area figures')
N = EU_Nodes()
F = abs(np.load('./ConstrainedFlowData/Europe_aHE_0.05q99_DC_lin_flows.npy'))
link_dic = link_dict(N, F)
nodes = range(len(N))
links = range(len(F))
names = np.array([str(N[i].label) for i in range(len(N))])
link_names = np.array(link_namer(N, F))
N = np.load('./ConstrainedFlowData/Europe_aHE_copper_DC_lin.npz', mmap_mode='r+')
node_mean_load = N['mean']
N = None
betas = np.linspace(0.05, 1.5, 30)
for n in ['', 'norm']:
if n == 'norm':
saveString = 'normed/'
else:
saveString = ''
# Country's usage of all links as function of b
for node in nodes:
plt.figure(figsize=(12, 5))
usages = []
scheme = 'lin'
for b in np.linspace(0.05, 1.5, 30):
# Load data and results
F = abs(np.load('./ConstrainedFlowData/Europe_aHE_' + str(b) + 'q99_DC_' + scheme + '_flows.npy'))
quantiles = np.load('./constrained/quantiles_' + scheme + '_b_' + str(b) + '.npy')
N_usages = np.load('./constrained/Node_contrib_' + scheme + '_combined_b_' + str(b) + '.npy')
if n == 'norm':
usages.append(.5 * N_usages[node] / quantiles)
else:
usages.append(.5 * N_usages[node])
usages = np.array(usages).transpose()
ax1 = plt.subplot(121)
max_usages = np.max(usages, 1)
sort_usages = usages[max_usages.argsort()]
if n == 'norm':
norm_usages = sort_usages / np.sum(sort_usages, 0)
else:
norm_usages = sort_usages
sort_link_names = link_names[max_usages.argsort()]
top_col = ["#cc66cc", "#cc6666", "#cc9966", "#66cc66", "#66cccc", "#6666cc"]
for a in links:
if a < len(links) - 6:
col = "#6e5160"
else:
col = top_col[len(links) - a - 1]
if a == 0:
ax1.fill_between(betas, 0, norm_usages[a, :], facecolor=col, alpha=.7)
baseline = norm_usages[a, :]
else:
plot_data = [norm_usages[a, i] + baseline[i] for i in range(len(baseline))]
ax1.fill_between(betas, baseline, plot_data, facecolor=col, alpha=.7)
if a >= len(links) - 10:
plt.text(1.51, 0 + baseline[-1] + (plot_data[-1] - baseline[-1]) / 2,
sort_link_names[a], color=col, va='center', fontsize=9)
baseline = [baseline[i] + norm_usages[a, i] for i in range(len(baseline))]
ax1.set_xticks(np.linspace(0, 1.5, 16))
ax1.set_xticklabels(np.linspace(0, 1.5, 16))
plt.axis([0.05, 1.5, 0, max(np.sum(norm_usages, 0))])
plt.xlabel(r'$\beta$')
plt.title('Network usage, DC')
if n == 'norm':
plt.ylabel(r'$\mathcal{K}^T_{ln}/\mathcal{K}^T_l$')
else:
plt.ylabel(r'$\mathcal{K}^T_{ln}$ [W]')
usages = []
scheme = 'minDis'
for b in np.linspace(0.05, 1.5, 30):
# Load data and results
F = abs(np.load('./ConstrainedFlowData/Europe_aHE_' + str(b) + 'q99_lin_flows.npy'))
quantiles = np.load('./constrained/quantiles_' + scheme + '_b_' + str(b) + '.npy')
N_usages = np.load('./constrained/Node_contrib_' + scheme + '_combined_b_' + str(b) + '.npy')
if n == 'norm':
usages.append(.5 * N_usages[node] / quantiles)
else:
usages.append(.5 * N_usages[node])
usages = np.array(usages).transpose()
ax2 = plt.subplot(122)
max_usages = np.max(usages, 1)
sort_usages = usages[max_usages.argsort()]
if n == 'norm':
norm_usages = sort_usages / np.sum(sort_usages, 0)
else:
norm_usages = sort_usages
sort_link_names = link_names[max_usages.argsort()]
top_col = ["#cc66cc", "#cc6666", "#cc9966", "#66cc66", "#66cccc", "#6666cc"]
for a in links:
if a < len(links) - 6:
col = "#6e5160"
else:
col = top_col[len(links) - a - 1]
if a == 0:
ax2.fill_between(betas, 0, norm_usages[a, :], facecolor=col, alpha=.7)
baseline = norm_usages[a, :]
else:
plot_data = [norm_usages[a, i] + baseline[i] for i in range(len(baseline))]
ax2.fill_between(betas, baseline, plot_data, facecolor=col, alpha=.7)
if a >= len(links) - 10:
plt.text(1.51, 0 + baseline[-1] + (plot_data[-1] - baseline[-1]) / 2,
sort_link_names[a], color=col, va='center', fontsize=9)
baseline = [baseline[i] + norm_usages[a, i] for i in range(len(baseline))]
ax2.set_xticks(np.linspace(0, 1.5, 16))
ax2.set_xticklabels(np.linspace(0, 1.5, 16))
plt.axis([0.05, 1.5, 0, max(np.sum(norm_usages, 0))])
plt.xlabel(r'$\beta$')
plt.title('Network usage, min. diss.')
plt.suptitle('Link usage by ' + names[node], fontsize=14)
plt.savefig(figPath + saveString + 'node-usage-area-' + str(node) + '.pdf', bbox_inches='tight')
plt.close()
# All countries usage of a single link as function of b
for link in links:
plt.figure(figsize=(12, 5))
usages = []
scheme = 'lin'
for b in betas:
# Load data and results
F = abs(np.load('./ConstrainedFlowData/Europe_aHE_' + str(b) + 'q99_DC_' + scheme + '_flows.npy'))
quantiles = np.load('./constrained/quantiles_' + scheme + '_b_' + str(b) + '.npy')
N_usages = np.load('./constrained/Node_contrib_' + scheme + '_combined_b_' + str(b) + '.npy')
if n == 'norm':
usages.append(.5 * N_usages[:, link] / quantiles[link])
else:
usages.append(.5 * N_usages[:, link])
usages = np.array(usages).transpose()
ax3 = plt.subplot(121)
max_usages = np.max(usages, 1)
sort_usages = usages[max_usages.argsort()]
if n == 'norm':
norm_usages = sort_usages / np.sum(sort_usages, 0)
else:
norm_usages = sort_usages
sort_names = names[max_usages.argsort()]
top_col = ["#cc66cc", "#cc6666", "#cc9966", "#66cc66", "#66cccc", "#6666cc"]
for a in nodes:
if a < len(nodes) - 6:
col = "#6e5160"
else:
col = top_col[len(nodes) - a - 1]
if a == 0:
ax3.fill_between(betas, 0, norm_usages[a, :], facecolor=col, alpha=.7)
baseline = norm_usages[a, :]
else:
plot_data = [norm_usages[a, i] + baseline[i] for i in range(len(baseline))]
ax3.fill_between(betas, baseline, plot_data, facecolor=col, alpha=.7)
if a >= len(nodes) - 10:
plt.text(1.51, 0 + baseline[-1] + (plot_data[-1] - baseline[-1]) / 2, sort_names[a], color=col, va='center', fontsize=9)
baseline = [baseline[i] + norm_usages[a, i] for i in range(len(baseline))]
ax3.set_xticks(np.linspace(0, 1.5, 16))
ax3.set_xticklabels(np.linspace(0, 1.5, 16))
plt.axis([0.05, 1.5, 0, max(np.sum(norm_usages, 0))])
plt.xlabel(r'$\beta$')
plt.title('Network usage, DC')
if n == 'norm':
plt.ylabel(r'$\mathcal{K}^T_{ln}/\mathcal{K}^T_l$')
else:
plt.ylabel(r'$\mathcal{K}^T_{ln}$ [W]')
usages = []
scheme = 'minDis'
for b in np.linspace(0.05, 1.5, 30):
# Load data and results
F = abs(np.load('./ConstrainedFlowData/Europe_aHE_' + str(b) + 'q99_lin_flows.npy'))
quantiles = np.load('./constrained/quantiles_' + scheme + '_b_' + str(b) + '.npy')
N_usages = np.load('./constrained/Node_contrib_' + scheme + '_combined_b_' + str(b) + '.npy')
if n == 'norm':
usages.append(.5 * N_usages[:, link] / quantiles[link])
else:
usages.append(.5 * N_usages[:, link])
usages = np.array(usages).transpose()
ax4 = plt.subplot(122)
max_usages = np.max(usages, 1)
sort_usages = usages[max_usages.argsort()]
if n == 'norm':
norm_usages = sort_usages / np.sum(sort_usages, 0)
else:
norm_usages = sort_usages
sort_names = names[max_usages.argsort()]
top_col = ["#cc66cc", "#cc6666", "#cc9966", "#66cc66", "#66cccc", "#6666cc"]
for a in nodes:
if a < len(nodes) - 6:
col = "#6e5160"
else:
col = top_col[len(nodes) - a - 1]
if a == 0:
ax4.fill_between(betas, 0, norm_usages[a, :], facecolor=col, alpha=.7)
baseline = norm_usages[a, :]
else:
plot_data = [norm_usages[a, i] + baseline[i] for i in range(len(baseline))]
ax4.fill_between(betas, baseline, plot_data, facecolor=col, alpha=.7)
if a >= len(nodes) - 10:
plt.text(1.51, 0 + baseline[-1] + (plot_data[-1] - baseline[-1]) / 2,
sort_names[a], color=col, va='center', fontsize=9)
baseline = [baseline[i] + norm_usages[a, i] for i in range(len(baseline))]
ax4.set_xticks(np.linspace(0, 1.5, 16))
ax4.set_xticklabels(np.linspace(0, 1.5, 16))
plt.axis([0.05, 1.5, 0, max(np.sum(norm_usages, 0))])
plt.xlabel(r'$\beta$')
plt.title('Network usage, min. diss.')
plt.suptitle('Usage of link ' + link_names[link], fontsize=14)
plt.savefig(figPath + saveString + 'link-usage-area-' + str(link) + '.pdf', bbox_inches='tight')
plt.close()