Validation 10 - Timeseries Minimum Up Time

In [1]:

%matplotlib inline

In [2]:

import psst

In [3]:

from psst.case import read_matpower
from psst.network import create_network
import pandas as pd

Validation of case 1

In [4]:

case = read_matpower('./cases/case7.m')

In [5]:

case.load = pd.read_csv('./cases/case7.csv', index_col=0)

In [6]:

network = create_network(case, prog='neato')
network.draw()
../../_images/notebooks_validation_Validation10-TimeseriesMinimumUpTime_7_0.png 
In [7]:

case

Out[7]:

<psst.case.PSSTCase(name=casematpower, Generators=2, Buses=2, Branches=1)>

In [8]:

case.bus

Out[8]:
TYPE PD QD GS BS AREA VM VA BASEKV ZONE VMAX VMIN
Bus1 3 0 131.47 0 0 1 1 0 230 1 1.1 0.9
Bus2 2 100 0.00 0 0 1 1 0 230 1 1.1 0.9 
In [9]:

case.branch

Out[9]:
F_BUS T_BUS BR_R BR_X BR_B RATE_A RATE_B RATE_C TAP SHIFT BR_STATUS ANGMIN ANGMAX
0 Bus1 Bus2 0.00281 0.0281 0.00712 800 800 800 0 0 1 -360 360 
In [32]:

case.gen.loc['GenCo1', 'MINIMUM_UP_TIME'] = 5

In [33]:

case.gen

Out[33]:
GEN_BUS PG QG QMAX QMIN VG MBASE GEN_STATUS PMAX PMIN PC1 PC2 QC1MIN QC1MAX QC2MIN QC2MAX RAMP_AGC RAMP_10 RAMP_30 RAMP_Q APF STARTUP_RAMP SHUTDOWN_RAMP MINIMUM_UP_TIME MINIMUM_DOWN_TIME
GenCo0 Bus1 200 0 30 -30 1 100 1 200 0 0 0 0 0 0 0 0 200 0 0 0 200 200 0 0
GenCo1 Bus2 500 0 30 -30 1 100 1 500 0 0 0 0 0 0 0 0 500 0 0 0 500 500 5 0 
In [34]:

case.gencost

Out[34]:
MODEL STARTUP SHUTDOWN NCOST COST_1 COST_0
GenCo0 1 0 0 2 10 0
GenCo1 1 5000 1000 2 14 2000 
In [35]:

import matplotlib.pyplot as plt

In [36]:

fig, axs = plt.subplots(1, 1, figsize=(8, 5))
ax = axs
case.load['Bus2'].plot.bar(ax=ax)
ax.set_ylim(0, 500);
../../_images/notebooks_validation_Validation10-TimeseriesMinimumUpTime_15_0.png 
In [37]:

from psst.model import build_model

In [38]:

model = build_model(case)

In [39]:

model

Out[39]:

<psst.model.PSSTModel(status=None)>

In [40]:

model.solve(solver='cbc', verbose=True)

Welcome to the CBC MILP Solver
Version: 2.9.6
Build Date: May 27 2016

command line - /usr/local/bin/cbc -mipgap 0.01 -printingOptions all -import /var/folders/wk/lcf0vgd90bx0vq1873tn04knk_djr3/T/tmpuYJYwx.pyomo.lp -import -stat=1 -solve -solu /var/folders/wk/lcf0vgd90bx0vq1873tn04knk_djr3/T/tmpuYJYwx.pyomo.soln (default strategy 1)
No match for mipgap - ? for list of commands
No match for 0.01 - ? for list of commands
Option for printingOptions changed from normal to all
Current default (if $ as parameter) for import is /var/folders/wk/lcf0vgd90bx0vq1873tn04knk_djr3/T/tmpuYJYwx.pyomo.lp
Presolve 284 (-638) rows, 383 (-370) columns and 1027 (-1387) elements
Statistics for presolved model
Original problem has 48 integers (48 of which binary)
Presolved problem has 24 integers (24 of which binary)
==== 190 zero objective 3 different
190 variables have objective of 0
49 variables have objective of 1
144 variables have objective of 1e+06
==== absolute objective values 3 different
190 variables have objective of 0
49 variables have objective of 1
144 variables have objective of 1e+06
==== for integers 24 zero objective 1 different
24 variables have objective of 0
==== for integers absolute objective values 1 different
24 variables have objective of 0
===== end objective counts


Problem has 284 rows, 383 columns (193 with objective) and 1027 elements
There are 193 singletons with objective
Column breakdown:
287 of type 0.0->inf, 48 of type 0.0->up, 0 of type lo->inf,
24 of type lo->up, 0 of type free, 0 of type fixed,
0 of type -inf->0.0, 0 of type -inf->up, 24 of type 0.0->1.0
Row breakdown:
24 of type E 0.0, 0 of type E 1.0, 0 of type E -1.0,
48 of type E other, 2 of type G 0.0, 0 of type G 1.0,
0 of type G other, 139 of type L 0.0, 0 of type L 1.0,
71 of type L other, 0 of type Range 0.0->1.0, 0 of type Range other,
0 of type Free
Continuous objective value is 47068 - 0.00 seconds
Cgl0003I 0 fixed, 0 tightened bounds, 23 strengthened rows, 0 substitutions
Cgl0004I processed model has 260 rows, 382 columns (24 integer (24 of which binary)) and 886 elements
Cbc0038I Initial state - 4 integers unsatisfied sum - 1.15
Cbc0038I Pass   1: suminf.    0.00000 (0) obj. 6.00037e+08 iterations 19
Cbc0038I Solution found of 6.00037e+08
Cbc0038I Relaxing continuous gives 6.00037e+08
Cbc0038I Before mini branch and bound, 20 integers at bound fixed and 263 continuous
Cbc0038I Full problem 260 rows 382 columns, reduced to 17 rows 13 columns
Cbc0038I Mini branch and bound did not improve solution (0.02 seconds)
Cbc0038I Round again with cutoff of 5.40038e+08
Cbc0038I Pass   2: suminf.    0.08727 (4) obj. 5.40038e+08 iterations 19
Cbc0038I Pass   3: suminf.    0.25000 (1) obj. 5.40038e+08 iterations 13
Cbc0038I Pass   4: suminf.    0.50000 (1) obj. 5.40038e+08 iterations 5
Cbc0038I Pass   5: suminf.    0.35417 (3) obj. 5.40038e+08 iterations 38
Cbc0038I Pass   6: suminf.    0.25000 (1) obj. 5.40038e+08 iterations 11
Cbc0038I Pass   7: suminf.    0.25000 (1) obj. 5.40038e+08 iterations 3
Cbc0038I Pass   8: suminf.    1.64258 (5) obj. 5.40038e+08 iterations 23
Cbc0038I Pass   9: suminf.    0.62500 (2) obj. 5.40038e+08 iterations 17
Cbc0038I Pass  10: suminf.    0.00000 (0) obj. 5.40038e+08 iterations 5
Cbc0038I Solution found of 5.40038e+08
Cbc0038I Relaxing continuous gives 84700
Cbc0038I Before mini branch and bound, 5 integers at bound fixed and 247 continuous
Cbc0038I Full problem 260 rows 382 columns, reduced to 62 rows 42 columns
Cbc0038I Mini branch and bound improved solution from 84700 to 58700 (0.03 seconds)
Cbc0038I Round again with cutoff of 56440
Cbc0038I Pass  11: suminf.    1.14997 (4) obj. 56440 iterations 7
Cbc0038I Pass  12: suminf.    0.25000 (1) obj. 56440 iterations 19
Cbc0038I Pass  13: suminf.    0.50000 (1) obj. 56440 iterations 5
Cbc0038I Pass  14: suminf.    1.58625 (5) obj. 56440 iterations 23
Cbc0038I Pass  15: suminf.    0.40556 (5) obj. 56440 iterations 13
Cbc0038I Pass  16: suminf.    1.24998 (4) obj. 56440 iterations 30
Cbc0038I Pass  17: suminf.    1.14997 (4) obj. 56440 iterations 5
Cbc0038I Pass  18: suminf.    0.25000 (1) obj. 56440 iterations 18
Cbc0038I Pass  19: suminf.    0.50000 (1) obj. 56440 iterations 2
Cbc0038I Pass  20: suminf.    0.97800 (5) obj. 56440 iterations 23
Cbc0038I Pass  21: suminf.    0.65000 (3) obj. 56440 iterations 16
Cbc0038I Pass  22: suminf.    0.95667 (3) obj. 56440 iterations 13
Cbc0038I Pass  23: suminf.    1.29364 (5) obj. 56440 iterations 4
Cbc0038I Pass  24: suminf.    0.95667 (3) obj. 56440 iterations 6
Cbc0038I Pass  25: suminf.    1.66229 (6) obj. 56440 iterations 16
Cbc0038I Pass  26: suminf.    1.58326 (6) obj. 56440 iterations 22
Cbc0038I Pass  27: suminf.    1.15000 (4) obj. 56440 iterations 23
Cbc0038I Pass  28: suminf.    0.28000 (2) obj. 56440 iterations 14
Cbc0038I Pass  29: suminf.    0.25000 (1) obj. 56440 iterations 5
Cbc0038I Pass  30: suminf.    0.50000 (1) obj. 56440 iterations 3
Cbc0038I Pass  31: suminf.    0.28000 (3) obj. 56440 iterations 27
Cbc0038I Pass  32: suminf.    1.42000 (6) obj. 56440 iterations 68
Cbc0038I Pass  33: suminf.    1.42000 (6) obj. 56440 iterations 8
Cbc0038I Pass  34: suminf.    1.14997 (4) obj. 56440 iterations 28
Cbc0038I Pass  35: suminf.    1.86249 (6) obj. 56440 iterations 14
Cbc0038I Pass  36: suminf.    1.86249 (6) obj. 56440 iterations 4
Cbc0038I Pass  37: suminf.    0.29000 (3) obj. 56440 iterations 28
Cbc0038I Pass  38: suminf.    0.25000 (1) obj. 56440 iterations 14
Cbc0038I Pass  39: suminf.    0.50000 (1) obj. 56440 iterations 5
Cbc0038I Pass  40: suminf.    1.10464 (5) obj. 56440 iterations 26
Cbc0038I No solution found this major pass
Cbc0038I Before mini branch and bound, 11 integers at bound fixed and 243 continuous
Cbc0038I Full problem 260 rows 382 columns, reduced to 21 rows 21 columns
Cbc0038I Mini branch and bound did not improve solution (0.05 seconds)
Cbc0038I After 0.05 seconds - Feasibility pump exiting with objective of 58700 - took 0.04 seconds
Cbc0012I Integer solution of 58700 found by feasibility pump after 0 iterations and 0 nodes (0.05 seconds)
Cbc0038I Full problem 260 rows 382 columns, reduced to 143 rows 260 columns - 5 fixed gives 128, 245 - still too large
Cbc0038I Full problem 260 rows 382 columns, reduced to 128 rows 245 columns - too large
Cbc0031I 3 added rows had average density of 8
Cbc0013I At root node, 16 cuts changed objective from 47400 to 58700 in 3 passes
Cbc0014I Cut generator 0 (Probing) - 28 row cuts average 4.4 elements, 3 column cuts (3 active)  in 0.001 seconds - new frequency is 1
Cbc0014I Cut generator 1 (Gomory) - 6 row cuts average 9.8 elements, 0 column cuts (0 active)  in 0.000 seconds - new frequency is 1
Cbc0014I Cut generator 2 (Knapsack) - 3 row cuts average 2.3 elements, 0 column cuts (0 active)  in 0.001 seconds - new frequency is 1
Cbc0014I Cut generator 3 (Clique) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.000 seconds - new frequency is -100
Cbc0014I Cut generator 4 (MixedIntegerRounding2) - 5 row cuts average 5.4 elements, 0 column cuts (0 active)  in 0.000 seconds - new frequency is 1
Cbc0014I Cut generator 5 (FlowCover) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.001 seconds - new frequency is -100
Cbc0014I Cut generator 6 (TwoMirCuts) - 9 row cuts average 6.0 elements, 0 column cuts (0 active)  in 0.001 seconds - new frequency is 1
Cbc0001I Search completed - best objective 58700, took 22 iterations and 0 nodes (0.07 seconds)
Cbc0035I Maximum depth 0, 15 variables fixed on reduced cost
Cuts at root node changed objective from 47400 to 58700
Probing was tried 3 times and created 31 cuts of which 0 were active after adding rounds of cuts (0.001 seconds)
Gomory was tried 3 times and created 6 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
Knapsack was tried 3 times and created 3 cuts of which 0 were active after adding rounds of cuts (0.001 seconds)
Clique was tried 3 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
MixedIntegerRounding2 was tried 3 times and created 5 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
FlowCover was tried 3 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.001 seconds)
TwoMirCuts was tried 3 times and created 9 cuts of which 0 were active after adding rounds of cuts (0.001 seconds)

Result - Optimal solution found

Objective value:                58700.00000000
Enumerated nodes:               0
Total iterations:               22
Time (CPU seconds):             0.08
Time (Wallclock seconds):       0.08

Total time (CPU seconds):       0.09   (Wallclock seconds):       0.10

Input data

In [41]:

import pandas as pd

In [42]:

pd.DataFrame(case.gen['PMAX'])

Out[42]:
PMAX
GenCo0 200
GenCo1 500 
In [43]:

case.load

Out[43]:
Bus1 Bus2
0 0.0 100.0
1 0.0 100.0
2 0.0 100.0
3 0.0 120.0
4 0.0 120.0
5 0.0 120.0
6 0.0 150.0
7 0.0 150.0
8 0.0 150.0
9 0.0 200.0
10 0.0 200.0
11 0.0 200.0
12 0.0 300.0
13 0.0 400.0
14 0.0 300.0
15 0.0 200.0
16 0.0 200.0
17 0.0 200.0
18 0.0 150.0
19 0.0 150.0
20 0.0 150.0
21 0.0 150.0
22 0.0 100.0
23 0.0 100.0

Model Results

In [44]:

model.results.unit_commitment

Out[44]:
GenCo0 GenCo1
0 1 0
1 1 0
2 1 0
3 1 0
4 1 0
5 1 0
6 1 0
7 1 0
8 1 0
9 1 0
10 1 0
11 1 1
12 1 1
13 1 1
14 1 1
15 1 1
16 1 0
17 1 0
18 1 0
19 1 0
20 1 0
21 1 0
22 1 0
23 1 0 
In [45]:

model.results.power_generated

Out[45]:
GenCo0 GenCo1
0 100 0
1 100 0
2 100 0
3 120 0
4 120 0
5 120 0
6 150 0
7 150 0
8 150 0
9 200 0
10 200 0
11 200 0
12 200 100
13 200 200
14 200 100
15 200 0
16 200 0
17 200 0
18 150 0
19 150 0
20 150 0
21 150 0
22 100 0
23 100 0 
In [46]:

model.results.commitment_cost

Out[46]:

6000

In [47]:

model.results.production_cost

Out[47]:

42700

In [48]:

model.results.noload_cost

Out[48]:

10000.0

In [49]:

model.results.line_power

Out[49]:
0
0 100
1 100
2 100
3 120
4 120
5 120
6 150
7 150
8 150
9 200
10 200
11 200
12 200
13 200
14 200
15 200
16 200
17 200
18 150
19 150
20 150
21 150
22 100
23 100 
In [51]:

from psst.plot import line_power, stacked_power_generation

In [52]:

stacked_power_generation(model.results, legend=True)
../../_images/notebooks_validation_Validation10-TimeseriesMinimumUpTime_32_0.png