Validation 09 - Timeseries Startup Ramp Rates

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]:

case.reserve_factor = 0.0

In [7]:

network = create_network(case, prog='neato')
network.draw()
../../_images/notebooks_validation_Validation09-TimeseriesStartupRampRates_8_0.png 
In [8]:

case

Out[8]:

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

In [9]:

case.bus

Out[9]:
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 [10]:

case.branch

Out[10]:
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 [11]:

case.gen.loc['GenCo1', 'RAMP_10'] = 50
case.gen.loc['GenCo1', 'STARTUP_RAMP'] = 25

In [12]:

case.gen

Out[12]:
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 50 0 0 0 25 500 0 0 
In [13]:

case.gencost.loc['GenCo1', 'STARTUP'] = 0
case.gencost.loc['GenCo1', 'SHUTDOWN'] = 0

In [14]:

case.gencost

Out[14]:
MODEL STARTUP SHUTDOWN NCOST COST_1 COST_0
GenCo0 1 0 0 2 10 0
GenCo1 1 0 0 2 14 2000 
In [15]:

import matplotlib.pyplot as plt

In [16]:

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_Validation09-TimeseriesStartupRampRates_17_0.png 
In [17]:

from psst.model import build_model

In [18]:

model = build_model(case)

In [19]:

model

Out[19]:

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

In [20]:

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/tmpF4LWAO.pyomo.lp -import -stat=1 -solve -solu /var/folders/wk/lcf0vgd90bx0vq1873tn04knk_djr3/T/tmpF4LWAO.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/tmpF4LWAO.pyomo.lp
Presolve 261 (-638) rows, 336 (-417) columns and 900 (-1411) elements
Statistics for presolved model
Original problem has 48 integers (48 of which binary)
Presolved problem has 24 integers (24 of which binary)
==== 120 zero objective 4 different
120 variables have objective of 0
48 variables have objective of 1
24 variables have objective of 2000
144 variables have objective of 1e+06
==== absolute objective values 4 different
120 variables have objective of 0
48 variables have objective of 1
24 variables have objective of 2000
144 variables have objective of 1e+06
==== for integers 0 zero objective 1 different
24 variables have objective of 2000
==== for integers absolute objective values 1 different
24 variables have objective of 2000
===== end objective counts


Problem has 261 rows, 336 columns (216 with objective) and 900 elements
There are 192 singletons with objective
Column breakdown:
240 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, 0 of type G 0.0, 0 of type G 1.0,
0 of type G other, 72 of type L 0.0, 0 of type L 1.0,
117 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 44300 - 0.01 seconds
Cgl0003I 0 fixed, 0 tightened bounds, 26 strengthened rows, 0 substitutions
Cgl0003I 0 fixed, 0 tightened bounds, 2 strengthened rows, 0 substitutions
Cgl0003I 0 fixed, 0 tightened bounds, 1 strengthened rows, 0 substitutions
Cgl0003I 0 fixed, 0 tightened bounds, 1 strengthened rows, 0 substitutions
Cgl0003I 0 fixed, 0 tightened bounds, 1 strengthened rows, 0 substitutions
Cgl0003I 0 fixed, 0 tightened bounds, 1 strengthened rows, 0 substitutions
Cgl0003I 0 fixed, 0 tightened bounds, 1 strengthened rows, 0 substitutions
Cgl0003I 0 fixed, 0 tightened bounds, 2 strengthened rows, 0 substitutions
Cgl0003I 0 fixed, 0 tightened bounds, 3 strengthened rows, 0 substitutions
Cgl0004I processed model has 238 rows, 336 columns (24 integer (24 of which binary)) and 830 elements
Cbc0038I Initial state - 11 integers unsatisfied sum - 1.47663
Cbc0038I Pass   1: suminf.    0.00000 (0) obj. 5.25043e+08 iterations 16
Cbc0038I Solution found of 5.25043e+08
Cbc0038I Relaxing continuous gives 4.50045e+08
Cbc0038I Before mini branch and bound, 13 integers at bound fixed and 194 continuous
Cbc0038I Full problem 238 rows 336 columns, reduced to 71 rows 52 columns
Cbc0038I Mini branch and bound improved solution from 4.50045e+08 to 7.50522e+07 (0.07 seconds)
Cbc0038I Freeing continuous variables gives a solution of 3.75529e+07
Cbc0038I Round again with cutoff of 3.38029e+07
Cbc0038I Pass   2: suminf.    0.80379 (9) obj. 3.38029e+07 iterations 19
Cbc0038I Pass   3: suminf.    0.00000 (0) obj. 3.38029e+07 iterations 34
Cbc0038I Solution found of 3.38029e+07
Cbc0038I Relaxing continuous gives 67700
Cbc0038I Before mini branch and bound, 13 integers at bound fixed and 193 continuous
Cbc0038I Full problem 238 rows 336 columns, reduced to 73 rows 55 columns
Cbc0038I Mini branch and bound improved solution from 67700 to 55700 (0.08 seconds)
Cbc0038I Round again with cutoff of 55090.2
Cbc0038I Pass   4: suminf.    1.15404 (9) obj. 55090.2 iterations 1
Cbc0038I Pass   5: suminf.    0.20490 (1) obj. 55090.2 iterations 26
Cbc0038I Pass   6: suminf.    0.20490 (1) obj. 55090.2 iterations 4
Cbc0038I Pass   7: suminf.    0.20000 (1) obj. 55090.2 iterations 7
Cbc0038I Pass   8: suminf.    1.26144 (6) obj. 55090.2 iterations 19
Cbc0038I Pass   9: suminf.    0.84335 (5) obj. 55090.2 iterations 4
Cbc0038I Pass  10: suminf.    0.20490 (1) obj. 55090.2 iterations 20
Cbc0038I Pass  11: suminf.    0.60490 (2) obj. 55090.2 iterations 1
Cbc0038I Pass  12: suminf.    0.60490 (2) obj. 55090.2 iterations 0
Cbc0038I Pass  13: suminf.    0.20490 (1) obj. 55090.2 iterations 6
Cbc0038I Pass  14: suminf.    0.20000 (1) obj. 55090.2 iterations 11
Cbc0038I Pass  15: suminf.    0.60490 (2) obj. 55090.2 iterations 9
Cbc0038I Pass  16: suminf.    1.16643 (6) obj. 55090.2 iterations 20
Cbc0038I Pass  17: suminf.    1.16643 (6) obj. 55090.2 iterations 0
Cbc0038I Pass  18: suminf.    0.20490 (1) obj. 55090.2 iterations 25
Cbc0038I Pass  19: suminf.    0.78660 (7) obj. 55090.2 iterations 15
Cbc0038I Pass  20: suminf.    0.45185 (8) obj. 55090.2 iterations 11
Cbc0038I Pass  21: suminf.    0.20490 (1) obj. 55090.2 iterations 31
Cbc0038I Pass  22: suminf.    0.20490 (1) obj. 55090.2 iterations 4
Cbc0038I Pass  23: suminf.    0.20000 (1) obj. 55090.2 iterations 13
Cbc0038I Pass  24: suminf.    0.60463 (3) obj. 55090.2 iterations 26
Cbc0038I Pass  25: suminf.    0.43809 (2) obj. 55090.2 iterations 16
Cbc0038I Pass  26: suminf.    0.20490 (1) obj. 55090.2 iterations 14
Cbc0038I Pass  27: suminf.    0.60490 (2) obj. 55090.2 iterations 3
Cbc0038I Pass  28: suminf.    0.60490 (2) obj. 55090.2 iterations 2
Cbc0038I Pass  29: suminf.    0.20490 (1) obj. 55090.2 iterations 5
Cbc0038I Pass  30: suminf.    0.20000 (1) obj. 55090.2 iterations 15
Cbc0038I Pass  31: suminf.    0.60490 (2) obj. 55090.2 iterations 14
Cbc0038I Pass  32: suminf.    0.60490 (2) obj. 55090.2 iterations 1
Cbc0038I Pass  33: suminf.    0.94133 (6) obj. 55090.2 iterations 13
Cbc0038I No solution found this major pass
Cbc0038I Before mini branch and bound, 7 integers at bound fixed and 196 continuous
Cbc0038I Mini branch and bound did not improve solution (0.12 seconds)
Cbc0038I After 0.12 seconds - Feasibility pump exiting with objective of 55700 - took 0.06 seconds
Cbc0012I Integer solution of 55700 found by feasibility pump after 0 iterations and 0 nodes (0.12 seconds)
Cbc0038I Full problem 238 rows 336 columns, reduced to 173 rows 278 columns - 2 fixed gives 173, 276 - still too large
Cbc0031I 1 added rows had average density of 8
Cbc0013I At root node, 26 cuts changed objective from 52651.023 to 55700 in 1 passes
Cbc0014I Cut generator 0 (Probing) - 16 row cuts average 2.8 elements, 2 column cuts (2 active)  in 0.001 seconds - new frequency is 1
Cbc0014I Cut generator 1 (Gomory) - 3 row cuts average 15.0 elements, 0 column cuts (0 active)  in 0.000 seconds - new frequency is 1
Cbc0014I Cut generator 2 (Knapsack) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.001 seconds - new frequency is -100
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) - 0 row cuts average 0.0 elements, 0 column cuts (0 active)  in 0.000 seconds - new frequency is -100
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) - 7 row cuts average 17.0 elements, 0 column cuts (0 active)  in 0.001 seconds - new frequency is 1
Cbc0001I Search completed - best objective 55700, took 11 iterations and 0 nodes (0.13 seconds)
Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost
Cuts at root node changed objective from 52651 to 55700
Probing was tried 1 times and created 18 cuts of which 0 were active after adding rounds of cuts (0.001 seconds)
Gomory was tried 1 times and created 3 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
Knapsack was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.001 seconds)
Clique was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
MixedIntegerRounding2 was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
FlowCover was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.001 seconds)
TwoMirCuts was tried 1 times and created 7 cuts of which 0 were active after adding rounds of cuts (0.001 seconds)

Result - Optimal solution found

Objective value:                55700.00000000
Enumerated nodes:               0
Total iterations:               11
Time (CPU seconds):             0.15
Time (Wallclock seconds):       0.19

Total time (CPU seconds):       0.19   (Wallclock seconds):       0.25

Input data

In [21]:

import pandas as pd

In [22]:

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

Out[22]:
PMAX
GenCo0 200
GenCo1 500 
In [23]:

case.load

Out[23]:
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 [24]:

model.results.unit_commitment

Out[24]:
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 1
10 1 1
11 1 1
12 1 1
13 1 1
14 1 1
15 1 0
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 [25]:

model.results.power_generated

Out[25]:
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
10 150 50
11 100 100
12 150 150
13 200 200
14 150 150
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 [26]:

model.results.commitment_cost

Out[26]:

0

In [27]:

model.results.production_cost

Out[27]:

43700

In [28]:

model.results.noload_cost

Out[28]:

12000.0

In [29]:

model.results.line_power

Out[29]:
0
0 100
1 100
2 100
3 120
4 120
5 120
6 150
7 150
8 150
9 200
10 150
11 100
12 150
13 200
14 150
15 200
16 200
17 200
18 150
19 150
20 150
21 150
22 100
23 100 
In [30]:

from psst.plot import line_power, stacked_power_generation

In [32]:

ax = stacked_power_generation(model.results, legend=True)

# (model.results.power_generated.sum(axis=1) + model.results.regulating_reserve_up_available.sum(axis=1)).plot(ax=ax)
../../_images/notebooks_validation_Validation09-TimeseriesStartupRampRates_34_0.png