Note
You can download this example as a Jupyter notebook or start it in interactive mode.
Optimization without pyomo
In this example we demonstrate the behaviour of the Linear Optimal Power Flow (LOPF) calculation without using pyomo. This requires to set pyomo to False in the lopf function. Then, the communication with the solvers happens via in-house functions which leads to a much faster solving process.
[1]:
import pypsa
import pandas as pd
import os
[2]:
n = pypsa.examples.ac_dc_meshed(from_master=True)
WARNING:pypsa.io:Importing network from PyPSA version v0.17.1 while current version is v0.21.1. Read the release notes at https://pypsa.readthedocs.io/en/latest/release_notes.html to prepare your network for import.
INFO:pypsa.io:Imported network ac-dc-meshed.nc has buses, carriers, generators, global_constraints, lines, links, loads
Modify the network a bit: We set gas generators to non-extendable
[3]:
n.generators.loc[n.generators.carrier == "gas", "p_nom_extendable"] = False
Add ramp limit
[4]:
n.generators.loc[n.generators.carrier == "gas", "ramp_limit_down"] = 0.2
n.generators.loc[n.generators.carrier == "gas", "ramp_limit_up"] = 0.2
Add additional storage units (cyclic and non-cyclic) and fix one state_of_charge
[5]:
n.add(
"StorageUnit",
"su",
bus="Manchester",
marginal_cost=10,
inflow=50,
p_nom_extendable=True,
capital_cost=10,
p_nom=2000,
efficiency_dispatch=0.5,
cyclic_state_of_charge=True,
state_of_charge_initial=1000,
)
n.add(
"StorageUnit",
"su2",
bus="Manchester",
marginal_cost=10,
p_nom_extendable=True,
capital_cost=50,
p_nom=2000,
efficiency_dispatch=0.5,
carrier="gas",
cyclic_state_of_charge=False,
state_of_charge_initial=1000,
)
n.storage_units_t.state_of_charge_set.loc[n.snapshots[7], "su"] = 100
Add an additional store
[6]:
n.add("Bus", "storebus", carrier="hydro", x=-5, y=55)
n.madd(
"Link",
["battery_power", "battery_discharge"],
"",
bus0=["Manchester", "storebus"],
bus1=["storebus", "Manchester"],
p_nom=100,
efficiency=0.9,
p_nom_extendable=True,
p_nom_max=1000,
)
n.madd(
"Store",
["store"],
bus="storebus",
e_nom=2000,
e_nom_extendable=True,
marginal_cost=10,
capital_cost=10,
e_nom_max=5000,
e_initial=100,
e_cyclic=True,
);
Extra functionalities:
[7]:
from pypsa.linopt import get_var, linexpr, join_exprs, define_constraints
One of the most important functions is linexpr which take one or more tuples of coefficient and variable pairs which should go into the left hand side (lhs) of the constraint.
Add mimimum for state_of_charge
[8]:
def minimal_state_of_charge(n, snapshots):
vars_soc = get_var(n, "StorageUnit", "state_of_charge")
lhs = linexpr((1, vars_soc))
define_constraints(n, lhs, ">", 50, "StorageUnit", "soc_lower_bound")
Fix the ratio between ingoing and outgoing capacity of the Store
[9]:
def fix_link_cap_ratio(n, snapshots):
vars_link = get_var(n, "Link", "p_nom")
eff = n.links.at["battery_power", "efficiency"]
lhs = linexpr(
(1, vars_link["battery_power"]), (-eff, vars_link["battery_discharge"])
)
define_constraints(n, lhs, "=", 0, "battery_discharge", attr="fixratio")
Every bus must in total produce the 20% of the total demand
This requires the function pypsa.linopt.join_exprs which sums up arrays of linear expressions
[10]:
def fix_bus_production(n, snapshots):
total_demand = n.loads_t.p_set.sum().sum()
prod_per_bus = (
linexpr((1, get_var(n, "Generator", "p")))
.groupby(n.generators.bus, axis=1)
.apply(join_exprs)
)
define_constraints(
n, prod_per_bus, ">=", total_demand / 5, "Bus", "production_share"
)
Combine them …
[11]:
def extra_functionalities(n, snapshots):
minimal_state_of_charge(n, snapshots)
fix_link_cap_ratio(n, snapshots)
fix_bus_production(n, snapshots)
…and run the lopf with pyomo=False
[12]:
n.lopf(
pyomo=False,
extra_functionality=extra_functionalities,
keep_shadowprices=["Bus", "battery_discharge", "StorageUnit"],
)
INFO:pypsa.linopf:Prepare linear problem
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.1/lib/python3.10/site-packages/pypsa/linopt.py:474: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
ref_dict.pnl[attr].loc[df.index, df.columns] = df
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.1/lib/python3.10/site-packages/pypsa/linopt.py:474: FutureWarning: In a future version, `df.iloc[:, i] = newvals` will attempt to set the values inplace instead of always setting a new array. To retain the old behavior, use either `df[df.columns[i]] = newvals` or, if columns are non-unique, `df.isetitem(i, newvals)`
ref_dict.pnl[attr].loc[df.index, df.columns] = df
INFO:pypsa.linopf:Total preparation time: 0.34s
INFO:pypsa.linopf:Solve linear problem using Glpk solver
INFO:pypsa.linopf:Optimization successful. Objective value: 1.43e+07
[12]:
('ok', 'optimal')
The keep_shadowprices argument in the lopf now decides which shadow prices (SP) should be retrieved. It can either be set to True, then all SP are kept. It also can be a list of names of the constraints. Therefore the name argument in define_constraints is necessary, in our case ‘battery_discharge’, ‘StorageUnit’ and ‘Bus’.
Analysing the constraints
Let’s see if the system got our own constraints. We look at n.constraints which combines summarises constraints going into the linear problem
[13]:
n.constraints
[13]:
| pnl | specification | ||
|---|---|---|---|
| component | name | ||
| Generator | mu_lower | True | non_ext, p |
| mu_upper | True | non_ext, p | |
| Line | mu_upper | True | s |
| mu_lower | True | s | |
| Link | mu_upper | True | p |
| mu_lower | True | p | |
| Store | mu_upper | True | e |
| mu_lower | True | e | |
| StorageUnit | mu_upper | True | p_dispatch, p_store, state_of_charge |
| mu_lower | True | p_dispatch, p_store, state_of_charge | |
| mu_state_of_charge_set | True | ||
| Generator | mu_ramp_limit_up | True | nonext. |
| mu_ramp_limit_down | True | nonext. | |
| StorageUnit | mu_state_of_charge | True | |
| Store | mu_state_of_charge | True | |
| SubNetwork | mu_kirchhoff_voltage_law | True | |
| Bus | marginal_price | True | |
| GlobalConstraint | mu | False | co2_limit |
| StorageUnit | soc_lower_bound | True | |
| battery_discharge | fixratio | False | |
| Bus | production_share | False |
The last three entries show our constraints. As ‘soc_lower_bound’ is time-dependent, the pnl value is set to True.
Let’s check whether out two custom constraint are fulfilled:
[14]:
n.links.loc[["battery_power", "battery_discharge"], ["p_nom_opt"]]
[14]:
| p_nom_opt | |
|---|---|
| Link | |
| battery_power | 900.0 |
| battery_discharge | 1000.0 |
[15]:
n.storage_units_t.state_of_charge
[15]:
| StorageUnit | su | su2 |
|---|---|---|
| snapshot | ||
| 2015-01-01 00:00:00 | 1835.74 | 1000.000 |
| 2015-01-01 01:00:00 | 1326.16 | 1000.000 |
| 2015-01-01 02:00:00 | 1376.16 | 1000.000 |
| 2015-01-01 03:00:00 | 1426.16 | 1000.000 |
| 2015-01-01 04:00:00 | 1986.06 | 1000.000 |
| 2015-01-01 05:00:00 | 50.00 | 50.000 |
| 2015-01-01 06:00:00 | 50.00 | 50.000 |
| 2015-01-01 07:00:00 | 100.00 | 156.727 |
| 2015-01-01 08:00:00 | 50.00 | 140.120 |
| 2015-01-01 09:00:00 | 50.00 | 50.000 |
[16]:
n.generators_t.p.groupby(n.generators.bus, axis=1).sum().sum() / n.loads_t.p.sum().sum()
[16]:
bus
Frankfurt 0.200000
Manchester 0.200000
Norway 0.637047
dtype: float64
Looks good! Now, let’s see which dual values were parsed. Therefore we have a look into n.dualvalues
[17]:
n.dualvalues
[17]:
| in_comp | pnl | ||
|---|---|---|---|
| component | name | ||
| StorageUnit | mu_upper | True | True |
| mu_lower | True | True | |
| mu_state_of_charge_set | True | True | |
| mu_state_of_charge | True | True | |
| Bus | marginal_price | True | True |
| StorageUnit | soc_lower_bound | True | True |
| battery_discharge | fixratio | False | False |
| Bus | production_share | True | False |
Again we see the last two entries reflect our constraints (the values in the columns play only a minor role). Having a look what the values are:
[18]:
from pypsa.linopt import get_dual
[19]:
get_dual(n, "StorageUnit", "soc_lower_bound")
[19]:
| StorageUnit | su | su2 |
|---|---|---|
| snapshot | ||
| 2015-01-01 00:00:00 | -0.00000 | -0.00000 |
| 2015-01-01 01:00:00 | -0.00000 | -0.00000 |
| 2015-01-01 02:00:00 | -0.00000 | -0.00000 |
| 2015-01-01 03:00:00 | -0.00000 | -0.00000 |
| 2015-01-01 04:00:00 | -0.00000 | -0.00000 |
| 2015-01-01 05:00:00 | -0.00000 | -0.00000 |
| 2015-01-01 06:00:00 | -157.42300 | -4.44444 |
| 2015-01-01 07:00:00 | -0.00000 | -0.00000 |
| 2015-01-01 08:00:00 | -0.00000 | -0.00000 |
| 2015-01-01 09:00:00 | -5.55556 | -67.84860 |
[20]:
get_dual(n, "battery_discharge", "fixratio")
[20]:
0 567.89
Name: fixratio, dtype: float64
[21]:
get_dual(n, "Bus", "production_share")
[21]:
Bus
London NaN
Norwich NaN
Norwich DC NaN
Manchester -45.4185
Bremen NaN
Bremen DC NaN
Frankfurt -35.2007
Norway -0.0000
Norway DC NaN
storebus NaN
Name: production_share, dtype: float64
Side note
Some of the predefined constraints are stored in components itself like n.lines_t.mu_upper or n.buses_t.marginal_price, this is the case if their are designated columns are spots for those. All other dual are under the hook stored in n.duals