Transformers¶

This example illustrates the use of transformers with non-trivial phase shift and tap ratio. The example is a copy of the pandapower minimal example.

In [2]:

import numpy as np
import pandas as pd

import pypsa

n = pypsa.Network()

n.add("Bus", "MV bus", v_nom=20, v_mag_pu_set=1.02)
n.add("Bus", "LV1 bus", v_nom=0.4)
n.add("Bus", "LV2 bus", v_nom=0.4)

n.add(
    "Transformer",
    "MV-LV trafo",
    type="0.4 MVA 20/0.4 kV",
    bus0="MV bus",
    bus1="LV1 bus",
)
n.add(
    "Line", "LV cable", type="NAYY 4x50 SE", bus0="LV1 bus", bus1="LV2 bus", length=0.1
)
n.add("Generator", "External Grid", bus="MV bus", control="Slack", marginal_cost=10)
n.add("Load", "LV load", bus="LV2 bus", p_set=0.1, q_set=0.05);

import numpy as np import pandas as pd import pypsa n = pypsa.Network() n.add("Bus", "MV bus", v_nom=20, v_mag_pu_set=1.02) n.add("Bus", "LV1 bus", v_nom=0.4) n.add("Bus", "LV2 bus", v_nom=0.4) n.add( "Transformer", "MV-LV trafo", type="0.4 MVA 20/0.4 kV", bus0="MV bus", bus1="LV1 bus", ) n.add( "Line", "LV cable", type="NAYY 4x50 SE", bus0="LV1 bus", bus1="LV2 bus", length=0.1 ) n.add("Generator", "External Grid", bus="MV bus", control="Slack", marginal_cost=10) n.add("Load", "LV load", bus="LV2 bus", p_set=0.1, q_set=0.05);

/home/runner/work/PyPSA/PyPSA/pypsa/network/io.py:2082: FutureWarning: pandas infers the `str` dtype for string data since its version 3.0. PyPSA still converts it back to numpy object dtype on import, but will keep it from PyPSA 2.0 on. Set `pypsa.options.api.legacy_string_dtype` explicitly to suppress this warning.
  new_static = _coerce_string_dtypes(new_static)

In [3]:

def run_power_flow(n: pypsa.Network) -> pd.DataFrame:
    n.lpf()
    n.pf(use_seed=True)
    return pd.DataFrame(
        {
            "Voltage Angles": n.buses_t.v_ang.loc["now"] * 180.0 / np.pi,
            "Voltage Magnitude": n.buses_t.v_mag_pu.loc["now"],
        }
    )

def run_power_flow(n: pypsa.Network) -> pd.DataFrame: n.lpf() n.pf(use_seed=True) return pd.DataFrame( { "Voltage Angles": n.buses_t.v_ang.loc["now"] * 180.0 / np.pi, "Voltage Magnitude": n.buses_t.v_mag_pu.loc["now"], } )

In [4]:

run_power_flow(n)

run_power_flow(n)

INFO:pypsa.network.power_flow:Performing linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7f2bb8902270> for snapshot(s) Index(['now'], dtype='str', name='snapshot')

INFO:pypsa.network.power_flow:Performing non-linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7f2b5252a350> for snapshots Index(['now'], dtype='str', name='snapshot')

Out[4]:

	Voltage Angles	Voltage Magnitude
name
MV bus	0.000000	1.020000
LV1 bus	-150.760126	1.008843
LV2 bus	-149.884141	0.964431

In [5]:

n.transformers.tap_position = 2
run_power_flow(n)

n.transformers.tap_position = 2 run_power_flow(n)

INFO:pypsa.network.power_flow:Performing linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7f2b5252a350> for snapshot(s) Index(['now'], dtype='str', name='snapshot')

INFO:pypsa.network.power_flow:Performing non-linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7f2b525702b0> for snapshots Index(['now'], dtype='str', name='snapshot')

Out[5]:

	Voltage Angles	Voltage Magnitude
name
MV bus	0.000000	1.020000
LV1 bus	-150.843911	0.959655
LV2 bus	-149.870837	0.912713

In [6]:

n.transformers.tap_position = -2
run_power_flow(n)

n.transformers.tap_position = -2 run_power_flow(n)

INFO:pypsa.network.power_flow:Performing linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7f2b525702b0> for snapshot(s) Index(['now'], dtype='str', name='snapshot')

INFO:pypsa.network.power_flow:Performing non-linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7f2b51d715b0> for snapshots Index(['now'], dtype='str', name='snapshot')

Out[6]:

	Voltage Angles	Voltage Magnitude
name
MV bus	0.000000	1.020000
LV1 bus	-150.681666	1.063133
LV2 bus	-149.896634	1.021202

Now play with tap changer on LV side

In [7]:

new_trafo_lv_tap = n.transformer_types.loc[["0.4 MVA 20/0.4 kV"]]
new_trafo_lv_tap.index = ["New trafo"]
new_trafo_lv_tap.tap_side = 1
new_trafo_lv_tap.T

new_trafo_lv_tap = n.transformer_types.loc[["0.4 MVA 20/0.4 kV"]] new_trafo_lv_tap.index = ["New trafo"] new_trafo_lv_tap.tap_side = 1 new_trafo_lv_tap.T

Out[7]:

	New trafo
f_nom	50.0
s_nom	0.4
v_nom_0	20.0
v_nom_1	0.4
vsc	6.0
vscr	1.425
pfe	1.35
i0	0.3375
phase_shift	150.0
tap_side	1
tap_neutral	0
tap_min	-2
tap_max	2
tap_step	2.5
references	pandapower;Oswald - Transformatoren - Vorlesun...

In [8]:

n.add("TransformerType", "New trafo", **new_trafo_lv_tap.iloc[0].to_dict())
n.transformers.type = "New trafo"
n.transformers.tap_position = 2
run_power_flow(n)

n.add("TransformerType", "New trafo", **new_trafo_lv_tap.iloc[0].to_dict()) n.transformers.type = "New trafo" n.transformers.tap_position = 2 run_power_flow(n)

INFO:pypsa.network.power_flow:Performing linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7f2b52525ae0> for snapshot(s) Index(['now'], dtype='str', name='snapshot')

INFO:pypsa.network.power_flow:Performing non-linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7f2b52525ae0> for snapshots Index(['now'], dtype='str', name='snapshot')

Out[8]:

	Voltage Angles	Voltage Magnitude
name
MV bus	0.000000	1.020000
LV1 bus	-150.755820	1.059317
LV2 bus	-149.964875	1.017221

In [9]:

n.transformers.T

n.transformers.T

Out[9]:

name	MV-LV trafo
bus0	MV bus
bus1	LV1 bus
type	New trafo
model	t
x	0.058283
r	0.01425
g	0.003375
b	-0.0
s_nom	0.4
s_nom_mod	0.0
s_nom_extendable	False
s_nom_min	0.0
s_nom_max	inf
s_nom_set	NaN
s_max_pu	1.0
capital_cost	0.0
overnight_cost	NaN
discount_rate	NaN
fom_cost	0.0
num_parallel	1.0
tap_ratio	1.05
tap_side	1
tap_position	2
phase_shift	150.0
phase_shift_min	0.0
phase_shift_max	0.0
active	True
build_year	0
lifetime	inf
v_ang_min	-inf
v_ang_max	inf
sub_network	0
x_pu	0.145712
r_pu	0.035618
g_pu	0.00135
b_pu	-0.0
x_pu_eff	0.152994
r_pu_eff	0.037406
s_nom_opt	0.0

In [10]:

n.transformers.tap_position = -2
run_power_flow(n)

n.transformers.tap_position = -2 run_power_flow(n)

INFO:pypsa.network.power_flow:Performing linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7f2b535f2150> for snapshot(s) Index(['now'], dtype='str', name='snapshot')

INFO:pypsa.network.power_flow:Performing non-linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7f2b6d8e1050> for snapshots Index(['now'], dtype='str', name='snapshot')

Out[10]:

	Voltage Angles	Voltage Magnitude
name
MV bus	0.000000	1.020000
LV1 bus	-150.765232	0.958366
LV2 bus	-149.789394	0.911353

Finally, consider the phase shift in the linear optimal power flow ([n.optimize()][pypsa.Network.optimize.call]). It solves a cycle-based linearised power flow, enforcing Kirchhoff's voltage law around the network's cycles. The radial network above has no cycle, so the phase shift cannot redistribute power and does not affect the optimised flows — it only offsets the absolute voltage angles seen in n.pf()/n.lpf(). The branch flows below are therefore unchanged by the phase shift:

In [11]:

n.generators.p_nom = 1
n.lines.s_nom = 1
n.optimize()
pd.DataFrame(
    {
        "Active Power p0 (MW)": pd.concat(
            [n.lines_t.p0.loc["now"], n.transformers_t.p0.loc["now"]]
        )
    }
)

n.generators.p_nom = 1 n.lines.s_nom = 1 n.optimize() pd.DataFrame( { "Active Power p0 (MW)": pd.concat( [n.lines_t.p0.loc["now"], n.transformers_t.p0.loc["now"]] ) } )

/tmp/ipykernel_8200/981123384.py:3: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable.
  n.optimize()
WARNING:pypsa.consistency:The following buses have carriers which are not defined. Run n.sanitize() to add them. Components with undefined carriers:
Index(['MV bus', 'LV1 bus', 'LV2 bus'], dtype='object', name='name')

WARNING:pypsa.consistency:Encountered nan's in varying data 'p' for columns ['External Grid'] of component 'Generator'.

WARNING:pypsa.consistency:The following lines have carriers which are not defined. Run n.sanitize() to add them. Components with undefined carriers:
Index(['LV cable'], dtype='object', name='name')

WARNING:pypsa.consistency:The following sub_networks have carriers which are not defined. Run n.sanitize() to add them. Components with undefined carriers:
Index(['0'], dtype='object', name='name')

INFO:linopy.model: Solve problem using Gurobi solver

INFO:linopy.model:Solver options:
 - log_to_console: False

INFO:linopy.io: Writing time: 0.04s

Set parameter WLSAccessID

Set parameter WLSSecret

Set parameter LicenseID to value 2537914

Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de

Read LP format model from file /tmp/linopy-problem-g9pnd7w6.lp

Reading time = 0.00 seconds

obj: 9 rows, 3 columns, 11 nonzeros

Set parameter LogToConsole to value 0

INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 3 primals, 9 duals
Objective: 1.00e+00
Solver: gurobi
Runtime: 0.00s
Dual bound: 1.00e+00
Solver model: available
Solver message: 2

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Line-fix-s-lower, Line-fix-s-upper, Transformer-fix-s-lower, Transformer-fix-s-upper were not assigned to the network.

Out[11]:

	Active Power p0 (MW)
name
LV cable	0.1
MV-LV trafo	0.1

Phase shift in a meshed network¶

To see the phase shift act through the optimisation we need a cycle. Below, two buses are joined by two parallel paths — an ordinary line and a phase-shifting transformer — with equal per-unit reactance. Without a phase shift the 50 MW load splits evenly between the two paths; a phase shift on the transformer drives a circulating flow around the cycle that redistributes the power. The optimisation now reproduces exactly what n.lpf() computes.

Note the input attribute is phase_shift; the realised/optimised shift is written back to the output n.transformers_t.phase_shift_opt.

In [12]:

def meshed_network(phase_shift: float) -> pypsa.Network:
    m = pypsa.Network()
    m.add("Bus", ["A", "B"], v_nom=1.0)
    m.add("Generator", "gen", bus="A", control="Slack", p_nom=100, marginal_cost=10)
    m.add("Load", "load", bus="B", p_set=50)
    m.add("Line", "line", bus0="A", bus1="B", x=0.01, r=1e-6, s_nom=100)
    m.add(
        "Transformer",
        "PST",
        bus0="A",
        bus1="B",
        x=1.0,
        r=1e-6,
        s_nom=100,
        phase_shift=phase_shift,
    )
    return m


rows = []
for angle in [0.0, 5.0, 10.0]:
    opt = meshed_network(angle)
    opt.optimize()
    ref = meshed_network(angle)
    ref.lpf()
    rows.append(
        {
            "phase_shift (deg)": angle,
            "line p0 — optimize": opt.lines_t.p0.loc["now", "line"],
            "PST p0 — optimize": opt.transformers_t.p0.loc["now", "PST"],
            "line p0 — lpf": ref.lines_t.p0.loc["now", "line"],
            "PST p0 — lpf": ref.transformers_t.p0.loc["now", "PST"],
        }
    )
pd.DataFrame(rows).round(3)

def meshed_network(phase_shift: float) -> pypsa.Network: m = pypsa.Network() m.add("Bus", ["A", "B"], v_nom=1.0) m.add("Generator", "gen", bus="A", control="Slack", p_nom=100, marginal_cost=10) m.add("Load", "load", bus="B", p_set=50) m.add("Line", "line", bus0="A", bus1="B", x=0.01, r=1e-6, s_nom=100) m.add( "Transformer", "PST", bus0="A", bus1="B", x=1.0, r=1e-6, s_nom=100, phase_shift=phase_shift, ) return m rows = [] for angle in [0.0, 5.0, 10.0]: opt = meshed_network(angle) opt.optimize() ref = meshed_network(angle) ref.lpf() rows.append( { "phase_shift (deg)": angle, "line p0 — optimize": opt.lines_t.p0.loc["now", "line"], "PST p0 — optimize": opt.transformers_t.p0.loc["now", "PST"], "line p0 — lpf": ref.lines_t.p0.loc["now", "line"], "PST p0 — lpf": ref.transformers_t.p0.loc["now", "PST"], } ) pd.DataFrame(rows).round(3)

/tmp/ipykernel_8200/3936709006.py:23: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable.
  opt.optimize()
WARNING:pypsa.consistency:The following buses have carriers which are not defined. Run n.sanitize() to add them. Components with undefined carriers:
Index(['A', 'B'], dtype='object', name='name')

WARNING:pypsa.consistency:The following lines have carriers which are not defined. Run n.sanitize() to add them. Components with undefined carriers:
Index(['line'], dtype='object', name='name')

INFO:linopy.model: Solve problem using Gurobi solver

INFO:linopy.model:Solver options:
 - log_to_console: False

INFO:linopy.io: Writing time: 0.04s

Set parameter WLSAccessID

Set parameter WLSSecret

Set parameter LicenseID to value 2537914

Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de

Read LP format model from file /tmp/linopy-problem-zi7njawy.lp

Reading time = 0.00 seconds

obj: 9 rows, 3 columns, 13 nonzeros

Set parameter LogToConsole to value 0

INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 3 primals, 9 duals
Objective: 5.00e+02
Solver: gurobi
Runtime: 0.00s
Dual bound: 5.00e+02
Solver model: available
Solver message: 2

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Line-fix-s-lower, Line-fix-s-upper, Transformer-fix-s-lower, Transformer-fix-s-upper, Kirchhoff-Voltage-Law were not assigned to the network.

INFO:pypsa.network.power_flow:Performing linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7f2b50fcfa10> for snapshot(s) Index(['now'], dtype='str', name='snapshot')

/tmp/ipykernel_8200/3936709006.py:23: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable.
  opt.optimize()
WARNING:pypsa.consistency:The following buses have carriers which are not defined. Run n.sanitize() to add them. Components with undefined carriers:
Index(['A', 'B'], dtype='object', name='name')

WARNING:pypsa.consistency:The following lines have carriers which are not defined. Run n.sanitize() to add them. Components with undefined carriers:
Index(['line'], dtype='object', name='name')

INFO:linopy.model: Solve problem using Gurobi solver

INFO:linopy.model:Solver options:
 - log_to_console: False

INFO:linopy.io: Writing time: 0.03s

Set parameter WLSAccessID

Set parameter WLSSecret

Set parameter LicenseID to value 2537914

Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de

Read LP format model from file /tmp/linopy-problem-ihirksxl.lp

Reading time = 0.00 seconds

obj: 9 rows, 3 columns, 13 nonzeros

Set parameter LogToConsole to value 0

INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 3 primals, 9 duals
Objective: 5.00e+02
Solver: gurobi
Runtime: 0.00s
Dual bound: 5.00e+02
Solver model: available
Solver message: 2

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Line-fix-s-lower, Line-fix-s-upper, Transformer-fix-s-lower, Transformer-fix-s-upper, Kirchhoff-Voltage-Law were not assigned to the network.

INFO:pypsa.network.power_flow:Performing linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7f2b7189d550> for snapshot(s) Index(['now'], dtype='str', name='snapshot')

/tmp/ipykernel_8200/3936709006.py:23: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable.
  opt.optimize()
WARNING:pypsa.consistency:The following buses have carriers which are not defined. Run n.sanitize() to add them. Components with undefined carriers:
Index(['A', 'B'], dtype='object', name='name')

WARNING:pypsa.consistency:The following lines have carriers which are not defined. Run n.sanitize() to add them. Components with undefined carriers:
Index(['line'], dtype='object', name='name')

INFO:linopy.model: Solve problem using Gurobi solver

INFO:linopy.model:Solver options:
 - log_to_console: False

INFO:linopy.io: Writing time: 0.03s

Set parameter WLSAccessID

Set parameter WLSSecret

Set parameter LicenseID to value 2537914

Academic license 2537914 - for non-commercial use only - registered to l.___@tu-berlin.de

Read LP format model from file /tmp/linopy-problem-jo6i1d9m.lp

Reading time = 0.00 seconds

obj: 9 rows, 3 columns, 13 nonzeros

Set parameter LogToConsole to value 0

INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 3 primals, 9 duals
Objective: 5.00e+02
Solver: gurobi
Runtime: 0.00s
Dual bound: 5.00e+02
Solver model: available
Solver message: 2

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Line-fix-s-lower, Line-fix-s-upper, Transformer-fix-s-lower, Transformer-fix-s-upper, Kirchhoff-Voltage-Law were not assigned to the network.

INFO:pypsa.network.power_flow:Performing linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7f2b7189edd0> for snapshot(s) Index(['now'], dtype='str', name='snapshot')

Out[12]:

	phase_shift (deg)	line p0 — optimize	PST p0 — optimize	line p0 — lpf	PST p0 — lpf
0	0.0	25.000	25.000	25.000	25.000
1	5.0	29.363	20.637	29.363	20.637
2	10.0	33.727	16.273	33.727	16.273

A positive phase shift moves flow off the transformer onto the parallel line, and the optimisation and linear power flow agree to numerical precision.