[bug] Wrong sign parameter `cp2_eur_per_mw2` of `create_poly_cost` for `load`

[kornerc]

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• Searched the issues page for similar reports

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• Browse the tutorials and tests for usefull code snippets and examples of use

• Reproduced the issue after updating with pip install --upgrade pandapower (or git pull)

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Reproducible Example

import pandapower as pp


def poly_costs(cp1_eur_per_mw: float, cp2_eur_per_mw2: float, load: bool, p_mw: float) -> None:
    element_name = 'load' if load else 'sgen'

    net = pp.create_empty_network()

    b1 = pp.create_bus(net, vn_kv=20.)
    b2 = pp.create_bus(net, vn_kv=20.)
    pp.create_line(net, from_bus=b1, to_bus=b2, length_km=2.5, std_type="NAYY 4x50 SE")
    pp.create_ext_grid(net, bus=b1)

    kwargs = dict(net=net, bus=b2, p_mw=p_mw, min_p_mw=p_mw, max_p_mw=p_mw, min_q_mvar=0., max_q_mvar=0., controllable=True)
    if load:
        flex = pp.create_load(**kwargs)
    else:
        flex = pp.create_sgen(**kwargs)

    pp.create_poly_cost(net, element=flex, et=element_name, cp1_eur_per_mw=cp1_eur_per_mw, cp2_eur_per_mw2=cp2_eur_per_mw2)

    pp.runopp(net)

    print(f"Element: {element_name}")
    print(f"Cost coefficients: (Linear: {net.poly_cost['cp1_eur_per_mw'].values[0]}, Quadratic: {net.poly_cost['cp2_eur_per_mw2'].values[0]})")
    print(f"Power: {(net.res_load if load else net.res_sgen)['p_mw'].values[0]:.1f} MW")
    print(f"Costs: {net.res_cost:.1f} Eur\n")


if __name__ == "__main__":
    poly_costs(load=True, p_mw=1., cp1_eur_per_mw=1, cp2_eur_per_mw2=0)
    poly_costs(load=True, p_mw=1., cp1_eur_per_mw=0, cp2_eur_per_mw2=1)
    poly_costs(load=True, p_mw=1., cp1_eur_per_mw=-1, cp2_eur_per_mw2=0)
    poly_costs(load=True, p_mw=1., cp1_eur_per_mw=0, cp2_eur_per_mw2=-1)
    poly_costs(load=True, p_mw=-1., cp1_eur_per_mw=1, cp2_eur_per_mw2=0)
    poly_costs(load=True, p_mw=-1., cp1_eur_per_mw=0, cp2_eur_per_mw2=1)
    poly_costs(load=True, p_mw=-1., cp1_eur_per_mw=-1, cp2_eur_per_mw2=0)
    poly_costs(load=True, p_mw=-1., cp1_eur_per_mw=0, cp2_eur_per_mw2=-1)

    poly_costs(load=False, p_mw=1., cp1_eur_per_mw=1, cp2_eur_per_mw2=0)
    poly_costs(load=False, p_mw=1., cp1_eur_per_mw=0, cp2_eur_per_mw2=1)
    poly_costs(load=False, p_mw=1., cp1_eur_per_mw=-1, cp2_eur_per_mw2=0)
    poly_costs(load=False, p_mw=1., cp1_eur_per_mw=0, cp2_eur_per_mw2=-1)
    poly_costs(load=False, p_mw=-1., cp1_eur_per_mw=1, cp2_eur_per_mw2=0)
    poly_costs(load=False, p_mw=-1., cp1_eur_per_mw=0, cp2_eur_per_mw2=1)
    poly_costs(load=False, p_mw=-1., cp1_eur_per_mw=-1, cp2_eur_per_mw2=0)
    poly_costs(load=False, p_mw=-1., cp1_eur_per_mw=0, cp2_eur_per_mw2=-1)

Element: load
Cost coefficients: (Linear: 1.0, Quadratic: 0.0)
Power: 1.0 MW
Costs: 1.0 Eur

Element: load
Cost coefficients: (Linear: 0.0, Quadratic: 1.0)
Power: 1.0 MW
Costs: -1.0 Eur

Element: load
Cost coefficients: (Linear: -1.0, Quadratic: 0.0)
Power: 1.0 MW
Costs: -1.0 Eur

Element: load
Cost coefficients: (Linear: 0.0, Quadratic: -1.0)
Power: 1.0 MW
Costs: 1.0 Eur

Element: load
Cost coefficients: (Linear: 1.0, Quadratic: 0.0)
Power: -1.0 MW
Costs: -1.0 Eur

Element: load
Cost coefficients: (Linear: 0.0, Quadratic: 1.0)
Power: -1.0 MW
Costs: -1.0 Eur

Element: load
Cost coefficients: (Linear: -1.0, Quadratic: 0.0)
Power: -1.0 MW
Costs: 1.0 Eur

Element: load
Cost coefficients: (Linear: 0.0, Quadratic: -1.0)
Power: -1.0 MW
Costs: 1.0 Eur

Element: sgen
Cost coefficients: (Linear: 1.0, Quadratic: 0.0)
Power: 1.0 MW
Costs: 1.0 Eur

Element: sgen
Cost coefficients: (Linear: 0.0, Quadratic: 1.0)
Power: 1.0 MW
Costs: 1.0 Eur

Element: sgen
Cost coefficients: (Linear: -1.0, Quadratic: 0.0)
Power: 1.0 MW
Costs: -1.0 Eur

Element: sgen
Cost coefficients: (Linear: 0.0, Quadratic: -1.0)
Power: 1.0 MW
Costs: -1.0 Eur

Element: sgen
Cost coefficients: (Linear: 1.0, Quadratic: 0.0)
Power: -1.0 MW
Costs: -1.0 Eur

Element: sgen
Cost coefficients: (Linear: 0.0, Quadratic: 1.0)
Power: -1.0 MW
Costs: 1.0 Eur

Element: sgen
Cost coefficients: (Linear: -1.0, Quadratic: 0.0)
Power: -1.0 MW
Costs: 1.0 Eur

Element: sgen
Cost coefficients: (Linear: 0.0, Quadratic: -1.0)
Power: -1.0 MW
Costs: -1.0 Eur

Issue Description and Traceback

The parameter cp2_eur_per_mw2 of create_poly_cost seems to have a different sign convention than the parameter cp1_eur_per_mw seems for load.

Element	Power (MW)	cp1_eur_per_mw	cp2_eur_per_mw2	Cost (Eur)
Load	1	0	1	-1
Load	1	0	-1	1
Load	-1	0	1	-1
Load	-1	0	-1	1

For sgen they are correct.

Element	Power (MW)	cp1_eur_per_mw	cp2_eur_per_mw2	Cost (Eur)
SGen	1	0	1	1
SGen	1	0	-1	-1
SGen	-1	0	1	1
SGen	-1	0	-1	-1

The parameter cp1_eur_per_mw works as expected.

Element	Power (MW)	cp1_eur_per_mw	cp2_eur_per_mw2	Cost (Eur)
Load	1	1	0	1
Load	1	-1	0	-1
Load	-1	1	0	-1
Load	-1	-1	0	1
SGen	1	1	0	1
SGen	1	-1	0	-1
SGen	-1	1	0	-1
SGen	-1	-1	0	1

Expected Behavior

Element	Power (MW)	cp1_eur_per_mw	cp2_eur_per_mw2	Cost (Eur)
Load	1	0	1	1
Load	1	0	-1	-1
Load	-1	0	1	1
Load	-1	0	-1	-1

Installed Versions

• python version: 3.13
• pandapower: 3.4.0
• pandas version: 2.3.3
• Operating System name/version: Debian

Label

• Relevant labels are selected

[kornerc]

It seems like cp0_eur has also the wrong sign convention for load.
Because a positive cp0_eur is counted negatively in the cost function.

The behavior can also be shown convert_pp_to_pm().

import pandapower as pp
import pandapower.converter.pandamodels

net = pp.create_empty_network()

b1 = pp.create_bus(net, vn_kv=20.)
b2 = pp.create_bus(net, vn_kv=20.)
pp.create_line(net, from_bus=b1, to_bus=b2, length_km=2.5, std_type="NAYY 4x50 SE")
pp.create_ext_grid(net, bus=b1)

load = pp.create_load(net=net, bus=b2, p_mw=0.0, min_p_mw=0.0, max_p_mw=0.0, min_q_mvar=0.0, max_q_mvar=0.0, controllable=True)
sgen = pp.create_sgen(net=net, bus=b2, p_mw=0.0, min_p_mw=0.0, max_p_mw=0.0, min_q_mvar=0.0, max_q_mvar=0.0, controllable=True)

pp.create_poly_cost(net, element=load, et="load", cp2_eur_per_mw2=2.0, cp1_eur_per_mw=1.0, cp0_eur=3.0)
pp.create_poly_cost(net, element=load, et="sgen", cp2_eur_per_mw2=20.0, cp1_eur_per_mw=10.0, cp0_eur=30.0)

pp.converter.pandamodels.convert_pp_to_pm(net, "poly_cost.json")

Generated JSON

{
    "ac": true,
    "baseMVA": 1,
    "branch": {
        "1": {
            "angmax": 1.0471975511965976,
            "angmin": -1.0471975511965976,
            "b_fr": 0.03298672286269282,
            "b_to": 0.03298672286269282,
            "br_r": 0.0040125,
            "br_status": 1,
            "br_x": 0.00051875,
            "f_bus": 1,
            "g_fr": 0.0,
            "g_to": 0.0,
            "index": 1,
            "rate_a": 0.0,
            "rate_b": 0.0,
            "rate_c": 0.0,
            "shift": 0.0,
            "t_bus": 2,
            "tap": 1.0,
            "transformer": false
        }
    },
    "bus": {
        "1": {
            "base_kv": 20.0,
            "bus_i": 1,
            "bus_type": 3,
            "index": 1,
            "va": 0.0,
            "vm": 1.0,
            "vmax": 1.00000001,
            "vmin": 0.99999999,
            "zone": 1
        },
        "2": {
            "base_kv": 20.0,
            "bus_i": 2,
            "bus_type": 1,
            "index": 2,
            "va": 0.0,
            "vm": 1.0,
            "vmax": 2.0,
            "vmin": 0.0,
            "zone": 1
        }
    },
    "correct_pm_network_data": true,
    "dcline": {},
    "gen": {
        "1": {
            "cost": [
                0.0,
                0.0,
                0.0
            ],
            "gen_bus": 1,
            "gen_status": 1,
            "index": 1,
            "model": 2,
            "ncost": 3,
            "pg": 0.0,
            "pmax": 1000000000.0,
            "pmin": -1000000000.0,
            "qg": 0.0,
            "qmax": 1000000000.0,
            "qmin": -1000000000.0,
            "shutdown": 0.0,
            "startup": 0.0,
            "vg": 1.0
        },
        "2": {
            "cost": [
                20.0,
                10.0,
                30.0
            ],
            "gen_bus": 2,
            "gen_status": 1,
            "index": 2,
            "model": 2,
            "ncost": 3,
            "pg": 0.0,
            "pmax": 1e-08,
            "pmin": -1e-08,
            "qg": 0.0,
            "qmax": 1e-08,
            "qmin": -1e-08,
            "shutdown": 0.0,
            "startup": 0.0,
            "vg": 1.0
        },
        "3": {
            "cost": [
                -2.0,
                -1.0,
                -3.0
            ],
            "gen_bus": 2,
            "gen_status": 1,
            "index": 3,
            "model": 2,
            "ncost": 3,
            "pg": -0.0,
            "pmax": 1e-08,
            "pmin": -1e-08,
            "qg": -0.0,
            "qmax": 1e-08,
            "qmin": -1e-08,
            "shutdown": 0.0,
            "startup": 0.0,
            "vg": 1.0
        }
    },
    "load": {},
    "name": "",
    "ne_branch": {},
    "per_unit": true,
    "pm_log_level": 0,
    "pm_mip_solver": "cbc",
    "pm_mip_time_limit": Infinity,
    "pm_model": "ACPPowerModel",
    "pm_nl_solver": "ipopt",
    "pm_nl_time_limit": Infinity,
    "pm_solver": "ipopt",
    "pm_time_limit": Infinity,
    "pm_tol": 1e-08,
    "shunt": {},
    "silence": true,
    "source_version": "2.0.0",
    "sourcetype": "matpower",
    "storage": {},
    "switch": {},
    "user_defined_params": {
        "gen_and_controllable_sgen": {
            "2": 2
        }
    }
}

The relevant part is generator 3 with the costs:

"cost": [
  -2.0,
  -1.0,
  -3.0
]

It seems like all signs of the coefficients are changed.
But in my opinion only the sign of the linear coefficient should be changed when transforming a load to a gen.

When changing the reference system of the power (as it is done for load).

$$a\cdot (-P)^2 + b\cdot (-P) + c = a\cdot P^2 - b\cdot P + c$$

Only the sign of the linear coefficient b must be changed internally not the signs of the quadratic coefficient a and the constant c.

[kornerc]

After some debugging I found the relevant function:

pandapower/pandapower/opf/make_objective.py

Line 81 in b0a54a3

def _fill_gencost_poly(ppci, net, is_quadratic, q_costs):

In here the variable signs can have the values -1 and 1 and it is multiplied with all all cost coefficients, e.g.:

    if is_quadratic:
        c2 = cost["cp2_eur_per_mw2"]
        ppci["gencost"][gens, NCOST] = 3
        ppci["gencost"][gens, COST] = c2 * signs
        ppci["gencost"][gens, COST + 1] = c1 * signs
        ppci["gencost"][gens, COST + 2] = c0 * signs