Sources and Price Zones

Renewable Source

Renewable source model

Renewable source model

For all renewable sources:

(1)\[0 \leq \gamma_{rg} \leq 1 \qquad \forall rg \in \mathcal{RG}\]

For renewables sources connected to AC nodes:

(2)\[\begin{split}\begin{align} Q_{rg}^{min} \leq Q_{rg} \leq Q_{rg}^{max} & \qquad \forall rg \in \mathcal{RG}_{ac} \\ (\gamma_{rg} P_{rg})^2 + Q_{rg}^2 \leq S_{rg,rating}^{2^{max}} & \qquad \forall g \in \mathcal{RG}_{ac} \end{align}\end{split}\]

Renewable source limits

Renewable source limits

Class Reference: pyflow_acdc.Classes.RenSource

class Ren_Source(name, node, PGi_ren_base, rs_type='Wind', S_base=100, installation_cost=0, Max_S_factor=1, np_rsgen=1)

Renewable generation source attached to a node.

Represents a (by default curtailable) renewable injection such as wind or solar, with its rated capacity, base/installation cost, and number of parallel units (np_rsgen). Powers and limits are tracked in per-unit on the source’s own S_base.

Parameters:

• name (str) – Renewable-source identifier.

• node (Node_AC or Node_DC) – Host bus (node name stored as Node).

• PGi_ren_base (float) – Rated active power in pu on S_base.

• rs_type (str, optional) – Technology label for plotting (e.g. 'Wind', 'solar').

• S_base (float, optional) – Per-unit power base in MVA.

• installation_cost (float, optional) – Installation cost for TEP (stored as base_cost before lambda_capex).

• Max_S_factor (float, optional) – Multiplier for apparent-power rating (Max_S = PGi_ren_base * Max_S_factor).

• np_rsgen (int, optional) – Number of parallel renewable units.

PGi_ren

Available active power in pu (PGi_ren_base * PRGi_available).

Type:

float

PRGi_available

Availability factor in [0, 1].

Type:

float

gamma

Curtailment factor in [min_gamma, 1].

Type:

float

min_gamma

Minimum allowed curtailment factor.

Type:

float

curtailable

Whether the source may be curtailed in OPF.

Type:

bool

Qmin, Qmax

Reactive power limits in pu (AC-connected sources).

Type:

float

Max_S

Apparent-power rating in pu.

Type:

float

Type	Figure for folium plotting
wind
offshore wind
onshore wind
solar

Generator

Generator model

Generator model

(3)\[\begin{split}\begin{align} P_{g}^{min} \leq P_{g} \leq P_{g}^{max} & \qquad \forall g \in \mathcal{G}_{ac} \\ Q_{g}^{min} \leq Q_{g} \leq Q_{g}^{max} & \qquad \forall g \in \mathcal{G}_{ac} \\ P_{g}^2+Q_{g}^2 \leq S_{g,rating}^{2} & \qquad \forall g \in \mathcal{G}_{ac} \end{align}\end{split}\]

Generator limits

Generator limits

Class Reference: pyflow_acdc.Classes.Gen_AC

class Gen_AC(name, node, Max_pow_gen, Min_pow_gen, Max_pow_genR, Min_pow_genR, quadratic_cost_factor=0, linear_cost_factor=0, fixed_cost=0, Pset=0, Qset=0, S_rated=None, gen_type='Other', installation_cost=0, S_base=100, np_gen=1)

AC generator connected to a bus.

Parameters:

• name (str) – Generator identifier.

• node (Node_AC) – Host bus.

• Max_pow_gen (float) – Maximum active power in pu on S_base.

• Min_pow_gen (float) – Minimum active power in pu on S_base.

• Max_pow_genR (float) – Maximum reactive power in pu on S_base.

• Min_pow_genR (float) – Minimum reactive power in pu on S_base.

• quadratic_cost_factor (float, optional) – Quadratic cost coefficient (stored as qf).

• linear_cost_factor (float, optional) – Linear cost coefficient (stored as lf).

• fixed_cost (float, optional) – Fixed cost coefficient (stored as fc).

• Pset (float, optional) – Per-unit active setpoint for one parallel unit.

• Qset (float, optional) – Per-unit reactive setpoint for one parallel unit.

• S_rated (float, optional) – Apparent-power rating in pu (stored as Max_S).

• gen_type (str, optional) – Fuel/technology label (e.g. 'natural gas', 'hydro').

• installation_cost (float, optional) – Installation cost for TEP (stored as base_cost before lambda_capex).

• S_base (float, optional) – Per-unit power base in MVA.

• np_gen (int, optional) – Number of parallel generator units.

PGen, QGen

Total dispatched active/reactive power (setpoint × np_gen; OPF result after solve).

Type:

float

price_zone_link

If True, lf/qf track the host price zone.

Type:

bool

is_ext_grid

External-grid (slack) generator flag.

Type:

bool

Type	Figure for folium plotting	Default cost
hydro
nuclear
hard coal
solid biomass
geothermal
lignite
natural gas
oil
waste
biogas
ccgt
diesel
shunt reactor
other

Price Zone

Price zone model

Price zone model

Price zone model is taken from [3]. The cost of generation quadratic curve is calculated in Market coefficients.

Class Reference: pyflow_acdc.Classes.Price_Zone

class Price_Zone(price=1, import_pu_L=1, export_pu_G=1, a=0, b=1, c=0, import_expand=0, curvature_factor=1, S_base=100, name=None, positive_price_delta=None)

Market price zone grouping AC nodes.

Holds a zonal price and demand-curve coefficients shared by its member nodes. Setting price propagates to the zone’s nodes and their price-zone-linked generators, and to any linked MTDC/offshore price zones. Specialised subclasses model MTDC and offshore zones.

Parameters:

• price (float, optional) – Zonal energy price.

• import_pu_L (float, optional) – Per-unit import load limit.

• export_pu_G (float, optional) – Per-unit export generation limit.

• a (float, optional) – Base quadratic cost coefficient (stored as a_base; effective a may differ).

• b (float, optional) – Linear cost-curve coefficient (see Market_Coeff).

• c (float, optional) – Constant cost-curve coefficient.

• import_expand (float, optional) – Import expansion offset in pu (used when expand_import is True).

• curvature_factor (float, optional) – Scales a_base when computing effective a.

• S_base (float, optional) – Per-unit power base in MVA.

• name (str, optional) – Price-zone identifier.

• positive_price_delta (float, optional) – Maximum allowed price increase; caps PGL_max when set.

nodes_AC, nodes_DC

Member AC and DC buses in the zone.

Type:

list

ConvACDC

AC/DC converters assigned to the zone.

Type:

list

PLi

Aggregated zone load in pu.

Type:

float

PLi_factor, PLi_inv_factor

Time-series and investment load scaling (propagate to linked nodes).

Type:

float

PGL_min, PGL_max

Minimum and maximum generation limits in pu.

Type:

float

PGL_min_base

Base lower generation limit before curve adjustments.

Type:

float

PN

Net active power at the zone.

Type:

float

expand_import

Import-expand mode flag (derives a and PGL_min from import_expand).

Type:

bool

linked_price_zone

Linked offshore or coupled price zone.

Type:

Price_Zone, optional

mtdc_price_zones

MTDC price zones notified when this zone’s price changes.

Type:

list

References

[3]

B. C. Valerio, V. A. Lacerda, M. Cheah-Mañe, P. Gebraad, and O. Gomis-Bellmunt, “Optimizing offshore wind integration through multi-terminal DC grids: a market-based OPF framework for the North Sea interconnectors,” IET Conference Proceedings, vol. 2025, no. 6, pp. 150–155, 2025. doi: 10.1049/icp.2025.1198