PyPSA: Python for Power System Analysis

Variable	Units	Definition
n, m		Bus labels
r		Generator energy carrier labels (e.g. wind, solar, gas, etc.)
s		Storage energy carrier labels (e.g. battery, hydrogen, etc.)
κ, ℓ		Branch labels
c		Cycle labels
t		Snapshot/time point labels
e_r/s	tCO₂eq/MWh_th	CO₂-equivalent emissions of energy carrier r or s
w_t	h	Weighting of snapshot in objective function
g_n,r,t	MW	Dispatch of generator at bus n with carrier r at time t
G_n,r	MW	Power capacity of generator n, r
g̅_n,r,t	MW/MW	Power availability per unit of generator capacity
η_n,r	MW_el/MW_th	Efficiency of generator
u_n,r,t		On/off binary status for generator unit commitment
$T_{n, r}^{min_down}$	h	Generator minimum down time
$T_{n, r}^{min_up}$	h	Generator minimum up time
ru_n,r	(MW/MW)/h	Generator ramp up limit per unit of capacity
rd_n,r	(MW/MW)/h	Generator ramp down limit per unit of capacity
c_n,r	€/MW	Generator capital (fixed) cost
o_n,r	€/MWh	Generator operating (variable) cost
suc_n,r(,t)	€	Generator start up cost (in time t)
sdc_n,r(,t)	€	Generator shut down cost (in time t)
h_n,s,t	MW	Dispatch of storage at bus n with carrier s at time t
H_n,s	MW	Power capacity of storage n, s
e_n,s,t	MWh	Storage state of charge (energy level)
E_n,s	MWh	Storage energy capacity
c_n,s	€/MW	Storage power capacity cost
ĉ_n,s	€/MWh	Storage energy capacity cost
o_n,s	€/MWh	Storage dispatch cost
d_n,t	MW	Electrical load at bus n at time t
λ_n,t	€/MWh	Marginal price at bus n at time t
V_n	kV	Complex voltage at bus n
θ_n	rad	Voltage angle at bus n
I_n	kA	Complex current at bus n
P_n	MW	Total active power injection at bus n
Q_n	MVAr	Total reactive power injection at bus n
S_n	MVA	Total apparent power injection at bus n
f_ℓ,t	MW	Branch active power flow
F_ℓ	MW	Branch active power rating
c_ℓ	€/MW	Branch capital cost
x_ℓ	Ω	Branch series reactance
r_ℓ	Ω	Branch series resistance
Variable	Units	Definition
z_ℓ	Ω	Branch series impedance
y_ℓ	S	Branch shunt admittance
τ_ℓ		Transformer tap ratio
$θ_{ℓ}^{shift}$	rad	Transformer phase shift
η_ℓ,t	MW/MW	Efficiency loss of a link
K_nℓ		N × L incidence matrix
C_ℓ_c		L × (L – N + 1) cycle matrix
Y_nm	S	Bus admittance matrix
B_ℓ_k	S	Diagonal L × L matrix of branch susceptances
BODF_ℓ_k		Branch Outage Distribution Factor

Table 2

PyPSA components.

Network	Container for all other network components.
Bus	Fundamental nodes to which all other components attach.
Carrier	Energy carrier (e.g. wind, solar, gas, etc.).
Load	A consumer of energy.
Generator	Generator whose feed-in can be flexible subject to minimum loading or minimum down and up times, or variable according to a given time series of power availability.
Storage Unit	A device which can shift energy from one time to another, subject to efficiency losses.
Store	A more fundamental storage object with no restrictions on charging or discharging power.
Shunt Impedance	An impedance in shunt to a bus.
Line	A branch which connects two buses of the same voltage.
Transformer	A branch which connects two buses of different voltages.
Link	A branch with a controllable power flow between two buses.

Electrical property definitions for passive branches (lines and transformers).

Example of the coupling in PyPSA between electricity (at top) and other energy sectors: transport, hydrogen, natural gas and heating. There is a bus for each energy carrier, to which different loads, energy sources and converters are attached.

Calculation times for performing a full load flow on the MATPOWER [6] standard cases using MATPOWER versus PyPSA.

Table 3

A comparison of selected features of selected software tools that are similar to PyPSA.

	Power Flow	Continuation Power Flow	Dynamic Analysis	Transport Model	Linear OPF	SCLOPF	Nonlinear OPF	Multi-Period Optimisation	Unit Commitment	Investment Optimisation	Other Energy Sectors
Power system tools	MATPOWER	6.0	[6]	✓	✓	✓		✓	✓		✓
	NEPLAN	5.5.8	[2]		✓		✓	✓	✓	✓	✓				✓
	pandapower	1.4.0	[9]	✓	✓			✓	✓		✓
	PowerFactory	2017	[1]		✓		✓		✓	✓	✓
	PowerWorld	19	[3]		✓		✓	✓	✓	✓	✓
PSAT	2.1.10	[7]	✓	✓	✓	✓		✓		✓	✓	✓
PSS/E	33.10	[4]		✓		✓		✓	✓	✓
PSS/SINCAL	13.5	[5]		✓		✓				✓				✓
PYPOWER	5.1.2	[8]	✓	✓			✓	✓		✓
PyPSA	0.11.0		✓	✓			✓	✓	✓		✓	✓	✓	✓
Energy system tools	calliope	0.5.2	[11]	✓				✓				✓		✓	✓
	minpower	4.3.10	[12]	✓					✓	✓			✓	✓
	MOST	6.0	[13]	✓	✓	✓		✓	✓	✓	✓	✓	✓
	oemof	0.1.4	[14]	✓				✓				✓	✓	✓	✓
	OSeMOSYS	2017	[15]	✓				✓				✓		✓	✓
PLEXOS	7.400	[16]					✓	✓	✓		✓	✓	✓	✓
PowerGAMA	1.1	[17]	✓				✓	✓			✓
PRIMES	2017	[18]					✓	✓			✓	✓	✓	✓
TIMES	2017	[19]					✓	✓			✓	✓	✓	✓
urbs	0.7	[20]	✓				✓				✓	✓	✓	✓

*Left*: Locational marginal prices (*λ_n,t* from equation (12)) for Germany in an hour with high wind and low load; *Middle*: Line loading during this hour: highly loaded lines in the middle of Germany prevent the transport of cheap wind energy to consumers in the South; *Right*: Reactive power feed-in (positive in red, negative in blue) necessary to keep all buses at unit nominal voltage.

Results of optimisation of generation and storage capacities in Europe to reduce CO₂ emissions in the European electricity sector by 95% compared to 1990 levels [32]. The grid topology is based on the GridKit network for Europe, clustered from 5000 buses to 256 buses.

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DOI: https://doi.org/10.5334/jors.188 | Journal eISSN: 2049-9647

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Language: English

Submitted on: Aug 2, 2017

Accepted on: Nov 12, 2017

Published on: Jan 16, 2018

Published by: Ubiquity Press

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Power system simulations,

energy system simulations,

Load flow calculations,

optimal power flow,

security-constrained optimal power flow,

unit commitment,

renewable energy

© 2018 Thomas Brown, Jonas Hörsch, David Schlachtberger, published by Ubiquity Press
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 6 (2018): Issue 1

PyPSA: Python for Power System Analysis

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