Newton-Raphson Power Flow¶

In this example, we are going to create a network with three nodes, three lines, one load, and one generator with given setpoints. We then solve the non-linear power flow equations using the Newton-Raphson method applied in n.pf().

In [2]:

import numpy as np

import pypsa

n = pypsa.Network()

N_BUSES = 3

import numpy as np import pypsa n = pypsa.Network() N_BUSES = 3

Add three buses:

In [3]:

for i in range(N_BUSES):
    n.add("Bus", f"My bus {i}", v_nom=20)

n.buses

for i in range(N_BUSES): n.add("Bus", f"My bus {i}", v_nom=20) n.buses

Out[3]:

	v_nom	type	x	y	carrier	unit	location	v_mag_pu_set	v_mag_pu_min	v_mag_pu_max	control	generator	sub_network
name
My bus 0	20.0		0.0	0.0	AC			1.0	0.0	inf	PQ
My bus 1	20.0		0.0	0.0	AC			1.0	0.0	inf	PQ
My bus 2	20.0		0.0	0.0	AC			1.0	0.0	inf	PQ

Add three lines in a ring

In [4]:

for i in range(N_BUSES):
    n.add(
        "Line",
        f"My line {i}",
        bus0=f"My bus {i}",
        bus1=f"My bus {(i + 1) % N_BUSES}",
        x=0.1,
        r=0.01,
    )

n.lines

for i in range(N_BUSES): n.add( "Line", f"My line {i}", bus0=f"My bus {i}", bus1=f"My bus {(i + 1) % N_BUSES}", x=0.1, r=0.01, ) n.lines

Out[4]:

	bus0	bus1	type	x	r	g	b	s_nom	s_nom_mod	s_nom_extendable	...	v_ang_min	v_ang_max	sub_network	x_pu	r_pu	g_pu	b_pu	x_pu_eff	r_pu_eff	s_nom_opt
name
My line 0	My bus 0	My bus 1		0.1	0.01	0.0	0.0	0.0	0.0	False	...	-inf	inf		0.0	0.0	0.0	0.0	0.0	0.0	0.0
My line 1	My bus 1	My bus 2		0.1	0.01	0.0	0.0	0.0	0.0	False	...	-inf	inf		0.0	0.0	0.0	0.0	0.0	0.0	0.0
My line 2	My bus 2	My bus 0		0.1	0.01	0.0	0.0	0.0	0.0	False	...	-inf	inf		0.0	0.0	0.0	0.0	0.0	0.0	0.0

3 rows × 35 columns

Add a generator at bus 0

In [5]:

n.add("Generator", "My gen", bus="My bus 0", p_set=100, control="PQ")

n.generators

n.add("Generator", "My gen", bus="My bus 0", p_set=100, control="PQ") n.generators

Out[5]:

	bus	control	type	p_nom	p_nom_mod	p_nom_extendable	p_nom_min	p_nom_max	p_nom_set	p_min_pu	...	min_up_time	min_down_time	up_time_before	down_time_before	ramp_limit_up	ramp_limit_down	ramp_limit_start_up	ramp_limit_shut_down	weight	p_nom_opt
name
My gen	My bus 0	PQ		0.0	0.0	False	0.0	inf	NaN	0.0	...	0	0	1	0	NaN	NaN	NaN	NaN	1.0	0.0

1 rows × 42 columns

Add a load at bus 1

In [6]:

n.add("Load", "My load", bus="My bus 1", p_set=100, q_set=100)

n.loads

n.add("Load", "My load", bus="My bus 1", p_set=100, q_set=100) n.loads

Out[6]:

	bus	carrier	type	p_set	q_set	sign	active
name
My load	My bus 1			100.0	100.0	-1.0	True

Do a Newton-Raphson power flow

In [7]:

n.pf()

n.pf()

INFO:pypsa.network.power_flow:Performing non-linear load-flow on AC sub-network <pypsa.SubNetwork object at 0x7a5e4000ae40> for snapshots Index(['now'], dtype='object', name='snapshot')

Out[7]:

{'n_iter': name      0
 snapshot   
 now       3,
 'error': name                 0
 snapshot              
 now       4.753531e-10,
 'converged': name         0
 snapshot      
 now       True}

Alright, it converged! Now, what is the active power flow on the lines?

In [8]:

n.lines_t.p0

n.lines_t.p0

Out[8]:

name	My line 0	My line 1	My line 2
snapshot
now	66.897487	-33.333333	-33.391038

...and what are the voltage angles on the buses?

In [9]:

n.buses_t.v_ang * 180 / np.pi

n.buses_t.v_ang * 180 / np.pi

Out[9]:

name	My bus 0	My bus 1	My bus 2
snapshot
now	0.0	-0.875939	-0.433813

...and their mangitudes?

In [10]:

n.buses_t.v_mag_pu

n.buses_t.v_mag_pu

Out[10]:

name	My bus 0	My bus 1	My bus 2
snapshot
now	1.0	0.981199	0.99057