Request for help with offdesign calculations

I have an issue with turning a design run into an offdesign one. The jacobian matrix is always ending up forming a singularity. I feel I am doing something wrong with what parameters I omit during offdesign. Any help is highly appreciated.

What I am trying to do is the follows:

1. If I change the mass flow rate, I want the turbine efficiencies to change and correspondingly its output powers.
2. If it is possible, I also want to be able to set a pressure change at crucial junctures and see its effect on the power output

Attached herewith is the design code. Do let me know how do I turn it into an offdesign case.

# %% Starting the Network
fluid_list = ['Ar', 'N2', 'H2O', 'CO2', 'O2']
nw = Network(fluids=fluid_list, T_unit='C', p_unit='bar', h_unit='kJ / kg')

# Parameters for fluid flow
flueflow = 604.8

hptsink = 45.3
waterflow = 425.8

iptsploffset = 0 # +-30% 190.25 | max value is 0.3*(waterflow-hptsink)/2 | min is -0.3*(waterflow-hptsink)/2

ipt1psink = 10.5 
ipt2psink = 10.5 

iptlptsink = 42.6

lptsploffset = 0 # Can be maximum of +-0.3*(waterflow-hptsink-ipt1psink-ipt2psink-iptlptsink)/2

lpt1spl = 6.1
lpt2spl = 6.1

lpt1pspl = 11.65
lpt2pspl = 11.65

lpt1dpspl = 5.1
lpt2dpspl = 5.1


# %% Instantiating Components

#src sink
wtr_src = Source('Water Source')
flue = Source('Flue Gas Source')
stack = Sink('Flue Gas Stack')

hpt_sink = Sink('HPT Sink')
ipt_sink_1 = Sink('IPT 1 & 2 Sink')
ipt_sink_2 = Sink('IPT 1p & 2p Sink')
lpt_sink_1 = Sink('LPT 1 & 2 Sink')
lpt_sink_2 = Sink('LPT 1p & 2p Sink')
lpt_sink_3 = Sink('LPT 1dp & 2dp Sink')
lpt_sink_4 = Sink('LPT 1tp & 2tp Sink')

#Heat Exhangers

evap_sup = SteamGenerator('Evaporator & Superheater')
reh = SteamGenerator('Reheater')

evap_sup.set_attr(pr1=0.98, pr2=0.888, design=['pr2'], offdesign=['zeta2','kA_char2'])
reh.set_attr(pr1=0.99, pr2=0.91, design=['pr2'], offdesign=['zeta2', 'kA_char2'])

#Splitter & Merger
hpt_spl = Splitter('HPT Splitter')

ipt_spl = Splitter('IPT Splitter')
ipt1_spl = Splitter('IPT1 Splitter')
ipt2_spl = Splitter('IPT2 Splitter')
ipt12_mrg = Merge('IPT1 & 2 Merger')
ipt12p_mrg = Merge('IPT1p & 2p Merger')

ipt_lpt_spl = Splitter('IPT to LPT Splitter')

lpt_spl = Splitter('LPT Splitter')
lpt1_spl = Splitter('LPT1 Splitter')
lpt1p_spl = Splitter('LPT1p Splitter')
lpt1dp_spl = Splitter('LPT1dp Splitter')
lpt2_spl = Splitter('LPT2 Splitter')
lpt2p_spl = Splitter('LPT2p Splitter')
lpt2dp_spl = Splitter('LPT2dp Splitter')

lpt12_mrg = Merge('LPT1 & 2 Merger')
lpt12p_mrg = Merge('LPT1p & 2p Merger')
lpt12dp_mrg = Merge('LPT1dp & 2dp Merger')
lpt12tp_mrg = Merge('LPT1tp & 2tp Merger')

#Turbines
hpt = Turbine('HPT', eta_s=0.89, design=['eta_s'], offdesign=['eta_s_char', 'cone'])

ipt1 = Turbine('IPT 1', eta_s=0.903, design=['eta_s'], offdesign=['eta_s_char', 'cone'])
ipt2 = Turbine('IPT 2', eta_s=0.903, design=['eta_s'], offdesign=['eta_s_char', 'cone'])
ipt1p = Turbine('IPT 1p', eta_s=0.903, design=['eta_s'], offdesign=['eta_s_char', 'cone'])
ipt2p = Turbine('IPT 2p', eta_s=0.903, design=['eta_s'], offdesign=['eta_s_char', 'cone'])

lpt1 = Turbine('LPT 1', eta_s=0.851, design=['eta_s'], offdesign=['eta_s_char', 'cone'])
lpt2 = Turbine('LPT 2', eta_s=0.851, design=['eta_s'], offdesign=['eta_s_char', 'cone'])
lpt1p = Turbine('LPT 1p', eta_s=0.851, design=['eta_s'], offdesign=['eta_s_char', 'cone'])
lpt2p = Turbine('LPT 2p', eta_s=0.851, design=['eta_s'], offdesign=['eta_s_char', 'cone'])
lpt1dp = Turbine('LPT 1dp', eta_s=0.851, design=['eta_s'], offdesign=['eta_s_char', 'cone'])
lpt2dp = Turbine('LPT 2dp', eta_s=0.851, design=['eta_s'], offdesign=['eta_s_char', 'cone'])
lpt1tp = Turbine('LPT 1tp', eta_s=0.851, design=['eta_s'], offdesign=['eta_s_char', 'cone'])
lpt2tp = Turbine('LPT 2tp', eta_s=0.851, design=['eta_s'], offdesign=['eta_s_char', 'cone'])

# %% Setting the Connections
# Air/Flue

flue_evap = Connection(flue, 'out1', evap_sup, 'in1')
evap_reh = Connection(evap_sup, 'out1', reh, 'in1')
reh_stack = Connection(reh, 'out1', stack, 'in1')

# Water
src_evap = Connection(wtr_src, 'out1', evap_sup, 'in2')
evap_hpt = Connection(evap_sup, 'out2', hpt, 'in1')

hpt_hptspl = Connection(hpt, 'out1', hpt_spl, 'in1')
hptspl_sink = Connection(hpt_spl, 'out1', hpt_sink, 'in1')
hptspl_reh = Connection(hpt_spl, 'out2', reh, 'in2')

reh_iptspl = Connection(reh, 'out2', ipt_spl, 'in1')
iptspl_1 = Connection(ipt_spl, 'out1', ipt1, 'in1')
iptspl_2 = Connection(ipt_spl, 'out2', ipt2, 'in1')

ipt1_1spl = Connection(ipt1, 'out1', ipt1_spl, 'in1')
ipt1spl_1p = Connection(ipt1_spl, 'out1', ipt1p, 'in1')
ipt1spl_mrg = Connection(ipt1_spl, 'out2', ipt12_mrg, 'in1')

ipt2_2spl = Connection(ipt2, 'out1', ipt2_spl, 'in1')
ipt2spl_2p = Connection(ipt2_spl, 'out1', ipt2p, 'in1')
ipt2spl_mrg = Connection(ipt2_spl, 'out2', ipt12_mrg, 'in2')

ipt12mrg_s = Connection(ipt12_mrg, 'out1', ipt_sink_1, 'in1')

ipt1p_mrg = Connection(ipt1p, 'out1', ipt12p_mrg, 'in1')
ipt2p_mrg = Connection(ipt2p, 'out1', ipt12p_mrg, 'in2')
ipt12pmrg_spl = Connection(ipt12p_mrg, 'out1', ipt_lpt_spl, 'in1')

iptlptspl_spl = Connection(ipt_lpt_spl, 'out1', lpt_spl, 'in1')
iptlptspl_s = Connection(ipt_lpt_spl, 'out2', ipt_sink_2, 'in1')

lptspl_1 = Connection(lpt_spl, 'out1', lpt1, 'in1')
lptspl_2 = Connection(lpt_spl, 'out2', lpt2, 'in1')

lpt1_1spl = Connection(lpt1, 'out1', lpt1_spl, 'in1')
lpt1spl_1p = Connection(lpt1_spl, 'out1', lpt1p, 'in1')
lpt1spl_mrg = Connection(lpt1_spl, 'out2', lpt12_mrg, 'in1')

lpt2_2spl = Connection(lpt2, 'out1', lpt2_spl, 'in1')
lpt2spl_2p = Connection(lpt2_spl, 'out1', lpt2p, 'in1')
lpt2spl_mrg = Connection(lpt2_spl, 'out2', lpt12_mrg, 'in2')

lpt12mrg_sink = Connection(lpt12_mrg, 'out1', lpt_sink_1, 'in1')

lpt1p_1spl = Connection(lpt1p, 'out1', lpt1p_spl, 'in1')
lpt1pspl_1dp = Connection(lpt1p_spl, 'out1', lpt1dp, 'in1')
lpt1pspl_mrg = Connection(lpt1p_spl, 'out2', lpt12p_mrg, 'in1')

lpt2p_2spl = Connection(lpt2p, 'out1', lpt2p_spl, 'in1')
lpt2pspl_2dp = Connection(lpt2p_spl, 'out1', lpt2dp, 'in1')
lpt2pspl_mrg = Connection(lpt2p_spl, 'out2', lpt12p_mrg, 'in2')

lpt12pmrg_sink = Connection(lpt12p_mrg, 'out1', lpt_sink_2, 'in1')

lpt1dp_1spl = Connection(lpt1dp, 'out1', lpt1dp_spl, 'in1')
lpt1dpspl_1tp = Connection(lpt1dp_spl, 'out1', lpt1tp, 'in1')
lpt1dpspl_mrg = Connection(lpt1dp_spl, 'out2', lpt12dp_mrg, 'in1')

lpt2dp_2spl = Connection(lpt2dp, 'out1', lpt2dp_spl, 'in1')
lpt2dpspl_2tp = Connection(lpt2dp_spl, 'out1', lpt2tp, 'in1')
lpt2dpspl_mrg = Connection(lpt2dp_spl, 'out2', lpt12dp_mrg, 'in2')

lpt12dpmrg_sink = Connection(lpt12dp_mrg, 'out1', lpt_sink_3, 'in1')

lpt1tp_mrg = Connection(lpt1tp, 'out1', lpt12tp_mrg, 'in1')
lpt2tp_mrg = Connection(lpt2tp, 'out1', lpt12tp_mrg, 'in2')
lpt12tpmrg_sink = Connection(lpt12tp_mrg, 'out1', lpt_sink_4, 'in1')

# %% Setting Connection Parameters
# Combustion
flue_evap.set_attr(p=1.01, T=1782.7, m=flueflow, fluid={'CO2': 0.25, 'N2': 0.709, 'Ar': 0.0102, 
                                            'O2': 0.0348, 'H2O': 0.028})

evap_reh.set_attr(T=802.3)
reh_stack.set_attr(T=529.8)

# Water
src_evap.set_attr(p=193.7, T=324, m=waterflow, fluid={'Ar': 0, 'N2': 0, 'H2O': 1,
                                                    'CO2': 0, 'O2': 0})

hpt_hptspl.set_attr(p=44.1)

hptspl_sink.set_attr(m=hptsink)

iptspl_1.set_attr(m=(waterflow-hptsink)/2+iptsploffset)

ipt1_1spl.set_attr(p=17.4)

ipt1spl_mrg.set_attr(m=ipt1psink)
ipt2spl_mrg.set_attr(m=ipt2psink)

ipt1p_mrg.set_attr(p=7.93)

iptlptspl_s.set_attr(m=iptlptsink)

lptspl_1.set_attr(m=(waterflow-hptsink-ipt1psink-ipt2psink-iptlptsink)/2+lptsploffset)

lpt1_1spl.set_attr(p=2.6)

lpt1spl_mrg.set_attr(m=lpt1spl)
lpt2spl_mrg.set_attr(m=lpt2spl)

lpt1p_1spl.set_attr(p=1.3)

lpt1pspl_mrg.set_attr(m=lpt1pspl)
lpt2pspl_mrg.set_attr(m=lpt2pspl)

lpt1dp_1spl.set_attr(p=0.26)

lpt1dpspl_mrg.set_attr(m=lpt1dpspl)
lpt2dpspl_mrg.set_attr(m=lpt2dpspl)


lpt1tp_mrg.set_attr(p=0.103)


nw.add_conns(flue_evap, evap_reh, reh_stack)
nw.add_conns(src_evap, evap_hpt, hpt_hptspl, hptspl_sink, hptspl_reh, reh_iptspl,
             iptspl_1, iptspl_2, ipt1_1spl, ipt1spl_1p, ipt1spl_mrg, ipt2_2spl, ipt2spl_2p, ipt2spl_mrg, ipt12mrg_s,
             ipt1p_mrg, ipt2p_mrg, ipt12pmrg_spl, iptlptspl_s, iptlptspl_spl,
             lptspl_1, lptspl_2, lpt1_1spl, lpt1spl_1p, lpt1spl_mrg, lpt2_2spl, lpt2spl_2p, lpt2spl_mrg, lpt12mrg_sink,
             lpt1p_1spl, lpt1pspl_1dp, lpt1pspl_mrg, lpt2p_2spl, lpt2pspl_2dp, lpt2pspl_mrg, lpt12pmrg_sink,
             lpt1dp_1spl, lpt1dpspl_1tp, lpt1dpspl_mrg, lpt2dp_2spl, lpt2dpspl_2tp, lpt2dpspl_mrg, lpt12dpmrg_sink,
             lpt1tp_mrg, lpt2tp_mrg, lpt12tpmrg_sink)

# %% Solving Plant for design
nw.solve('design')
nw.print_results()
nw.save(path='./my_char')

If it helps I have also attached a diagram of the plant

Note: The combustor was removed because of inadequate data I had

[fwitte]

For completion, solution is to fix the lowest turbine stage outlet pressure for offdesign:

# %% Importing modules

from tespy.networks import Network
from tespy.connections import Connection
from tespy.components import Sink, Source
from tespy.components import HeatExchangerSimple, Turbine
from tespy.components import Merge, Splitter

import numpy as np

# %% Network

fluid_list = ['BICUBIC::H2O']
nw = Network(fluids=fluid_list, T_unit='C', p_unit='bar', h_unit='kJ / kg')

# %% Starting the components

wtr = Source("Water")
sink_1 = Sink("HPT Sink")
sink_2 = Sink("IPT 1 Sink")
sink_3 = Sink("LPT 1 Sink")
sink_4 = Sink("LPT 2 Sink")
sink_5 = Sink("LPT 3 Sink")
sink_6 = Sink("LPT 4 Sink")

heat_ex_1 = HeatExchangerSimple('Evaporator and Superheater', pr=0.98, design=['pr'], offdesign=["zeta"])
heat_ex_2 = HeatExchangerSimple("Reheater", pr=0.98, design=['pr'], offdesign=["zeta"])

turbine_1 = Turbine('HPT', eta_s=0.89, design=["eta_s"], offdesign=["eta_s_char", "cone"])
turbine_2 = Turbine('IPT 1', eta_s=0.903, design=["eta_s"], offdesign=["eta_s_char", "cone"])
turbine_3 = Turbine('IPT 2', eta_s=0.903, design=["eta_s"], offdesign=["eta_s_char", "cone"])
turbine_4 = Turbine('LPT 1', eta_s=0.85,design=["eta_s"], offdesign=["eta_s_char", "cone"])
turbine_5 = Turbine('LPT 2', eta_s=0.85, design=["eta_s"], offdesign=["eta_s_char", "cone"])
turbine_6 = Turbine('LPT 3', eta_s=0.85, design=["eta_s"], offdesign=["eta_s_char", "cone"])
turbine_7 = Turbine('LPT 4', eta_s=0.85, design=["eta_s"], offdesign=["eta_s_char", "cone"])

spl_1 = Splitter('HPT Splitter')
spl_2 = Splitter('IPT Splitter')
spl_3 = Splitter('LPT 1 Splitter')
spl_4 = Splitter('LPT 2 Splitter')
spl_5 = Splitter('LPT 3 Splitter')

# %% Building Connections
water = Connection(wtr, 'out1', heat_ex_1, 'in1')
evap_hpt = Connection(heat_ex_1, 'out1', turbine_1, 'in1')
hpt_spl = Connection(turbine_1, 'out1', spl_1, 'in1')
spl1_water = Connection(spl_1, 'out1', sink_1, 'in1')
spl1_reh = Connection(spl_1, 'out2', heat_ex_2, 'in1')
reh_ipt = Connection(heat_ex_2, 'out1', turbine_2, 'in1')
ipt1_spl = Connection(turbine_2, 'out1', spl_2, 'in1')
spl2_water = Connection(spl_2, 'out1', sink_2, 'in1')
spl2_ipt2 = Connection(spl_2, 'out2', turbine_3, 'in1')
ipt2_lpt1 = Connection(turbine_3, 'out1', turbine_4, 'in1')
lpt1_spl = Connection(turbine_4, 'out1', spl_3, 'in1')
spl3_water = Connection(spl_3, 'out1', sink_3, 'in1')
spl3_lpt2 = Connection(spl_3, 'out2', turbine_5, 'in1')
lpt2_spl = Connection(turbine_5, 'out1', spl_4, 'in1')
spl4_water = Connection(spl_4, 'out1', sink_4, 'in1')
spl4_lpt3 = Connection(spl_4, 'out2', turbine_6, 'in1')
lpt3_spl = Connection(turbine_6, 'out1', spl_5, 'in1')
spl5_water = Connection(spl_5, 'out1', sink_5, 'in1')
spl5_lpt4 = Connection(spl_5, 'out2', turbine_7, 'in1')
lpt4_water = Connection(turbine_7, 'out1', sink_6, 'in1')

# %% Setting Connection Params
water.set_attr(T=170, m=425.8, fluid={'H2O': 1})
evap_hpt.set_attr(p=187, T=537, design=["p"])
hpt_spl.set_attr(p=44.1, design=["p"])
spl1_water.set_attr(m=45)
reh_ipt.set_attr(T=537)
ipt1_spl.set_attr(p=17.4, design=["p"])
spl2_water.set_attr(m=40)
ipt2_lpt1.set_attr(p=7.93, design=["p"])
lpt1_spl.set_attr(p=2.6, design=["p"])
spl3_water.set_attr(m=24)
lpt2_spl.set_attr(p=1.3, design=["p"])
lpt3_spl.set_attr(p=0.26, design=["p"])
spl4_water.set_attr(m=15)
spl5_water.set_attr(m=10)
lpt4_water.set_attr(p=0.103)

# %% Adding Connections to Network

nw.add_conns(water, evap_hpt,hpt_spl, spl1_water, spl1_reh, reh_ipt,
            ipt1_spl, spl2_water, spl2_ipt2, ipt2_lpt1, lpt1_spl,
            spl3_water, spl3_lpt2, lpt2_spl, spl4_water, spl4_lpt3,
            lpt3_spl, spl5_water, spl5_lpt4, lpt4_water)

# %% Solving the plant

nw.solve('design')
nw.save('./srinath')
nw.print_results()
# %% Turbine Power
print(turbine_1.P.val + turbine_2.P.val + turbine_3.P.val + turbine_4.P.val
        + turbine_5.P.val + turbine_6.P.val + turbine_7.P.val)

# %% Offdesign
for m in np.linspace(24, 34, 11):
    spl3_water.set_attr(m=m)
    nw.solve(mode='offdesign', design_path='./srinath', max_iter=75)
    print(lpt4_water.h.val)

[fwitte]

For now, just comment that you like to participate. We will publish a schedule and more detailed information in a separate wiki https://github.com/oemof/oemof/wiki.