7. Generator Model Examples
Understanding the generator examples is most easily done with the companion report for GeneratorSE. The design variables in the examples relate to both the electromagnetic and structural design. The five generator example files relate to the five different generator architectures available:
PMSG-Outer: Permanent magnet synchronous generator (outer generator - inner stator)
PMSG-Disc: Permanent magnet synchronous generator (inner generator - outer stator) with solid disc stator support
PMSG-Arms: Permanent magnet synchronous generator (inner generator - outer stator) with arm/spoke stator support
EESG: Electrically excited synchronous generator
DFIG: Doubly fed induction generator
SCIG: Squirrel-cage induction generator
Each of the technologies have slightly different sets of required inputs so while the examples follow the same pattern, the specific design variables and constraints will vary from one to the other. For brevity, only the pmsg_outer.py script is presented here.
First, we import the modules we want to use,
import numpy as np
import openmdao.api as om
import wisdem.commonse.fileIO as fio
from wisdem.drivetrainse.generator import Generator
Next, we initialize the problem and set some script parameters,
# Whether or not to run optimization
opt_flag = False
# Number of points in efficiency table
n_pc = 20
# Initialize problem instance
prob = om.Problem(reports=False)
prob.model = Generator(design="pmsg_outer", n_pc=n_pc)
If running an optimization, we set the design variables, constraints, and objectives. These are most easily understood with the report linked above. Note that the optimization driver in the script is SLSQP from the OpenMDAO Scipy Driver, as that is available in the regular Conda-based installation of WISDEM. However, we have had some better experience using the CONMIN driver available in the pyOptSparse library.
if opt_flag:
# Add optimizer and set-up problem (using user defined input on objective function)
prob.driver = om.ScipyOptimizeDriver()
prob.driver.options["optimizer"] = "SLSQP"
prob.driver.options["tol"] = 1e-6
# prob.driver = om.pyOptSparseDriver()
# prob.driver.options["optimizer"] = 'CONMIN' # 'SNOPT'
# Specificiency target efficiency(%)
Eta_Target = 0.955
# Design variables
prob.model.add_design_var("rad_ag", lower=3.0, upper=6.0)
prob.model.add_design_var("len_s", lower=1.5, upper=2.5)
prob.model.add_design_var("h_s", lower=0.1, upper=1.00)
prob.model.add_design_var("p", lower=50.0, upper=100.0, ref=1e2)
prob.model.add_design_var("h_m", lower=0.01, upper=0.2, ref=1e-2)
prob.model.add_design_var("h_yr", lower=0.035, upper=0.22, ref=1e-2)
prob.model.add_design_var("h_ys", lower=0.035, upper=0.22, ref=1e-2)
prob.model.add_design_var("B_tmax", lower=1, upper=2.0)
prob.model.add_design_var("t_r", lower=0.05, upper=0.3, ref=1e-2)
prob.model.add_design_var("t_s", lower=0.05, upper=0.3, ref=1e-2)
prob.model.add_design_var("h_ss", lower=0.04, upper=0.2, ref=1e-2)
prob.model.add_design_var("h_sr", lower=0.04, upper=0.2, ref=1e-2)
# Constraints
prob.model.add_constraint("B_symax", lower=0.0, upper=2.0)
prob.model.add_constraint("B_rymax", lower=0.0, upper=2.0)
prob.model.add_constraint("b_t", lower=0.01, ref=1e-2)
prob.model.add_constraint("B_g", lower=1.19, upper=1.2)
prob.model.add_constraint("A_Cuscalc", lower=5.0, upper=600, ref=1e1)
prob.model.add_constraint("K_rad", lower=0.15, upper=0.3)
prob.model.add_constraint("Slot_aspect_ratio", lower=4.0, upper=10.0)
prob.model.add_constraint("generator_efficiency", lower=Eta_Target, indices=[-1])
prob.model.add_constraint("A_1", upper=110000.0, ref=1e6, indices=[-1])
prob.model.add_constraint("T_e", lower=21.03e6, upper=21.1e6, ref=1e6)
prob.model.add_constraint("J_actual", lower=3, upper=6, indices=[-1])
# prob.model.add_constraint("con_uar", lower=1e-2, ref=1e-2)
# prob.model.add_constraint("con_yar", lower=1e-2, ref=1e-2)
# prob.model.add_constraint("con_uas", lower=1e-2, ref=1e-2)
# prob.model.add_constraint("con_yas", lower=1e-2, ref=1e-2)
Objective_function = "generator_cost"
prob.model.add_objective(Objective_function, scaler=1e-5)
Now, the long list of electromechanical and structural inputs are set prior to execution,
prob.setup()
# Specify Target machine parameters
prob["machine_rating"] = 15e6
prob["shaft_rpm"] = np.linspace(5.0, 7.56, n_pc)
prob["rated_torque"] = 21030561.0
prob["P_mech"] = 15354206.45251639
# Drivetrain
prob["D_shaft"] = 3.0
prob["D_nose"] = 2.2
# Generator inputs
prob["B_g"] = 1.38963289
prob["B_r"] = 1.279
prob["B_rymax"] = 1.63478983
prob["B_symax"] = 1.63455514
prob["B_tmax"] = 1.88378905
prob["E_p"] = 3300.0 / np.sqrt(3)
prob["L_s"] = 0.01138752
prob["N_c"] = 2
prob["P_Fe0e"] = 1.0
prob["P_Fe0h"] = 4.0
prob["R_s"] = 0.02457052
prob["S"] = 240
prob["S_N"] = -0.002
prob["alpha_p"] = 1.0995574287564276 # 0.5*np.pi*0.7
prob["b"] = 2.0
prob["b_m"] = 0.1288363023
prob["b_r_tau_r"] = 0.45
prob["b_ro"] = 0.004
prob["b_s"] = 0.05121796888
prob["b_s_tau_s"] = 0.45
prob["b_so"] = 0.004
prob["b_t"] = 0.08159225451
prob["c"] = 5.0
prob["cofi"] = 0.85
prob["freq"] = 60.0
prob["h_0"] = 0.005
prob["h_i"] = 0.004
prob["h_m"] = 0.0995385122
prob["h_s"] = 0.37694491492
prob["h_sr"] = 0.04677
prob["h_ss"] = 0.04651
prob["h_sy0"] = 0.0
prob["h_t"] = 0.3859449149
prob["h_w"] = 0.005
prob["h_yr"] = 0.0361759511
prob["h_ys"] = 0.03618114528
prob["k_fes"] = 0.8
prob["k_fillr"] = 0.55
prob["k_fills"] = 0.65
prob["k_s"] = 0.2
prob["len_s"] = 2.23961662
prob["m"] = 3
prob["mu_0"] = 1.2566370614359173e-06 # np.pi*4e-7
prob["mu_r"] = 1.06
prob["p"] = 100
prob["phi"] = 1.5707963267948966 # 90 deg
prob["q1"] = 5
prob["q2"] = 4
prob["rad_ag"] = 0.5 * 10.25246718
prob["ratio_mw2pp"] = 0.8
prob["resist_Cu"] = 2.52e-8 # 1.8e-8*1.4
prob["sigma"] = 60e3
prob["t_r"] = 0.061
prob["t_s"] = 0.061
prob["tau_p"] = 0.1610453779
prob["tau_s"] = 0.1339360726
prob["u_allow_pcent"] = 8.5
prob["y_allow_pcent"] = 1.0
prob["y_tau_p"] = 0.8 # 12./15.
prob["y_tau_pr"] = 0.8333333 # 10. / 12
prob["z_allow_deg"] = 0.05
# Specific costs
prob["C_Cu"] = 4.786 # Unit cost of Copper $/kg
prob["C_Fe"] = 0.556 # Unit cost of Iron $/kg
prob["C_Fes"] = 0.50139 # specific cost of Structural_mass $/kg
prob["C_PM"] = 95.0
# Material properties
prob["rho_Fe"] = 7700.0 # Steel density Kg/m3
prob["rho_Fes"] = 7850 # structural Steel density Kg/m3
prob["rho_Copper"] = 8900.0 # copper density Kg/m3
prob["rho_PM"] = 7450.0 # typical density Kg/m3 of neodymium magnets (added 2019 09 18) - for pmsg_[disc|arms]
prob["E"] = 2e11
prob["G"] = 79.3e9
The script can now be executed. If running an optimization, we activate finite differencing for the total derivatives instead of the partials,
if opt_flag:
prob.model.approx_totals()
prob.run_driver()
else:
prob.run_model()
prob.model.list_inputs(units=True)
prob.model.list_outputs(units=True)
print("Efficiency table:")
print(" rpm converter transformer generator ")
print("-------------------------------------------")
print(np.c_[prob["shaft_rpm"],
prob["converter_efficiency"],
prob["transformer_efficiency"],
prob["generator_efficiency"],
])