Battery and ESC selection

Written by Marc Budinger (INSA Toulouse), Scott Delbecq (ISAE-SUPAERO) and Félix Pollet (ISAE-SUPAERO), Toulouse, France.

Design graph

The following diagrams represent the design graphs of the battery and ESC selection.

Fig. 22 Battery design graph

Fig. 23 ESC design graph

The design graphs for the overall drone system can be found in here.

Sizing code

# Specifications
N_pro = 4.0  # [-] Number of propellers
M_pay = 1.0  # [kg] Payload mass
nu_esc = 0.95  # [–] ESC efficiency

# Reference parameters for scaling laws
# Ref : MK-quadro
M_bat_ref = 0.329  # [kg] mass
E_bat_ref = 220.0 * 3600.0 * 0.329  # [J]
C_bat_ref = 5  # [Ah] Capacity
I_bat_max_ref = 50 * C_bat_ref  # [A] max discharge current

# Ref : Turnigy K_Force 70HV
P_esc_ref = 3108.0  # [W] Power
M_esc_ref = 0.115  # [kg] Mass

# Assumptions
U_bat_est = 14.0  # [V] Battery voltage estimation
P_el_mot_hov = 10.0  # [W] Electrical power consumption for one motor during hover
P_el_mot_to = 30.0  # [W] Electrical power consumption for one motor during takeoff
U_mot_to = 12.0  # [V] Motor voltage during takeoff

# Design variables
k_vb = 1.0  # oversizing coefficient for voltage evaluation
k_mb = 1.0  # ratio battery/load mass

# Equations

# Voltage selection with takeoff scenario
U_bat = k_vb * 1.84 * P_el_mot_to ** (0.36)  # [V] battery voltage estimation

# Energy selection with payload mass
M_bat = k_mb * M_pay  # [kg] Battery mass
E_bat = (
    E_bat_ref * M_bat / M_bat_ref * 0.8
)  # [J] Energy  of the battery (.8 coefficient because 80% use only of the total capacity)

# Estimation models
C_bat = E_bat / U_bat  # [A*s] Capacity  of the battery
I_bat_max = I_bat_max_ref * (C_bat / C_bat_ref)  # [A] Max discharge current
P_bat_max = U_bat * I_bat_max  # [W] Max power

# Performance in hover
I_bat_hov = (P_el_mot_hov * N_pro) / nu_esc / U_bat  # [A] Current of the battery


#% ESC
# ---
# Power selection with takeoff scenario
P_esc = (
    P_el_mot_to * U_bat / U_mot_to
)  # [W] power electronic power (corner power or apparent power)

# Estimation models
U_esc = 1.84 * P_esc**0.36  # [V] ESC voltage
M_esc = M_esc_ref * (P_esc / P_esc_ref)  # [kg] Mass ESC

%whos

Variable        Type     Data/Info
----------------------------------
C_bat           float    101212.39316709602
C_bat_ref       int      5
E_bat           float    633600.0
E_bat_ref       float    260568.0
I_bat_hov       float    6.725969774527912
I_bat_max       float    5060619.658354801
I_bat_max_ref   int      250
M_bat           float    1.0
M_bat_ref       float    0.329
M_esc           float    0.0005790796638241396
M_esc_ref       float    0.115
M_pay           float    1.0
N_pro           float    4.0
P_bat_max       float    31680000.0
P_el_mot_hov    float    10.0
P_el_mot_to     float    30.0
P_esc           float    15.650257349264573
P_esc_ref       float    3108.0
U_bat           float    6.260102939705829
U_bat_est       float    14.0
U_esc           float    4.952740310797201
U_mot_to        float    12.0
k_mb            float    1.0
k_vb            float    1.0
nu_esc          float    0.95