CALC-096

Why a 5 kV bus is affordable to one architecture and not to the other

Feeds CLM-0888. Answers QST-004. Basis: kg of conductor.

Why it was needed. CLM-0879 records that the register's two stated SPS bus voltages disagree by a factor of eight, with the later and smaller design using the LOWER voltage, and that no source reconciles them. The 1978 report justifies its 40 kV in one line, on "power conductor and conditioning equipment mass considerations", and never writes the relation down. Writing it down explains the disagreement.

Relationship, derived rather than quoted.

I = P/V                    current at bus voltage V
loss = I^2 R = f P         a fractional resistive loss f
   ->  R = f V^2 / P
R = rho_e L / A            a conductor of length L, area A
   ->  A = rho_e L P / (f V^2)
m = 2 rho_m L A            two conductors, out and return

   m = 2 rho_m rho_e L^2 P / (f V^2)

CONDUCTOR MASS SCALES AS THE SQUARE OF LENGTH AND THE INVERSE SQUARE OF VOLTAGE.

Inputs.

Working. 2 rho_m rho_e = 1.5228e-04.

1978, 5 GW at 40 kV, L = 5 km      595 t of conductor
      against 5,863 t stated for power distribution and control - about 10 per cent of it

CAST, 1 GW at 5 kV, L = 5 km       7,614 t of conductor
      against 1,360 t stated for power transmission and management - 5.6 TIMES THE WHOLE SUBSYSTEM

CAST per module, 48 MW at 5 kV, L = 310 m    1,405 kg
      across all fifty modules                   70 t
      (corrected 2026-10-22: this used 32 MW and an assumed 100 m, giving 97 kg and 4.9 t)

Result. A single 5 kV bus carrying 1 GW over kilometres does not fit inside CAST's own mass budget. Its architecture is why it never has to: it never routes full power over full length. THE EIGHT-FOLD DISAGREEMENT IS NOT ABOUT ELECTRICAL PRACTICE, IT IS ABOUT WHETHER THE SATELLITE IS MONOLITHIC OR MODULAR. The 1978 design moves 5 GW from array to antenna as one system and needs 40 kV to afford it.

Sensitivity, because L is assumed and the relation is quadratic in it.

CAST single bus at L = 10 km    30,456 t     (four times)
CAST single bus at V = 10 kV    1,904 t     (one quarter)

The finding that a monolithic 5 kV bus does not fit CAST's budget survives any run length above about 2 km. The specific tonnages do not stand on their own.

What this does not establish. CAST's paper gives its own reason (SRC-169 PDF p.5, printed 111): the 310 m distance "allows for the use of relatively shorter cables and lower voltage (5 kV)". It gives no conductor mass, so the relation shows that reason is consistent with CAST's mass budget, not that the paper used this relation. (Corrected 2026-10-22: this said no source states why CAST chose 5 kV.) And the 595 t against 5,863 t comparison is a CONSISTENCY CHECK, not a validation - the stated mass covers switchgear, conditioning and structure as well as conductor, so agreement to an order of magnitude is all it can show.

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