Power computation over several orbits.

Create a CubeSat model with large deployed arrays. Compute the power generated by the arrays assuming LVLH pointing. ------------------------------------------------------------------------ See also RVFromKepler, Date2JD, JD2T, julianCent, SunV1, Eclipse, SolarCellPower ------------------------------------------------------------------------

Contents

%--------------------------------------------------------------------------
%   Copyright (c) 2011, 2020 Princeton Satellite Systems.
%   All Rights Reserved.
%--------------------------------------------------------------------------
%   Since 2020.1
%--------------------------------------------------------------------------

Constants

solarFlux   = 1367;             % W
radiusEarth = 6378.165;         % km

Battery parameters

capacity    = 7.4*0.830;        % W-hr
dOD         = 0.6;              % Depth of discharge

Compute semi-major axis from altitude

altitude    = 500;              % km
inc         = 51.6*pi/180;   % deg - launch from KSFC
sma         = radiusEarth + altitude;

We need the date in Julian Centuries for the sun model

jD0         = Date2JD([2021 1 2 0 0 0]);
t           = linspace(0,6*3600,300);
julianDate  = jD0 + t/86400;

Compute trajectory from orbital elements

[rs,vs,t]   = RVFromKepler( [sma inc 0 0 0 0], t );
m           = length(t);
PlotOrbit( rs, t, jD0 );

CubeSat model including the deployed solar panels

d                       = CubeSatModel( 'struct' );
d.massComponents        = 3;
d.solarPanel.dim        = [100 100 10];	% [side attached to cubesat, side perpendicular, thickness]
d.solarPanel.nPanels    = 3; % Number of panels per wing
d.solarPanel.rPanel     = [-150 -150 -150 -150;100 200 -100 -200;50 50 50 50]; % Location of inner edge of panel
d.solarPanel.sPanel     = [1 1 1 1;0 0 0 0;0 0 0 0];
d.solarPanel.cellNormal = [0 0 0 0;0 0 0 0;1 1 1 1]; % Cell normal
d.solarPanel.sigmaCell  = [1;0;0];    % [absorbed; specular; diffuse]
d.solarPanel.sigmaBack  = [0;0;1];    % [absorbed; specular; diffuse]
d.solarPanel.mass       = 0.1;

[v, f, data]            = CubeSatModel( [3 1 1], d );
hF                      = DrawCubeSat( v, f, data );

Initialize the array to save time

dT                      = t(2) - t(1);
tE                      = 0;
p                       = zeros(1,m);
nEcl                    = zeros(1,m);
uSunBody                = zeros(3,m);
uNadir                  = zeros(3,m);

Track LVLH coordinates;

z is in the -r direction y is in the - rxv direction x completes the set; along v in a circular orbit q transforms from ECI to LVLH coordinates

qs     = QLVLH(rs,vs);
qPoint = Eul2Q( [pi;0;0] );   % Swap Z axes by rotating 180 around X

Compute the power in a loop

for k = 1:m
	[uSun, rSun]	= SunV1( julianDate(k) );
	nEcl(k)       = Eclipse( rs(:,k), rSun*uSun );
  qECIToBody    = QMult( qs(:,k), qPoint );
  uSunBody(:,k) = QForm(qECIToBody,uSun); % the vector to the sun, body frame
  uNadir(:,k)   = QForm(qECIToBody,-Unit(rs(:,k))); % vector to the Earth
  pSunBody      = solarFlux*nEcl(k)*uSunBody(:,k);
	p(k)          = SolarCellPower( data.power, pSunBody );
	tE            = (1-nEcl(k))*dT + tE;
  if 1
    if k == 1
      figure(hF)
      hA = gca;
      q(1) = quiver3(hA,0,0,0,uSunBody(1,k),uSunBody(2,k),uSunBody(3,k),0.5,'color',[0.93 0.69 0.13]);
      q(2) = quiver3(hA,0,0,0,uNadir(1,k),uNadir(2,k),uNadir(3,k),0.5,'color',[0 0.8 0.1]);
      aa = axis;
      limit = max(abs(aa));
      axis(limit*[-1 1 -1 1 -1 1]);
    else
      set(q(1),'UData',uSunBody(1,k));
      set(q(1),'VData',uSunBody(2,k));
      set(q(1),'WData',uSunBody(3,k));
      set(q(2),'UData',uNadir(1,k));
      set(q(2),'VData',uNadir(2,k));
      set(q(2),'WData',uNadir(3,k));
      pause(0.1)
    end
  end
end

tOrb = Period(sma);
Plot2D(t/tOrb,qs,'Time (orbits)', {'q_1' 'q_x', 'q_y' 'q_z'}, 'LVLH Quaternion' );
Plot2D(t/tOrb,[rs;p],'Time (orbits)', {'x (km)' 'y (km)', 'z (km)' 'Power (W)'}, 'Power' );
hold on
plot(t/tOrb,max(p)*nEcl,'k')
legend('Power','Sun')

Size the battery

pTotal          = sum(p)*dT;
pAve            = pTotal/t(end);
pStored         = pAve*tE/3600;
batteryCapacity = pStored/(1-dOD);

fprintf('Total time         %8.1f hr\n',t(end)/3600);
fprintf('Eclipse Time       %8.1f hr\n',tE/3600);
fprintf('Total power input  %8.1f Wh\n',pTotal/3600);
fprintf('Depth of discharge %8.1f%%\n',dOD*100);
fprintf('Battery Storage    %8.1f Wh\n',pStored);
fprintf('Battery Capacity   %8.1f Wh\n',batteryCapacity);
fprintf('Li-Ion Polymer     %8.1f Wh\n',capacity);

%--------------------------------------

Total time              6.0 hr
Eclipse Time            2.3 hr
Total power input      60.9 Wh
Depth of discharge     60.0%
Battery Storage        23.0 Wh
Battery Capacity       57.5 Wh
Li-Ion Polymer          6.1 Wh

Published with MATLAB® R2019a