Optimizing Solar Panel Placement through Passive Architectural Design

Data Availability Statement

Acknowledgments

Notation

$E_b^{(h,t)}$

The state of charge (kWh) of home h’s battery at time t;

E_max

The maximum state of charge of the communal battery over time (kWh);

$E_{max}^{(h)}$

The maximum state of charge of home h’s battery over time (kWh);

${\mathcal{F}}_h$

The set of roof facets belonging to house h;

$\mathcal{H}$

The set of houses in the community;

I_beam

Beam irradiance profile (W);

I_dif

Diffuse irradiance profile (W);

I_glo

Global irradiance profile, incident on plane (W);

I_horz

Horizontal irradiance profile (W);

$n_p^{(h,i)}$

The number of panels on a given facet i of the roof of house h;

${\overline{n}}^{(h,i)}$

The maximum number of panels that fit on facet i of house h;

$P_{\mathrm{buy}}^{(h,t)}$

The power imported to home h at time t (kW);

$P_{\mathrm{cons}}^{(h,t)}$

The total consumption of house h at time t (kW);

$P_{\mathrm{gen}}^{(h,t)}$

The total generation of house h at time t (kW);

${\overline{P}}_{\mathrm{gen}}^{(h,t)}$

The maximum total generation of house h at time t (kW);

$P_{\mathrm{net}}^{(h,t)}$

The net import/export of power to home h at time t (kW);

$P_{\mathrm{sell}}^{(h,t)}$

The power exported to the grid h at time t (kW);

${\hat{p}}^{(h,i,t)}$

The power production of a single solar panel of house h, facet i at time t (kW);

t′

Time elapsed since midnight of the previous day (hr);

α

Multiobjective optimization tuning parameter;

δ

Solar declination;

η_ch

The efficiency of the battery during charge (including inverter efficiency);

η_dis

The efficiency of the battery during discharge (including inverter efficiency);

η_PV

The efficiency of the solar panel installation (including inverter efficiency);

θ_h,i

The angle of roof facet i on house h;

θ_n

Angle of incidence on plane;

θ_p

Vertical orientation angle of the plane;

θ_s

Solar zenith angle;

λ

Latitude angle of the plane’s location;

ρ_g

Ground reflectance;

ϕ_h

The orientation of house h (angle from true north to project north);

ϕ_h,i

The orientation of facet (angle from true north) i on house h;

ϕ_p

Horizontal orientation angle of the plane;

ϕ_s

Solar azimuth angle; and

ω

Hour angle of the day.

References