Renewable Energy Systems Workbench

Interactive workspace initializes in your browser. Engineering method, assumptions, validation, and references are available below.

Engineering reference

Renewable Energy Systems: theory, method, and sources

This environmental & energy engineering workspace publishes 9 governing equations, 7 stated assumptions, 1 documented boundary, and 2 sources so the numbers it returns can be checked rather than taken on trust.

Calculations run locallyCalculation & source methodology

How this tool works

Ten modules cover photovoltaic output, wind turbine power, hydropower, solar thermal, geothermal, biomass, capacity factor, levelized cost of energy, and renewable portfolio share.

Wind output is computed from a user-supplied power coefficient, which should be checked against the Betz limit of 16/27 ≈ 0.593 that no turbine can exceed.

Calculators and topics covered

solar
wind
hydro
renewable energy
PV output
wind power
hydropower
geothermal
capacity factor
LCOE

Core equations

\text{photovoltaic power:}\quad P = I \cdot A \cdot \eta \cdot \text{derate}

\text{annual energy:}\quad E = P_{\mathrm{rated}} \cdot CF \cdot 8760

\text{wind power:}\quad P = \frac{1}{2} \rho Av^{3} \cdot C_{p} \cdot \eta \; \text{with}\; A = \frac{\pi D^{2}}{4}

\text{hydropower:}\quad P = \rho gQH \cdot \eta

\text{solar thermal:}\quad Q = I \cdot A \cdot \eta

\text{geothermal:}\quad P = \dot{m} \cdot c_{p} \cdot \Delta T \cdot \eta

\text{biomass energy:}\quad E = m \cdot LHV \cdot \eta

\text{capacity factor:}\quad CF = \frac{\text{actual}\; MWh}{\text{rated}\; MW \times \mathrm{hours}}

\text{levelized cost:}\quad LCOE = \frac{CAPEX \cdot CRF + O \text{\&} M}{\text{annual}}\; MWh,\; CRF = \frac{r \left(1 + r\right)^{n}}{\left(1 + r\right)^{n} - 1}

Method and assumptions

Assumptions

Resource inputs — irradiance, wind speed, flow — are single representative values, not time series, so output scales linearly rather than following a real resource distribution.
Wind power uses the cube of a single speed, which understates energy from a variable wind resource compared with a full Weibull distribution.
Photovoltaic derate factors bundle soiling, temperature, wiring, and inverter losses into one number.
LCOE uses a constant discount rate with level annual output and no degradation, tax treatment, or fuel escalation.
Grid integration constraints, curtailment, and transmission losses are not included.
The wind power coefficient is entered by the user and is not checked against the Betz limit of 16/27; a value above it is not physically achievable.
Hydropower uses a fixed water density of 998.2 kg/m³ rather than a temperature-dependent value.

Limitations and design boundaries

Educational screening calculations only. Project design and investment decisions require site resource data, equipment curves, hourly simulations, grid studies, environmental review, finance models, and qualified engineering analysis.

Sources and references

Primary sources are preferred for ratings, standards, manufacturer data, and externally defined constants.

Source policy

Masters, Renewable and Efficient Electric Power Systems
Boyle, Renewable Energy: Power for a Sustainable Future