Renewable Energy Investment

Overview

Engineering reference data for Renewable Energy Investment in dynamics.

Key Formulas

Newton's Second Law

$F = ma$

Force = mass × acceleration.

Kinetic Energy

$E_k = \frac{1}{2}mv^2$

Energy of motion.

Momentum

$p = mv$

Mass × velocity.

Work

$W = Fd\cos\theta$

Force × displacement × cos(angle).

Variables

Payback Time Method

The payback time calculates how many years it takes for an investment to pay for itself through energy savings or earnings.

Formula: $t = \frac{I}{A} = \frac{I}{E \cdot c}$

Variables:

• $t$ = payback time (years)
• $I$ = investment
• $A$ = annual net income or savings
• $E$ = energy produced or saved per year (kWh/year)
• $c$ = cost or savings per energy unit (1/kWh)

Example:
Investment: 100,000
Energy production: 8,000 kWh/year
Grid energy cost: 1 per kWh
Annual savings: $A = 8{,}000 \text{ kWh/year} \times 1 \text{ kWh}^{-1} = 8{,}000$
Payback time: $t = \frac{100{,}000}{8{,}000} = 12.5 \text{ years}$

---

Simple Annual Method

This method calculates the average cost per unit of energy over the system's lifetime, accounting for initial investment and operating costs.

Formula: $c = \frac{\frac{I}{y} + C}{E}$

Variables:

• $c$ = cost or savings per energy unit (1/kWh)
• $I$ = investment
• $y$ = investment lifetime (years)
• $C$ = average annual running costs (1/year)
• $E$ = energy produced or saved per year (kWh/year)

Example:
Investment: 50,000
System lifetime: 25 years
Annual operating costs: 1,200/year
Annual energy production: 4,000 kWh/year
Cost of energy:
$c = \frac{\frac{50{,}000}{25} + 1{,}200}{4{,}000} = \frac{2{,}000 + 1{,}200}{4{,}000} = 0.8 \text{ per kWh}$

---

Discounted Cash Flow Method

Accounts for the time value of money—future cash flows are discounted to present value.

Present Value Formula: $P = \frac{F_0}{(1+i)^0} + \frac{F_1}{(1+i)^1} + \frac{F_2}{(1+i)^2} + \cdots + \frac{F_n}{(1+i)^n}$

Annual Cash Flow: $F_n = E_n \cdot c_n - C_n$

Real Interest Rate: $i_n = \frac{1 + i_{mn}}{1 + i_{in}} - 1$

Variables:

• $P$ = present value
• $F_n$ = cash flow per year (1/year)
• $E_n$ = energy produced or saved per year (kWh/year)
• $c_n$ = costs or savings per energy unit (1/kWh)
• $C_n$ = running costs (1/year)
• $i_n$ = real interest rate
• $i_{mn}$ = nominal interest rate
• $i_{in}$ = rate of inflation

Example Parameters:
Initial investment: 100,000
Annual energy savings: 15,000 kWh/year
Energy cost: 1 per kWh
Annual operating costs: 1,000
Inflation rate: 0.02 (2%)
Monetary interest rate: 0.05 (5%)
Over 10 years, the discounted present value is 23,305.

References

• Original Source