### 1.2 Efficiency of Conversion

Efficiency is a very important metric in energy conversion. It is most commonly used for evaluating and comparing various methods and devices in terms of technical performance, which is, in turn, related to cost of the technology.

Efficiency is the term we often hear and use in daily life, and it comes up frequently in various system analyses, cost estimates, and decision making studies. So, we should spend some time on refreshing our basic understanding of the efficiency as a universal metric of conversion systems.

#### Reading Assignment

So, first of all, please refer to this Efficiency of Energy Conversion book chapter, and refresh your basic knowledge of the efficiency definition and use. This text uses a number of simple efficiency calculation examples describing fossil fuel systems. I encourage you to learn from them, and further we will see how the same approaches may apply to solar energy systems and facilities.

Based on this reading, can you answer the following questions?

#### Check Your Understanding - Essay Question 6

If an electric motor consumes 150 W of electrical power to produce 120 W of mechanical power, what is the efficiency of this device?

#### Check Your Understanding - Essay Question 7

How would you determine the energy conversion efficiency of a power plant that consists of three conversion sub-systems with efficiencies *η*1, *η*2, and *η*3, respectively?

#### Check Your Understanding - Essay Question 8

A light bulb converts electric energy to light and heat. Can you estimate efficiency of a 40 W light bulb emitting 950 lumens of light energy (assume 1 lumen equivalent to 0.001496 W of power)?

We see that **efficiency of conversion **η is an important metric of system performance. When applied to solar energy conversion systems, efficiency of solar energy conversion (η) is defined as the ratio of the useful output power (delivered by the conversion device) to the incident power (of the solar radiation):

$\eta =\frac{{P}_{out}}{{P}_{in}}\times 100\%$

#### What can we learn from efficiency analysis?

- What fraction of available energy is lost in the conversion
- How one device is compared to another
- What is the performance limit

Photovoltaic cells are compared by nominal efficiency measured at standard conditions [ASTM G173 guide]:

- Air temperature 25
**°**C - Irradiance of 1000 W/m
^{2}(clear sky) - Air mass (AM) of 1.5G
- Panel oriented perpendicular to the light beam

When the exterior conditions are kept constant, measured efficiency is solely a device characteristic. If we have solar irradiance measured and device performance data collected, we can tell at what efficiency the system operates.

**[Solar Conversion Efficiency Cheat Sheet]**.

### Example of Efficiency Calculation

Generally, to estimate the efficiency of solar energy conversion, you would need:

- solar irradiance data, and
- performance data

Consider the example below, which shows estimation of the standard efficiency of a PV module.

Standard solar input (irradiance) at the module surface: S = 1000 W/m^{2}

Identifying power input to the PV cell: P_{in }= S =1000 W/m^{2}

Identifying power output from the PV cell: P_{out }= E × I / Area = 112.5 W/m^{2 }(Note: from physics, power is equal voltage times current)

Then, for efficiency, we can write: η = P_{out} / P_{in} = 112.5 / 1000 ×100% = 11.25%

Conclusion: only 11.25% of energy flowing to the panel is converted to electricity.

$$

The reason that energy conversion systems have less than 100% efficiency is that there are losses. The origin of those losses can be a complex issue, which could be better understood based on the physics and design of a particular conversion device – PV cell, concentrator, or thermal collector. We will get back to those considerations when talking about specific conversion technologies in detail in respective lessons of this course.

There is an important distinction between the total power (measured in W) and power density or flux (measured in W/m^{2}). When we talk about the performance of a particular solar energy conversion device (for example, a solar cell), power density characterizes the "quality" of the energy conversion - how much power is generated by each square meter of the cell area. That may depend on various properties of the cell material, design, and physical principles behind the conversion process. In contrast, the total power reflects the overall output - the "quantity" of usable energy generated by the whole device per unit of time. In applications of solar energy (say, if we want to power a building), we always look at the total wattage of the system and ways to maximize that total "quantity" of energy supply.

For example, imagine a solar module. At a particular moment of operation, the output power of the device can be expressed as

P_{out} (total) = P_{in}(total) (η/100%) = S A (η/100%)

- η = efficiency (%)
- S = sunlight power density (irradiance) at the cell surface (W/m
^{2}) - A = total cell area (m
^{2})

Logically, to increase the total output from that module, we need to either increase the efficiency or increase the total input power.

The avenue of raising cell efficiency leads us to the physics of the conversion process, materials properties, and cell design. The main research and development question here is how to make a better working cell.

The avenue of increasing the total input power lead us to three issues: (i) concentration of light, (ii) sun tracking, and (iii) system scale-up. Concentrating the ambient incident light would indeed increase the amount of energy supplied to the module per unit of time via increasing the S parameter in the above equation. Tracking - i.e., the orientation of the solar panel perpendicular to the sunlight beam - is another way to maximize the amount of absorbable radiation and also contributes to increasing the S parameter. Finally, increasing the size of the module by adding more cells to the system, increasing cell area, or multiplying modules (scale-up) would increase the total active area of conversion (A).

The technology scale-up is the way to match the solar power to commercial applications and consumer's needs. The utility-scale solar power, which is the primary focus of this course, is discussed in the next section.