Digital Workbench: Bay Area Solar Simulator

Ever wonder about the benefits of putting solar panels on your roof? The model below provides an example of a rooftop solar installation in the San Francisco Bay Area. It calculates the value of the solar energy generated from a typical solar system of your own design.

Which way would you face solar panels to maximize the value of the system? The answer depends not only on the amount of energy generated but also the time the energy is produced. Trying different layouts and time-of-use (TOU) rate schedules will help you understand how these affect the value of solar energy generation.

Although the model is functional on smaller screens, to see all six responsive charts at one time, a screen of at least 1,300 pixels in width is recommended.

INSTRUCTIONS:

On the rooftop, click and drag the installation crew to create a new panel layout on the rooftop. The distribution of panels affects how much and when energy is generated (see Generation Profile chart).
Observe the impact of time of generation and unit price of electricity on overall value. The value of the energy is represented by the sum of the four areas in the Value Pool chart and shown in green bar in the Energy and Value Comparison chart.
Optimize the value of the rooftop solar system by configuring the panel layout to maximize the height of the green bar for the "Current Case".
Once you are comfortable with the model outputs and have found the optimal for the default rate schedule, try to find optimal layouts for other rate schedule options or a rate schedule of your own design.
Further usage instructions, model details, and guiding questions are provided below.

Line generator

NOTE: Peak time-of-use is 3:00 to 8:00 pm daily.

Expert Panel of Judges

😑🤨😐

Larry Moe Curly

Digital Workbench Info

Usage
Assumptions
Resources
Quiz
About

General
Inputs
Outputs
Guages
Optimization

Welcome to TCG's Digital Workbench. Here we test concepts and try to gain insights beyond the strategy work we do during the day.

The Bay Area Solar Simulator was created to visualize the impact of solar panel distribution on energy revenue and to provide an example of what interests us. Details of the model are contained in this folder.

The good news is that you don't need any of these details to get started. Just click on roof and see what happens.

The model has been tested on Chrome, Edge and Safari browsers. If you have any issues running the model, please leave a note below.

DISCLAIMER: Many simplifying assumptions have been made in creating this model. Although the results are valid under these assumptions, the model is meant for educational purposes and not to be used as a substitute for an energy assessment based on the real-world conditions. TCG assumes no liabilty (or credit) for use of model results for purposes that were never intended.

The model has two main inputs: rate schedule and solar panel distribution.

Rate schedule: the drop-down menu has pre-populated values for peak and off-peak rates for "summer" and "winter" seasons. Using PG&E's rate structure "winter" is October through May and "summer" is June through September. Peak pricing start at 3pm and ends at 8pm. Beside the prepopulated values, you may also enter custom rates for each. Although other values will work, a realistic maximum for each is $0.70/kWh, at least within our lifetimes.

Solar Panel distribution: the distribution is controlled by the position of the installation crew on the roof. All practical and some not so practical configurations can be created by dragging the installation crew around the roof. You may also click a location on the roof to create a new configuration (useful for older or slower browsers).

Model outputs are shown in four charts:

Generation Profile

This chart show the generation profile for "summer" which is June through September and "winter" which is June through September seasons defined by PG&E. The value of the curve represents the total geneneration for the entire season for the hour of the day.

As you change panel distribution, note how generation decreases as panels are moved from south to north, and how generation shifts from AM to PM as panels are moved from east to west.

Value Pool

The Value Pool shows the source of energy revenue based a one year period. The rate schedule defines electricity rates for 4 regimes: summer and winter, with peak and off-peak times for each season. Based on the ability to sell surplus energy back to the utility (i.e. net-metering), the value of energy generation is used as a measure of performance.

The area of each value pool is product of the electricity rate and the amount energy that qualifies for that rate based on season and time of day. The sum of the four areas in the chart represent the total annual value of the energy generated.

As you change the panel distribution, observe how the distribution of value changes between the 4 rate regimes. For example, moving panels from east to west shifts energy into peak pricing regimes in both winter and summer seasons.

Energy and Value Bar Chart

The Energy and Value Bar Chart shows annual energy production in blue and annual value of energy in green. The blue bar represents the combined areas under the summer and winter curves in the generation profile, and the green bar represents the area of the 4 value pool components. The best and worst cases under PG&E's E-TOU Option A rate schedule are provided for comparison.

As you change the panel distribution from east to west, energy value increases faster than energy production due to increasing production during peak pricing regimes.

Contour Plot

The contour plot represents the entire solution space for the selected rate schedule. The location of the blue pin on the contour plot mirrors the position of the installation crew on the roof and therefore corresponds to a distribution of solar panels.

The color of the contour represents the value of energy at that point (i.e. for that panel distribution). Red is the lowest value (worst cast). Green is the best.

As you move the installation crew on the roof, the blue pin shows the corresponding value for that distribution. Equivalently, when the blue pin is moved on the contour plot, the corresponding solar panel distribution is shown on the roof.

Change the rate schedule and see how the optimum panel distribution changes.

How can you tell whether your solution is good? With an overarching goal of maximizing energy revenue (i.e. value) from the rooftop solar panels, there are many value indicators on the page:

The Judges: When you have best possible solution, the future will be so bright they'll have to wear 😎. As you might guess, Curly is easiest to please, Moe thinks he is smartest and is most critical, and Larry is somewhere in between.
The value bar chart: maximize the height of the green bar and you've found the optimal solution. Note that the best and worst values presented for comparison are based on the 'E-TOU Option A' rate schedule. It is possible to find better and worst cases than these for other rate schedules.
The contour plot: the darkest green contour is where you will get the most value from your system.

Optimize the distribution of solar panels for any rate structure by locating the greenest part of the contour plot. The optimal distribution of panels depends on the rate schedule, particularly the difference between peak and off-peak rates (i.e. the spread).

With the ability to analyze different rate structures, now answers can be found to questions such as "what peak/off-peak spread rewards solar panels facing west rather than south?". Optimizing solar panel distribution for different rate structures will provide the answer.

_{Cantabia Digital Workbench: Bay Area Solar Simulator v1.0}

Site
Solar Resource
PV System
Rate Schedules
Economics

The model was built using insights from a client's site near San Francisco. The solar energy system in the model is assumed to be roof mounted. The roof pitch is assumed to be 40° from horizontal. As another simplifying assumption, the rooftop has four sides. The roof is oriented 20° counter clockwise from true north.

For the purposes of this model, we consider no blockage or shading from trees or building structures.

Data for solar energy production was generated using NREL's PVWatts® Calculator. The primary inputs needed to estimate solar energy production on each side of the roof are provided below.

Module Type	Premium
Array Type	Roof Mount
System Losses	14.08% (PVWatts Default)
Azimuth	North: 340°, South: 160°, East: 70°, West: 250°
Shading	None

The solar energy system capacity is fixed at 5 kW composed of 20 - 250W solar panels. System losses are adopted from PVWatt's default for residential roof mounted solar.

With the current panel distribution algorith, not every configuration is possible. For example, layouts with panels only on opposing facings of the roof cannot be configured. However, the layouts that can be configured are guaranteed to include the configurations that produce the best and worst possible value.

The rate schedules are modeled after Pacific Gas & Electric's Residential Tiered Electric Rates and Residential Time-of-Use Electric Rates.

Although PG&E provides options for several peak/offpeak regimes, this model defines peak as 3:00 to 8:00 pm daily. The chosen definition provides the maximum amount of generation during peak rates therefore maximizing the overall value of generation. This is the most aggresive assumption that can be made when evaluating the benefits of TOU rate schedules on solar generation.

The economics of this model only focus on energy revenue to determine the relative merits of solar panel configurations. The scope of this model does not cover returns on investment or life-cycle costs. In this model, system cost, financing, escalation of rates, operations and maintenance costs and other are economic factors not considered.

With the goal of comparing panel distributions, the economics do not consider differences in solar panels or performance degradation over time. The model results can be interpreted as first year energy revenue results.

With these simplifications, this model does not provide an economic basis for purchasing or investing in a solar energy system.

At this scale, the difference between a good and great 5kW rooftop layout only amounts to a few hundred dollars in revenue per year. But when the same considertions are applied to a 100 MW solar farm, the impact on revenue can be on the order of $5,000,000 per year. For utliity-scale solar projects, an understanding of the impact of rate structures in Power Purchase Agreements is especially important in developing and financing any project.

_{Cantabia Digital Workbench: Bay Area Solar Simulator v1.0}

Acknowledgments
Solar Resource
Web Coding
D3 Charts

This model was build with permission of TCG's solar clients. Insights derived from evaluating economics of evolving rate structures and solar tracking systems provided the basis for this simple model.

Many online resources were used in the process of building this simulator. Some of these resources are provided in this section.

Solar energy generation data was calculated using NREL's PVWatts® Calculator. The tool has been developed by the National Renewable Energy Laboratories at the US Department of Energy and other US government partners to support solar development throughout the world. Estimates are based on measured solar insolation data, and include impacts of real-life conditions such as temperature effects on solar efficiency.

Description from NREL's website: NREL's PVWatts® Calculator estimates the energy production and cost of energy of grid-connected photovoltaic (PV) energy systems throughout the world. It allows homeowners, small building owners, installers and manufacturers to easily develop estimates of the performance of potential PV installations.

Each of these resources helped directly or indirectly to the creation of this model. They are listed in no particular order.

jsfiddle.net

www.w3schools.com

www.rgbtohex.net/rgb/

javascript-get-x-and-y-coordinates-on-mouse-click

obj_mouseevent.asp

colors_picker.asp

grid-grail

common-responsive-layouts-with-css-grid-and-some-without

shorthand-javascript-techniques

Easy-Responsive-Tabs-to-Accordion

Using ‘$’ instead of ‘jQuery’ in WordPress

complete-guide-grid

developer.mozilla.org CSS Reference

Collapse-O-Matic

One of the joys of producing this simulation was using D3 charting libaries to create responsive and interactive charts. This responsiveness adds a new dimension to visualing the relationships between data elements. Some resources are provided below. They are listed in no particular order.

dont-show-negative-sign-d3-axis-labels

Wrapping Long Labels

svg-group-element-and-d3js

d3-contour plot examples

D3 v4 Line Chart

Reusable Responsive Multiline Chart

Responsive Multiline Chart

Creating SVG groups using D3.js - an example

making-dashed-line-in-d3js

how-to-use-svg-file-for-image-source-in-d3

combining-translate-and-rotate-with-d3

_{Cantabia Digital Workbench: Bay Area Solar Simulator v1.0}

K-8
High School
Bachelors
Masters
Doctorate

Why does the sun rise and set everyday?

Hint

The earth spins around once every day.

Answer

The part of the earth facing the sun is considered to be day and the shadowed part, night. When the earth spins, it appears from earth that the the sun rises and sets. Too easy?

When panels are moved from the east side of the roof to the west, why does the generation profile shift to the right?

Hint

It has to do with where the sun rises and sets.

Answer

The east face of the roof captures more sunlight in the morning and the west face gets more in the evening.

For the average year, which side of the roof captures the most solar energy? Why?

Hint

It is the side that faces most directly into the sun.

Answer

The south face gets the most direct sunlight because San Francisco is north of the equator. Confirm your answer by comparing generation profiles for north and south facing panels.

For the average year, which side of the roof captures the least solar energy? Why?

Hint

It is the side that faces most directly away from sun.

Answer

The north face gets the least direct sunlight because San Francisco is north of the equator. Confirm your answer by comparing generation profiles for north and south facing panels.

On the generation profile, why is there usually greater energy production in the winter than the summer?

Hint

How are summer and winter defined?

Answer

On a daily basis, there is better solar energy in the summer than winter. However, using PG&E's definitions for rate schedules, "winter" is 8 months (October through May) and "summer" is 4 months (June through September). The generation profiles represent total energy production at the same time of day for an entire season. Since "winter" is roughly twice as long as "summer", there is usually greater energy production during the winter season.

What is the ideal tilt angle for solar panels mounted on the south side of the roof?

Hint

To get the most direct sunlight from a fixed solar panel throughout the year, the tilt angle should match the latitude of the site.

Answer

The latitude of San Francisco is about 38°N, so the optimal tilt measured from horizontal is 38°. The rooftop in our model is 40°, so not too far from ideal. You can find out more about optimizing tilt angle here:

What is the best configuration for PG&E's 'E-TOU Option A' rate schedule?

Southward facing panels only.

Set the rate schedule to $0.20/kWh spread. Can you find a more optimal layout than facing all panels south?

Hint

From the value pool chart, where do you get the most value from peak rates?

Answer

West facing panels will never produce more energy than south facing panels. However, under this rate schedule, you get paid much more for energy after 3pm. Because of this, panels on the west face will produce more value than those on the south face. Check your answer using the value pool, value contour and bar charts above.

Under the current TOU definitions of summer/winter and peak/off-peak, how could panels facing east or north deliver more value than facing south or west?

Hint

Experiment with different combinations of summer/winter/peak/off-peak rates.

Answer

In The Bay Area, solar panel on east and north will never deliver more value than south or west.

Why is there greater energy production when all panels face west compared to east?

Hint

Does the roof line up with cardinal compass directions?

Answer

The roof rotated is 20° CCW from cardinal directions. The west side of the roof faces slightly south and the east side slightly north. If these facings were perfectly east and west, the difference in production would be much smaller. There would still be difference due to atmospheric conditions and temperature related solar efficiencies that change throughout the day.

When the peak/off-peak spread is $0.166/kWh, why doesn't the value change when panels are moved between south and west faces

The value of each panel facing south and west is equivalent at this rate spread. When moving from south to west, the decrease in value due to lower energy production is offset by a higher on-peak rate.

What do you think causes the out-of-place increase in production at 6am in the summer for panels on the east side?

I don't have the answer and have not asked NREL. In looking at the hourly data from PVWatts, the increase happens daily so not likely to be a bad data point. The data from PVWatts is based on measured data. My best guess is that during the summer, the position of the sun was just right so a reflection (from glass or still water) hit the measurement array at 6am. Post your theories in the comments section below.

Could the duck curve in California be helped by pointing single-sided rooftop solar panels west?

Hint

When is peaking generation most needed? When are ramp rates the highest? Based on the generation profile, will solar energy ever be able to ramp up in the evening?

Answer

No. In this case, the traditional rooftop installations that are contributing to the issue in the first place cannot be part of the solution. The best we can do is to reduce required peaking capacity by shifting the ramping down of solar in the evening by pointing panels toward the west. Utility TOU rates need to be structured to encourage solar energy system owners to do this without losing energy revenue. This variable rate schedules in this model help us understand how electricity pricing can be designed to encourage solar energy systems to go west.

In this model, the roof tilt angle is fixed at 40° and single-sided or monofacial solar modules are used. If the tilt angle can be increased to 90° (i.e. vertical) then it would be possible to shift generation much later (and earlier) in the day using bifacial modules. This configuration may not be practical or economical for pitched roofs, but would be an option for flat roofs and ground mounted arrays. More about bifacial modules can be found here.

When would it make sense for a utility to structure TOU rates to reduce ramp rates for peaking generation?

Hint

Consider the alternatives and follow the money.

Answer

Punitive limits for daytime generation may be an option albeit likely not easy to implemented. Utility payment for curtailing solar generation might also be a lower cost near-term option than trying to manage the full capacity and evening ramp rate of solar. Barring these, it's highly unlikely that positive incentives in TOU structure will help. To reach parity on south and west faces, a $0.166/kWh spread needs to exist. At such a large spread, many other technology solutions are lower cost options (e.g. demand-side-management, peaking generation, thermal storage, pumped hydro). At these spreads, even some forms of electro-chemical storage start to make economic sense.

How can the duck curve be managed in the course of complying with California's Senate Bill 100 (passed in the State Assembly 8/28/18) with renewable goals of 50% by 2026, 60% by 2030 and 100% by 2045?

Hint

Based on the latest research into technology, policy, economics, and regulation, the solution will require a combination of all of these. As solar growth is a significant component in meeting the SB 100 goals, other forms of complementary or dispatchable generation will also be essential. An incomplete list of options is below:

Demand-side-management: regulate load as solar production drops.
Katabatic wind flows driven by daytime desert heating provide a potential renewable option for evening upramp that is naturally complementary to solar downramp.
In the near-term, with policy support, modifying under-utilized base-load gas turbines to support flexible peaking generation will continue be a stopgap option.
There are limited opportunities for pumped hydro storage which has its own challenges with environmental regulation, transmission, construction permitting and last but not least bankability.
In time, electrochemical and thermal storage might be also be a cost-effective options to level variable solar generation.
Bifacial solar panels mounted facing east/west have the great potential to reshape the generation profile of solar. Testing of this technology for widespread commercial adoption is underway.

Answer

As a proper grad-school-level question, the solution is left as an exercise to the reader. Please post your insights in the comments section below.

Only for the most brilliant among us...

? Please answer the last question smarty pants!

_{Cantabia Digital Workbench: Bay Area Solar Simulator v1.0}

This webpage was create for multiple reasons.

To share insights from our work.
To create a platform for discussion and learning.
To understand issues the solar industry is facing and evaluate possible solutions.
Out of curiosity about responsive charts, d3.js and coding in Javascript and CSS.

One thing this webpage is not meant to be is an uber-efficient, well-programmed web application. Our digital workbench is a testbed for algorithms and technologies. The components of the website were hastenly programmed for functionality without much focus on efficiency or style. Additionally, code snippets were used from various sources and modified for current use. Between these, fumbling through many new techniques, limits of WordPress and my own ineptitude, there is no doubt great opportunity exists for improvements in coding efficiency.

There are people who do this type of programming for a living. Any similarity between the quality of their work and mine is purely accidental.

Having said that, if there are suggestions or better yet offers of help to improve the code they are most welcome!

If you like the webpage, please consider responding:

Share something you learned with others in the comments section below.
Leave feedback on my LinkedIn article. If you like the model, encourage others to try it.
Tell those you know who many have an interest in the site (e.g. twitter, instagram, LinkedIn, pintrest)
Provide suggestions or offer help for improvements.
Find out about our consulting services. Contact us here.

Revision v1.0 This is the initial release.

The following are know issues with the site.

The plots are too wide to fit on many mobile screens.
In one and two column grid mode, blue pin on contour plot is not limited in +x direction and exhibits strange behavior at the bottom of the chart.
Formatting of notes in tabs and accordion folders is subpar.
The min and max on rates in the rate schedule do not limit inputs as they should.
Not all Larry, Moe, Curly emojis are not pre-loaded on some browsers.

Thanks for your interest! I'm Mark and I put this webpage together. This is an example of what energy geeks do for fun.

Many years ago, I worked with computational methods, data analytics and visualization in grad school. I still love technology and programming but don't have much time for it these days. Building this webpage took much of my spare time, but was a great opportunity to learn something about data visualization!

Thank you for trying out this webapp and especially for your interest in finding out more as evident from you being this deep in the site content!

That is all I've got for you about this webpage. I leave you with some of my inspiration for this project:

Thank you for visiting!

_{Cantabia Digital Workbench: Bay Area Solar Simulator v1.0}

Leave a Reply