How much electricity does a rooftop solar panel produce?

Calculating the Electrical Energy Output of a Solar Panel

When choosing a rooftop solar panel, estimating the average daily electrical energy output is always a challenge.  Data sheet of a solar panel specifies only the power output while it is the energy output that is required for sizing most applications. The purpose of this blog-post is to describe some basic principles that will help with the estimation of energy output. Once you know the expected average energy output, it is possible to size the panels for a particular application. If you want to skip all the theory, jump directly to this calculator where you can enter the parameters for your system to calculate the monthly and yearly output. To get a deeper understanding of the subject read on:

Power output of a solar panel is specified in Watts for Standard Test Conditions (STC). The STC corresponds to a solar insolation (radiation) of 1000 W/m² and a cell temperature of of 25º Celsius. For instance, the LONGi LR6-72-340M panel is rated to produce 340 Watts when solar insolation is 1000 W/m² and solar-cell temperature is 25º Celsius. This output power is rarely achieved in practice. There are several reasons for the reduction in output. Each of these reasons correspond to a down-rating factor to apply to the published power output:

• Solar insolation: An insolation of 1000 W/m² is probably achieved in a desert when the sun is directly overhead! In practice, insolation varies considerably across the globe. Absorption of sunlight in air varies depending on the volume of air through which the sunlight passes. The volume depends on the latitude and the season. At latitudes far away from the equator, sun never comes directly overhead and the sunlight must pass through a larger volume of air. During the winter season, there is a further increase in the volume of air through which the sunlight must pass as the declination of sun in the sky is higher. Absorption in the atmosphere also depends upon factors such as humidity, dust particles and aerosols present in the air. Moreover, there are cloudy days, during which the insolation reduces significantly. Another factor that affects insolation is the horizontal tilt at which the solar panel is installed. For most locations in the northern hemisphere the panels must be facing south with a horizontal tilt that equals the latitude for the location for optimal average insolation. A horizontal panel may experience significantly lower insolation. Given these variables, how do we estimate the amount of energy that a solar panel will deliver? Thankfully, NASA has gathered data for solar insolation for almost every part of the globe and averaged it over 22 years. This data was gathered using satellites. For instance, here’s the data for Pune, India, and San Jose, California, USA.

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec	Avg
Pune, India kWh/m2/day	6.09	6.45	6.75	6.63	6.34	4.31	3.46	3.39	4.47	5.51	5.83	5.77	5.41
San Jose, CA kWh/m2/day	3.74	4.69	5.98	6.59	6.82	7.03	7.12	7.07	6.78	6.13	4.52	3.69	5.85

Insolation Data for Pune, India and San Jose, CA, USA, for a surface tilted at “latitude” degrees towards south

• Operating Temperature: A solar panel can never operate continuously at a cell temperature of 25º Celsius. In a tropical country like India, it is more common for the cell temperature to rise to above 50º Celsius. At this temperature, the power output from a solar panel is significantly less compared to that at  25º Celsius. For the LONGi solar panel, a 10% drop in power output is expected at the cell temperature of 50º Celsius. The cell temperature is strongly correlated with ambient temperature and hence with the weather for a given location. Secondly, the cell temperature varies throughout the day, which too makes it difficult to estimate the exact impact on output. However, it is possible to estimate the loss due to rise in cell temperature by using statistical analysis along with the average monthly weather data for a given location. The impact of weather on operating temperature and the output of solar panels is a topic of research. The details of this are beyond the scope of this blog. However, it can be assumed that for most tropical locations an impact of 5% to 12% (depending on the month) on output is expected. Certain locations with very cold weather may actually have a better power output as compared to STC conditions. For the purpose of this blog-post, a down-rating factor of 0.93 is assumed, which could correspond to a typical location in India in March.
• Electronics associated with using the energy produced by the solar panel can’t operate at 100% efficiency. However, well designed inverters operate at a very high efficiency, with many inverters claiming 96 to 98% efficiency. The inverters also track the peak power generation point of the solar panels. However, a small error in tracking is always possible. Considering these factors, a down-rating factor due to associated electronics is 0.96.
• Cabling Losses: Several solar panels are connected in series to form a system that operates at high voltage and (relatively) low current. Lower current implies a lower power loss in cables. For the purpose of this document, the cabling loss is assumed to be 2%, implying a down-rating factor of 0.98. The length and diameter of cables and configuration of a given system will decide the actual loss; but a down-rating factor of 0.98 is achievable.
• Dust and Cell Mismatch.: Solar panels collect a lot of dust and bird droppings on the glass surface. This reduces the output significantly. Even when the panels are cleaned periodically, some residue remains. Reduction in output of even a single solar cell affects the power output from the panel since all solar cells within the panel are connected in series. Reduction in current output causes a corresponding reduction in power and energy output of the panel. The reduction in output of a solar panel due to this factor is mostly a guess since conditions are different for every installation. It is assumed that the down-rating factor on this account will be 0.93.
• Aging: Output of solar panels reduces with age. The panels generally come with a guarantee of 90% output after 10 years and 80% output after 25 years. During the very first year of operation there is about 2.5% loss as the panels are exposed to sunlight. A down-rating factor of 0.975 is used for calculation for the first year of operation.
• COS(θ) Effect: During the course of the day, as the sun traverses the sky, angle of incidence of sunlight on the solar panel keeps changing. The angle of incidence is maximum early in the morning and late in the evening. Near noon, this angle is at a minimum and hence maximum solar radiation in incident on the panel. Thus, the 100W panel cannot output 100W throughout the day. This is called the COS(θ) effect, since the output is proportional to the cosine of angle of incidence.  There is one more factor that results in another COS(θ) effect. Throughout the year, as seasons change, the declination of sun in the sky changes. This results in an additional cosine factor. The COS(θ) effect is taken into account in the insolation data reported by NASA for a given location. A separate down-rating factor is not necessary for this.
• Availability: A grid connected system operated only as long as the electric grid is available. Such a system is required to shut down when the grid is down. There could be other reasons such as faults, regular maintenance, etc. that may result in availability to be less than 100%. It is fair to assume 98% availability and hence a down-rating factor of 0.98

Calculation of Output:

Electricity output is obtained by multiplying the panel power rating by insolation and the total down-rating factor. The total down-rating factor is simply a multiplication of all the factors mentioned above. Temperature compensation is dependent on location and month. As a result, the total down-rating factor changes based on location and month. Let us calculate the output for Pune, India for the month of March:

total_down_rating_factor = 0.93 * 0.96 * 0.98 * 0.93 * 0.975 * 0.98 = 0.78

output for March = panel_rating * insolation * total_down_rating_factor * days

output for March = .340 kW * 6.75 * .78 *31 = 55.5 kWh

A similar calculation for San Jose, CA, with temperature compensation = 0.97 yields an output electrical energy of 51.1 kWh.

Yearly Output Calculation for Various Locations:

I am using this calculator to estimate the outputs. It provide estimates for almost any location in the world.

Location	Mumbai, India	Bengaluru, India	Kolkata, India	Delhi, India	Sunnyvale, CA	Tampa, FL	Seattle, WA	Phoenix, AZ	Sydney, Australia
Yearly kWh for a 340 W panel	588	502	461	513	513	536	370	559	479

Yearly Output for a 340 Watt Panel Tilted at Latitude Degrees for Various Locations

Reference: Solar Generation Calculator

Suboptimal Generation in a Solar PV System under Shading Conditions

If you have a solar PV system that uses a string inverter and does not produce the expected output when certain solar panels are shaded then you may find this article of interest.

Modern solar systems utilize half-cut panels equipped with bypass diodes, alongside string inverters capable of maximum power power tracking (MPPT). Despite the inclusion of these components it’s often observed that some systems fail to deliver optimal power output under shading conditions. Personally, I have a rooftop system where certain panels are shaded in the morning. Upon observation, it became apparent that this system was generating significantly lower output when only a couple of panels were affected by shading. In response to this issue, I conducted a root cause analysis, the findings of which are detailed in this blog post. It is my hope that sharing these results will assist others facing similar challenges.

Configuration:

My system is rated at 7.56 kW and utilizes Waree 540 W Mono PERC half-cut panels paired with a Havells on-grid inverter. The configuration comprises 14 panels arranged in a single string. The panels are oriented southwards and tilted at 18 degrees, aligning with the installation location in Pune, situated at a latitude of 18 degrees north.

Observations:

Despite only a portion of two panels being shaded in the morning, the system exhibited significantly low power generation. For instance, at 9:12 AM on January 15th, the power output was recorded at 0.36 kW, with a current of 0.5 A and a string voltage of 626 V. However, within a span of just ten minutes, the power output surged to 3.25 kW by 9:22 AM, accompanied by a current increase to 6.6 A, while the voltage dropped to 506 V.

Inverter Generation

The graph distinctly illustrates a sudden increase in both current and power output around 9:22 AM. Prior to this time, shading affected two panels in the string. However, after 9:22 AM, only one panel remained partially shaded, with the shadow covering solely the bottom portion of the panel. Additionally, a marginal increase in voltage can be observed following 9:22 AM. The voltage peaked around 9:38 AM when all panels were free from shadows.

Discussion

It is generally expected that modern inverters can efficiently manage a string of solar panels equipped with half-cut cells and bypass diodes, ensuring operation at the optimal power point even when some panels are shaded. Bypass diodes are designed to conduct for the set of cells affected by shadows, resulting in a lower voltage output of the string compared to when no shadows are present. However, the current output should remain consistent with the solar insolation levels for the panels in sunlight. For example, if the maximum power point (MPP) current of panels in sunlight is 6 A and the MPP current of shaded panels is 0.6 A, the string should ideally operate at a current close to 6 A while bypass diodes are activated for shaded panels. Consequently, the voltage output of the string must be lower than usual due to the activation of bypass diodes, assuming that the number of shaded panels is less than half of the total panels in the string.

However, observations from my installation revealed a different scenario. Despite two panels being partially shaded, the voltage was unexpectedly high, while the current was low. Subsequently, there was a sudden increase in current and power output, accompanied by a decrease in string voltage, when the second panel emerged from the shadow, leaving only one panel shaded.

The MPPT function in an inverter is designed to sweep the voltage/current range to achieve the maximum power point (MPP). However, it’s important to note that when shadows are present, there isn’t a single MPP for a string of panels. Each panel within the string may have its own local MPP, while the string as a whole has a global MPP. In our observation, the inverter we employed struggled to track the global MPP when more than one panel was shaded. Instead, it operated at a current corresponding to the shaded panels, resulting in a high string voltage and low power output. Only when only one panel remained in shadow did the MPP tracker finally adjust to operate the string at the global MPP. However, until this adjustment occurred, the string operated well below its optimal capacity.

Conclusion

It is important to assess how well an inverter can track MPP when certain number of panels are shaded. While the datasheets of most inverters lack detailed information in this regard, it may be useful to consider white papers by manufacturers. Fronius is one brand that describes the MPPT operation in detail. However, many popular (and inexpensive) inverters in the market do not publish any details. It is worth evaluating if investing in a better brand will yield better returns in the long term.

Solar Electricity Generation in One Year

Our 12.24 kW rooftop solar PV system in Pune, India, recently completed one year of operation. This blog-post reports the total electricity generation as well as the monthly numbers. It also compares the generation with theoretical estimates for each month. The total generation from July 1, 2018 to June 30, 2019 was 17,791 kWh. The average daily generation was 48.7 kWh/day. Since this generation was for a 12.24 kW system, the efficiency is calculated to be 3.98 kWh/kW/day. The estimated values based on insolation data for Pune are, 18,276 kWh for yearly generation and an estimated efficiency of 4.09 kWh/kW/day.

Monthly Generation Statistics

Month	Actual and (expected) Generation (kWh)	Efficiency (kWh/kW/Day)
July 2018	800 (993)	2.11
August 2018	953 (1031)	2.51
September 2018	1330 (1283)	3.65
October 2018	1473 (1632)	3.88
November 2018	1375 (1681)	3.74
December 2018	1249 (1643)	3.29
January 2019	1629 (1796)	4.29
February 2019	1728 (1615)	5.04
March 2019	2052 (1913)	5.41
April 2019	1868 (1805)	5.09
May 2019	1925 (1713)	5.07
June 2019	1399 (1171)	3.69

Observations:

• March, April, and May are predictably the best months for electricity generation with ideal conditions: almost no cloud cover, low humidity, and good number of daylight hours with sun rising almost to the zenith point.
• July and August, with monsoon at its peak, are the worst months, in spite of long daylight hours.
• Generation  in October, November and December was worse than expected. The primary reason for this was a lack of proper cleaning. In the preceding months, rainy season had ensured that the panels remained clean. The dust accumulating on the panels reduced generation significantly. In December, the generation was 24% lower than the theoretically expected value. This was corrected in mid January with a strict, biweekly, cleaning schedule.

Return on Investment (ROI)

During this period, the savings in electricity bill amounted to ₹ 2,88,525/-. The system cost was ₹ 7,63,000/-. There were no maintenance expense. The ROI is calculated to be 37.8%. This implies a payback period of less that 3 years. We did not use any subsidy from the government while purchasing the system. An installation that makes use of subsidy can enjoy an even shorter payback period.

Conclusion

An average generation of about 4 kWh/kW/day is close to the theoretical value of 4.09 for Pune. This slight reduction (3%) is primarily due to the accumulation of dust and a lack of cleaning. A strict biweekly cleaning schedule is necessary to ensure efficient generation. In any case, a generation of 4kWh/kW/day can be used as a reference to estimate generation of a solar PV system in Pune. This number will be valid for most regions in India, except the far north, north east and some hill-stations in the western ghats. Generation will be slightly higher in the desert region of Rajasthan and at many locations in the northern Maharashtra and parts of Gujarat. The payback period and ROI for this system is one of the best that I have seen reported. This is thanks to optimal sizing of the system in a region with high tariff for electricity.

Reference: Solar Generation Calculator

How to Size a Rooftop Solar Power System

A rooftop solar power system requires significant investment. The return on investment (ROI) of this system is dependent on selecting the right size for the system. The suppliers/providers of such systems tend to over-size them because a larger system implies a higher price and therefore higher profits for the provider. Their goal is rarely to optimize the ROI for the customer. This blog post aims to guide the customer in selecting the correct size for their rooftop solar power system.

Executive Summary:

Size the system such that the yearly generation is slightly less than the yearly consumption. For most locations in India, a rooftop solar system will generate 4 kWh/kW/day, when averaged over a year. The size of the rooftop solar system in kW is calculated to be: yearly_consumption/(4 * 365).  Therefore a 20,000 kWh yearly consumption will require a 13.7 kW system. If the available space cannot accommodate this system then it is recommended to go for a lower size. Never try to ‘fit’ a large system by cramping together rows of panels. This is because  shadows will reduce the output significantly. The solar system needs 8 shadow-free hours in the middle of the day (8 am. to 4 pm.) for optimal generation, even during the winter months.

Assumptions:

1. The discussion applies to a system in India but could be extended to systems in other parts of the world.
2. The electricity utility company supports net-metering for rooftop solar systems.
3. The rate at which the utility company purchases excess electricity is significantly lower than the marginal rate at which the consumer purchases electricity.

Rows of Tilted Solar Panels in the USA (Credits: Pixabay)

A Tilted Single Row with 4×2 Arrangement of 330 W Solar Panels in Pune, India

Step-by-Step Procedure to Size the System:

• Identify the application which will be supplied solar power. For instance, lifts (elevators), common lighting, water pumps, air conditioning, etc.
• Collect monthly bills for one full year and note the consumption in kWh for each month. Calculate the yearly consumption in kWh.
• The yearly consumption is the target yearly generation for the solar photo-voltaic (PV) system.
• The capacity of a solar PV system is measured in kilowatts (kW). A grid-tied system consists of solar panels and an inverter. The solar panels generate DC output while the inverter output is AC. The inverter and panels generally have the same capacity. So, a system with solar panels of 10 kW DC capacity should use an inverter with 10 kW AC capacity. However, a 10 kW DC system will rarely generate 10 kW output since the solar panel rating is specified for ideal conditions. Such conditions are rarely present in practice unless the installation is in the Sahara desert and the sun is shining directly overhead. Hence, it is perfectly safe to use an inverter that has 10 to 15% lower capacity than the solar panels.
• Calculate solar panel capacity (DC kW) using the following formula:

Capacity (kW) = (target_ yearly_generation in kWh)/(365 * 4)

In this formula, the number ‘4’ is the typical generation in kWh/kW/day for most locations in India. This generation is for a system with solar panels facing south, tilted at ‘latitude’ degrees. For instance, latitude for Pune is 18 degrees and hence the solar panels should be tilted at 18 degrees to ground. This website provides a good estimate of monthly and yearly generation for most locations in the world.

• This capacity is the target capacity for the system. Never buy a system with larger capacity.
•  Measure the area (in square meters) on the roof that will be used to install solar panels. The area should be with a clear view of the south and there should be no obstructions such as trees, water tanks, elevator rooms, etc. Note that parapet walls are not a concern since the panels can be installed elevated.  The idea is to avoid shadow on panels from 8 AM to 4 PM in all seasons, as far as possible.
• Multiply the area by power density to obtain the approximate capacity of panels in kW that can be installed in the area. The power density depends on several factors. If multiple rows of tilted solar panels are installed then the panels in front cast a shadow on the back row. An adequate distance is necessary between rows to avoid the shadow. The angle of tilt is generally the same as the latitude of the location. Higher the latitude, higher the tilt and hence more distance is necessary between rows, implying a lower power density.
• For small systems, say less than 4kW, a single row of panels may be sufficient (see the picture above). For such a configuration, a power density of 170 W/m² can be used to calculate the system size. For larger systems with multiple rows of panels, following table summarizes approximate power density for different latitudes:

Latitude	Power Density
0	170
5	157
10	142
15	127
18	117
20	111
25	93
30	75

• For instance, in Pune, India, with a latitude of 18 degrees, an area of 100 m² can support a 11.7 kW installation. If the target capacity calculated based on consumption is 15 kW, this space will be insufficient. Cramping a 15 kW system will result in shadows that will reduce generation. A low generation implies a correspondingly low ROI. In this situation, it will be best to install a system with 11.7 kW (DC) capacity. The inverter, or the AC capacity of the system, should be chosen to be 10 kW.

Note:

This blog-post will help the customer optimize solar system size for most installations. It should also help while verifying proposals from solar installers. While the information provided will apply to most situations, there are cases when deeper analysis may be necessary. For instance, at certain locations, it may be better to install panels without a tilt. The power density in this case will be the same as that for latitude 0.

Reference: Calculators for Solar Generation and System Sizing

 

Solar Generation During Monsoon

Solar Electricity Generation During the Monsoon

A frequently asked question for rooftop solar power is: “Will my rooftop solar PV system be useful during the monsoon season?”. I did some theoretical analysis as well as practical measurements to answer this question. The analysis pertains to Pune, India and the measurements were for a rooftop solar PV system of capacity 12.2 kW, installed in Pune. Based on this analysis, a prediction will be made for other locations in India too. The discussion assumes a PV system with net-metering.

The monsoon in Pune is characterised by extremely overcast conditions in the month of July. The month of August is very similar to that of July. June and September are the other two months of the monsoon season, characterised by more sunshine as compared to July and August. The average solar insolation in Pune in May is 6.34 kWh/m²/day for a surface facing south and tilted at an angle of 18 (latitude) degrees. The corresponding number for July is only 3.46 kWh/m²/day (Source: NASA Data). In other words, the solar insolation in July is only about 55% of that in May. Most of this solar insolation is diffused in nature, with very little direct sunlight. The question is whether this diffused solar radiation generates sufficient electricity. The monsoon was very active in Pune in July 2018. It rained almost every day. In fact, it was reported that, on average, there was just one hour of clear sunshine per day in this month and the insolation averaged 3.23 kWh/m²/day .

Our 12.2 kW rooftop solar system generated about 53 kWh/day in May, while in July, the generation averaged 31 kWh/day. Thus, the generation in July was about 58% of that in May. The observed results are quite close to the prediction based on NASA data. There were a few days in July when it rained very hard and the sky had a thick cloud cover. One such day was July 15th, when the solar generation was only 9.6 kWh. However, the average generation for July was slightly higher than predicted values.

Compared to Pune, most cities in India report a higher insolation in July:

1. Mumbai: 5.06 kWh/m²/day (72% of May)
2. Bangalore: 4.44 kWh/m²/day (74% of May)
3. Delhi: 4.75 kWh/m²/day (81% of May)
4. Kolkata: 3.84 kWh/m²/day (71% of May)
5. Nagpur: 3.78 kWh/m²/day (62% of May)

(Source: NASA Data)

A solar PV system in these cities will perform even better than that in Pune in July. In other months during the monsoon season, the insolation is higher than that in July. I measured the generation in August. It was 37 kWh/day, higher than that in July. The generation in September was even higher, at 53.6 kWh/day. However, this September was considerably dry. The average generation in the monsoon season (June to September) was 43.3 kWh/day and considering that this is a 12.2 kW system, the average generation per kW per day is calculated to be 3.55 kWH. Thus, any concerns regarding very low generation during the monsoon season are misplaced. The only days when the generation is extremely low (< 25% of average) are the days of continuous heavy rain throughout the day. It is expected that most rooftop solar systems will be in a net-metering configuration. For such systems, the grid acts as storage. On the days that generation is very low, electricity will be imported from the grid.

However, for an off-grid system, the monsoon season can be very challenging. It is rather difficult to size the solar panels and batteries for uninterrupted operation during the monsoon season. There is a significant chance that days of heavy rainfall are consecutive along with several days of extreme cloudiness. I will cover this in detail in another blog-post.

 

Don’t Oppose Large Dams: Hydro Power is Necessary for Solar Power to Succeed!

India has a long history of opposition to the construction of large dams. The opposition to the Saradar Sarovar project in the form of Narmada Bachav Andolan and the opposition to the Tehri dam are some of the most notable ones. There is opposition to even smaller dams and associated hydroelectric power. The reasons for this are many, the most prominent being the displacement of people and the destruction of the ecosystem. The proponents of the dams highlight the advantages: flood control, irrigation, and electricity.

However, there is one point that both sides miss completely: Opposing large dams is equivalent to opposing solar power and supporting ever increasing coal mining. Here’s why:

The growing economy of India is hungry for electric power. Electricity generation increased from 744 TWh in 2006 to 1401 TWh in 2016, an increase of 88.3% [1]. Quite predictably, during the same period, coal consumption increased by 88% [1]. In fact, the demand for coal could not be satisfied with domestic production, and as a result, the import of coal increased 5 times from 2006 to 2016. During the same period, hydroelectricity consumption increased by just 14% [1]. Moreover, natural gas production in India shows a worrying trend, declining from 29.3 BCM in 2006 to 27.6 BCM in 2016 [1]. In short, it is coal that supports the rising economy of India. Unless solar power can somehow replace the electricity produced using coal, coal mining is only going to increase.

Solar Power Needs Hydroelectricity:

The resource with the highest potential to produce electricity is solar, more specifically photovoltaic electricity. However, this resource is an intermittent but predictable resource. A 1 MW solar power plant will not produce 24 MWh of electricity in a day. In fact, the long term average is likely to be only about 4.25 MWh/day [4], depending on the location of the plant. Thus, solar power either needs a backup or some type of storage to cover the time when the sun is not shining or shining not very brightly. When solar power is not available, the backup source needs to take over. This is best explained with a load curve aka load profile. The figure below shows an ideal theoretical load curve [see note at the end] for the state of Maharashtra in India:

The red line shows the load (demand) on the grid. It can be observed that in an ideal situation, load on the grid corresponds to human activity. The demand is at its lowest from 1 AM to 4 AM. There are two peaks in the demand, one at noon and another at about 8 PM in the evening. It can be observed that solar power, if it were installed, can fulfil the demand as it rises in the morning. Solar power is not available in the evening or at night. The demand in the evening and night can be fulfilled by hydro power and natural gas. A small amount of base load can be served by coal or nuclear power. In such an ideal scenario, solar power can fulfil about 45% of the total electricity demand, hydro power and natural gas would serve about 37% and coal/nuclear power will fulfil about 18% of the demand. This is without any type of storage of electricity. Development of either pumped hydro storage or other modern storage solutions can help solar power serve an even higher percentage of the total electricity demand.

Large scale storage solutions are still very expensive and using a backup power source is the most viable option. A backup power source needs to be dispatchable, meaning it should be possible to turn it on or off on-demand and the output power should follow the demand from the grid. Electricity from coal or nuclear power is not very dispatchable. The best resources from this perspective are hydroelectricity and natural gas. However, potential for natural gas in India seems rather bleak, with production on the decline in the past few years. Considering this, hydroelectricity is the only viable resource that can serve as backup for solar power.

Hydroelectricity Potential in India:

India has a hydro power potential of 146 GW at 60% load factor [2]. Thus, in a year, 767 TWh of electricity can be generated using hydroelectric power stations. This number does not take into account the potential for pumped storage hydro power, the potential for which is about 90 GW [3]. Total electricity generation in India in the year 2016 was 1401 TWh. Thus, fully realising the hydroelectric potential in India could easily support 55% of generation. More importantly, 1 unit of hydro generation supports more than one unit of solar generation by taking over when solar power is not available. Availability of pumped storage hydro power and with some support from natural gas based power stations, solar power can serve more than 50% of the total electricity requirement. In the absence of support from hydroelectric power, solar power cannot succeed since coal or nuclear power will not be able to serve as a viable backup when solar power is not available. By realising the full hydroelectricity potential, solar power can can grow and provide more electricity than hydro.

Conclusion:

Opposing dams is a folly. They are absolutely necessary for solar power to succeed and to avoid all the damaging effects of using coal as the primary source of electricity. Large dams do have their disadvantages. However, those disadvantages must be weighed against the environmental benefits of moving away from coal as the primary source of electricity.

Note on load curve: The actual load curve for Maharashtra is quite flat with only a small dip in the night. The load curve discussed above was for an ideal situation. Presently, the grid is mostly powered by coal and these power stations are not very good at handling a load curve that corresponds to human activity. As a result, electricity consumers are forced or provided with an incentive to use power in the middle of the night. While such staggered usage of electricity is necessary for coal power, it takes a toll on farmers and workers who are forced to work at odd hours. Using solar power in conjunction with hydro power and natural gas will allow the load curve to resemble human activity. Incentives for working in the night will no longer be necessary, In fact, incentives may be provided to work more during the daytime. A large number of farmers and workers will benefit from this.

References:

1. BP Statistical Review of World Energy 2017: BP
2. http://powermin.nic.in/en/conten…
3. India Wants to Build 10 Gigawatts of Pumped Hydro Storage to Support Solar
4. How much energy does a 100W rooftop solar panel generate?

Solar Electric Power from Rooftop Reaches Tipping Point

Executive Summary

Falling prices of solar panels and rising electricity rates have profoundly changed the economics of solar power. In India, solar photovoltaic electricity has reached a tipping point as the return on investment has become very attractive for many applications. It has become extremely economical to install rooftop solar panels with net-metering. This has the potential to start a revolution where most buildings in cities will install solar panels to generate electricity. This change can potentially happen faster than the proliferation of television and the Internet.

Introduction

Most states in India now allow net-metering. It is now possible for a home, housing-society, commercial establishment, or an industrial unit to feed power to the grid and get paid for it. A net-metering system will charge the consumer only for the net consumption of electricity. For instance, a home can feed power to the grid during day-time when household requirement for electricity is low and consume power from grid during evening and night when solar generation is zero. The consumer gets charged only for the consumption that is more than the energy delivered to the grid. This blog-post presents calculations to prove that it is much better to invest in solar power than a bank deposit or a debt mutual fund. Such an attractive investment option can result in a rapid change in the way electricity is generated in the country from a completely centralised generation to a more distributed generation architecture.

Calculation for Return on Investment (ROI) for Solar Power

System Sizes and Cost

The investment in a roof-top solar, grid-connected PV system is expressed in terms of Rupees per kilowatt (₹/kW). These rooftop systems are available in various power ratings, ranging from 1 kW to about 25 kW. Largest systems have the lowest price per kW and smaller systems are more expensive. A 1 kW system is expected to cost almost ₹100,000/- while a 10 kW system costs about ₹70,000/kW. A 25 kW system may cost only ₹60,000/kW. These prices include solar panels, synchronous inverter, cabling, accessories, installation, and taxes.

Electricity Generation by Solar Panels

The electricity generated per year varies based on system size and location. For the purpose of this blog, I am only considering the major parts of India that have ample sunshine. Please refer to my earlier blog-post for calculation of electricity generation by a solar panel. Based on that blog-post, a 1 kW panel in India will generate about 4.24 kWh of electricity per day, or about 155 kWh per year. There will be some variation from city to city. For instance, Pune is expected to generate about 4.19 kWh/day and New Delhi will generate about 4.25 kWh, while Jaisalmer in Rajasthan will generate 4.46 kWh per day. These are numbers averaged over a year. For calculating the return on investment, I will use the number for Pune since it is slightly lower than average and will provide a safety factor.

Electricity Rate and Monthly Bill

I will use the electricity tariffs in Maharashtra for residential and commercial low tension (LT) supply for the purpose of these calculations. Residential electricity rates are organised in slabs:

Slab (kWh)	Total Tariff (₹/kWh)
0-100	4.88
100-300	9.21
300-500	12.66
500-1000	14.40
1000+	15.88

The tariff includes wheeling charges and taxes. Electricity rates for commercial consumers are arranged in slabs that depend on the maximum power rating (kW) for the connection:

Slab (kWh and/or kW)	Total Tariff ( ₹/kWh)
0-200 (< 20 kW Connection)	8.47
>200 (<20 kW Connection)	12.21
20 kW – 50 kW Connection	12.98
> 50 kW Connection	15.96

It can be observed that higher the consumption, higher the rate charged to the customer. Following table lists the typical monthly bills for different types of consumers:

Consumer/Rate	Monthly Consumption (kWh)	Bill (₹)
Residential	250	1,870
Residential (Uses AC)	500	4,862
Housing Society Water Pump/Resdential	1600	21,588
Housing Society Lifts and Lights/Residential	1000	12,059
Commercial (100 sq meters)/LT20kW	1500	17,567
Large Commercial (400 sq meters)/LT20-50kW	6000	77,880

Consumers with high consumption pay a higher rate per unit of electricity. Use of solar power with net-metering saves tremendously for such high consumers. For residential consumers and commercial consumers with a lower power connection (<20 kW), net-metering effectively brings down the slab under which the consumer gets billed.

Calculation for Return on Investment (ROI)

It is easy to calculate ROI, given all the preceding data. High consumers get the best ROI as they are being charged a high rate for their electric consumption. To calculate ROI, it is necessary to start with system size in kW and price/kW. The system size translates into average electricity generated per month. For the purpose of this blog, I am using the number for Pune of 4.19 kWh/kW/day. This implies that a 1 kW solar panel in Pune will generate on the average 4.19 kWh/day. This requires the solar panel to be installed at an optimal angle, pointing south. The generation for Pune is slightly less than the average for India. The daily generation is multiplied by 30 to calculate the monthly generation. To calculate ROI it is necessary to know the average monthly consumption and the corresponding tariff. The generated units are subtracted from average consumption to calculate the billable units and the monthly bill. This directly translates into monthly and yearly savings. For instance, water pumping in our housing society consumes 1600 units per month on the average. We are evaluating a 12 kW system with a price of ₹70,000/- per kW. This corresponds to a total investment of ₹8,40,000/-. The 12 kW system will generate 1508 kWh/month. This will result in a savings of ₹21,140/- per month and ₹2,53,683/- per year. The yearly savings correspond to a gross return of 30.2% on the investment. This ROI is excellent and corresponds to a payback period of a little over 3 years. Since the life of system is very long (25 years) and there is hardly any maintenance requirement apart from weekly cleaning of panels, the net return on investment is expected to be well over 20%.

The gross ROI will vary depending on the system installed and the average monthly consumption for the given application. The following table summarises the ROI values for various combinations:

Application	Monthly Consumption (kWh)	System Size (kW)	Price	Monthly Generation (kWh)	ROI %
Residential	250	1	₹1,00,000/-	126	13.89%
Residential	500	3	₹2,55,000/-	377	19.59%
Housing Society	1000	5	₹3,75,000/-	629	28.24%
Housing Society	1600	12	₹8,04,000/-	1508	31.55%
Commercial (<20 kW)	1500	10	₹7,00,000/-	1257	26.31%
Commercial (20-50 kW)	6000	25	₹15,00,000/-	3143	32.63%

Understanding the Impact of ROI Numbers

• For a residential customer consuming 500 units per month, it will be very attractive to get an ROI of 19.59% on investment. Even after subtracting 7% for depreciation and maintenance, the ROI works out to be 12.59%. This is much better than investment in a bank fixed deposit or a debt mutual fund, both of which typically yield 7% – 9% before income tax.
• For housing societies, electricity bills for pumping water, common lighting, and lifts are usually the major contributors in monthly expenses. These societies typically have fixed deposits in bank and the interest on the same is used to pay a part of the bills. An ROI in the range of 30% makes solar power so attractive that I don’t see any reason not to switch to solar power, unless there is no shadow-free rooftop space available.
• For a commercial establishment, an ROI in the range of 26 to 32% is extremely attractive. It is also possible to claim the benefit of accelerated depreciation, which will increase the ROI to more than 40%. It will be worth taking a loan to install such a system. It may even be worth paying for the space on terrace to install such a system.
• For smaller residential customers (250 kWh/month) the ROI of 13.89% is marginally better than a fixed deposit in bank. Electricity rates are expected to keep rising in the future and the ROI will only improve.

Conclusion

A revolution is now underway and I won’t be surprised if every building with a shadow-free rooftop space starts using solar electric power in the next 3 years.

Reference: Calculators for Solar Energy

CO2 At Record Levels and the Brightest Minds on Earth

There were three interesting news items in the Times of India, Pune Edition, today. The first one talked about CO2 in atmosphere reaching levels not seen in a million years. The Mauna Loa Observatory recorded CO2 at 410.28 ppm. Slowly, but surely, the CO2 levels are leading earth to a permanent climate change and associated disaster. The second news item on the same page relates to Google Inc. which, after a decade of research, opened the self-driving cars to general public. Surely, this technology requires the brightest minds on earth to develop the necessary algorithms and technology. The third news item on the page shows a picture of Larry Pages’s flying car. Again a demonstration of brightest engineers at work for a project with investment from a very intelligent and rich investor!

It is indeed sad that the brightest minds are working on solving problems that hardly are problems in the first place. If anything, self-driving cars and flying cars will lead to more cars, more energy consumption, and more CO2 in atmosphere. In a certain sense, the innovations behind these technologies are hardly innovations when you compare them with the work of scientists and mathematicians a century or more ago. For instance, compare these with the work of Newton, Edison, Tesla, Leibniz, Bernoulli, Pasteur, Fleming and hundreds more which profoundly made a difference. I know that this can be a very controversial statement. I am not saying that it is ‘simple’ to develop self-driving cars; it is just not a problem for the brightest minds on earth to spend their time on. It seems that a majority of bright young people are attracted to study computer science and associated specializations. Who doesn’t want to work on cool stuff that also is very likely to lead to tremendous prosperity? However, climate change and associated topics are very often perceived as ‘old world’ and non-cool. Considering the pace at which CO2 levels are increasing, it is very clear that only a few bright people are working on that problem. They need lots more…..

 

Now Saving 30,000 Liters/Day in Our Pune Housing Society

Simple Engineering Solutions to Save Water

This year (2015-16) has been a year of severe water crisis in Pune and our housing society faced a major reduction in water supply from the Pune Municipal Corporation. This housing society consists of four buildings, each with 11 floors and 33 apartments. The water use in our society has always been excessive. The bathroom fittings installed by the builder are of great quality as far as looks are concerned. However, they assume an infinite supply of water! These bathroom fittings were the primary reason for the excessive water use. Once the water crisis hit us, we implemented a number of innovative but simple measures which are helping save about 30,000 liters of water each day. This blog-post describes some of the simple engineering solutions that helped us save water. They can potentially be implemented in every housing society with high-rise buildings and the so-called modern bathroom fittings.

Key Principle:

Water saving can be achieved by reducing the flow of water from each outlet. In our case, the water flow ranged from 7 liters/minute to more than 20 liters/minute, depending on the floor where the measurement was carried out. It was considered necessary to reduce the flow to, 3 to 5 liters/minute for every outlet, except the toilet flush. At this flow rate, usability is not affected in any way. Water flow through any outlet is directly proportional to the area of aperture (of washer) of an outlet and to the square-root of the pressure head. This implies that the water flow is proportional to the square of radius for a circular aperture and to the square-root of height of water tank above. Hence, water flow can be reduced significantly by simply using washers which have a smaller aperture. [Ref: Bernoulli’s Principle]

Implementation:

We implemented special washers for washbasin taps and showers. Since ‘water-saving’ washers were not available in the market, we made tap washers at home. For the shower, it was necessary to use Aluminum washers, which were made with the help from a local workshop. The cost of making washers for the washbasin was less than Rs. 5/- per outlet. These washers were made using a 1.5 mm thick sheet of Silicone rubber. The washers for shower were made in Aluminum by a local workshop for less than Rs. 20/- per piece. For the kitchen taps, it was possible to implement a solution similar to the washbasin. However, we chose to replace the complete aerator assembly with a flow controller available in the market. This flow-controller is well designed but costs Rs. 300/- per outlet. It wasn’t an option to use this flow-controller for every faucet and for every apartment in the entire society as the cost would be prohibitive. Secondly, these flow-controllers were not available for the shower and we desperately needed to save the water used for taking showers.

Design:

The washers for washbasin are mounted on the aerator assembly, which is removable. The washer is cut from a Silicone rubber sheet. Silicone rubber is easy to cut and can sustain high temperatures. The washer in the picture below has a central hole of 4 mm diameter. There is another (optional) hole of 1.5 mm diameter between the central hole and the edge. The second hole is useful to obtain a better aerated flow on the upper floors. The size and the number of holes can be changed, depending on the type of aerator and the desired water flow on a given floor. The central hole was punched with the help of a single-hole punch, available in stationery shops. The smaller hole was punched with a leather punching tool, available online or in some hardware shops. Even a cobbler can help punch the holes.

Water-Saving Washer

Aerator Assembly

Aerator Assembly With Water-Saving Washer

The washer for shower is made using Aluminum since the support provided by an aerator (as a base) is not available for the shower. Aluminum, being stronger than rubber, does not buckle due to water pressure. This washer is installed by first unscrewing the shower-head with a spanner and then installing the Aluminum washer below the original rubber washer. The diameter of the central hole depends on the floor (pressure head). On lower floors, with higher water pressure, a 2 mm or 2.5 mm hole was used. On upper floors, a 3 or 3.5 mm hole was necessary. These washers were made with the help of a local workshop that worked with sheet metals.

Aluminum Washer for Shower

Shower Head and Aluminum and Rubber Washers

Shower Head with Washers Installed

Calculations:

In my apartment on the 8th floor, water savings were calculated to be 320 liters/day:

1. Kitchen sink: 125 liters/day : 25 minutes/day * 5 liters/minute
2. Washbasin: 90 liters/day : 30 minutes/day * 3 liters/minute
3. Shower: 105 liters/day : 30 minutes/day * 3.5 liters/minute

The amount of savings on the lower floors is expected to be higher. It was estimated that about 30,000 liters of water is being saved per day, based on actual measurement of water usage from the underground tank. This water saving also implies a saving in the energy use, both for the society and for the individual apartments.

Caveats:

1. This implementation assumes that an easily removable aerator is part of the faucets. This is true for most modern faucets. The aerator provides space for fitting the water-saving washer. The shower-head also needs to be removable.
2. We did not implement any solution for the toilet flush valves. While it is certainly possible to use the same principle, it was observed that the installed flush valves do not provide an easy access to implement a modification.

Note:

1. We did not require a skilled plumber to carry out the installation. Either the apartment resident or a handy-man installed the washers.
2. Silicone rubber sheet is available fairly easily. In Pune, I purchased it from Budhwar Peth. Workshops that work with sheet metals are generally present in most cities.
3. It is necessary to clean the aerator and washer under running water to avoid accumulation of dirt etc. This is required anyway, whether water-saving washers are installed or not.
4. On the lower floors, where pressure can be very high, it is necessary to use a Teflon tape (white tape used by plumbers) when installing to avoid leakage. This is available in any hardware store.
5. For someone interested in implementing this in their society, I can be reached via comments on this blog, where you can provide your contact information. I don’t have any commercial interest in this; the idea is to save water in high-rise buildings where excessive water use takes place.
6. Last, but not the least, this change requires cooperation by society management and a few willing residents who don’t mind experimentation in their home, before a large scale implementation.

The Concept of Entropy and its Importance

A Simple Explanation of Entropy

<Based on my book: http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=ISBN+148409834X&gt;

The concept of entropy originates from the second law of thermodynamics. Energy tends to flow from a concentrated form to a dispersed form. For instance, petrol (gasoline) is an example of energy stored in a concentrated form. When an automobile engine burns petrol, the energy stored in petrol is released and gets dispersed in various forms. The energy is partly dispersed as hot gases, as heat transferred to the parts of the engine, and partly as mechanical work that gets done in the engine to move the automobile. Finally, all the energy obtained by burning petrol gets dispersed in the surroundings as heat. The energy so dispersed is not accessible anymore to do any useful work and such energy is termed as the unavailable energy. Entropy is essentially the unavailable energy and the second law of thermodynamics states that the entropy of the universe always increases. This implies that every energy conversion adds to unavailable energy.

To do any useful work, we need concentrated sources of energy and the ability to control when and how much energy will be released and utilized. In this process the concentrated source of energy gets dispersed and a part of the energy becomes unavailable. It is not possible to create a concentrated source of energy without giving a larger energy input that must come from some other concentrated source! For instance, hydrogen gas has a stored energy content of 123 MJ/kg. It has more stored energy per kg than petrol. However, hydrogen gas is not found in nature in the basic molecular form (H₂) required for combustion. To obtain hydrogen gas by electrolysis of water, it is necessary to provide an energy input that is larger than the energy contained in hydrogen. Quite obviously, it is meaningless to carry out the electrolysis using electricity obtained by burning coal. There will be multiple energy conversions in the entire process and primary energy spent per kg of hydrogen so obtained will be much larger than the 123 MJ obtained by combustion of hydrogen. Petroleum is a concentrated source of energy that was created in the crust of the earth as a part of various geological processes. While it is possible to create petroleum products in the lab, the primary energy required to create such products will always be larger than what is obtained by their combustion.

These examples illustrate the fact that as energy sources are consumed, it is not possible to create them by processes that do not use some other concentrated source of energy. In other words, the depletion of energy sources is an irreversible process. The only energy source that won’t deplete for about a billion years is the sun. Hence, the civilization cannot hope to be dependent on the fossil fuels forever. The decline of fossil fuels is inevitable and at some point in the future, it will be necessary to switch entirely to the use of solar energy, either in direct or indirect form.

Another important point that comes up based on the concept of entropy is that before proposing or advocating any new method of energy conversion or a new source of energy, detailed thermodynamic analysis is an absolute necessity. In absence of such an analysis, a wonderful idea in the lab may not provide any net energy.

To sum up, entropy and the second law of thermodynamics occupies a prime position among the laws of nature. Most of the struggle to find alternative sources of energy is essentially a struggle against entropy, which makes it so difficult. It is fairly common to read in newspapers about entrepreneurs, enthusiasts, and economists to have found a solution to the energy crisis. Yet, none of them turn out to be real solutions that are actually workable. It will be worthwhile to use an old quote from Sir Arthur Stanley Eddington that sums up the problem that most enthusiasts do not realize:

“If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations – then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation – well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.”

This quote may be modified in the current context to be:

“You may find the elusive Higgs Boson at CERN by putting together the most brilliant scientific minds and spending billions of dollars; but finding a solution to the energy crisis that somehow beats the second law thermodynamics is a hopeless quest.”

Solar Water Heaters Without Vent Pipes

Air-vent pipes are integral parts of most solar water heaters. This blog-post discusses the design of solar water heating systems without vent pipes. My previous blog-post discussed some of the problems due to vent pipes for systems installed on high-rise buildings. However, these problems may be relevant even when solar water heating systems are installed on not-so-tall structures. Before finding alternatives for vent pipes, let us understand the function that vent pipes perform.

Vent Pipes: Function

As the name suggests, the primary function of a vent pipe is to vent air from a solar water heater and associated pipes. As a solar water heater is filled with water, air needs to be vented out. Air, being lighter than water, tends to rise to the highest point in the system. The vent pipe, which rises a few meters above the heater, provides a path for air to be vented out to the atmosphere. Once air has been vented out, water rises in the vent pipe up to a level that corresponds to the input water pressure. For instance, a solar water heater connected to an input water tank that rises 4 meters above the water heater must have a vent pipe that rises to the same height.

Another important function of a vent pipe is to accommodate the thermal expansion of water. Water expands with the rise in temperature. For a 150 litre water heater, the expansion in volume is about 30 ml per degree Kelvin rise in temperature. Since water is not a compressible liquid, space must be provided to allow for this expansion. In a system with a vent pipe, water level will rise in the pipe with a rise in temperature. Allowing space for water to expand in the vent pipe prevents an excessive rise in pressure inside the water heater.

An air-vent pipe also protects the solar water heater by preventing vacuum formation. It provides path for air to enter the system if water were to be drained out of the storage tank for whatever reason. Without path for air to enter the tank, atmospheric pressure may cause the tank to collapse.

Vent Pipes: Problems

My previous blog-post discussed problems related to the use of vent pipes. Here is a quick summary:

• There is a risk of lightning strike when vent pipes rise high above the roof. This risk is elevated in the case of high-rise buildings.
• Long vent pipes result in an additional loss of heat and reduce the net thermal efficiency.
• It is necessary to tie vent pipes with strong cables to avoid damage in the case of strong winds. Installation of several solar water heaters on the roof creates a big mess and an eye-sore.

Solar Water Heaters Without Vent Pipes

A system that does not make use of a vent pipe must make alternative arrangements that perform the function of a vent pipe.:

Venting Air:

It is possible to make use of air-vent valves to perform this function. An air-vent valve typically contains a plastic float and a lever that can operate to seal an air-passage. The air-vent valve is installed at the highest point in the system. As water is filled in the solar water heater, air escapes to atmosphere via the air-vent valve. Water rises and eventually reaches the float in the vent valve. Rising water raises the float which operates a lever to close the air-passage. This closes the system, implying that it is no longer open to atmosphere. A closed system must be protected against excessive rise of pressure and also from vacuum formation. An air-vent valve usually protects against vacuum formation too. When hot water in a solar water heater is used, it is replenished with cold water that enters via the inlet. However, if the inlet valve is closed for any reason, there is a risk of vacuum formation when water is drained. With an air-vent valve, any reduction in the water level causes the float in the valve to lower, opening the air-passage, preventing vacuum formation.

Pressure Release Valve:

An air-vent valve does not address the problem of excessive pressure rise due to increase in water temperature. Water is not a compressible liquid. Lack of space inside the storage tank for water to expand can result in a buildup of pressure that can damage the storage tank as well as other parts of the solar water heater. Typically, the hot-water tank has some space above the water outlet, where air is trapped. As water expands, this air is compressed to allow for the expansion of water. However, this causes a rise in the pressure inside the tank. This pressure rise is governed by gas laws and is not as dramatic as the one caused by a lack of space for expansion of water. However, even a temperature rise of 10 degree Celsius can result in sufficient pressure rise to cause problems. For instance, the version of Honeywell evacuated tube solar water heater installed at my place is rated for an operating pressure of 0.5 bar. A rise in pressure to 1 bar results in the evacuated tubes and tanks to shift which lead to leakages. An even higher rise in pressure can result in damage too. A Pressure Release Valve (PRV) is required to protect against such damage. A PRV is preset to operate at a certain pressure. When pressure inside the solar water heater tank rises above this pressure, it causes the PRV to operate to release some water/air to the surroundings. This action reduces the pressure inside the system and the PRV closes automatically to seal back the system. Care must be taken to choose the preset pressure to match the specifications of the solar water heater. In such a system, the PRV should operate whenever there is a significant temperature rise. The amount of water released on operation of the PRV is very small compared to the capacity of the solar water heater. For instance, for a 150 litre system, a 10 degree Celsius rise in temperature implies a 300 ml increase in the volume of water. It will be sufficient to drain this volume of water to normalize the pressure. Care must be taken to test the valve periodically to make certain that the valve is not stuck. Salts and other impurities in water can make the valve ‘stick’ as water dries.

Expansion Tank:

An expansion tank can be used as an alternative to PRV. It provides space for thermal expansion of water, avoiding excessive rise in pressure. No maintenance is generally necessary for expansion tanks, unlike PRVs which require periodic checking. The size of expansion tank is large, as compared to a PRV. For instance, for a 150 litre solar water heater, an eighty degree temperature rise will result in an additional space requirement of 2.4 litres due to thermal expansion of water. The expansion tank must provide for this space and more in order to avoid excessive pressure rise.