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.

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

 

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