PV Row to Row Spacing


If your system consists of two or more rows of PV panels, you must make sure that each row of panels does not shade the row behind it. To determine the correct row-to-row spacing, refer to the figure above.

There is no single correct answer since the solar elevation starts at zero in the morning and ends at zero in the evening. The sunshine (irradiation) on an array has three components, direct beam, diffuse (blue sky and overcast), and reflected from the ground in front of the array. Here we will consider only the direct beam that is subject to shadowing by the row in front (or even a wall).

The elevation of the sun at noon on December 21st in the Northern Hemisphere is basically 90-23.45-latitude (in degrees). In most cases 90% of the unobstructed irradiation on the array occurs when the solar elevation is above 50% of the maximum winter elevation. The elevation correction is therefore 50%. This may be excessive for rows that are less than about 4 times the height of the panel.

To solve for X (the minimum distance between the rows), use the equation below:

X = L (cos(tilt)+ (sin (tilt) * tan (lat + 23.5+(50% of elevation))))


L = panel length
tilt= panel tilt angle
lat= geographic latitude of your system.

Calculated values are:

Winter minimum noon solar elevation = 90-23.45-latitude
90% of unobstructed elevation = 50% of Winter minimum solar elevation

The Excel spreadsheet version of this is:

Spacing Excel

The Excel formula can be copied >>> =B1*(COS(B2*PI()/180)+(SIN(B2*PI()/180)*TAN((B3+23.5+B5)*PI()/180)))

Effect of PV Array Orientation - Phoenix AZ

The following chart shows the calculated PV system output for a system in the Phoenix, Arizona area for a variety of array orientations. The calculations assume an open array in free air such as a pole mount or parking canopy without anything under the modules. Mounting PV modules on a roof reduces the output due to the higher temperatures. PV modules mounted flush with a roof, but with at least 3” of space below the modules and mounting structures that allow some air flow, will have an annual energy reduction of about 6%. Of course, these calculationa assume no shadows on the PV array.  The calculations include normal inverter efficiency, wire loss, and an allowance for dirt.
In the chart the upper line shows the roof pitch (4/12 represents 4" of slope per 12" of roof), the angle the pitch represents, and the direction the PV module face (NW=North-West, etc.).The larger number is the annual output in kilo-Watt-hours (kWhr) per year for a PV array with a nominal rating of 1000 Watts.  For instance, if the PV array has 20 PV modules with a rating of 310 watts (STC) per module, the array is rated 6.2 kilo-Watts DC (kWdc). To estimate the annual output using this chart, simply select the closest orientation, such as South facing at 3/12 pitch, and multiply the 1668 by 6.2 to get the annual output of 103,416 kWhr.
kWhr vs orientation Phx

The Challenge of Storing Energy


All sources of energy have some level of intermittency, they are not always available when needed. The reliability range is wide, utility supplied electric or gas energy seldom fails while we know that the sun is not available to operate photovoltaic (PV) or thermal systems at night. Our needs for energy also vary from critical full time (example: network computer servers), to critical when needed (example: emergence lighting), to use it while it is available with no problem with loss of operation (example: cathodic protection systems).

Key to reliable power is redundancy, having multiple sources of power. For utilities this usually means multiple generating stations and multiple transmission paths to ensure delivery of power. For applications not connected to a reliable power grid, the alternate power source can be small emergency generators or battery backup.

Most renewable energy sources, solar and wind being the main sources, are intermittent by their very nature. If continuous power is required, they need to be backed up by energy storage or generators. The most common combination is PV power systems with batteries. In these systems the PV system is designed to provide enough energy to meet the energy needs and recharge the battery. As such the size is based the worst case during the year with safety factors added for year to year differences, longest expected periods of low sunshine, and the expected degradation of equipment as it ages. The result is rather high energy costs because at many times of the year the energy produced by the PV array exceeds needs and is not harvested.

More popular these days are PV systems that are utility connected and any excess energy is either banked with the utility (net metering) or sold to the utility (net billing). Since most of these utility connected systems generate energy only when the utility is functioning, there is also the ability to design the system to include energy storage. There are many options, see the AZSC separate article on (title and article needed covering AC vs DC coupled storage, demand reduction, backfeed limiting, etc. based on 2019 products).

There are many aspects to energy storage, size can range from very small (battery or capacitor) to very large (pumped hydro), many technologies, safety aspects, to name a few.  There is no easy way of describing this wide range of technologies, but we will start with some definitions.

There are two basic terms for defining storage, Power and Energy:

Watt: A unit of Power, one Watt is the rate at which work is done when one ampere (A) of current flows through an electrical potential difference of one volt (V). Items like light bulbs are rated in watts. Power is the rate at which energy is generated or consumed and hence is measured in units (e.g. watts) that represent energy per unit time. Electrical demand is a power term, usually measured in kilo-Watts (kW).

Watt-hours: A unit of Energy, defined as power over a time interval. One watt of power for one hour is one Watt-Hour. Often used with the prefixes Mega for 1-million (mWh) and Kilo for 1-thousand (kWh).


The suitability of a storage technology is determined primarily by its power and energy capacity and the rate at which these can be stored and delivered. Other characteristics to consider are round-trip efficiency (how much energy is lost from charging and discharging), cycle life (how many times the technology can charge and discharge at a particular depth of discharge [e.g., 80% or 100%]), safety, and ramp rate (how fast the technology can respond to a command).

Other metrics to consider include specific energy and specific power. Specific energy is a measure of energy per unit mass of an energy storage system. Specific power is defined as the power per unit mass of an energy storage system. When specific power and energy are high, the weight of the energy storage system tends to be lower per kW/kWh. See the Figure below for a comparison of specific power and specific energy for each of the many of the energy storage technologies presently available. Optimal characteristics of energy storage technology include high specific energy and specific power, but these features are often costly and not necessary for every application.

 Comparison of Specific Power and Specific Energy

The above graphic covers battery technologies from the point of view of large scale energy storage.  It was extracted from a good report that is worth reading: ENERGY STORAGE TECHNOLOGIES WHITE PAPER by the Port of Long Beach

The basic physics of energy storage

There are three basic ways to store energy; electrochemical, mechanical and electrical.

Electrochemical methods basically change one element or compound into another wherein the process is reversible (the energy can later be recovered). Examples include breaking water into its components of hydrogen and oxygen (H₂O into H₂ and O₂) and lead-acid batteries (PbO₂ + Pb + 2H₂SO₄ into 2PbSO₄ + 2H₂0), more on these later. 

Mechanical methods utilize physical forces such as gravity (pumped hydro), angular momentum (flywheels), pressure (compressed air), and heat.

Electrical storage includes capacitors and inductors. Some energy storage combine elements of these ways.


After APS explosion injures 4 firefighters, Arizona cities enact battery storage laws for utilities, homeowners

There is an interesting, but non-technical, article in the Arizona Republic about batteries in PV systems.

Most of the major Phoenix area cities have documents that detail the requirements for new solar systems and it is likely that the cities will be updating their documents soon with battery requirements.

After APS explosion injures 4 firefighters, Arizona cities enact battery storage laws for utilities, homeowners