Is (Wind + Solar) Better Than (Wind or Solar)?

IEEE-PES Little Rock Chapter Virtual Meeting

Prof. Mack Grady, ECE, Baylor UniversityProf. Emeritus at U.T. Austin

IEEE Fellow

December 15, 2020

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ERCOT has added Solar MW to their Real Time Web Site(Here is what I have thus far. If any of you want recorded once-per-

minute data, let me know)

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Month-Day

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1,500,000 W ÷ 4657 m2 = 322 W / m2

Note - in bright sun, PV produces about 150 W / m2

GE 1.5 MW

1 m / sec = (1 / 1609) miles / sec = (1 / 1609) miles / sec * 3600 sec / hour = (1 / 1609) miles / sec * 3600 sec / hour 1 m / sec = 2.237 miles / hour

31 mph

8 mph

56 mph

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GE 2.5 MW

2,500,000 W ÷ 7854 m2 = 318 W / m2

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GE 3.6 MW

3,600,000 W ÷ 9677 m2 = 372 W / m2

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Most Efficient Energy Capture is whenDownwind Wind Speed = 1/3 of Upwind Wind Speed

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Betz Limit

Wind turbines do have inertia. Separate from physical positioning, wind turbines constantly “dither” blade pitch angles to find Pmax for the given wind intensity.

If a number of turbines were used to find report Pmax to other turbines, the other turbines could be forced to at (Pmax minus a desired Pinertia = 5%,10%, etc.)

In case of a system wide event that requires more inertia, the turbine could quickly adjust to Pmax, thus having a response similar to inertia.

sec)/()(sec)/(

mvmRrad

vSpeedTipTSR

wind

rotorrotor

wind

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2

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21

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21..

,21..

AvdtdxAvP

dtdmvEK

dtdP

mvEK

x distance

Power is Proportional to Air Density, Blade Swept Area, and (Wind Velocity)^3

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For any given temperature, air density (and wind power) drop about 15% per 1000 meter rise in elevation.

To have the same air density as sea level, temperature must drop about 35 degrees C per 1000 meter rise in elevation (which is not likely to happen).

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Hey, I’m down here

From Google Earth, the “Heading” is 339.7⁰, so the Sun’s Azimuth φ is (337.7 – 180) = 159.7⁰. From the 1-min data columns underneath the figures, the time corresponding to 159.7⁰ is 11:55 CST, and the Sun’s Zenith angle is ϴ=51.0⁰ . Hub height H is calculated according to the diagram on the right. L is shadow length

ϴ

H

L

Vertical

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July 1 through July 31, 2020. Vertical lines are at Midnight UTC (7pm CDT). Wind generation tends to peak when total load is moving rapidly down to minimums.

On the other hand, maximum solar power will be in the 12:15pm to 1pm time period across Texas. Dual tracking panels, commonly seen in West Texas, will extend into higher load levels in late afternoons.

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Where is the Sun?

Figure 4. Sun Zenith and Azimuth Angles

West

North(x axis)

Line perpendicular to horizontal plane

East(y axis)

Horizontal plane

Up (z axis)

zenithsun

azimuthsun

Note – because of magnetic declination, a compass in Austin points approximately 6º east of north.

• (Latitude) at the spring and fall equinoxes,

• (Latitude – 23.5º) at the summer solstice,

• (Latitude + 23.5º) at the winter solstice.

The sun’s zenith angle at solar noon is

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Panel Orientation is Important

• Best all-year tilt = Latitude

• Best winter tilt = Latitude + 15°

• Best summer tilt = Latitude – 15°

tiltpanel

Line perpendicular to horizontal plane

tiltpanel

Horizontal plane

Figure 6. Panel Tilt Angle

Line perpendicular to panel surface

Edge of panel

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Computing Incident Power, cont.

panelincidentzenithsun

incident ADHGHDHP

)cos(

)cos()(

The incident solar radiation, in kW, on a panel surface is approximated by

About 14% is converted to electricity

Est. disk of sun component on sensor pointed toward sun

Measured sky on shadowed horizontal sensor (excludes

disk of sun)

Est. disk of sun component on panel surface

Multiply by surface area

Est. Watts on panel surface

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90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 2700

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Array Azimuth

Array TiltPredicted PV Performance in Austin for September 2008, Daily kWH per kW Installed

5.6-5.85.4-5.65.2-5.45-5.24.8-54.6-4.84.4-4.64.2-4.44-4.23.8-43.6-3.83.4-3.63.2-3.43-3.2

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0.00.20.40.60.81.01.21.4

0 30 60 90 120 150 180 210 240 270 300 330 360 390Day of Year

SAN ANGELO.  Ratio of Actual PV kWh/kW to Corresponding Weather and Angle Corrected Estimate

0.00.20.40.60.81.01.21.4

0 30 60 90 120 150 180 210 240 270 300 330 360 390Day of Year

CEDAR HILL.  Ratio of Actual PV kWh/kW to Corresponding Weather and Angle Corrected Estimate

Analysis of PV Performance for Texas Parks and WildlifeFactors in Actual Sun Intensity and Fixed PV Mounting Angles

100524.034.5)( 1777.0 VeVI

Solar Panel I-V Curve

Voc

Isc

Pmax at approx. 30V

Pmax 0.7 • Voc • Isc

PV Station 13, Bright Sun, Dec. 6, 2002

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0 5 10 15 20 25 30 35 40 45

V(panel) - volts

I - a

mps

Isc

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PV Station 13, Bright Sun, Dec. 6, 2002

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

0 5 10 15 20 25 30 35 40 45

V(panel) - volts

P(pa

nel)

- wat

ts

The Maximum Power Point

Pmax

On a good solar day in Texas, you get about 1kWh per square meter of solar panels

(corresponds to about 150W rated)

P=0 at short circuit P=0 at open circuit

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PV has no inertial. Separate from physical solar tracking, inverters constantly “dither” to find Pmax for the given sun position and intensity.

If a number of panels were used to find and report Pmax to other panels, the other panels could be forced to operate at (Pmax minus a desired Pinertia = 5%, 10%, etc.

In case of a system wide event that requires more inertia, the inverters could quickly adjust to Pmax, thus having a response similar to inertia.

Partly Cloudy Afternoon

Amorphous Array Pmax (Rated = 150W)

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11.5 12.0 12.5 13.0 13.5 14.0Hour

W

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Corresponding P Drawn from Neighboring 190W Panel Connected to a Back-of-the-Panel 240Vac Inverter

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Cloud pattern moving 10-20 meters/sec

A repeating pattern.  The circles represent moving shadows due to clouds.  When no shadow, use panel clear sky Pmax for the given time of day and panel 

orientation.  When inside a 50‐second diameter (see A), use Pmax / 3.  When inside a 5‐second circular transition ring (see C – A), assume linear variation 

between Pmax and Pmax / 3. 

2 mins 

5 sec 

50 sec 

A C 

For cloud shadow speed = 10 m/s, A =   500 meters, C =   600 meters

For cloud shadow speed = 20 m/s, A = 1000 meters, C = 1200 meters27

• Cloud shadow pattern moves across the distribution system in 1-second steps.

• Shadow depth at each bus is computed, and the PV power at that bus is adjusted accordingly.

• Loadflow and Harmonic Loadflow Re-Solved• Process continues in 1-second steps, saving

bus voltages and powers at each step

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-0.018-0.016-0.014-0.012-0.010-0.008-0.006-0.004-0.0020.000

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PU V

olta

ge D

rop

Minutes

Voltage Magnitude Ripple, 50% PV, Wind = 10 m/s, Azimuth = 315 deg

Bus 15

-0.018-0.016-0.014-0.012-0.010-0.008-0.006-0.004-0.0020.000

0 5 10 15 20 25

PU V

olta

ge D

rop

Minutes

Voltage Magnitude Ripple, 50% PV, Wind = 10 m/s, Azimuth = 0 deg

Bus 15

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Sun Zenith Angles for Little Rock

June 22

September 1

December 15

PV is great in summer time

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ERCOT Load MW, Nov 22 - 28, 2020

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ERCOT Load MW, Nov 29 – Dec 05, 2020

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ERCOT Load MW, Dec 06 – Dec 12, 2020

ERCOT;s Comments: Solar and wind may be complementary resources With wind and solar variability, the two resource types may be able to assist one another during the course of a day. In general, wind tends to blow more during the late afternoon to mid-morning hours during the summer, while the solar potential occurs during the day. In the future, solar power may be able to help meet load demands when wind is lower during the middle of the day; likewise, wind power can ramp up to meet decreasing solar output in the evening and overnight hours.

areare

will

MG’s suggestions

Is (Wind + Solar) Better than (Wind or Solar)?The Answer is YES!

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Smart Grid Course Design Project. 2020_1130. This 25 bus subset of ERCOT shown on the next slide has 138kV and 69kV transmission lines. Not all busses are shown around Marfa and Alpine due to congestion. The arrows at the top are connections to the “stiff” portion of ERCOT. There are three power paths to Marfa, and one path from Marfa to Shafter and Presidio.

Step #1. Use the PCFLO loadflow program to analyze the grid “as is.” Use bus 6655 Barilla as the swing bus with V = 1.05 pu, and 6630 Fort Stockton as a fixed voltage bus that can be adjusted 1% to 2% from Barilla V to help prevent line overloads on the three red-circled transmission lines flowing toward Marfa. If necessary, you can add shunt capacitors at busses, in 300 kVAr increments, to hold bus voltages in the (0.95 to 1.05 pu range). Perimeter busses are usually the best locations.

Step #2. Individually outage the three red-circled transmission lines to determine how much load must be shed (if any) to prevent line overloads, and determine where additional shunt capacitors (in 300 kVAr increments) should be added to hold bus voltages in the (0.90 to 1.05 pu) range. (lower voltage is acceptable during outages).

Step #3. Using your Step #1 modifications (not your Step #2 modifications), determine the largest integer MW solar plant that can be installed at your assigned blue bus. The solar plant does not produce MVArs, so you can add shunt capacitors at any busses, in 300 kVAr increments, to hold bus voltages in the (0.95 to 1.05 pu range). It is possible that, with generation, some voltages will go above 1.05.

Step #4. Repeat the Step #2 procedure using your Step #3 plan. Develop a PPT that shows your results, and illustrates how your proposed solar MW affects the grid. Are more capacitors required? Do solar MW reduce the load shedding needed when individual red-circled lines are outaged?

Step #5. Next, using what you learn in the above steps, what else can be done to increase the solar MW capability? For example, are larger transmission line conductors needed, i.e., wires paralleled to reduce resistance and approximately double the line rating? Are higher-rated substation transformers needed? Do some lines need a parallel line?

Step #6. Prepare a PPT that explains your recommendations of the amount of solar MW that can be added, how it can reduce load shedding during outages, and how that value can be larger is selected grid modification improvements are made.

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665366556630

6680

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6668

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6663

6002

66676666

38496676

66916692

6677

6689

66826690

6683

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Shafter

Presidio

69 kV138 kVMcDonald Observatory

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#1 #2#3

#4#5

#6

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41MG’s photo of Shafter. A silver mine was here prior to WW2. It is the ghost town in Sci-Fi movie “The Andromeda Strain.”

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Photo courtesy of McDonald Observatory. The Observatory has hosted our first remote Texas Synchrophasor Network PMU since 2008.