Solar energy: photovoltaic and solar thermal

The price of solar photovoltaic modules has fallen by roughly 90 percent over the past fifteen years, and solar is now the largest source of new generating capacity in much of the world. Winnipeg is not a sunny place in winter, but its summers are long and bright, and its annual sunshine is better than that of much of Germany, which has built a very large solar industry. Northgate owns a large flat roof on its plant building, several hectares of land beside its yard, and a network that could take solar heat in summer. Tomás has been asked to estimate what solar electricity and solar heat could each contribute, and how well they match the network's needs.

The solar resource

Outside the atmosphere the Sun delivers about 1,361 W/m² on a surface facing it. At the ground on a clear day near noon the irradiance is about 1,000 W/m², the reference value used to rate solar modules. Irradiance has a direct component, the beam from the Sun's disc, and a diffuse component scattered by the sky and clouds; on cloudy days nearly all of it is diffuse. Over a year the energy received depends on latitude, climate and the orientation of the surface. It is measured in kilowatt-hours per square metre per day or per year, and one kilowatt-hour per square metre is the energy of one hour of sunshine at the reference irradiance, which is why the daily value is often called peak-sun hours.

Tilting a surface toward the equator increases the energy it collects. In Winnipeg, at about 50° N, a south-facing surface tilted at roughly the latitude angle collects about 1,600 to 1,750 kWh/m² a year, compared with about 1,300 to 1,400 kWh/m² on a horizontal surface. Steeper tilts favour winter production and shed snow better; flatter tilts favour summer. Single-axis trackers, which turn the modules to follow the Sun from east to west, add 15 to 25 percent more energy at extra cost and are common on large solar farms.

How a photovoltaic cell works

A photovoltaic cell is a semiconductor junction, usually in crystalline silicon. A photon with enough energy frees an electron from its bond, creating an electron and a hole; the electric field at the junction separates them, driving a current through an external circuit. Photons with less energy than silicon's band gap of about 1.1 eV pass through unused, and the extra energy of more energetic photons becomes heat. These two effects limit a single-junction silicon cell to an efficiency of about 30 percent in theory. Commercial modules today convert about 20 to 23 percent of sunlight to electricity at standard test conditions of 1,000 W/m², 25 °C cell temperature and a standard spectrum. A module rated at 400 W under those conditions is said to be 400 Wp, watts peak.

Cell efficiency falls as temperature rises, by about 0.3 to 0.4 percent per kelvin for crystalline silicon. In full sun a module runs 20 to 30 K above the air, so summer output is lower than the rating suggests, while on a cold, bright winter day it can exceed its rating. Bifacial modules, which collect light on both faces, gain extra energy from light reflected off the ground, especially from snow.

From modules to a system

Modules are wired in series strings to reach a voltage suitable for an inverter, which converts their direct current to alternating current synchronized with the grid. The performance ratio of a system is the ratio of its actual energy to the energy its rated modules would produce at the measured irradiance with no losses; it captures temperature effects, inverter efficiency, wiring losses, soiling, shading, mismatch between modules and downtime. Well-designed systems reach performance ratios of 0.80 to 0.88. In snowy climates, snow cover can remove a large share of winter output from modules tilted at shallow angles.

# Solar PV yield by month with a temperature derate, and a flat-plate solar thermal collector
SITE = 'ca'
# Monthly plane-of-array irradiation (kWh/m2 per month, south-facing, tilt about 45 degrees) and mean daytime air temperature (C)
d = {'ca': dict(city='Winnipeg',
                poa=[95, 125, 160, 165, 170, 165, 175, 170, 140, 110, 75, 75],
                tair=[-14, -11, -3, 7, 15, 20, 23, 22, 15, 7, -3, -11]),
     'us': dict(city='Minneapolis',
                poa=[100, 125, 155, 160, 170, 170, 180, 170, 145, 120, 85, 80],
                tair=[-8, -5, 2, 10, 17, 23, 25, 24, 18, 10, 2, -5])}[SITE]
kWp = 1000.0                     # 1 MWp array
gamma = -0.0035                  # power temperature coefficient per K (crystalline silicon)
pr_other = 0.86                  # inverter, wiring, soiling, mismatch, availability
snow = [0.70, 0.80, 0.90, 1, 1, 1, 1, 1, 1, 1, 0.95, 0.75]   # fraction of output kept after snow cover
months = 'Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec'.split()
tot = 0.0; rows = []
for m in range(12):
    tcell = d['tair'][m] + 25.0               # cell runs about 25 K above air in sun
    ft = 1 + gamma*(tcell - 25.0)
    E = kWp*d['poa'][m]*ft*pr_other*snow[m]/1000   # MWh (irradiation in kWh/m2 = peak-sun hours)
    tot += E; rows.append((months[m], E, ft))
print(f"{d['city']}: 1 MWp south-facing array")
for name, E, ft in rows:
    print(f"  {name}: {E:6.1f} MWh   temperature factor {ft:.3f}")
print(f"Annual yield {tot:,.0f} MWh, specific yield {tot*1000/kWp:,.0f} kWh/kWp, capacity factor {tot/(kWp/1000*8760):.3f}")
print(f"Share produced Nov-Feb (heating season peak): {sum(r[1] for r in rows if r[0] in ('Nov','Dec','Jan','Feb'))/tot*100:.0f} %")
# Flat-plate thermal collector efficiency  eta = eta0 - a1 (Tm - Ta)/G
eta0, a1 = 0.78, 3.8
for Tm, Ta, G in ((40, 20, 800), (60, -10, 600), (75, 20, 800)):
    eta = eta0 - a1*(Tm - Ta)/G
    print(f"Collector at mean {Tm} C, air {Ta} C, sun {G} W/m2: efficiency {max(eta,0):.2f}")

Winnipeg: 1 MWp south-facing array
  Jan:   60.0 MWh   temperature factor 1.049
  Feb:   89.3 MWh   temperature factor 1.038
  Mar:  125.1 MWh   temperature factor 1.010
  Apr:  138.4 MWh   temperature factor 0.976
  May:  138.5 MWh   temperature factor 0.948
  Jun:  132.0 MWh   temperature factor 0.930
  Jul:  138.4 MWh   temperature factor 0.919
  Aug:  134.9 MWh   temperature factor 0.923
  Sep:  114.1 MWh   temperature factor 0.948
  Oct:   92.3 MWh   temperature factor 0.976
  Nov:   61.9 MWh   temperature factor 1.010
  Dec:   50.2 MWh   temperature factor 1.038
Annual yield 1,275 MWh, specific yield 1,275 kWh/kWp, capacity factor 0.146
Share produced Nov-Feb (heating season peak): 21 %
Collector at mean 40 C, air 20 C, sun 800 W/m2: efficiency 0.69
Collector at mean 60 C, air -10 C, sun 600 W/m2: efficiency 0.34
Collector at mean 75 C, air 20 C, sun 800 W/m2: efficiency 0.52

The specific yield of about 1,280 kWh per kilowatt-peak a year, a capacity factor of about 0.15, is typical of the northern plains. A 1 MWp array produces about 1.3 GWh a year, about what a 0.5 MW heat pump uses in 2,600 hours at full load. But the timing is poor for heating: only about a fifth of the output comes in the four darkest months, when Winnipeg's heat demand peaks.

Rooftops, fields and long-term performance

Solar arrays can be mounted on roofs, over parking lots, on the ground or on floating platforms. Rooftop systems use space that has no other value and deliver power at the point of use, but they are smaller, cost more per watt and must respect roof loads, fire access paths and wind uplift. Ground-mounted arrays are cheaper per watt and can use trackers, but they need land, a fence and a grid connection. Some farms now combine solar with grazing or crops beneath raised modules, an approach called agrivoltaics. Over their 25 to 35 year lives, modules lose about 0.3 to 0.7 percent of their output a year, and inverters usually need replacing once or twice. Snow loads, hail and freeze-thaw cycles are the main weather risks in the northern plains, and modules and racking are tested for them. A long-term yield estimate should include degradation, inverter replacement and occasional storm damage as well as the first-year output.

Cost and the value of solar electricity

Large ground-mounted solar farms in North America now cost roughly 1 to 1.5 million per megawatt of alternating-current capacity, and rooftop systems more. Their levelized cost is among the lowest of any new generation in sunny regions and is competitive in the north. The value of solar electricity is a separate question. Because all solar plants in a region produce at the same time, a large amount of solar on a grid depresses prices in sunny hours, and its value per megawatt-hour falls as more is built. Storage, flexible loads and the ability to export restore some of that value.

For Northgate, a solar array on its own land would supply electricity mostly in summer, when its heat pumps run little. Manitoba Hydro buys small amounts of customer generation under net metering rules, but Northgate's electricity is already almost carbon free and cheap, so an array would cut costs only modestly and cut carbon hardly at all.

Solar thermal collectors

Solar thermal collectors turn sunlight directly into heat. A flat-plate collector has a dark absorber plate under a glass cover, with fluid tubes bonded to the plate and insulation behind. Evacuated-tube collectors surround each absorber with a vacuum to cut heat loss and suit higher temperatures and cold climates. The instantaneous efficiency of a collector is often written

where \(\eta_0\) is the optical efficiency, \(a_1\) the heat loss coefficient, \(T_m\) the mean fluid temperature, \(T_a\) the air temperature and \(G\) the irradiance. At low temperature differences a good collector converts 70 to 80 percent of sunlight to heat, far more than a photovoltaic module converts to electricity. At the 60 to 80 °C supply temperatures of a district network in cold weather, efficiency falls sharply.

Large solar thermal fields connected to district heating networks are common in Denmark, where dozens of towns have fields of several hectares, many with large seasonal storage pits that hold summer heat for the autumn. In a fourth-generation network with low return temperatures, a solar field can supply 10 to 20 percent of annual heat, and with seasonal storage up to about half. The field and the storage pit both need land near the network, which Northgate has at its yard. Solar thermal fields compete with photovoltaic arrays driving heat pumps; at high latitudes and with low-temperature networks, the two are often close in cost, and photovoltaics have the advantage that their electricity can be sold when heat is not needed.

The team's conclusion is that solar energy is a modest contributor for a northern heating utility: valuable in summer, cheap per kilowatt-hour, but unable to help on the design day. Its role in the plan is to supply part of the summer heat and electricity and to reduce the hours that other plant must run, not to provide capacity.