Main author

Paul Dodgshun Engineer
Last edited 07 Dec 2016

Domestic heat pumps and the electricity supply system

This article can be read as an extension of Kevin Pennycook's article: Air-source heat pumps - pros, cons and considerations for specifiers, January 2009.

Contents

[edit] Findings

1: An efficient, small, air-to-air (A2A) heat pump has an efficiency that is twice the average of that demonstrated by big air-to-water (A2W) pumps tested by the Energy Saving Trust (EST). This results in the small A2A running at half the cost of mains gas. This might also be expected to halve the electricity consumption (and generation) needed for domestic heat pumps.

2: Both A2A and A2W heat pumps can operate in an 'under-sized' condition where the economics of operation are compromised. The 'under-sized' condition is unstable and considerable reductions in heat load on the pump must be made to get a pump to recover to normal running. 'Under-sized' running requires yet more generation.

3: As heat engines, heat pumps obey Carnot's Law and the pressure/enthalpy diagram for the refrigerant in question. Making a domestic heat pump pump to high temperature (say 60C), as compared to pumping to a low temperature (say 30C) halves the efficiency (Coefficient of Performance CoP) is general terms. It also halves the maximum capacity. Efficiency and capacity get worse when 'under-sizing' starts.

4: The consequences of the three previous points on the generation, transmission and distribution system can be demonstrated. The biggest single issue raised is the distribution system. Currently, this loses about 8% of the electricity that passes through it.

Doubling the distribution currents in the same wires would cause the losses to rise by a factor of four to 32%. The fitting of big heat pumps in houses requires significant reinforcement of the underground cabling and its transformers and that requires works to all the roads with supply cables underneath, possibly repeatedly. The renewable generation with backup plant, as well as the grid system will also require significant reinforcement. All this must be made large enough to meet peak loads when all the big heat pumps start up together on a cold winter's evening.

This suggests that the concept needs changing to a system based on small A2A that runs continuously through the winter heating season. A 1kW(electrical) A2A in each of 29 million homes would require peak generation of 29GW. That is a bit more than half the current maximum demand and on that basis is at least a credible target. It is probable that this demand could be met by a doubling of the distribution system.

It is even possible that domestic CHP generation will take over and little of this will be needed at all.

[edit] An evaluation of the efficiency of an A2A heat pump installed in my house

'If a heat pump is used in place of a modern gas-condensing boiler, the carbon savings may be less clear-cut.’ Ref BSRIA.

Burning 6000kWh of gas at a cost of 5p/kWh and producing 5000kWh of heat in a 'modern gas-condensing boiler' costs 6000*0.05=£300. Using 1000kWh of electricity at a price of £0.15p/kWh in a heat pump with a Seasonal Coefficient of Performance (SCoP) of 5.0 produces 5000kWh of heat at a cost of 1000*0.15=£150. The pump runs at half the cost of mains gas. My A2A pump used 921kWh last winter and I believe that the above calculation is accurate, so I think that the quote must refer to A2W pumps with an average SCoP of 2.5.

The Effect on the Annual Billing of Running a 0.45kW A2A Heat Pump in my house:


Elec Domestic

Elec Pump

Mains Gas Burn

Gas Reduction at Autumn 2014

W14/15

3417

953

8214

3468

921

9446

1232

3321

921

9383

1169

W13/14

3373

808

11732

3518

3285

190

16081

7867

3524

0

20441

12226

3267

0

20535

12321

W12/13

3184

0

19872

11658

3010

18766

10552

2848

15291

7077

2671

15165

6950

W11/12

2695

14090

5876

Notes:

  1. Readings are from the electricity and gas billing meters and an in-line meter on the pump supply.
  2. Readings are in kWh on a rolling annual basis i.e. the summation of four quarterly bills, the current quarter and the three previous quarters.
  3. The W12/13 winter was long and cold. The W11/12 winter is a better match to W13/14.
  4. On the basis of this table, it is considered that a saving of 6000kWh of gas, through the use of a bit less than 1000kWh of electricity in the pump is a reasonable presentation.
  5. The rated CoP of the pump is 5.7 @A7/A20.

[edit] An evaluation of the consequences of running A2A and A2W heat pumps in the 'under-sized' condition

A2A Heat Pump 'under-sizing' Performance Test on 29/12/2014.

The appended test report demonstrates the complete economic failure that attaches to running in the 'under-sized' condition. 'Under-sizing' is a physical condition where the heat pump loses its ability to generate sufficient heat to prevent the actual temperature in the house falling below the desired temperature.

When a pump slips into 'under-sizing' its electrical power rises to a maximum whilst its heat output falls. The crucial point is that to remove the pump from this 'under-sized' state without shutting down requires a major reduction in the heat demand of the house. In other words, the 'under-sized' condition is unstable. If you go a little bit into 'under-sizing', you go all the way and stay there until you do something fairly drastic. That is where the high heat pump bills come from.

A lot of the poorly performing A2W pumps in DECC's test report spend a lot of time in the 'under-sized' condition. The A2W tested last winter certainly did. It ran 'under-sized' continuously in ambient temperatures of 5C at a cost of 4*24*0.15=£14.40 per day or £432 per 30 day month. The A2A, running properly and continuously at about 333watts, uses 0.33*24*0.15=£1.20 per day or £36 per 30 day month.

Which is the better choice? An 'under-sized' 4kW A2W or an efficient 0.45kW A2A; just a factor of 12 difference in running cost. The A2W failed to heat the house properly, whilst the A2A was fine. Also the A2W cost about eight times as much to buy as the A2A.

Ambient temperatures were -1.5C at 0600.

The sky was cloudless and ambient temperatures rose steadily throughout the test.

Time_ _ Pwr_ _ Blr In_ Out _ _Set Pt _Amb _ Notes

0950 _ 300 _ _ 19.2 _ _ 28.5 _ _ 21 _ _ 1.0 _ _ All doors shut except 3 1000_ _ 293 _ _ 19.0 _ _ 27.4 _ _ 21 _ _ 2.0 _ _ 1005_ _ 295 _ _ 18.9 _ _ 27.2 _ _ 21 _ _ 2.5 _ _ All doors opened 1010_ _ 385 _ _ 18.7 _ _ 29.0 _ _ 21 _ _ 2.5 _ _

1015_ _ 480 _ _ 18.6 _ _ 32.4 _ _ 21 _ _ 3.0 _ _ Whole house heated

… stable at high load ... 1050_ _ 470 _ _ 18.7 _ _ 34.0 _ _ 21 _ _ 5.5 _ _

Set Pt +1 → 22C. Fan noise up.

'Under-sized' condition starts 1055_ _ 645 _ _ 18.8 _ _ 35.9 _ _ 22 _ _ 6.0 _ _ 1100_ _ 675 _ _ 18.8 _ _ 36.2 _ _ 22 _ _ 6.0 _ _ Set Pt -1 → 21C 1105_ _ 560 _ _ 18.7 _ _ 33.7 _ _ 21 _ _ 6.5 _ _ 1110_ _ 640 _ _ 18.7 _ _ 35.0 _ _ 21 _ _ 6.5 _ _ No recovery of normal running 1115_ _ 665 _ _ 18.7 _ _ 36.3 _ _ 21 _ _ 7.0 _ _ 1120_ _ 665 _ _ 18.8 _ _ 36.5 _ _ 21 _ _ 7.0 _ _ 1125_ _ 665 _ _ 18.8 _ _ 36.4 _ _ 21 _ _ 7.5 _ _ 1130_ _ 665 _ _ 18.9 _ _ 36.4 _ _ 21 _ _ 7.5 _ _ Lounge door shut 1135_ _ 655 _ _ 18.9 _ _ 36.4 _ _ 21 _ _ 8.0 _ _ 1140_ _ 670 _ _ 19.0 _ _ 36.7 _ _ 21 _ _ 8.0 _ _ 3 bedroom doors shut 1145_ _ 630 _ _ 19.0 _ _ 36.4 _ _ 21 _ _ 8.0 _ _ Fan noise down 1150_ _ 605 _ _ 19.2 _ _ 36.0 _ _ 21 _ _ 8.5 _ _ 1155_ _ 605 _ _ 19.5 _ _ 36.0 _ _ 21 _ _ 9.0 _ _ 1200_ _ 560 _ _ 19.6 _ _ 34.7 _ _ 21 _ _ 9.0 _ _ 1205_ _ 535 _ _ 19.6 _ _ 34.4 _ _ 21 _ _ 9.5 _ _ 4th bedroom door shut 1210_ _ 430 _ _ 19.7 _ _ 33.3 _ _ 21 _ _ 9.5 _ _ 1215_ _ 315 _ _ 20.0 _ _ 31.6 _ _ 21 _ _ 9.5 _ _ 'Under-sized' condition ends

1220_ _ 316 _ _ 20.0 _ _ 30.1 _ _ 21 _ _ 10.0 _ _ Normal running.

1225_ _ 319 _ _ 20.0 _ _ 30.3 _ _ 21 _ _ 9.5 _ _ 4 bedroom doors opened 1230_ _ 310 _ _ 19.5 _ _ 29.0 _ _ 21 _ _ 10.0 _ _ Lounge door opened 1240_ _ 312 _ _ 19.1 _ _ 29.1 _ _ 21 _ _ 10.0 _ _

1250_ _ 445 _ _ 18.9 _ _ 33.7 _ _ 21 _ _ 9.5 _ _

… stable at high load ... 1400_ _ 415 _ _ 19.0 _ _ 33.0 _ _ 21 _ _ 9.0 _ _ Test ends. All doors open

Notes:

1: 'Doors' means internal doors (8 in total) that connect to the hall where the pump is located. 2: From stable high load at 1050 at Set Pt 21C, a Set Pt increase of 1C increased Pwr from 470 to 675watts. This increase started the 'under-sizing' test. 3: Recovery from 'under-sizing' lasts from 1100 to 1215. Progressively the Set Pt was reduced back to 21C, the lounge door shut, 3 bedroom doors shut and finally a 4th bedroom door shut to get back to normal running. 4: With normal running achieved at 1220, all doors were open at 1400 when the test ended. By then the ambient temperature had increased from 2.5C at 1005 to 9.5C which should have assisted the recovery of normal running. 5: This test provides an indication of the large heat load reduction required to recover a pump in the 'under-sized' condition. 6: The quick reversal of the Set Pt increase of 1C failed to return the pump to the previously stable condition. Five more doors had to be closed to recover normal running whilst the ambient temperature also rose by about 6.5C between 1005 and 1250. 7: The 'under-sized' condition is an instability that requires considerable intervention to reduce heat loads to recover the normal operation. 8: The 'under-sized' condition compromises the economics of running a heat pump. This has nothing to do with the excessive operation of back-up resistive electrical heaters which are another cause of high bills.

[edit] The basic theory of heating a house with a heat pump

'An advantage of air-to-air heat pumps over air-to-water heat pumps is the lower sink temperature (the temperature of the air passing over the condenser coil). This results in a higher COP and increased heat output. (COPs increase with reduced difference between source and sink temperatures.)… At temperatures higher than these the COP (and heat output) will fall. This means that heat pumps, although potentially suited to low temperature heating systems (such as underfloor heating), have poor COPs when used with conventional hydronic heating systems with high circulation temperatures, such as 60oC or higher. High flow temperatures will result in a lower heat pump COP, while lower flow temperatures will require greater radiator surface area.' ’ Ref BSRIA.

The heat output of a heat pump is equal to the electrical power times the CoP.

Heat = Power x CoP

Heat pumps are limited by the size of the compressor motor, so the maximum heat output of a pump is also limited. From the equation above, it can be seen that the maximum heat output of a fixed size pump is also a variable that depends on the CoP. Halve the CoP and you halve the maximum heat output.

So what can be done to halve the CoP of a pump at the design stage? Instead of making the pump pump to 30C, make it pump to 60C. Carnot's Law provides the formula and the pressure/enthalpy diagram the engineering evaluation. The maximum theoretical CoP is equal to the Th/(Th-Tc) where Th and TC are the hot and cold refrigerant temperatures in a running pump, expressed in degrees absolute.

CoP(5/30)=(273+30)/(30-5)=303/25=12.12

CoP(5/60)=(273+60)/(60-5)=333/55=6.05

The ratio is 12.12/6.05=2

A pump, pumping between 5 and 30C, uses half as much electricity as a pump, pumping between 5 and 60C to deliver the same amount of heat. Alternatively, a pump pumping between 0 and 60C can only produce half the maximum heat output of the same pump pumping between 0 and 30C. One statement deals with economy and the other deals with capacity and both are true at the same time.

To run a pump at 60C outlet temperatures, it has to double the size of a pump running at 30C outlet temperatures, in order to heat the same house. This is a big problem if the pump size is based on the standard conditions of A7/W(30/35) and it drives the radiators of a fossil-fired boiler that operates at 65C. This is certainly one cause of 'under-sizing'.

[edit] An evaluation of the overall efficiency of A2A and A2W supplied by fossil-fired generation from the grid

'Electrical energy from the National Grid is carbon inefficient when the low thermal efficiency of power stations is taken into consideration, along with distribution losses over the grid.' Ref BSRIA.

General:

  • Fuel Supply: Fossil, nuclear, renewables
  • Generation: Spin an AC generator but Solar PV is static
  • If fuel supply is renewable, add in a backup generator, almost certainly mains gas
  • Winter wind is about 25% of capacity, so backup is 75% gas
  • Transmission: Mostly long-distance wires on pylons at up to 400kV
  • Distribution: Mostly local and underground cable at 11kV, 3.3kV and 415V
  • Heat Pumps: Commercial and domestic

Specific:

  • Methane: Mains gas
  • CCGT: Close cycle gas turbines
  • 400kV: High voltage grid system
  • 11/3.3kV/415V: Distribution cabling and transformers
  • Domestic A2A or A2W: Air-to-Air or Air-to-Water Heat Pumps

Efficiency:

  • CCGT: 0.80
  • Grid: 0.97 # National Grid number
  • Distribution: 0.92 # National Grid number
  • 1: A2A: SCoP 5.0 # My own pump with a rated CoP of 5.7 at A7/A20
  • 2: A2W: SCoP 2.5 # EST Field Trials
  • 3: 'Under-sized' A2W: SCoP 1.64 # Test result

Overall Efficiency:

CCGT generation:

  • 1: = 0.80*0.97*0.92*5 = 3.57 # So 1kW of gas gives 3.57kW of heat in a house
  • 2: = 0.80*0.97*0.92*2.5 = 1.78 # So 1kW of gas gives 1.78kW of heat in a house
  • 3: = 0.80*0.97*0.92*1.64 = 1.17 # So 1kW of gas gives 1.17kW of heat in a house

This paints a rosy view of overall generation efficiency.

A typical large coal efficiency would be 0.35:

  • 1: = 0.35*0.97*0.92*5 = 1.56 # So 1kW of coal gives 1.56kW of heat in a house
  • 2: = 0.35*0.97*0.92*2.5 = 0.78 # So 1kW of coal gives 0.78kW of heat in a house
  • 3: = 0.35*0.97*0.92*1.64 = 0.51 # So 1kW of coal gives 0.51kW of heat in a house

Double the grid currents without reinforcement due to heat pump load with CCGT:

Heat losses are proportional to current squared (so-called I^2*R losses), so grid efficiencies become (1-4*0.03)=0.88.

  • 1: = 0.80*0.88*0.92*5 = 3.24
  • 2: = 0.80*0.88*0.92*2.5 = 1.62
  • 3: = 0.80*0.88*0.92*1.64 = 1.06

Double the distribution and grid currents without reinforcement due to heat pump load with CCGT:

  • 1: = 0.80*0.88*0.68*5 = 2.4
  • 2: = 0.80*0.88*0.68*2.5 = 1.2
  • 3: = 0.80*0.88*0.68*1.64 = 0.79

0.88*0.68 = 0.60 # The electricity losses in grid and distribution are 40%.

Essentially, with the highest possible CCGT efficiency and an A2W pump, you are achieving almost nothing. With 1kW of coal and an A2W, the answer becomes 0.35*0.60*2.5 = 0.53kW. 1KW of coal, 'under-sized' A2W and doubled currents give 0.35*0.6*1.62 = 0.34kW.

In practice you cannot double the currents, as the power dissipation heats the wires and that makes them expand. The grid system is limited by line sag. If you want to double the grid currents then you need to add a parallel line of pylons. There is a current example of this; the constraint payments to Scottish wind farms have rocketed recently because the four grid circuits into England are overloaded. A sub-sea cable from Hunterston on the Clyde to Connah's Quay on The Wirral is currently being installed to take this constrained output.

The underground distribution cabling is similarly limited as are all the transformers, so you need a parallel line of underground cabling and parallel transformers.

In conclusion, new heat pumps in aggregate will require in quantity new, matching:

  • Distribution systems, including the various transformers.
  • Grid lines, and conventional generation, or renewable generation with backup which may have to be the less efficient OCGT.
  • The aggregate cost of big A2W is very high.

This article was created by --Paul_Dodgshun

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