# Heat pumps and useful heat Level two · L2-HEAT · 12.09.2026 Source, heat user, seasonal operation and measured system performance. ## Starting asset Teaching system T-01 has four operating bins lasting 1,200, 1,600, 1,200 and 400 hours. Heat loads are 3, 5, 8 and 10 kW; heat-pump COP values are 4.5, 3.7, 2.8 and 2.2. External auxiliaries consume 450 kWh per season. These are teaching characteristics and do not describe a particular equipment brand. ## Outcome Calculate a system across operating conditions and prepare its test and acceptance programme. ## 1. Start with source and heat user Describe both sides of the installation: where heat originates and where it becomes useful. The source needs temperature, available flow, seasonality, contamination and permitted cooling. The user needs supply and return temperatures, flow, demand schedule and backup requirements. Refrigeration heat may be available in summer when space-heating demand is low. Its usefulness depends on matching schedules, required temperature and transfer cost. Keep both time series in the project record. For each source, identify operating constraints and the owner confirming availability. ## 2. Choose the performance boundary Operating-point COP is useful heat output divided by electrical input at the same point and boundary. Seasonal performance uses energy totals. Establish whether circulation pumps, defrost, controls and backup heating are included. The protocol needs a diagram showing heat and electricity meter locations. When both cooling and heating are useful products, show both outputs and the chosen cost-allocation method. Adding flows requires a defined balance and clearly described useful services. ```text COP = P_heat / P_electric SPF_system = Σ Q_useful / (Σ E_heat_pump + E_aux + E_backup) ``` ## 3. Calculate the season by operating bins Multiply each bin’s heat load by its duration and divide by the matching COP. T-01 delivers 3,600, 8,000, 9,600 and 4,000 kWh across the bins, totalling 25,200 kWh. Heat-pump electricity is approximately 8,208.92 kWh. Including external loads gives 8,658.92 kWh and a system seasonal factor of about 2.91. The arithmetic average of four COP values ignores the energy distribution. Choose bin resolution to suit the calculation. A final design needs equipment performance data and a time series covering material operating conditions. ```text Q_i = P_heat,i × hours_i E_heat_pump = Σ (Q_i / COP_i) ``` ## 4. Temperature lift and heat distribution For comparisons, fix source temperature and the temperature required by the heat user. Obtain pump data for that operating point. Changes to emitters and supply temperature can affect whole-system efficiency and required capacity. Use a flow heat balance for a water loop. At 10 kW and a 5 K water temperature difference, required flow is about 0.478 kg/s, or 1.72 m³/h at 1,000 kg/m³ density. The specific heat of 4.18 kJ/(kg·K) is an approximation here. For glycol mixtures, verify properties and pressure losses at the actual concentration and temperature. ```text P_heat,kW = mass_flow,kg/s × cp,kJ/(kg·K) × ΔT,K ``` ## 5. Cold conditions, backup and starts Compare unit capacity under the coldest condition with building load under that same condition. Define backup heat share, electrical capacity and coordination logic. In T-01, replacing one quarter of the final bin’s heat with resistance heating transfers 1,000 kWh of heat to backup. This increases seasonal electricity by about 545.45 kWh: backup uses 1,000 kWh instead of 454.55 kWh from the heat pump. Separately check simultaneous starts, defrost, minimum load and start frequency. Include manufacturer limits in the control specification. ## 6. Buffer storage and timing Estimate stored water heat from mass, specific heat and the usable temperature swing. A 500-litre tank with a 10 K usable swing theoretically stores about 5.81 kWh. At a 5 kW load this is approximately 1.16 hours before losses, mixing and supply-temperature constraints. A tank should solve a stated problem: hydraulic coordination, fewer starts or load shifting. For each purpose, check losses, added pumps and temperature changes. Design around usable volume and measured behaviour, particularly where stratification matters. ```text E_buffer,kWh = mass_kg × cp_kJ/(kg·K) × ΔT_K / 3600 ``` ## 7. Measure the economics of useful heat Useful-heat cost includes all electricity within the chosen boundary, maintenance and capital. A boiler comparison needs fuel price and seasonal efficiency; direct electric heating has a different baseline. Record tariff, currency and calculation date. At a hypothetical €0.18/kWh, T-01 seasonal electricity costs approximately €1,558.60. Dividing by 25,200 kWh of heat gives about €0.06185 per useful kWh for electricity alone. Maintenance and investment increase full cost. Test future prices through scenarios. ## 8. Acceptance and deviation diagnosis Before testing, specify measurement points and conditions: useful heat, electrical energy, temperatures, flow, starts, defrost and backup. Give each check a tolerance and valid measurement conditions. Qualified personnel perform installation and electrical and refrigerant work. If measured seasonal performance falls below the calculation, examine metering boundaries, sensors, temperature schedules, backup operation, hydraulics and demand in sequence. Preserve original settings before changing them. The final report records the discrepancy’s cause and a new test after correction. ## Calculation laboratory Four temperature bins are combined by energy. Change the coldest-bin COP or backup-heating share and compare seasonal SPF. https://x5power.com/Academy/Cold/heat-pumps/?lang=en#lab Each bin COP includes internal unit consumption. External auxiliaries are added once. Backup replaces the specified share of bin-4 heat at a factor of 1. Capacity, defrost and allowable-temperature checks require the equipment documentation. ## Exercises 1. Seasonal energy Sum heat delivered in the four T-01 bins. **Method and reference result** 3,600 + 8,000 + 9,600 + 4,000 = 25,200 kWh. ## Exercises 2. Whole-system factor Calculate electricity including external loads and the seasonal factor. **Method and reference result** 8,658.92 kWh and approximately 2.9103. The factor uses total heat divided by total electricity. ## Exercises 3. Backup heating Transfer 25% of the last bin’s heat to electric backup with a factor of 1. **Method and reference result** Additional electricity is 545.45 kWh; total is about 9,204.37 kWh; system factor is about 2.738. ## Exercises 4. Heat-transfer fluid flow Calculate water flow at 10 kW and a 5 K difference. **Method and reference result** 10 / (4.18 × 5) = 0.4785 kg/s, approximately 1.7225 m³/h at the stated density. ## Exercises 5. Buffer limit How much energy is stored in 500 litres of water over a usable 10 K swing? How long can it cover 5 kW? **Method and reference result** About 5.81 kWh and 1.16 hours in the idealized balance. Include losses and usable delivery temperature in a design. ## Exercises 6. Compare two installations Unit A has a higher rated COP but needs a hotter supply on the actual asset. What data is needed to choose? **Method and reference result** Performance maps under matched conditions, seasonal hours and loads, auxiliaries, backup, available capacity and full useful-heat cost. ## Field project Select a source and heat user. Prepare their records and time series, compare two architectures, calculate seasonal bins and determine backup, flow and electrical capacity. Produce the metering diagram, acceptance programme and settings log. For practical assessment, submit measurements from an installation or tested rig, explain the measured factor’s boundary and analyse deviations from calculation. A brief single-point test supports that operating point. A seasonal claim requires a matching observation period and evaluation method. ## How the work is assessed Academy teaching rubric: 100 points maximum. The calculation defence requires at least 80 points and all mandatory checks. Practical assessment additionally requires an implemented project and measurements. This page prepares the work; it does not issue certificates automatically. - Problem and boundaries: 20. Asset, useful service, units and constraints are defined. - Calculation and data: 25. The main result is reproducible and inputs are traceable. - Result verification: 20. Measurement, comparison and uncertainty match the claim. - Adverse conditions: 15. Failure, changed conditions and recovery are examined. - Operational handover: 10. Owners, acceptance programme and actionable instructions are present. - Transfer to a new asset: 10. New conditions and required adaptations are demonstrated. ### Mandatory checks Units and boundaries are consistent. Every material input has a source. Assumptions and measurements are identified separately. An adverse scenario is tested. The submitted result is reproducible. Practical claims are backed by implemented work. ## Project workbook - Asset and useful service - Boundary, period and units - Inputs and their provenance - Design and alternatives considered - Calculation and testable result - Uncertainty and missing information - Adverse scenario and recovery - Acceptance, owners and follow-up ## Agent assignment Study the book and prerequisites. Reproduce the reference calculation. Solve the exercises before reading the methods. Prepare a project for a new asset. Return inputs with units and provenance, calculation, applicability limits, an adverse scenario, a measurement plan and questions for the human. Give the package to another agent for independent checking. ## Books and primary sources - [SEAI · Publications](https://www.seai.ie/publications). Find Homeowners Guide to Heat Pumps and building assessment material. Compare the guidance with the selected unit documentation. - [EVO · International Performance Measurement and Verification Protocol](https://evo-world.org/en/products-services-mainmenu-en/protocols/ipmvp). Measurement boundaries, baseline and a savings verification plan. Record the chosen protocol edition when applying it. - [NASA · Systems Engineering Handbook](https://www.nasa.gov/reference/systems-engineering-handbook/). Requirements, life cycle, system verification and decision traceability. ## After implementation After one month, check metering and operating conditions. After a season changes, review the forecast and limits. Verify the final claim over its complete stated period. Add new observations to the project history and use them to develop the next exercise. XPower Academy · Alex Ananin and the Echelon group