Match power, energy and service timing

Define the requested quantity before comparing totals

Power describes how quickly energy is transferred. Energy describes the amount transferred over an interval. The model requests 4 kW of electrical service during each of four consecutive one-hour intervals, totaling 16 kWh. This is a four-hour study window, not a complete day or a measured school load.

A defined electrical request is not automatically equal lighting, comfort or other end-use service across different devices. For this investigation, the load at the modeled electrical bus is stipulated. Write that boundary and the time window beside your prediction so a comparison does not quietly change its purpose.

Convert power to energy with units attached

For a constant power P over duration h, energy E = P × h. A 2 kW device operating for 3 hours uses 6 kWh. It does not have a resulting power of 6 kW. Return to circuit power for the connection between electrical quantities and this energy account.

Within each one-hour model bin, numerical kW and kWh values happen to match. This is a duration convention, not an identity between their units. A 4 kW output sustained for half an hour supplies 2 kWh; the same power for two hours supplies 8 kWh.

Make a paper table with one column for interval power and another for interval energy. Do not combine them into a single unlabeled axis. A total-energy comparison can conceal a time mismatch even when every arithmetic conversion is correct.

Compare equal available totals at different times

Select no storage and steady generation. Available powers are [4,4,4,4] kW, matching demand in every bin. All 16 kWh is delivered locally; grid import and unserved demand are zero. Record this baseline before changing the generation timing.

Now choose middle periods, [0,8,8,0] kW, with no storage. It has the same 16 kWh available. In the two middle bins, demand uses 4 kWh each and the other 4 kWh per bin is curtailed potential. In the first and last bins, the grid provides its allowed 1 kWh each but leaves 3 kWh per bin unserved.

The result is 8 kWh used local generation plus 2 imported, giving 10 served and 6 unserved. Capture both settings. Explain why equal available energy did not establish equal supplied service: neither timing nor the limited support source can be discarded from the comparison.

Close two distinct accounts

The middle-period case has an availability allocation of 16 available + 2 grid = 10 served + 8 curtailed potential. Its physical bus account is 8 used local + 2 grid = 10 served. The second account excludes potential that was never generated into this bus.

Unserved demand compares a requested 16 with delivered 10. It is not another 6 kWh of physical output. Similarly, do not add local supply a second time merely because it appears as both an arrow and a contribution to served demand. Keep the request ledger and physical account separate.

The dispatch rule uses local input first and grid support last, with storage between them if selected. It is a stipulated policy, not optimized scheduling. A real system study would need more detailed demand, resource and equipment evidence before translating these four bins into reliability claims.

Transfer: change the duration

A separate fictional interval requests 3 kW for two hours. An available generator can supply 2 kW throughout, with no storage or grid support. Calculate requested, delivered and unserved energy. State why an unserved-energy result alone does not describe every consequence of the interruption.