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Learn through experiments

Enough energy, at the wrong time

Why can equal daily generation and demand still require grid energy?

1 · Try

Start with a concrete question

Original synthetic six-period energy schedule in kWh: generation [0, 2, 8, 4, 0, 0] and demand [2, 2, 2, 2, 4, 2]. Storage starts empty.

Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.

Go directly to the experiment · Review basic mathematics

2 · Predict

What do you expect?

Generation and demand both total 14 kWh at scale 1. Predict grid imports with no storage and with a 4 kWh battery.

3 · Experiment

Change one thing. Inspect what happens.

  1. Set capacity to zero and inspect when generation is unused and demand unmet locally.
  2. Set capacity to 4 and efficiency to 100%; compare imports and curtailed energy.
  3. Reduce efficiency to 80% and inspect charge input separately from stored energy.
  4. Increase capacity to 12. Explain why the first period still requires the grid even with ample later generation.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Grid import4 kWh
Curtailed energy3 kWh
Charge losses1 kWh
Energy remaining0 kWh

Compare the current results

Every bar starts at zero and uses the same numeric scale in this chart. The upper bound automatically adjusts to the largest current value (at least 1), so compare the numbers when changing inputs. Units and quantities come from each label; different kinds of quantity are not interchangeable. Displayed values are rounded to at most six significant digits.
02
  • Period 1 grid (kWh)2
    Period 1 grid (kWh): 2Horizontal bar from zero to 2, on the shared zero to 2 numeric axis.
  • Period 2 grid (kWh)0
    Period 2 grid (kWh): 0Horizontal bar from zero to 0, on the shared zero to 2 numeric axis.
  • Period 3 grid (kWh)0
    Period 3 grid (kWh): 0Horizontal bar from zero to 0, on the shared zero to 2 numeric axis.
  • Period 4 grid (kWh)0
    Period 4 grid (kWh): 0Horizontal bar from zero to 0, on the shared zero to 2 numeric axis.
  • Period 5 grid (kWh)0
    Period 5 grid (kWh): 0Horizontal bar from zero to 0, on the shared zero to 2 numeric axis.
  • Period 6 grid (kWh)2
    Period 6 grid (kWh): 2Horizontal bar from zero to 2, on the shared zero to 2 numeric axis.

Follow the calculation

  1. Period 1: generation 0.00, demand 2, direct 0.00; charge input 0.00, loss 0.00, discharge 0.00, grid 2.00, stored 0.00 kWh.
  2. Period 2: generation 2.00, demand 2, direct 2.00; charge input 0.00, loss 0.00, discharge 0.00, grid 0.00, stored 0.00 kWh.
  3. Period 3: generation 8.00, demand 2, direct 2.00; charge input 5.00, loss 1.00, discharge 0.00, grid 0.00, stored 4.00 kWh.
  4. Period 4: generation 4.00, demand 2, direct 2.00; charge input 0.00, loss 0.00, discharge 0.00, grid 0.00, stored 4.00 kWh.
  5. Period 5: generation 0.00, demand 4, direct 0.00; charge input 0.00, loss 0.00, discharge 4.00, grid 0.00, stored 0.00 kWh.
  6. Period 6: generation 0.00, demand 2, direct 0.00; charge input 0.00, loss 0.00, discharge 0.00, grid 2.00, stored 0.00 kWh.

Total generation alone does not determine grid reliance: timing, storage capacity, and conversion losses also matter.

Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.

4 · Understand

Explain the mechanism

What the experiment explains

Original synthetic six-period energy schedule in kWh: generation [0, 2, 8, 4, 0, 0] and demand [2, 2, 2, 2, 4, 2]. Storage starts empty.

Energy totals hide timing. Direct generation is used first; surplus can charge storage, but future generation cannot supply an earlier shortfall.

At 80% charging efficiency, accepting 5 kWh stores 4 kWh and loses 1 kWh. A full 4 kWh store cannot accept the entire 6 kWh surplus in period three.

The model counts grid imports, unused surplus, charging losses, and ending storage separately so the energy balance can be checked. It does not convert energy into emissions without an explicit emissions model.

Read the relationship

Charge input = min(surplus, free capacity / efficiency). Added storage = charge input × efficiency. Grid import = demand − direct generation − storage discharge. All energies are kWh.

Use the trace as evidence

The trace recomputes from your current controls. Change one control at a time, record what changed, and compare the result with your prediction. The bars use the same quantities as the numerical trace; a larger bar is not automatically a better outcome.

Boundaries of the model

  • No charge/discharge power limits, self-discharge, prices, lifecycle impacts, or grid emissions.
  • Only charging has losses; discharge is ideal. Schedule and parameters are invented teaching values.

Continue with A full reservoir can hide a shortage to investigate a different mechanism.

5 · Apply

Try a fresh case

New two-period case: demand [1, 4], generation [6, 0], empty storage capacity 3 kWh, charging efficiency 100%. How many kWh must the grid supply?

This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.

Take the investigation further

Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.

School investigation

Check that generation plus imports equals demand plus losses, curtailment, and final storage.

College investigation

Add power limits and implement a dispatch policy that can be compared with this greedy rule.

Workplace investigation

Write an energy proposal separating measured demand, assumed generation, cost, and emissions evidence.

6 · Continue

Keep the evidence, choose your next step

Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.