From 54e877db9b812b8724615fab3835ba5c62933c1f Mon Sep 17 00:00:00 2001 From: Matthew Daubney Date: Thu, 24 Sep 2026 12:47:12 +0100 Subject: [PATCH] Add exercise documents and battery dispatch implementation plan Commits the three source documents for the battery trading exercise (task brief, battery specification, and three years of half-hourly Market 1 and hourly Market 2 prices) together with PLAN.md, the implementation plan for the dispatch model. The plan covers a rolling-horizon MILP on the half-hourly grid with a 48-hour lookahead and 24-hour commitment, solved with PuLP/CBC, plus degradation and cycle-life reporting, an independent schedule validator, charts and tests. Co-Authored-By: Claude Opus 5 (1M context) --- 2nd Round Technical Question.pdf | Bin 0 -> 108246 bytes Attachment 1.xlsx | Bin 0 -> 22861 bytes Attachment 2.xlsx | Bin 0 -> 1606661 bytes PLAN.md | 241 +++++++++++++++++++++++++++++++ 4 files changed, 241 insertions(+) create mode 100644 2nd Round Technical Question.pdf create mode 100644 Attachment 1.xlsx create mode 100644 Attachment 2.xlsx create mode 100644 PLAN.md diff --git a/2nd Round Technical Question.pdf b/2nd Round Technical Question.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8435e5a55ca36d2dc5a8e9aae7295b321b178638 GIT binary patch literal 108246 zcmdSA1yo$kwlxYNxF)y+8Yd9k-6g?2xHeAXZoxuucL?t84grE&aCdjtAg{xBzH^d$ zuKfRacZ@e4gWX+Sd#zn-Rn1*hJ?Cz6IT0~hMmlz61o9g2A2I?XfB|5oZ-$J(!$Ys+ zVhyAh*0a~Murj8X(=!Iz0hqw273ih(K*m%+&|3h#qP?wyfxVI~5U5~fWe;Ftc|I?# zXKVf*WMl=t#;+pK5CAp<^6}A21MT$;!50KDvami|s+aLxW7s)0LJG!a7v=i_Tq~6 zdiFrDkGLW`fc@D*T#*C7@v8*3kh8TiPz2g*(1ZJ$UJ2-IPygN$+?hguy$S#I_WoDQ 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implementation plan + +## Context + +The folder contains a second-round technical exercise (`2nd Round Technical Question.pdf`) asking for a +Python package that models a 2 MW / 4 MWh battery charging and discharging across two wholesale +electricity markets to maximise profit, as a price taker. `Attachment 1.xlsx` gives the battery +specification, `Attachment 2.xlsx` gives three years of prices. Nothing has been built yet — this plan +covers the package from scratch. The exercise is explicitly judged on practical design, clear +communication of process and outcomes, and a codebase that is easy to review — not on squeezing out the +last pound of revenue. + +Decisions already taken with the user: model the **full three years across both markets**, use +**PuLP with the bundled CBC solver**, and include **degradation / cycle-life reporting** plus **charts and +a written results file**. Investment economics (NPV, IRR, payback) and heuristic benchmark comparisons +are deliberately out of scope. + +## What the data actually looks like + +Verified by reading both workbooks directly: + +| Item | Value | +|---|---| +| Market 1 | half-hourly, 52,608 rows, 2018-01-01 00:00 → 2020-12-31 23:30, 465 negative prices, mean £44.45/MWh | +| Market 2 | hourly, 26,304 populated rows (rows 26,306+ of the sheet are blank and must be dropped), mean £47.96/MWh | +| Battery | 2 MW charge, 2 MW discharge, 4 MWh, 5% charge loss, 5% discharge loss, 10 yr / 5,000 cycles, 1e-3 %/cycle fade, £500k capex, £5k/yr opex | + +Two data quirks the loader must handle explicitly: + +1. **Market 2 trailing blanks** — the sheet is 52,608 rows long but only the first 26,304 carry prices. +2. **Spring clock-change labelling** — Market 1 timestamps duplicate `02:00`/`02:30` and skip `01:00`/`01:30` + on 2018-03-25, 2019-03-31 and 2020-03-29. Row counts are nevertheless a clean 48/day (1,096 × 48) and + Market 2 is a clean 24/day (1,096 × 24). The loader will rebuild a regular half-hourly index from the + series start, assert the expected row counts, log the discarded anomalies, and align Market 2 to + Market 1 by integer position (2 half-hours per hour) rather than by timestamp join. This is documented + as an assumption in the README. + +Sizing sanity check: mean daily Market 1 spread is £39/MWh and hourly-averaged Market 1 correlates with +Market 2 at 0.983 (mean absolute gap £4.22/MWh), so a two-cycle-per-day strategy lands in the tens of +thousands of pounds per year. Cross-market optimisation adds value but intraday arbitrage dominates. + +## Approach + +Discretise everything onto the half-hourly grid — the finest market resolution — and express dispatch as a +**mixed-integer linear program** solved over a **rolling horizon**: a 48-hour lookahead window of which only +the first 24 hours is committed, with state of charge carried forward. This keeps each solve tiny (96 +binaries) while avoiding the myopia of independent daily solves, and it makes the three-year run tractable +in minutes rather than attempting one 52,608-period monolith. + +Market 2's hourly commitment rule is enforced structurally: one decision variable per *hour* that applies +to both of that hour's half-hours, so the constraint is impossible to violate rather than merely checked. +The "cannot sell the same unit of energy into both markets" rule falls out for free from a single shared +state-of-charge balance. + +Because both price series contain negative prices, the LP relaxation can genuinely prefer to charge and +discharge simultaneously (get paid at both ends). The solver therefore runs **LP-first with an MILP +fallback**: solve the relaxation, detect any window where charge and discharge are both non-zero in the +same half-hour, and re-solve that window with binaries. This is exact, and fast in the common case. + +## Formulation + +Per solve window, index half-hours by `t` and hours by `h`, with `H(h)` the two half-hours in hour `h`. +Δt = 0.5 h, η_c = η_d = 0.95, P_c = P_d = 2 MW, E_max = current degraded capacity. + +Variables: + +- `c1[t], d1[t] ∈ [0, P]` — MW committed to Market 1 for half-hour `t` +- `c2[h], d2[h] ∈ [0, P]` — MW committed to Market 2 for the whole of hour `h` +- `e[t] ∈ [0, E_max]` — energy stored at end of `t` +- `z[t] ∈ {0,1}` — charging indicator (MILP pass only) + +Constraints for every half-hour `t`, with `h = hour(t)`: + +``` +c1[t] + c2[h] <= P_c * z[t] +d1[t] + d2[h] <= P_d * (1 - z[t]) +e[t] = e[t-1] + Δt * ( η_c * (c1[t] + c2[h]) - (d1[t] + d2[h]) / η_d ) +0 <= e[t] <= E_max +``` + +`e[-1]` is the carry-in state of charge from the previous window. In the LP pass, `z[t]` is dropped and the +two power constraints become `c1+c2 <= P_c`, `d1+d2 <= P_d`. + +Objective (maximise): + +``` +Σ_t Δt * p1[t] * (d1[t] - c1[t]) + Σ_h 1.0 * p2[h] * (d2[h] - c2[h]) +``` + +Discharge accounting matches the spec: to deliver `D` MWh to the grid the battery draws `D / 0.95` MWh from +storage; to store `S` MWh it imports `S / 0.95` MWh from the grid — i.e. revenue and cost are settled on the +grid-side quantity, which is what the market pays for. + +Degradation is applied **between** windows rather than inside the LP (which would make it non-linear): +after each committed day, cumulative equivalent full cycles are updated as +`cycles += discharged_from_storage_MWh / E_nominal`, and usable capacity is set to +`E_max = E_nominal * (1 - 1e-5 * cycles)` for the next window. + +## Package layout + +Built in `/Users/matt/aurora_task` as a git repository (`git init` locally; nothing pushed anywhere without +asking). The two spreadsheets are copied into `data/` so the repo is self-contained and reproducible. + +``` +pyproject.toml # deps: pandas, openpyxl, pulp, matplotlib; dev: pytest +README.md # setup, how to run, assumptions, one-paragraph approach summary +RESULTS.md # headline outcomes, tables, embedded charts +data/ # copies of Attachment 1.xlsx and Attachment 2.xlsx +outputs/ # committed reproducible results (csv, json, png) +src/battery_dispatch/ + __init__.py + config.py # BatterySpec + RunConfig dataclasses; parse Attachment 1 + data.py # price loading, index rebuild, count assertions, market alignment + markets.py # Market dataclass (name, periods_per_halfhour, prices) + optimiser.py # window problem construction, LP/MILP solve, rolling horizon driver + battery.py # SoC state, cycle counting, capacity fade + validation.py # independent post-hoc schedule checker + metrics.py # annual/monthly KPIs, cycle and capacity reporting + plots.py # matplotlib figures + cli.py # `battery-dispatch run ...` +tests/ + test_data.py + test_optimiser.py + test_validation.py + test_battery.py +``` + +## Implementation steps + +### Task 1 — Data and configuration +1. `config.py`: `BatterySpec` dataclass (`max_charge_mw`, `max_discharge_mw`, `capacity_mwh`, + `charge_efficiency`, `discharge_efficiency`, `lifetime_years`, `lifetime_cycles`, + `degradation_pct_per_cycle`, `capex_gbp`, `fixed_opex_gbp_per_year`) with a `from_excel()` classmethod + that reads `data/Attachment 1.xlsx` by row label, converting the two loss fractions into + `efficiency = 1 - loss`. Also `RunConfig` (start, end, window hours, commit hours, solver options, + output directory, optional degradation cost). +2. `data.py`: `load_prices()` returning a single half-hourly `DataFrame` with columns + `market_1_price`, `market_2_price`, `hour_index`. Drops blank rows, asserts 1,096×48 and 1,096×24 rows, + rebuilds the regular index, logs clock-change anomalies, broadcasts hourly prices onto half-hours, and + exposes a `slice(start, end)` helper that clips to whole days. + +### Task 2 — Optimiser +3. `optimiser.py`: `build_window(prices_window, spec, soc_start, capacity, relaxed: bool)` returning a PuLP + problem plus a handle on the variable dictionaries. One `c2`/`d2` variable per hour, referenced by both + of its half-hours. +4. `solve_window()`: solve relaxed; if any half-hour has both charge and discharge above 1e-6, rebuild with + binaries and re-solve. Raise on non-optimal solver status rather than silently returning a bad schedule. + Expose `--milp-always` / `--lp-only` overrides. +5. `run_rolling_horizon()`: iterate windows of `window_hours` committing `commit_hours`, carry SoC, + update capacity fade via `battery.py` after each commit, and concatenate committed half-hours into one + result frame (`timestamp, p1, p2, c1, d1, c2, d2, soc, capacity, revenue_m1, revenue_m2`). + +### Task 3 — Battery state and degradation +6. `battery.py`: `BatteryState` tracking SoC, cumulative charged/discharged MWh, equivalent full cycles and + degraded capacity; `apply_cycles()` implementing the 1e-3 %/cycle fade; helper for implied end of life, + `min(10 years, 5000 / cycles_per_year)`. + +### Task 4 — Independent validation +7. `validation.py`: `validate_schedule(result, spec)` re-checking, from the output frame alone and without + reference to solver internals: + - `0 <= c1 + c2 <= max_charge`, `0 <= d1 + d2 <= max_discharge` + - no half-hour with both charge and discharge non-zero (tolerance 1e-6) + - Market 2 power identical across both half-hours of every hour + - SoC recomputed from scratch stays in `[0, capacity]` and matches the reported SoC + - revenue recomputed from prices and powers matches the reported revenue + Returns a structured report; the CLI fails loudly if any check fails. + +### Task 5 — Metrics, plots, CLI +8. `metrics.py`: totals and per-year / per-month breakdowns — gross trading profit split by market, MWh + charged and discharged, equivalent full cycles, capacity remaining, average captured spread £/MWh, + share of revenue from each market. +9. `plots.py`: (a) one representative week showing both prices, dispatch by market and SoC; + (b) monthly revenue stacked by market; (c) cumulative cycles and capacity fade over three years; + (d) distribution of captured spread. +10. `cli.py`: `battery-dispatch run --start 2018-01-01 --end 2020-12-31 --out outputs/` writing + `dispatch.csv`, `summary.json`, and the PNGs; prints a compact summary table and the validation verdict. + Deterministic: no randomness anywhere, fixed solver settings. + +### Task 6 — Tests +11. `tests/test_optimiser.py` — small hand-checkable cases: + - two half-hours priced £0 then £100, Market 1 only → charges then discharges; revenue equals + `2 MW × 0.5 h × 0.95 × 0.95 × £100 = £90.25` + - an hour whose two half-hours have opposite Market 1 signals → confirms Market 2 power stays flat + across the hour + - negative prices in both markets → confirms the MILP fallback triggers and no simultaneous + charge/discharge survives + - a case where the optimum splits power across both markets within one hour, respecting the 2 MW cap +12. `tests/test_data.py` — blank-row dropping, row-count assertions, hourly→half-hourly broadcast. +13. `tests/test_validation.py` — validator catches each injected violation type. +14. `tests/test_battery.py` — cycle counting and capacity fade arithmetic. + +### Task 7 — Documentation and committed results +15. Run the full three years, commit `outputs/` and write `RESULTS.md`: headline gross profit, per-year + table, revenue split between markets, cycles per year against the 5,000-cycle budget, capacity fade, + solver statistics and wall-clock runtime. +16. `README.md`: install (`uv sync` or `pip install -e .`), run commands, the modelling assumptions + (efficiency convention, clock-change handling, rolling-horizon perfect foresight within the window, + degradation applied between windows), known simplifications, and the required one-paragraph summary. + +## Acceptance criteria + +- `pip install -e .` (or `uv sync`) succeeds on Python 3.11+ with no non-pip dependencies; CBC ships with PuLP. +- `battery-dispatch run --start 2018-01-01 --end 2020-12-31` completes in under 10 minutes on a laptop and + exits 0. +- `validate_schedule` reports zero violations on the full three-year run, checked independently of the solver. +- Every half-hour satisfies `c1+c2 <= 2 MW`, `d1+d2 <= 2 MW`, `0 <= SoC <= capacity`, and never both charges + and discharges (tolerance 1e-6). +- Market 2 committed power is constant within every hour, verified across all 26,304 hours. +- Revenue recomputed independently from `dispatch.csv` matches the optimiser objective to within £0.01. +- `pytest` passes, including the £90.25 analytic two-period case to within £0.01. +- Re-running the CLI twice produces byte-identical `summary.json`. +- `RESULTS.md` reports gross profit per year, revenue split by market, cycles per year, and end-of-life + capacity, each traceable to a file in `outputs/`. + +## Verification + +1. `pytest -q` — unit tests, including analytic known-answer cases. +2. `battery-dispatch run --start 2018-01-01 --end 2018-01-07 --out /tmp/smoke` — fast smoke run; eyeball the + week plot against the price series to confirm it buys the overnight trough and sells the evening peak. +3. `battery-dispatch run --start 2018-01-01 --end 2020-12-31 --out outputs/` — the reproducible headline run. +4. Confirm the validation report at the end of the full run shows all checks passed. +5. Spot-check a single day by hand: pull one day from `dispatch.csv`, recompute revenue and SoC in a + scratch script, and confirm agreement. +6. Edge cases to exercise: a day containing negative prices in both markets, the three spring clock-change + days, and the first and last day of the series (window boundary behaviour). + +## Risks and mitigations + +- **CBC runtime on 1,096 windows.** Mitigated by the LP-first strategy — binaries only appear in the rare + windows where the relaxation cheats. If it is still slow, widen `commit_hours` or add a + `--max-seconds-per-window` solver cap; both are config, not redesign. +- **Rolling horizon is not globally optimal.** A 48-hour window with 24-hour commitment captures essentially + all intraday value for a 2-hour-duration battery. This will be stated plainly in the README as a + deliberate trade-off rather than left implicit. +- **Efficiency convention could be read the other way.** The spec's wording is unambiguous (losses occur + before storage on import and before the grid on export), but the convention will be written out in the + README and pinned by a unit test so a reviewer can see exactly what was assumed. +- **Clock-change timestamps.** Rebuilding a regular index is the pragmatic choice given clean 48/day counts; + the discarded anomalies are logged so the decision is visible rather than hidden. +- **Scope creep into investment economics.** Explicitly excluded per the user's decision; the package reports + cycles and capacity fade but stops short of NPV, keeping the deliverable within the exercise's time box.

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