Power, Energy & Watts
Why a 100MW BESS and a 100MW/400MWh BESS are two completely different machines — and the one distinction that governs every spec sheet in the energy industry.
Musk's Rocket Science · Part 1 — Electricity Basics · Chapter 6 · 16 min read
Two BESS projects are announced in the same week. Project A is described as “100MW”. Project B is described as “100MW / 400MWh”. A casual reader might think these are the same size. They are not — Project B can sustain its full 100MW output for four hours, while Project A’s duration is unstated, and without it the number “100MW” alone tells you almost nothing about how much total energy the project can actually deliver.
This confusion — power versus energy — is arguably the single most common source of miscommunication in the entire energy industry, from grid operators to journalists to procurement teams. This chapter exists to make sure you never make that mistake.
6.1 — Power: the rate of doing work
Power is the rate at which energy is transferred or work is done, measured in Watts (W), where one Watt equals one Joule per second.
P = W / t
P is power in Watts, W is work or energy in Joules, and t is time in seconds.
Combining this with definitions from earlier chapters gives electrical power its most useful working form. Recall from Chapter 2 that V = W/Q, so W = V × Q. Substituting:
P = (V × Q) / t = V × (Q/t) = V × I
Q/t is exactly the definition of current from Chapter 1.
This gives the single most-used power equation in electrical engineering.
P = V × I
Combining it with Ohm’s Law from Chapter 3 gives two more equivalent forms, each useful in different situations.
P = I² × R and P = V² / R
Substituting V = IR into P = VI gives the first; substituting I = V/R gives the second.
Worked example 6.1 — Power delivered by a BESS PCS
A BESS string’s Power Conversion System operates its DC input at V = 1,500V, drawing I = 300A from the string during a discharge event.
P = V × I = 1,500 × 300 = 450,000W = 450 kW
This is the instantaneous power flowing from the string into the PCS at that moment — the foundation figure that, sustained over time, becomes the energy delivered.
6.2 — How much power? Across the energy stack
Power ratings span an extraordinary range across the modern energy industry — from a 7kW home EV charger to a 1.6GW nuclear reactor, a span of nearly six orders of magnitude.
Table 6.1 — Power ratings across the energy stack
| System | Typical power | Context |
|---|---|---|
| EV home AC charger (Level 2) | 7 kW | Overnight residential charging |
| Data centre AI GPU rack (dense) | 100 kW | Modern AI training clusters now regularly exceed traditional server rack densities by 5–10× |
| EV DC fast charger | 350 kW | Public ultra-fast charging infrastructure |
| Offshore wind turbine (single unit) | 8 MW | A single modern offshore turbine |
| Utility-scale BESS project | 100 MW | A representative grid-connected battery storage project |
| SMR (Small Modular Reactor) | 300 MW | Next-generation nuclear, designed for factory fabrication and faster deployment |
| Large nuclear reactor (single unit) | 1.6 GW | Among the largest single generating units in operation globally |
6.3 — Energy: power sustained over time
If power is the rate of energy transfer, then energy is simply power sustained over a duration.
E = P × t
The SI unit of energy is the Joule, but a Joule is an inconveniently small quantity for describing real energy systems — a single AA battery holds several thousand of them. The energy industry overwhelmingly uses Watt-hours instead: the energy delivered by one Watt of power sustained for one hour. Because an hour is 3,600 seconds, 1 Wh = 3,600 Joules.
Table 6.2 — Energy units in practice
| Unit | Equivalent | Typical use |
|---|---|---|
| Watt-hour (Wh) | 3,600 J | Small electronics, individual cells |
| Kilowatt-hour (kWh) | 1,000 Wh | EV battery packs, household electricity billing, small BESS units |
| Megawatt-hour (MWh) | 1,000 kWh | Utility-scale BESS, commercial and industrial energy use |
| Gigawatt-hour (GWh) | 1,000 MWh | Grid-scale generation and storage, annual gigafactory output |
Worked example 6.2 — From power to energy
The BESS PCS from Worked Example 6.1 sustains its 450kW discharge for exactly two hours during an evening peak event.
E = P × t = 450 kW × 2 h = 900 kWh = 0.9 MWh
This is the total energy delivered — the number that determines how much stored charge was actually consumed, appears on a settlement invoice, and is what a BESS’s Ah or kWh capacity rating is fundamentally describing.
6.4 — The critical BESS distinction: power rating and energy rating
A BESS project is always specified by two numbers — a power rating in MW and an energy rating in MWh — because they answer two independent engineering questions: how fast can the system deliver energy, and for how long can it sustain that rate? Dividing one by the other gives the system’s duration.
Duration (hours) = Energy (MWh) / Power (MW)
This single ratio is arguably the most important spec in grid-scale battery storage, because different grid services fundamentally require different durations.
Table 6.3 — BESS applications by typical duration
| Application | Typical duration | Why |
|---|---|---|
| Frequency regulation | 15–30 minutes | Corrects rapid, small grid frequency deviations — needs to be fast, not long |
| Peak shaving / price arbitrage | 2–4 hours | Covers evening demand peaks, or captures daily price spreads |
| Renewables time-shifting | 4–8 hours | Shifts midday solar generation into the evening demand peak |
| Long-duration storage (LDES) | 8–24+ hours | Bridges multi-day renewable generation gaps; an active area for flow batteries and other emerging chemistries beyond Li-ion |
Worked example 6.3 — Comparing two BESS projects
Project A: 100MW / 100MWh → duration = 100/100 = 1 hour
Suited to fast-response grid services, but cannot sustain output through a multi-hour evening peak.
Project B: 100MW / 400MWh → duration = 400/100 = 4 hours
The same power rating, but four times the battery cells, sized specifically for extended peak-shaving duty. Both projects can deliver the same instantaneous 100MW — but Project B costs roughly four times as much in battery hardware for the same power electronics, because energy capacity (cells) and power capacity (PCS and inverters) are largely independent design choices in a BESS.
Why this matters later
This is precisely why a BESS’s power rating and energy rating must always be quoted together, never one alone. It is also why BESS design allows real flexibility: a system can be built “power-heavy” — few cells, big inverters, short duration — or “energy-heavy” — many cells, modest inverters, long duration — depending entirely on which grid service it is contracted to provide.
6.5 — Charging time: power determines how fast, energy determines how far
The same power-versus-energy distinction governs EV charging. A vehicle’s range depends on its battery’s energy capacity in kWh; how quickly that battery refills depends entirely on the charger’s power rating in kW.
Charge time (hours) = Energy needed (kWh) / Charger power (kW)
Worked example 6.4 — Estimating a fast-charging session
A passenger EV needs 50kWh to go from 10% to 80% state of charge, plugged into a 150kW DC fast charger.
Charge time = 50 kWh / 150 kW = 0.33 hours ≈ 20 minutes
In practice, charging is rarely delivered at perfectly constant power — the charge curve tapers as the battery approaches full, similar in spirit to the CC-CV behaviour in our balancing and capacity test procedure — so real-world sessions typically run somewhat longer than this simplified constant-power estimate.
6.6 — Efficiency: not all power delivered is power used
No real energy conversion is perfect. Efficiency is the ratio of useful output power to input power.
Efficiency (%) = (P_out / P_in) × 100
The remaining fraction is lost, almost always as heat — a direct consequence of the I²R losses introduced in Chapter 3. Conversion efficiency varies enormously by technology.
Worked example 6.5 — Sizing electrolyser input for a hydrogen target
A PEM electrolyser plant needs to produce 1,000 kg of green hydrogen per day. Its specific energy consumption — a standard efficiency metric in the hydrogen industry — is 55 kWh per kg of H₂ produced.
Total electrical energy: 1,000 kg × 55 kWh/kg = 55,000 kWh = 55 MWh per day
Average input power over 24h: 55 MWh / 24h ≈ 2.29 MW
This is the figure a plant developer would use to size the grid connection and, potentially, a co-located solar or wind power purchase agreement.
Technical framing
The 70% efficiency figure for PEM electrolysers in Figure 6.4 corresponds to roughly 50–55 kWh of electrical input per kg of hydrogen produced, against hydrogen’s higher heating value of about 39.4 kWh/kg. The gap between those two numbers is exactly the electrolyser’s conversion loss — dissipated as heat and lost overpotential across the activation, ohmic and mass-transport regions of the polarisation curve from Chapter 3.
6.7 — Quick reference
Power and energy cheat sheet
| Quantity | Formula | Unit |
|---|---|---|
| Power | P = VI = I²R = V²/R | Watt (W) |
| Energy | E = P × t | Watt-hour (Wh, kWh, MWh, GWh) |
| BESS duration | Duration (h) = Energy (MWh) / Power (MW) | Hours |
| Charge time | Time (h) = Energy needed (kWh) / Charger power (kW) | Hours |
| Efficiency | η (%) = (P_out / P_in) × 100 | Percent |
Chapter summary
- ✓Power (P) is the rate of energy transfer, P = W/t, measured in Watts. Combining with earlier chapters gives P = VI = I²R = V²/R.
- ✓Energy (E) is power sustained over time, E = P × t. The energy industry uses Watt-hours — Wh, kWh, MWh, GWh — rather than Joules, for practical convenience.
- ✓Power ratings across the energy industry span from single-digit kilowatts (EV home chargers) to gigawatts (large nuclear reactors) — nearly six orders of magnitude.
- ✓A BESS, or any storage system, must always be specified by both power (MW) and energy (MWh). Their ratio gives duration, which determines what grid service the system can actually provide — from 15-minute frequency regulation to 12-hour-plus long-duration storage.
- ✓EV charging time follows the same logic: charge time = energy needed / charger power, which is why the charger’s power rating, not just battery size, dominates real-world charging speed.
- ✓Efficiency (P_out/P_in) varies enormously by technology — from about 99% in modern SiC and GaN power electronics down to roughly 70% in green-hydrogen electrolysis and 35% in a combustion engine — and directly determines the true input power needed to hit a target output.
Test your understanding
- 1A wind turbine’s generator operates at 690V and delivers 4,000A at rated output. What is its power output, in MW?
- 2A BESS sustains 50MW of discharge for 6 hours. How much energy, in MWh, did it deliver?
- 3Two BESS projects are both rated 50MW. Project X is 50MWh; Project Y is 200MWh. What is each project’s duration, and which is better suited to frequency regulation versus multi-hour peak shaving?
- 4An EV needs 40kWh to reach full charge and is plugged into a 22kW AC charger. Roughly how long will charging take?
- 5A grid-tied inverter is rated 97% efficient at converting a solar array’s 500kW DC input to AC. How much power, in kW, is lost as heat?
- 6Challenge: a green-ammonia plant’s electrolyser stage consumes 48 kWh per kg of hydrogen produced, and the plant needs 2,000 kg of hydrogen per day for downstream ammonia synthesis. If the plant operates 20 hours per day, accounting for maintenance and grid curtailment, what average power draw in MW must the electrolyser’s grid connection support during those 20 operating hours?
Frequently asked questions
What is the difference between kW and kWh?+
kW is power — the rate at which energy moves, right now. kWh is energy — that rate sustained over time, since E = P × t. A 7kW charger delivers 7 kWh in one hour. Quoting one without the other is the most common source of confusion in the energy industry: a battery rated only in MW tells you how fast it can discharge, but nothing about for how long.
What does a BESS rated “100MW / 400MWh” actually mean?+
The first number is its power rating — the maximum rate it can charge or discharge. The second is its energy rating — the total it can store. Dividing energy by power gives duration: 400/100 = 4 hours, meaning it can sustain full 100MW output for four hours. A 100MW/100MWh project has the same power but only one hour of duration, and costs far less in cells for identical power electronics.
How do you calculate BESS duration?+
Duration in hours = energy rating (MWh) divided by power rating (MW). The result determines what grid service a system can provide: roughly 15–30 minutes suits frequency regulation, 2–4 hours suits peak shaving and price arbitrage, 4–8 hours suits shifting midday solar into the evening peak, and 8–24 hours or more is long-duration storage territory.
How long does it take to charge an EV?+
Charge time in hours = energy needed (kWh) divided by charger power (kW). Delivering 50kWh takes about 35.7 hours on a 1.4kW household outlet, 7.1 hours on a 7kW home charger, 20 minutes on a 150kW DC fast charger and about 3 minutes on a 1MW Megawatt Charging System. Real sessions run longer than this because the charge curve tapers as the battery fills.
What are the three forms of the electrical power equation?+
P = V × I is the base form, derived by combining P = W/t with the definition of voltage (V = W/Q) and current (I = Q/t). Substituting Ohm’s Law gives two more: P = I²R, used for calculating resistive heat loss in cables and busbars, and P = V²/R, useful when voltage and resistance are the known quantities.
How efficient are batteries compared with other energy conversions?+
Li-ion battery storage achieves roughly 90% round-trip efficiency, and an EV powertrain about 85% from battery to wheels. Modern SiC and GaN power electronics reach around 99%, and grid transformers and HVDC converter stations about 98%. PEM electrolysis for green hydrogen sits near 70%, and an internal combustion engine is fundamentally limited to roughly 35%.
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Musk's Rocket Science is an original educational series explaining the physics and chemistry behind everyday electricity and battery technology. Figures and worked examples use standard physical constants and representative real-world values for illustration.