How Should a Battery Decide When to Charge and Discharge?

A practical introduction to BESS dispatch, showing why battery arbitrage requires decisions across time and how physical and economic constraints lead naturally to optimization.

The basic idea

So far, we’ve looked at individual arbitrage opportunities.

We know that a battery needs to consider:

  • the charging price
  • the selling price
  • round-trip efficiency
  • battery-use costs
  • its available energy
  • its power limits
  • its SOC

But a real BESS doesn’t operate one trade at a time.

Electricity prices change continuously.

A battery may have several opportunities to charge and discharge throughout the day, but its energy capacity is limited.

That creates a different question:

Given electricity prices over the next 24 hours, when should the battery charge and discharge?

This is the beginning of battery dispatch optimization.

1. Start with our battery

We’ll continue using the same: 100 MW / 200 MWh BESS

For this simplified example, assume:

  • Maximum charge power = 100 MW
  • Maximum discharge power = 100 MW
  • Energy capacity = 200 MWh
  • Starting SOC = 50%
  • Round-trip efficiency = 90%
  • Battery-use cost = ignored initially

Starting stored energy is:200×50%200\times50\%=100 MWh=\boxed{100\ MWh}

So the battery begins the day with 100 MWh available.

2. Give the battery a price signal

Suppose tomorrow’s electricity prices look like this:

HourElectricity price
00:00$50/MWh
01:00$40/MWh
02:00$30/MWh
03:00$25/MWh
04:00$30/MWh
05:00$45/MWh
06:00$60/MWh
07:00$70/MWh
08:00$65/MWh
09:00$55/MWh
10:00$45/MWh
11:00$40/MWh
12:00$35/MWh
13:00$30/MWh
14:00$35/MWh
15:00$50/MWh
16:00$75/MWh
17:00$100/MWh
18:00$140/MWh
19:00$160/MWh
20:00$130/MWh
21:00$90/MWh
22:00$70/MWh
23:00$55/MWh

At first glance, the answer seems obvious:

Charge at the lowest prices and discharge at the highest prices.

But the battery can’t simply buy all the cheap electricity and sell all the expensive electricity.

Its capacity is limited.

3. The battery can’t charge indefinitely

Our battery can store a maximum of:200 MWh200\ MWh

It starts with:100 MWh100\ MWh

So it has room for only:200−100200-100=100 MWh=\boxed{100\ MWh}

of additional energy.

At a maximum charging rate of 100 MW, it could fill that available space in one hour.

Suppose it charges 100 MWh at the lowest price:

$25/MWh at 03:00.

The energy cost is:100×25100\times25=$2,500=\boxed{\$2,500}

The battery is now full, at least under our simplified treatment of efficiency.

But that decision matters. By filling the battery at 03:00, we have used its available storage capacity.

We can’t also charge another 100 MWh at 13:00 when electricity is $30/MWh unless we’ve discharged some energy first.

4. The battery can’t discharge everything at once

The battery contains:200 MWh200\ MWh

But its maximum discharge power is:100 MW100\ MW

So even though it has 200 MWh available, it cannot deliver all of it during one hour.

At maximum power:100MW×1h=100MWh100MW\times1h=100MWh

So it would take two hours to discharge 200 MWh.

This is the power constraint we established earlier.

The battery therefore has to manage both:

How much energy it has

and

how quickly it can move that energy.

5. Now look at the evening prices

The highest prices occur at:

18:00 → $140/MWh

19:00 → $160/MWh

Suppose the battery has 200 MWh available.

It could discharge:

100 MWh at 18:00

and:

100 MWh at 19:00

giving:100×140=$14,000100\times140=\$14,000

and:100×160=$16,000100\times160=\$16,000

Total revenue:$30,000\boxed{\$30,000}

This is already more interesting than simply saying:

“Sell when the price is highest.”

The battery has to decide how much to sell at each hour.

6. What if there is an even better opportunity later?

Suppose the battery knows that at 19:00 the price will be:$160/MWh\$160/MWh

while at 18:00 it is:$140/MWh\$140/MWh

Should it discharge 100 MWh at 18:00?

Maybe.

But doing so leaves less energy for 19:00.

The battery could instead preserve some energy for the higher price.

For example:

18:00: discharge 50 MWh

19:00: discharge 100 MWh

Now the battery has preserved another 50 MWh for the higher-priced period.

The value of that decision depends on what happens before, during and after those hours.

This is the beginning of intertemporal optimization:

A decision made now changes the choices available later.

7. This is why the highest price isn’t always the whole answer

Imagine the battery has two possible strategies.

Strategy A

Discharge: 100 MWh at $140/MWh

and: 100 MWh at $160/MWh.

Revenue:100(140)+100(160)100(140)+100(160)=$30,000=\boxed{\$30,000}

Strategy B

Discharge:50 MWh at $140/MWh

and: 100 MWh at $160/MWh.

Revenue from these two hours:50(140)+100(160)50(140)+100(160)=$23,000=\boxed{\$23,000}

Strategy A produces more revenue if the battery already has 200 MWh available and there is no more valuable opportunity being sacrificed.

But now suppose the battery could use that preserved 50 MWh at 21:00 for a different market opportunity worth $200/MWh.

Suddenly the decision changes.

So, “What’s the highest price?” is oversimplification. The battery is essentially asking:

“What is the highest-value use of each available MWh over the entire decision horizon?”

That’s the deeper problem.

8. SOC links every decision together

This is where the SOC concept becomes particularly important.

Suppose the battery starts with 100 MWh.

If it discharges:50 MWh50\ MWh

then its stored energy becomes:100−50=50 MWh100-50=50\ MWh

Its SOC becomes:50200=25%\frac{50}{200}=25\%

That means the decision at one hour changes the starting point for the next hour.

Similarly, charging increases future available energy.

So we can think of the battery as moving through a sequence:

SOCt→Charge/Discharget→SOCt+1SOC_t \rightarrow Charge/Discharge_t \rightarrow SOC_{t+1}

The decision at time tt affects what is possible at time t+1t+1.

9. Now we can describe the dispatch problem

For every hour, the battery needs to determine:

  • Should I charge? If electricity is sufficiently cheap.
  • Should I discharge? If electricity is sufficiently valuable.
  • How much? Subject to its power and energy constraints.
  • Should I wait? Because a better opportunity may appear later.

All of these decisions affect the battery’s future SOC.

So instead of one calculation, we now have a sequence of linked decisions.

10. From intuition to an optimization problem

We can express the objective in a simplified way as:

Maximize total revenue−energy costs−battery-use costs\boxed{ \text{Maximize total revenue} – \text{energy costs} – \text{battery-use costs} }

subject to constraints such as:0≤SOCt≤SOCmax0\le SOC_t\le SOC_{max}0≤Charget≤Chargemax0\le Charge_t\le Charge_{max}0≤Discharget≤Dischargemax0\le Discharge_t\le Discharge_{max}

and the SOC must evolve according to the energy entering and leaving the battery.

We’re not solving the optimization yet. The important thing is understanding what the optimization is trying to decide.

The mental model

We’ve now seen how the different pieces of a BESS fit together:

  • Power and energy determine what the battery can physically do.
  • State of charge determines how much energy is available at any given time.
  • Efficiency determines how much energy is lost when the battery charges and discharges.
  • Degradation gives battery usage an economic cost.
  • And arbitrage turns these physical constraints into an economic decision.

The next step is to bring these pieces together over time.

Battery arbitrage isn’t simply about finding the biggest price spread. It’s about allocating a finite, state-dependent asset across time.

That’s the intuition underneath battery optimization.

The next question

How would we actually tell the battery which decisions to make?

That’s where the basic structure of an optimization problem comes in:

objective function → decision variables → constraints.

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