Exercise set
Energy Storage and Grid Flexibility Exercises
Worked engineering exercises for energy storage and grid flexibility covering usable energy, SOC reserve, duration, peak shaving, renewable shifting, round-trip efficiency, inverter loading, and validation.
These exercises practise first-pass engineering calculations for energy storage and grid flexibility systems. The aim is to connect power, energy, state of charge, reserve, efficiency, inverter loading, and validation evidence to the service that the storage system is expected to deliver.
Assume simplified steady values unless an exercise states otherwise. Real projects require time-series simulation, manufacturer limits, protection studies, grid-code review, degradation modelling, thermal analysis, fire-safety review, controls validation, and contractual service definitions.
How to Use These Exercises
For each problem, state four things before calculating:
- the grid or site service being delivered;
- the measurement boundary, such as cell, DC block, AC terminals, point of interconnection, or customer meter;
- the usable state-of-charge window and reserve that cannot be dispatched;
- whether the result is a sizing screen, operating limit, dispatch instruction, or commissioning check.
The most common error is comparing storage projects by nameplate energy alone. A storage asset is useful only if it can deliver the required power for the required duration while preserving reserve, lifetime, safety, grid compatibility, and recovery capability.
For each result, state whether it supports procurement sizing, dispatch scheduling, grid-service qualification, reserve policy, inverter loading, recovery charging, or commissioning acceptance. The boundary matters: cell energy, DC-block energy, AC delivered energy, and point-of-interconnection service are not interchangeable.
Exercise 1: Usable Energy from Nameplate Capacity
A battery energy storage system has a beginning-of-life nameplate capacity of 120\ \text{MWh}. The allowed operating state-of-charge window is from 15\% to 90\%. The operator also withholds 10\% of the window for emergency reserve. End-of-life capacity is expected to be 86\% of beginning-of-life capacity.
Estimate the usable energy available for routine dispatch at end of life.
Solution
Allowed SOC window:
Routine dispatch fraction after emergency reserve:
End-of-life usable energy:
The battery has about 69.7\ \text{MWh} available for routine dispatch at end of life.
Engineering Comment
The answer is much lower than the nameplate value. This does not mean the battery is poorly designed. It means the service calculation respects SOC limits, emergency reserve, and degradation. A dispatch schedule based on 120\ \text{MWh} would overstate the serviceable capability.
Exercise 2: Duration at Contracted Power
Using the 69.7\ \text{MWh} usable energy from Exercise 1, determine how long the system can discharge at a contracted power of 30\ \text{MW}.
Solution
Approximate discharge duration is:
The system can support 30\ \text{MW} for about 2.3\ \text{h} under the assumed usable-energy boundary.
Engineering Comment
This is a screening duration. Actual duration depends on inverter limits, auxiliary loads, low-temperature derating, SOC estimation error, thermal constraints, minimum reserve policy, and whether the battery must still provide another service during or after the event.
Exercise 3: Peak Shaving Energy
A site has a demand limit of 6.0\ \text{MW}. During a production peak, demand is expected to be:
- 7.2\ \text{MW} for 30\ \text{min};
- 6.8\ \text{MW} for 45\ \text{min};
- 6.4\ \text{MW} for 60\ \text{min}.
Estimate the minimum battery energy discharged at the AC point of connection to keep demand below the limit.
Solution
Only demand above the limit must be shaved.
First interval:
Second interval:
Third interval:
Total delivered energy:
Minimum power rating at the point of connection is set by the largest required reduction:
Engineering Comment
The calculation shows that both power and energy matter. The battery must deliver at least 1.2\ \text{MW}, but it must also sustain a total delivered energy of 1.60\ \text{MWh}. The recovery charge should be scheduled carefully; charging immediately after the peak can create a second demand peak.
Exercise 4: Renewable Energy Shifting with Round-Trip Efficiency
A solar plant has 18\ \text{MWh} of midday energy that would otherwise be curtailed because of an export limit. The battery can accept all of this energy within its SOC window. The AC-to-AC round-trip efficiency for the planned operating point is 88\%.
Estimate the energy delivered during the evening discharge period.
Solution
Delivered energy is:
The battery can deliver about 15.8\ \text{MWh} during the evening period.
Engineering Comment
The missing 2.16\ \text{MWh} is not an accounting error. It represents conversion and auxiliary losses within the selected AC-to-AC boundary. A financial or carbon analysis should use delivered energy, not charged energy, when evaluating the useful grid service.
Exercise 5: SOC Reserve Conflict Between Services
A battery has 40\ \text{MWh} of usable energy in its normal operating window. A contract requires 12\ \text{MWh} to remain reserved for emergency support at all times. The operator wants to schedule a peak-shaving event that requires 24\ \text{MWh} and then hold 8\ \text{MWh} for evening frequency-response availability.
Check whether the planned service stack is feasible within the same operating window.
Solution
Energy committed inside the usable window:
Available usable energy:
Energy shortfall:
The service stack is not feasible as stated. It exceeds the usable energy window by 4\ \text{MWh}.
Engineering Comment
Service stacking fails when several products rely on the same constrained resource at the same time. The correction could be a smaller peak-shaving commitment, different SOC reserve rule, additional installed energy, revised frequency-response availability, or a dispatch priority rule that makes one service interruptible.
Exercise 6: Inverter Apparent Power for Active and Reactive Support
A battery inverter must provide 8.0\ \text{MW} of active power while also supplying 3.0\ \text{MVAr} of reactive power for local voltage support. Estimate the minimum apparent power rating at that operating point.
Solution
Apparent power requirement:
The inverter must be capable of at least 8.54\ \text{MVA} at that operating point.
Engineering Comment
An inverter rated only for 8.0\ \text{MVA} could not provide both services simultaneously at those values. Grid support often consumes current headroom. A storage design should state whether active-power delivery, reactive-power support, fault response, and thermal derating can coexist.
Exercise 7: Frequency-Response Energy Budget
A battery provides a fast frequency-response service. During one event it injects 12\ \text{MW} for 8\ \text{min}. The discharge-path efficiency over the event is 94\% from stored battery energy to AC output.
Find the AC energy delivered and the stored energy consumed.
Solution
Event duration:
AC energy delivered:
Stored energy consumed:
Engineering Comment
Short-duration services can still consume meaningful energy when events repeat. Operators should track event count, recovery charge, SOC confidence, thermal response, and whether reserve remains available after several events close together.
Exercise 8: Commissioning Capacity Test
A storage system is commissioned with a constant AC discharge of 20\ \text{MW} for 2.5\ \text{h} before it reaches its agreed lower SOC limit. The commissioning plan requires at least 48\ \text{MWh} delivered at the AC terminals.
Determine whether the test passes the delivered-energy requirement.
Solution
Delivered AC energy:
Compare with acceptance criterion:
The test passes the delivered-energy requirement with:
of margin.
Engineering Comment
Passing delivered energy is necessary but not sufficient. The commissioning record should also include SOC estimate before and after the test, temperature, auxiliary loads, inverter limits, alarms, cell imbalance, voltage limits, recovery charge behavior, and measurement uncertainty.
Review Checklist
Before accepting an energy-storage calculation, check:
- whether the service is frequency response, peak shaving, backup, renewable shifting, microgrid resilience, or voltage support;
- whether energy values are nameplate, DC usable, AC delivered, or measured at the point of interconnection;
- whether SOC reserve and end-of-life degradation are included;
- whether power rating and energy capacity are both adequate;
- whether active and reactive power can be delivered simultaneously;
- whether charging recovery creates a new constraint;
- whether service stacking uses a clear dispatch priority;
- whether degradation, temperature derating, auxiliary loads, SOC estimation error, and warranty limits are included in available capacity;
- whether commissioning evidence includes delivered energy, power response, alarms, thermal behavior, recovery charge, and measurement uncertainty;
- whether commissioning tests measure the same boundary assumed in design.
Good storage engineering is not a search for the largest battery. It is the discipline of matching stored energy, converter capability, reserve policy, controls, safety, and evidence to the grid service being promised.