Engineering & Technology · Electrical Power, Conversion & Machines

Electrical storage, batteries and coupled energy systems

Two storage systems can have the same energy capacity but very different power capability. One may supply a small load for hours while being unable to start a larger load at all. A useful storage model therefore needs state, conversion boundaries and operating limits together.

Electrical Circuits supplies current/voltage, power, rms, phase and ideal storage relations. Engineering Thermodynamics supplies energy balances, losses and system boundaries. This chapter introduces magnetic flux and pole count before using them, derives the simple machine/converter relations and labels every invented parameter. All diagrams and numerical cases are original teaching models. They do not specify equipment construction, protective settings, installation, switching or qualification.

Back to the chapter

After reading, you can

Relate storage state, usable energy, power and efficiency without treating a nominal capacity as a guaranteed delivered service.

Specify what actually stores the energy

Batteries store energy through electrochemical state; electrons move in an external circuit while ionic processes inside support charge balance. Charging and discharging alter that state. Incomplete reversibility and other degradation processes can reduce performance over time. The energy is not simply a tank of free electrons waiting to leave.

Other electrical-storage systems use mechanical, gravitational, thermal or field energy and converters to accept and return electrical power. Their service depends on the whole chain. Selecting one chemistry or mechanism requires its conditions, timescale, losses and lifecycle rather than a universal ranking.

Connect electrode reactions to two different charge carriers

An electrode is a conducting interface between the external electronic circuit and the cell chemistry. The electrolyte provides an internal ionic route: ions are atoms or groups of atoms with a net electric charge. A separator can prevent direct electronic contact between electrodes while allowing ionic transport through its electrolyte-filled structure. A useful cell therefore supports two coupled routes rather than sending the same electrons through every part of one metal loop.

During discharge, a reaction at the negative electrode releases electrons to the external circuit. Losing electrons is oxidation. A reaction at the positive electrode accepts electrons arriving through the load; gaining electrons is reduction. The external electron motion is from negative to positive through the load, while conventional current has the opposite direction. Internal ion movement maintains charge balance as the interfacial reactions proceed. The ion species and directions depend on the chemistry; not every cell sends one kind of positive ion in the same direction.

The diagram deliberately chooses one abstract rechargeable host model. Let AM be a neutral host A containing an inserted species M. At the negative interface, AM → A+M⁺+e⁻: one positively charged ion enters the ionic route while one electron enters the external electronic route. At the positive interface, B+M⁺+e⁻ → BM. Adding the two reactions gives AM+B → A+BM. A and B stand for different host materials, not real element symbols or a proposed battery recipe. Each local reaction balances charge, and M is transferred rather than created.

For this chosen discharge direction, M⁺ travels internally from the A side toward the B side, while electrons reach B through the load. The change in material state can release energy: some transfers electrically through the load, while losses can produce heat. The stored chemical energy belongs to that material state, rather than to a pile of surplus electrons. Charge conservation alone cannot predict the cell voltage. Electrode materials, state, temperature and losses matter. With the external path open, only a limited transient charge separation can occur before sustained reaction current stops; an ionic path alone does not supply continuous external power.

Blocking ionic transport also prevents sustained discharge in this model, even if an external conductor remains connected. Charge would accumulate near the interfaces and oppose further reaction; brief capacitive transients do not establish continued chemical transport. Conversely, an unintended internal electronic path can allow reactions without useful work in the intended load. The existence of reactive material is not enough: the permitted charge and energy paths determine the service.

Charging a rechargeable cell requires an external source to drive appropriate net reactions in reverse and increase the stored chemical energy. This does not guarantee a perfect return to the previous state: side reactions, structural changes and transport losses can reduce capability. “Anode” means the oxidation electrode and “cathode” the reduction electrode in strict reaction terminology, so their reaction roles reverse on charge; using the physical positive and negative electrode names avoids that ambiguity here. No charging voltage, current or method follows from this conceptual account.

An abstract discharge model has negative host AM on the left and positive host B on the right. Electrons released by AM travel through an external load to B; conventional current is opposite. Internally, M-plus ions travel through an electronically blocking, ion-permitting electrolyte/separator to B. The two stipulated interfaces are AM → A + M⁺ + e⁻ and B + M⁺ + e⁻ → BM, giving net AM + B → A + BM. This one-ion host model is not a universal battery mechanism or a construction diagram.

Keep charge, energy and power separate

Ampere-hours measure charge: 1 Ah=3600 C. Watt-hours measure energy: 1 Wh=3600 J. A voltage-weighted charge integral gives electrical energy; multiplying Ah by one nominal voltage is an approximation whose usefulness depends on voltage variation and the stated capacity basis.

Power is the rate of energy transfer. A nominal kWh capacity does not establish a maximum kW output, charge rate, startup capability or remaining usable state. State of charge is an estimate relative to a defined reference capacity; state of health concerns changed capability relative to another defined baseline. Neither is directly established by one unloaded terminal-voltage observation alone.

Define the boundary of efficiency. Cell, pack, DC bus and delivered AC energy can have different losses, auxiliary loads and usable windows. Round-trip efficiency compares returned energy with charging energy over a defined cycle and state condition. Avoid multiplying unrelated specifications as if they came from the same operating point.

Include the allowed state window and receiving load

The original figure distinguishes installed nominal energy from an assumed usable internal window, then accounts for discharge and converter losses. The values are mathematical teaching assumptions, not a battery specification. Its bars share one energy scale and label the losses rather than hiding them in a vague percentage.

A real system also depends on temperature, aging, current, thermal management, protection, self-discharge and the time profile of demand. Coupling to a generator or heat system introduces more interfaces. Recovered heat may be useful in a suitable application, but it cannot also be counted as extra electrical output without a separate conversion account.

Retain capacity basis, initial/final state, duty cycle, environmental conditions and energy-meter boundaries when comparing storage claims. Otherwise a capacity improvement might merely reflect a wider allowed state window or a different test, rather than changed material performance.

Vertical energy 0–12 kWh at 25 units/kWh; categorical bars nominal 12, usable internal 9, delivered AC 7.695 kWh. Allowed internal window is 75% of nominal, not a 3 kWh energy dissipation. Discharge path 95% and AC conversion 90% give 1.305 kWh losses between 9 and 7.695. Output power limit separately 3 kW and not represented by bar height. All model parameters hypothetical; auxiliaries, self-discharge and condition dependence omitted.

Check energy duration and instantaneous power

An invented pack has nominal energy 12 kWh, with 75% allowed as the usable internal window: 9 kWh. Suppose discharge-path efficiency is 95% and the following AC converter is 90% efficient at this model operating point. Delivered energy is 9×0.95×0.90=7.695 kWh, omitting auxiliaries and self-discharge only for this calculation.

For a constant 2.5 kW AC load within an assumed 3 kW output limit, duration is 7.695/2.5=3.078 h, about 3.08 h. A constant 4 kW demand exceeds that output limit even though an energy-only division would produce a duration. Capacity alone does not meet the power requirement.

If charging efficiency from the same external boundary to the internal store is 90%, restoring 9 kWh needs 10 kWh input. Returning 7.695 kWh gives round-trip efficiency 76.95% for these declared factors and boundaries. The difference is not all attributed to the cells; it includes the specified conversion paths.

A separate nominal 20 Ah, 12 V description would suggest 240 Wh only if the voltage/capacity approximation were justified. It does not automatically describe our 12 kWh pack or guarantee its usable energy, current limit or lifetime.

A separate original charge-and-energy case uses a cell stipulated to deliver a constant 3.0 V terminal voltage and 1.0 A for 60 s. Charge through the external load is It=60 C, equal to 60/3600=1/60 Ah. Delivered electrical energy is VIt=180 J=0.050 Wh. In the ideal one-electron-per-M⁺ host account, the interfacial reaction throughput corresponds to that same 60 C of charge equivalents, not an additional 60 C to add to the external reading. Chemical transport and external charge flow are coupled descriptions of the same reaction progress.

Now stipulate a different discharge interval: 2.0 A for 30 s at a constant 2.7 V terminal voltage. The external charge is still 60 C, but delivered energy is 2.7×60=162 J=0.045 Wh. Equal Ah did not give equal Wh because the terminal voltage differs. These supplied intervals do not establish the cause of the voltage change, the cell chemistry or its permissible rate. They connect the physical reaction paths to the earlier distinction between charge capacity, energy and power.

Try the reasoning

Are Ah and Wh interchangeable capacity units?
Show the answer and reasoning
No. Ah is charge and Wh is energy; energy also depends on voltage through the transfer.
Why can a 4 kW load fail the example even with substantial remaining energy?
Show the answer and reasoning
The assumed AC power limit is 3 kW, independent of how many kWh remain.
Does 76.95% identify a universal battery round-trip efficiency?
Show the answer and reasoning
No. It is the product of explicitly assumed path efficiencies for this constructed cycle and boundary.
A model retains an external electronic connection but makes the internal electrolyte unable to transport ions. Can its original constant discharge current continue indefinitely?
Show the answer and reasoning
No. Sustained interfacial reactions would leave uncompensated charge near the electrodes and oppose further transfer. A brief charge-separation transient can occur, but the coupled ionic route is needed for the sustained current assumed by the cell model.
In the abstract AM+B discharge, one M⁺ and one electron are transferred per reaction event. Does this double the externally measured charge?
Show the answer and reasoning
No. They follow different internal and external routes required by the same coupled reaction. The external current counts charge through its own cross-section; adding internal charge equivalents to it would count reaction progress twice.
A fresh stipulated interval delivers 1.5 A for 40 s at 2.5 V. Compare its charge and energy with the earlier 1 A, 60 s, 3 V interval.
Show the answer and reasoning
Both transfer 60 C, or 1/60 Ah. The new interval delivers 2.5×60=150 J, about 0.04167 Wh, compared with 180 J or 0.050 Wh. Equal charge does not fix electrical energy when voltage differs; neither interval supplies a chemistry or operating limit.

What to carry forward

Describe the state and usable window, then check energy, power, losses and conditions at the same system boundary.

References

Teaching resources and research supporting this lesson’s explanations and examples.