Difficulty: Intermediate | Prerequisites: Basic chemistry (redox reactions), Lecture 2 notes on battery manufacturing and construction
Lithium-ion batteries come in several chemistries (LFP, LMO, LTO, LCO, NCA, NMC), each with distinct trade-offs in energy density, power, cycle life, and cost. The C-rate tells you how fast a battery charges or discharges relative to its capacity. Manufacturer datasheets give you the operating envelope (voltage limits, capacity, temperature range) that any battery model must respect.
Open circuit voltage (OCV)
The voltage measured across a battery's terminals when no current is flowing. Think of it as the battery's "resting" voltage at a given state of charge.
C-rate
A normalised measure of charge or discharge current relative to battery capacity. A 1C current fully charges or discharges the battery in one hour. In simple terms, it tells you how fast you are pushing energy in or pulling it out.
State of charge (SOC)
The fraction of remaining charge in a battery, normalised between 0 (empty) and 1 (full). Denoted z. In simple terms, it is the battery's fuel gauge.
Internal resistance (R_int)
The lumped resistance inside the battery that causes a voltage drop when current flows. Think of it as the friction that wastes energy whenever the battery does work.
Terminal voltage (V_t)
The voltage you measure at the battery's external terminals while current is flowing. It equals OCV minus the resistive drop during discharge, or OCV plus the resistive drop during charge.
Nominal voltage (V_nom)
The manufacturer's stated average working voltage for a cell, used for pack-level calculations.
Specific energy (Wh/kg)
Energy stored per unit mass. Higher values mean a lighter battery for the same energy. In simple terms, this is your "range per kilogram" figure.
Energy density (Wh/L)
Energy stored per unit volume. Higher values mean a smaller battery for the same energy.
Specific power (W/kg)
Peak power deliverable per unit mass. Higher values mean the battery can supply large bursts of current without being too heavy.
Cycle life
The number of full charge/discharge cycles a battery can undergo before its capacity drops below a specified threshold (often 80% of original).
Self-discharge (% per month)
The rate at which a battery loses charge while sitting idle with no load connected.
Coulomb counting
Estimating SOC by integrating the current over time. The governing equation is z-dot = -(1 / 3600 C_n) * I, where C_n is the nominal capacity in Ah.
Half-cell potential
The voltage of a single electrode measured against a lithium metal reference. The full-cell OCV is the cathode half-cell potential minus the anode half-cell potential.
Anode
The negative electrode in a lithium-ion cell during discharge. Typically graphite (Li_xC_6).
Cathode
The positive electrode in a lithium-ion cell during discharge. Common materials include LCO, NMC, NCA, LFP, and LMO.
Intercalation
The reversible insertion of lithium ions into the layered crystal structure of an electrode material. This is the physical mechanism behind charging and discharging in lithium-ion cells.
Lithium-ion cell manufacturing has two broad phases: electrode preparation and cell assembly.
Electrode preparation
Receiving raw materials (active material powders, binders, solvents, current collector foils)
Mixing and coating the slurry onto foils: positive electrode slurry on aluminium, negative electrode slurry on copper
Solvent evaporation and recovery
Calendering: compressing the coated electrode to target thickness and porosity
Vacuum drying to remove residual moisture
Electrode slitting to final dimensions
Cell assembly (performed in a dry room)
Cell stacking or winding of alternating anode, separator, and cathode layers
Current collector welding (tabs connecting the electrode stack to the terminals)
Enclosing the stack in its container (pouch, prismatic can, or cylindrical can)
Electrolyte filling and cell sealing
Formation cycling: the first controlled charge/discharge that forms the solid-electrolyte interphase (SEI) layer
Charge-retention testing and final cell sealing
Quality checks, module assembly, and pack assembly
ANL BatPac model
Argonne National Laboratory's BatPac model lets engineers study design trade-offs such as electrode thickness and porosity against energy density, power capability, and cost. A 2020-era cost breakdown shows materials accounting for roughly 49% of cell cost, with purchased items at 16% and the remaining slices spread across labour, overhead, R&D, depreciation, profit, and warranty.
Real-world context. This is the manufacturing pipeline behind every EV battery pack. Understanding it matters because design choices at the electrode level (thickness, porosity, active material loading) directly determine the cell's electrical performance, which feeds into every model you will build in this course.
Six common cathode chemistries dominate the lithium-ion landscape. The table below summarises the key performance figures from the lecture.
Property | LFP | LMO | LTO | LCO | NCA | NMC |
|---|---|---|---|---|---|---|
Specific energy (Wh/kg) | 80–130 | 105–120 | 70 | 120–150 | 80–220 | 140–180 |
Energy density (Wh/L) | 220–250 | 250–265 | 130 | 250–450 | 210–600 | 325 |
Specific power (W/kg) | 1400–2400 | 1000 | 750 | 600 | 1500–1900 | 500–3000 |
C-rate range | 10–30C | 8–10C | 10C | 2–4C | 5–20C | 2–20C |
Volts per cell (V) | 3.2–3.3 | 3.8 | 2.2–2.3 | 3.6–3.8 | 3.6 | 3.6–3.7 |
Cycle life | 1000–2000 | >500 | >4000 | >700 | >1000 | 1000–4000 |
Self-discharge (%/month) | <1% | 5% | 2–10% | 1–5% | 2–10% | 1% |
Cost ($/kWh) | $400–$1200 | $400–$900 | $600–$2000 | $250–$450 | $600–$1000 | $500–$900 |
Operating temp (°C) | -20 to +60 | -20 to +60 | -40 to +55 | -20 to +60 | -20 to +60 | -20 to +55 |
How to read the trade-offs:
High energy applications (range matters most): LCO, NCA, NMC. These chemistries pack the most Wh/kg and Wh/L.
High power applications (acceleration, regenerative braking): LFP, NCA, NMC. High C-rate capability and specific power.
High cycle life (longevity, grid storage): LFP, LTO, NMC. LTO stands out with >4000 cycles.
Lowest cost: LCO and LMO sit at the lower end of the price range, though raw material prices shift this constantly.
Source: The Handbook of Lithium-Ion Battery Pack Design, by John T. Warner.
C-rate is the current (in Amperes) at which a battery would be fully charged or discharged in exactly one hour. It normalises current against capacity, so you can compare batteries of different sizes on a level playing field.
Core rule: A rate of nC means the battery completes charge/discharge in 1/n hours. A rate of C/n means it takes n hours.
Worked examples from the lecture:
2C charging: the current that would charge the battery in 0.5 hours
C/10 discharge: the current that would deplete the battery in 10 hours
Numerical example (2 Ah battery):
1C = 2 A (fully discharge in 1 hour)
C/5 = 0.4 A (fully discharge in 5 hours)
3C = 6 A (fully discharge in 20 minutes)
General formula:
I = (C-rate) x (rated capacity in Ah)
Time to full discharge = 1 / (C-rate) in hours
Real-world context. When a datasheet says a cell supports "10C discharge," it means the cell can safely deliver ten times its Ah rating as current. This matters for EV applications where high peak power (acceleration) demands very high C-rates for short bursts.
The lecture uses the Panasonic NCR18650A as a reference cell. Key specs from its datasheet:
Parameter | Value |
|---|---|
Rated capacity | Min. 2900 mAh |
Typical capacity | 3070 mAh |
Nominal voltage | 3.6 V |
Charging method | CC-CV, std. 1475 mA, 4.20 V, 4.0 hrs |
Max weight | 47.5 g |
Charge temp. | 0 to +45 °C |
Discharge temp. | -20 to +60 °C |
Storage temp. | -20 to +50 °C |
Volumetric energy density | 620 Wh/L |
Gravimetric energy density | 225 Wh/kg |
Key datasheet plots to understand (and eventually model):
Charge characteristics: voltage and current versus time during CC-CV charge
Cycle life characteristics: capacity versus cycle count
Discharge characteristics by temperature: voltage versus discharge capacity at different temperatures
Discharge characteristics by rate: voltage versus discharge capacity at different C-rates (0.2C, 0.5C, 1C, 2C)
The overarching goal of the OCV-R model (and later, more complex models) is to mathematically describe and predict these four characteristic plots.
What to extract from a datasheet:
V_min and V_max: the voltage window the cell operates in (here roughly 2.5 V to 4.2 V)
Rated capacity: the Ah figure used for C-rate calculations
Temperature limits: charging is more restrictive than discharging
CC-CV charging protocol: constant current until V_max, then constant voltage until current tapers
Cell structure. A lithium-ion cell has a negative electrode (anode, typically graphite on a copper current collector), a positive electrode (cathode, a lithiated metal oxide on an aluminium current collector), and a lithium-ion-conducting electrolyte with a separator between the electrodes.
Discharge: lithium ions move from the anode through the electrolyte to the cathode. Electrons flow through the external circuit in the same direction (anode to cathode externally), providing useful current.
Charge: the process reverses. An external voltage forces lithium ions back into the anode.
Half-cell reactions (LCO/graphite example):
Anode: Li_xC_6 ⇌ xLi+ + xe- + C_6
Cathode: LiCoO_2 ⇌ Li_(1-x)CoO_2 + xLi+ + xe-
Full cell: LiCoO_2 + 6C ⇌ Li_yC_6 + Li_(1-x)CoO_2
The stoichiometric range for x at the cathode is 0 to 0.5 (you cannot safely extract all the lithium from LCO).
Cathode half-cell potentials (measured against lithium metal):
LiCoO_2 (LCO): roughly 3.5 to 4.3 V, with a relatively sloped curve as a function of lithium concentration y
LiMn_2O_4 (LMO): roughly 3.8 to 4.3 V, with a characteristic two-plateau shape
LiFePO_4 (LFP): very flat plateau near 3.4 V across most of the lithium concentration range
Anode half-cell potential (graphite against lithium metal):
Graphite shows a staged intercalation profile between 0 and 0.4 V. The potential curve has distinct flat regions corresponding to phase coexistence between different staging configurations (Dilute 1, Stage 4, Stage 3, Stage 2, Stage 1). Each stage has a characteristic voltage plateau and lithium concentration range.
Full-cell OCV:
OCV = U_p(y_0 - Q/C_p) - U_n(x_0 + Q/C_n)
where U_p is the cathode potential function, U_n is the anode potential function, Q is the charge throughput, and C_p and C_n are the cathode and anode capacities respectively.
State of charge: z = Q/C = (y_0 - y)/(y_0 - y_100) = (x - x_0)/(x_100 - x_0)
Total capacity: C = C_p(y_0 - y_100) = C_n(x_100 - x_0)
Real-world context. The shape of the OCV curve is ultimately determined by the thermodynamics of lithium intercalation at each electrode. LFP's flat voltage plateau makes SOC estimation from voltage alone very difficult in the middle range, which is one reason more sophisticated estimation algorithms (covered later in the course) are needed.
Students often think "higher C-rate" means "higher capacity." It does not. C-rate is about speed of charge/discharge, not how much energy the battery holds. A higher C-rate means faster, not bigger.
Students sometimes confuse anode and cathode naming conventions. In a lithium-ion cell, the graphite electrode is always called the anode (and is the negative terminal), regardless of whether the cell is charging or discharging. Some textbooks on general electrochemistry swap the labels depending on current direction, but battery convention does not.
A common error is to assume the full-cell voltage equals the cathode potential. It equals cathode minus anode potential. Because graphite sits near 0.1 V vs Li metal, the difference between the cathode potential and the full-cell OCV is small but not zero.
Students sometimes assume all lithium-ion chemistries behave the same. The OCV curve shape varies dramatically: LFP is nearly flat, LCO is steeply sloped, and graphite anodes show distinct staging plateaus. These differences affect every aspect of modelling and SOC estimation.
⚠️ Be able to calculate the current in Amps for any given C-rate and battery capacity. This is a near-certain exam question.
⚠️ Know which chemistries suit which applications (energy vs power vs cycle life). The comparison table is a favourite source for short-answer questions.
⚠️ Understand how the full-cell OCV is constructed from the two half-cell potentials. You may be asked to sketch OCV as a function of SOC given the half-cell curves.
⚠️ Know the physical meaning of each datasheet parameter (rated capacity, nominal voltage, V_min, V_max) and how they feed into the OCV-R model covered in Part 2.
True or False: A 2C discharge rate on a 5 Ah battery means 10 A of current. True.
Fill in the blank: The full-cell OCV equals the ______ potential minus the ______ potential. (cathode, anode)
True or False: LFP has the highest energy density of all common lithium-ion chemistries. False. LCO, NCA, and NMC have higher energy densities.
Fill in the blank: A C/10 discharge on a 3 Ah battery draws ______ A and takes ______ hours. (0.3 A, 10 hours)
True or False: Graphite anode potential vs lithium metal is roughly 3.5 V. False. It is roughly 0 to 0.4 V.
Q: A battery is rated at 2900 mAh. What current corresponds to a 0.5C discharge, and how long will the discharge take?
A: 0.5C x 2.9 Ah = 1.45 A. The discharge takes 1/0.5 = 2 hours.
Q: Name two lithium-ion chemistries best suited for a grid-storage application where cycle life is the primary concern. Justify your choice.
A: LFP and LTO. LFP offers 1000 to 2000 cycles and LTO exceeds 4000 cycles, both far above LCO (>700). Grid storage does not require high energy density, so the lower Wh/kg of these chemistries is an acceptable trade-off.
Q: Explain why the terminal voltage during discharge is lower than the OCV at the same SOC.
A: During discharge, current flows through the battery's internal resistance, creating a voltage drop V_drop = I x R_int. The terminal voltage is V_t = OCV - I x R_int, so it sits below the OCV curve by that resistive drop.
Q: Given the half-cell potentials U_p(y) for a cathode and U_n(x) for a graphite anode, write the expression for the full-cell OCV as a function of charge throughput Q.
A: OCV(Q) = U_p(y_0 - Q/C_p) - U_n(x_0 + Q/C_n), where y_0 and x_0 are the initial lithium concentrations, and C_p and C_n are the electrode capacities.
Q: Why is SOC estimation from voltage alone particularly difficult for LFP cells?
A: LFP has a very flat OCV plateau across most of its SOC range (roughly 20% to 80%). A small measurement error in voltage maps to a large uncertainty in SOC, because the OCV-SOC curve has almost zero slope in that region.
This material connects directly to Lecture 2 (battery manufacturing and construction), which covered how cells are physically built. The chemistries and half-cell potentials here explain why those manufacturing choices matter.
The OCV curve and C-rate concepts are prerequisites for Part 2 of this lecture's notes, which covers the OCV-R equivalent circuit model, Coulomb counting, and how to parameterise the OCV curve from experimental data.
Later in ME565, you will build on the OCV-R model with more complex equivalent circuit models (adding RC pairs for dynamic behaviour), state estimation algorithms (extended Kalman filters), and thermal modelling, all of which rely on the battery fundamentals covered here.
OCV, open circuit voltage, C-rate, state of charge, SOC, lithium-ion battery, LFP, LCO, NMC, NCA, LMO, LTO, half-cell potential, intercalation, graphite anode, cathode potential, battery datasheet, Panasonic NCR18650A, specific energy, energy density, cycle life, Coulomb counting, battery manufacturing, electrode preparation, calendering, formation cycling, BatPac, ME565, battery control and systems, University of Michigan