How does everything connect? Stocks, flows, feedback and the whole-system map

Fill a reservoir, close a feedback loop, then pull a lever and watch the whole system ripple

F2 of Energy Systems, Step by Step: run a stock-and-flow simulator (a reservoir, a battery, a carbon budget), sign and name feedback loops (chargers and EVs, the rebound effect), then pull four levers on a whole-system map and follow the ripples across technology, cost, emissions, people and security.
  • Foundations to Analyst · L1–L2
  • 25 min guided · about 10 min practice
  • After F1 and lesson 6

The lab's three stations, in brief

A reservoir
Holding up to 350 GWh and fed by a river averaging 101 MW, it gets through the year without spilling or running dry only with a steady release from 100 to 115 MW (the slider moves in 5 MW steps).
A battery
A 25 MW, 100 MWh battery that loses 20% on charging must buy 125 MWh to deliver 100.
A carbon budget
If an illustrative nation halves its 100 Mt a year by 2035 and holds there, its cumulative emissions still rise, from 825 Mt to 2,575 Mt by 2070, past a 1,500 Mt budget.
Feedback loops
More EVs bring more chargers, which bring more EVs: a reinforcing loop. Longer queues at chargers slow the growth, and the rebound effect takes back part of an efficiency saving: balancing loops.
The system map
Each of four levers reaches technology, cost, emissions, people and security within three waves.
Lever First wave Later waves
Gas price doubles Wholesale price rises; gas heating costs more; the gas import bill rises Plant mix shifts; CO₂ depends on what replaces gas; energy burden rises; investment shifts and dependence on imported gas falls
A heat wave Demand rises; lines carry less; spare capacity falls; heat-related health risk rises Prices and CO₂ can rise; bills and burden can rise later; tight hours can encourage new capacity
A carbon price Gas plants can move ahead of coal plants; wholesale price rises If gas replaces coal, CO₂ and local pollution fall; bills rise if the tariff passes the price on; the burden depends on the revenue; jobs shift
A new data center Demand rises; it needs new connections; spare capacity falls when it connects; jobs and tax base can rise; cooling water depends on the design CO₂ depends on what serves it; who pays for upgrades depends on the tariff; new supply may follow

With JavaScript on, you run these yourself: three tanks, two loops and four levers.

Tanks: the reservoir, lesson 9's battery and the nation's budget are illustrative.
Units: Mt = million tonnes; GWh = a thousand MWh.
Map: first-round directions of change, other things equal, for a grid like the Plains Grid; it states no sizes.
Waves: steps in tracing causes; each label says roughly when a step plays out.
Data center: an illustrative 300 MW load.

What you just did, as diagrams

Stock
A stock is an amount that builds up or drains: water, stored energy, cumulative CO₂, cars on the road.
Flow
A flow is a rate that fills or drains a stock; only flows change a stock.
Reinforcing loop
An even number of − links round a feedback loop: change feeds itself (reinforcing).
Balancing loop
An odd number of − links: the loop opposes the change that started it (balancing); with long delays it can overshoot.
Ripple
One change spreads step by step across technology, cost, emissions, people and security: some effects at once, some years later.
Go deeper · AnalystThe stocks that shape energy systems

Many slow, hard questions are questions about stocks.

  • Equipment. Power plants, buildings, cars and boilers last for decades, so today’s choices stay in the stock long after: new purchases are the inflow, retirements the outflow. National pathways track this (Analyst lesson A20; Modeler lesson M13).
  • Fuel. Gas in storage and emergency oil stocks buffer a supply shock (Analyst lesson A21).
  • Stored energy. Reservoirs and batteries move energy in time (lesson 9; Analyst lesson A8).
  • Cumulative CO₂ emissions. Warming tracks them: the IPCC’s best estimate is 0.45 °C for each 1,000 Gt of CO₂ (Gt = billion tonnes; likely 0.27 to 0.63 °C).
  • Net zero. Stabilising human-induced warming requires net zero CO₂. The lab’s counter records emissions only; land and oceans absorb part, so the CO₂ left in the air is a different stock.
Go deeper · ModelerFrom diagrams to equations

A stock is a state variable that carries over from one step to the next:

\[ S_{t+1} = S_t + \big(\mathit{in}_t - \mathit{out}_t\big)\,\Delta t, \qquad 0 \le S_t \le \bar{S} \]

with \(S_t\) the stock, \(\mathit{in}_t\) and \(\mathit{out}_t\) the flows, \(\Delta t\) the step and \(\bar{S}\) the ceiling. Flow × time must come out in the stock’s unit:

  • Reservoir: change in GWh = (river in − release, in MW) × 168 hours ÷ 1,000, since 1 GWh = 1,000 MWh.
  • Carbon: change in Mt = emissions in Mt a year × 1 year.
  • Battery: the rule of lesson 9, with an efficiency on the inflow.

A loop appears when a flow depends on a stock, such as sales that depend on the EVs already on the road.

  • Simulation steps such rules forward from given decisions; system dynamics, one method family in R3, writes the loops as equations.
  • Optimization chooses the decisions (lessons 10 to 13).
  • Which one a study needs is Researcher lesson R3.
Go deeperWhat this lab leaves out
  • Sizes: the map shows directions, not how much. Sizes need a model with data, prices and rules (Analyst and Modeler tiers).
  • Place and time: the same lever plays out differently in another region, market or year.
  • Many more links: a real system has far more parts and loops than fifteen cards and two diagrams.
  • Who decides: each ripple crosses the scales of F1, and trade-offs between goals are Analyst lesson A22.

Check yourself

Practice, about 10 minutes: four myths, then five questions.

Myth or fact? “If the inflow to a stock is falling, the stock is falling.”

  • Myth
  • Fact
Answer

Myth. A stock falls only when its outflow exceeds its inflow. In one test, business-school students new to these ideas showed a poor grasp of stocks and flows (Booth Sweeney and Sterman, 2000).

Myth or fact? “Holding CO₂ emissions steady holds the warming they cause steady.”

  • Myth
  • Fact
Answer

Myth. Warming tracks cumulative CO₂ emissions, a stock: steady emissions keep adding to it. The IPCC finds net zero CO₂ is required to stabilise human-induced warming.

Myth or fact? “A reinforcing loop always means growth.”

  • Myth
  • Fact
Answer

Myth. It reinforces whichever way it turns: fewer EVs, fewer chargers built, fewer EVs.

Myth or fact? “If people use a more efficient appliance more, the efficiency gain is wasted.”

  • Myth
  • Fact
Answer

Myth: one review concludes that the direct rebound for household energy services in OECD (mostly high-income) countries should generally be less than 30%, so most of the saving is kept (Sorrell et al., 2009).

Prairie Town's battery is rated 25 MW and 100 MWh. Which number limits the stock?

  • 25 MW
  • 100 MWh
  • Both equally
Answer

100 MWh is the stock it can hold; 25 MW limits the flow in or out. Together: 4 hours at full power.

More rooftop solar → lower midday prices → less income per new panel → less new rooftop solar. Which kind of loop?

  • Reinforcing
  • Balancing
Answer

Balancing: one − link (more solar, lower prices), so the loop pushes back on its own growth.

Why does a heat wave squeeze spare capacity from both sides?

  • Demand rises while hot lines and some thermal plants deliver less
  • Prices rise, so plants sell less
  • Solar stops at noon
Answer

Demand rises for cooling while hot lines sag and carry less and some thermal plants lose output: both sides of the balance move against the grid.

A 300 MW data center connects, and no new supply comes with it. When does spare capacity shrink?

  • Years later, after a second event
  • At once, as soon as the load connects
  • Never: demand and supply are separate
Answer

At once: the extra demand uses up spare capacity when it connects. The map's waves trace causes in order; they are not always apart in time.

The map says bills “rise” after a carbon price. What would you need to say by how much?

  • More arrows on the map
  • A survey of opinions
  • A model with data: plants, fuel prices, the carbon price and the tariff
Answer

A model with data. The map shows directions; sizes come from models like the ones the Analyst and Modeler tiers build.

Numbers, sources and what’s next

Numbers to remember

Number What it means Source
0.45 °C Best estimate of the warming caused by each 1,000 Gt of cumulative CO₂ (likely 0.27 to 0.63 °C): warming follows the stock. IPCC AR6 WG I, Summary for Policymakers, D.1.1, p. 28 · 2021
30% One review's conclusion: the direct rebound for household energy services in OECD countries should generally be less than this. Sorrell, Dimitropoulos and Sommerville, Energy Policy · 2009, abstract
759,180 MW The Lower 48 states' record hour of demand, on 29 July 2025, in hot weather. EIA, Today in Energy · 5 August 2025, preliminary data
4.4% Share of U.S. electricity used by data centers in 2023: a load the system map treats like any other. U.S. DOE, on a Lawrence Berkeley National Laboratory report · 20 December 2024

Next

A22 · Cheap, clean, reliable, fair, secure: can you have them all?

In the real world

  1. Measured: a study of 353 U.S. metro areas, 2011 to 2013, found effects running both ways, stronger on the car-buying side: chargers drew EV buyers, and EVs drew chargers (Li et al., 2017, abstract).
  2. Sized with data: real studies measure how strong such loops are; the lab only shows their shape.

Sources and further reading

Spotted an error, or stuck? Write to hlli@ksu.edu. Corrections are made in place and dated here.

Text licensed CC BY 4.0, code MIT: teachers and students may reuse and adapt it, with credit to Honglin Li.