Module 8 — A Control-Theoretic Perspective on Electricity Markets
Lesson 3 of 8
State, Feedback and Observability
Learning objectives
By the end of this lesson you should be able to:
- Understand the concepts of state, feedback and observability.
- Explain why feedback is fundamental to controlling dynamic systems.
- Recognise the relationship between measurements and decision-making.
- Appreciate why observability limits what any controller can achieve.
- Understand how these concepts can be applied to electricity markets.
Introduction
In the previous lesson, we saw that prices communicate information and influence behaviour.
This naturally raises an important question.
Where does that information come from?
To answer this, we turn to ideas from control theory.
Control theory studies how dynamic systems observe their own behaviour, make decisions and respond to changing conditions.
Although originally developed for engineering systems such as aircraft, industrial processes and robotics, these concepts can also provide a useful perspective for understanding electricity systems and electricity markets.
Dynamic systems
A dynamic system is one whose behaviour changes over time.
Examples include:
- a vehicle travelling along a road,
- an aircraft maintaining altitude,
- a factory production line,
- a heating system controlling room temperature,
- an electricity network balancing supply and demand.
In each case, the system evolves continuously as conditions change.
Effective operation therefore requires decisions to be updated over time rather than made only once.
What is state?
The state of a system describes its current condition.
For a car, the state might include:
- speed,
- position,
- direction,
- fuel level.
For a heating system, the state may include:
- room temperature,
- outside temperature,
- heater output.
For an electricity system, the state could include:
- demand,
- generation,
- power flows,
- voltages,
- network loading,
- available flexibility.
The state represents the information needed to understand how the system is currently behaving.
Why state matters
Imagine trying to drive a car without knowing your speed.
Or flying an aircraft without knowing its altitude.
Without information about the current state, it becomes extremely difficult to make good decisions.
The same principle applies to electricity systems.
Operators need information about the current condition of the network before deciding how it should be operated.
Decision-making depends upon understanding the present state of the system.
Feedback
Feedback is the process of using measurements of the current state to influence future decisions.
A familiar example is a household thermostat.
The thermostat measures the room temperature.
If the room becomes too cold, it switches the heating on.
As the room warms, the thermostat measures the new temperature and eventually switches the heating off.
The system continuously observes its own behaviour and adjusts accordingly.
This is known as a feedback loop.
Feedback in everyday life
Many systems use feedback.
Examples include:
- cruise control adjusting vehicle speed,
- aircraft autopilots maintaining altitude,
- smartphone screen brightness adjusting to ambient light,
- industrial robots correcting their movements,
- traffic signals adapting to vehicle flows.
In each case, measurements are used to improve future decisions.
Without feedback, systems often become less accurate, less efficient or less stable.
Observability
Feedback depends upon information.
This leads to another important concept: observability.
Observability describes how well the internal state of a system can be determined from available measurements.
If important information cannot be observed, decision-making becomes more uncertain.
For example, a pilot cannot safely control an aircraft without instruments.
Similarly, an electricity operator cannot confidently manage a network if key parts of the system cannot be observed.
Observability therefore limits what any controller can achieve.
Measurements and uncertainty
In practice, no system can be measured perfectly.
Sensors may fail.
Communications may be delayed.
Measurements may contain errors.
Some quantities cannot be measured directly and must instead be estimated.
Decision-makers therefore often work with incomplete information.
Engineering is frequently about making the best possible decisions despite uncertainty.
State estimation
When direct measurements are unavailable, engineers often estimate the state of the system.
State estimation combines:
- available measurements,
- mathematical models,
- engineering knowledge,
- statistical techniques,
to infer quantities that cannot be observed directly.
State estimation is widely used throughout engineering, including in modern electricity systems.
It allows operators to build the best possible picture of current system conditions using the information available.
Feedback and markets
Control theory is most commonly associated with engineering systems.
However, similar ideas can also be applied when analysing markets.
Prices influence participant behaviour.
Participant behaviour changes supply and demand.
These changes affect future prices.
Viewed in this way, markets contain feedback processes in which information influences decisions, and those decisions alter future system conditions.
This does not mean markets are identical to engineering controllers.
Rather, it suggests that feedback provides a useful framework for understanding how markets evolve over time.
Information drives coordination
Throughout this course we have seen that modern electricity systems are becoming increasingly digital.
Sensors provide more measurements.
Communications networks distribute information more rapidly.
Software processes larger volumes of data.
These developments improve our understanding of the current state of the electricity system.
Better information generally enables better coordination, whether decisions are made by human operators, automated controllers or market participants.
A key insight
Every dynamic system requires information about its current condition before effective decisions can be made.
Control theory describes this through the concepts of state, feedback and observability.
These ideas provide a useful framework for analysing how electricity systems—and the markets that coordinate them—adapt to changing conditions over time.
Key takeaways
- Dynamic systems change continuously over time.
- The state of a system describes its current condition.
- Feedback uses information about the current state to influence future decisions.
- Observability describes how well the system's state can be determined from available measurements.
- Limited observability increases uncertainty and can reduce decision quality.
- State estimation helps infer system conditions when direct measurements are unavailable.
- Concepts from control theory provide a useful perspective for understanding the coordination of modern electricity systems and markets.
Looking ahead
In this lesson, we introduced the concepts of state, feedback and observability.
These ideas apply whether decisions are made centrally or by many independent participants.
In the next lesson, we compare centralised optimisation and distributed coordination, exploring different approaches to making decisions within complex electricity systems.