Causal Loop Diagrams (CLD)

It has been shown in Section 3.1 that causal or feedback loops exist in all complex systems and gives the cause and effect that determine the structure and behaviour of the system. Causal loop diagrams (CLDs) are flexible and useful tools for diagramming the system feedbacks and the mental models of the system structure. According to Sterman (2000), CLDs are simple maps for illustrating

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the causal relationships among variables, visually represented by arrows from a cause to an effect.

The arrows indicate either a positive (self-reinforcing) or negative (self-correcting or balancing) feedback between system variables. Reinforcing feedback loops are generated when there is an even number (possibly zero) of negative cause to effect relationships, whilst balancing feedback loops are generated when there are an odd number of these relationships. These loops are important to understand the feedback interactions within the system. Reinforcing loops produce growth and amplify these interactions, whilst balancing loops are counteracting and oppose the effects of the interacting variables.

A simple example of a reinforcing loop and a balancing loop, relevant to this thesis and illustrating the mental model of the initial dynamic hypothesis, is shown in Figure 3.4. There are three main interacting variables, namely, low-carbon based capacity mix (electricity generation mainly composed of renewable sources), long-term effective supply (a self-sufficient/sustainable electricity supply that is not dependent on fossil fuel imports) and CO2 emissions (carbon-dioxide emissions from burning fossil fuels for electricity generation). The energy security loop (based on the concept of fossil fuel import independence) is reinforcing (denoted R) since low-carbon based capacity mix has a positive effect on the long-term effective supply which in turn has a positive effect back onto the low-carbon based capacity mix. This loop shows that if there is more low-carbon based capacity this will lead to more long-term effective supply, which will, in turn, lead to even more low-carbon based capacity. Given the structure of SD archetypes, if this loop operated independently, both the low-carbon based capacity mix and the long-term effective supply would typically change exponentially. This is mainly due to the fact that it is a positive reinforcing loop which will have an exponential archetype (Sterman, 2000).

On the other hand, the low CO2 emissions target loop is balancing (denoted B), since low-carbon based capacity mix has a negative effect on the CO2 emissions which then has a positive effect onto the low-carbon based capacity mix. This loop shows that increasing the low-carbon based capacity

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mix this will lead to fewer CO2 emissions, which will, in turn, lead to less low-carbon based capacity mix since it is reinforced by that later relationship. If this loop was operated independently, increases in the low-carbon based capacity mix will be counteracted and this variable would stabilise at some goal value. An SD archetype for this loop will be a goal-seeking archetype (Sterman, 2000). However, as these loops are interacting the low-carbon based capacity mix will be reinforced by the energy security loop and balanced by the low CO2 emissions target loop leading to an eventual dynamic equilibrium. The SD archetype that will exist for this two loops interacting will be an S-shaped archetype (Sterman, 2000). This observation underpins the initial hypothesis of this case study of a low-carbon electricity system.

Figure 3.4 Example simple CLD diagram of the mental model of the low-carbon electricity system

3.2.3 Stock and Flow Diagrams (SFD)

As shown in the previous subsection, CLDs are useful to elucidate the feedback structure of a complex system. However, stock and flow diagrams focus on the physical structures within the system. Stock and flow diagrams (SFDs) track these physical structures such as the accumulations or measurable quantities of the system. In so doing, they characterise the state of the system, the sources of inertia and memory, and generate the quantifiable information upon which decisions

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within the system are based. Stocks usually represents a noun and do not disappear if a time snap shot of the system is taken. Stocks usually decouples flows, create delays and hence can be said to have memory. Flows usually represents verbs and disappears if a time snap shot of the system is taken. Flows usually defines the change in the state of the stocks. Stocks and flows coexists and are mathematically defined for the system. The mathematical formulation requires detailed relationships between the different elements, for shaping a consistent basis, which often challenges and evolves the assumed mental model of how the system is thought to work. SFD diagramming

gives the complete mathematical formulation of all aspects of the mental model.

Figure 3.5 Example of a simple SFD diagram representing the low-carbon capacity mix

For example, as shown in Figure 3.5, the stock will be the measurable quantity of the installed low-carbon capacity and is illustrated as a box with arrows going into and out of it. The arrows represent the flows that influence the stock and reflects the rates at which this stock increase or decrease.

The inflow is the low-carbon investment rate which is the rate at which the stock increases, whilst the outflow is the carbon decommissioning rate which is the rate at which the installed low-carbon capacity decreases. These flows can be nonlinear and operate at different rates that are dependent on other variables and/or link into the rest of the model. For example, the CO2 emissions together with other variables can affect the inflow and/or outflow. Hence the casual relationships can be adequately expanded and be incorporated into the stocks and flows of the system. The clouds at the outer ends of the diagram represents the sources and sinks for the flows. Sources and sinks are assumed to have infinite capacity and do not restrict the flows to which they support. The source represent the stocks from which a flow originating from outside the boundary of the model

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arises whilst a sink represent the stocks into which flows leaving the model boundary drains. Hence, in this example, low-carbon investment rate has infinity capacity and low-carbon decommissioning

rate is not restricted from outside the model boundary.

Although the relationships between model variables are normally determined by simple mathematical equations, there is some interaction that might require a different approach such as the use of non-linear approximations or look-up tables. Key lookup tables and equations for this research are detailed in Appendix A. In addition, more details of this and other CLD and SFD diagramming conventions such as the resulting modes of dynamic behaviours can be found in Sterman (2000). The following section highlights the model testing approaches that are important for developing useful SD models.