Agent based modelling of local energy networks as instances of complex infrastructure systems

Power flow analysis

The electrical network is represented as a directed, weighted graph G=(V,E), where V is the set vertices (or nodes) and E is the set of edges (or lines) in the network. Weights are usually be given by the so called admittance matrix Y=[y_ij] that is the Laplacian Matrix, or Kirchhoff Matrix of G.

Engineers use models of the electrical power grid to calculate voltages and currents anywhere in a circuit. If voltages (or intensity sources) at generators are given and voltages and intensities at loads are unknown, then a linear system of equations results and mesh (or nodal) analysis can be used to solve the problem, using standard linear algebra methods.

But in the most usual problem in electrical power systems engineering, the statement is different and it leads to a non-linear system of equations. In this case, the most common method used is power-flow analysis. A very short summary of the method, explained in detail in classical power system books1^,2, follows.

There are three node types, slack (only one), control and load, each denoted by a symbol,

Given the specification: v is known and s is unknown for slack bus, (v,p) are known and (?,q) are unknown for control buses, s is known and v is unknown for load buses, then a non-linear system of equations is posed, for which the so called power-flow iterative approach (based on the Gauss-Seidel method) is usually used to calculate the unknowns. The resulting useful formulae, for each i-th bus,

This method is specially well suited to be adapted to agent-based modelling, because calculations are iterative and local at each node, so it is very easy to do it, simply by representing nodes by agents.

Extending the electrical grid

As agent-based models of the electrical grid were already made by the authors, for microgrids3, the method proposed in this article is extending these models to also cover Energy Networks.

But electrical elements are not enough for this, a more sophisticated idea if node, able to accommodate multidimensional flows, is needing.

This conceptualization is interesting because it could be extended further, to Infrastructure Network models, simply by adding more lines (for communications, policies, regulations, water flows, transport flows, etc.) and allowing hubs to implement conversion points8.

Energy kinds

The electric power it is not the only possible energy carrier, also gas and heat utilities are very useful to cover domestic energy demand. In the gas utility, a gas is flowing through pipes from some generator nodes where the fluid is pushed into the network to other consumer nodes where the chemical energy in the gas is transformed into heat for use it. In the heat utility, usually water (sometimes as steam) is flowing through the pipes from generators to consumers, where the thermo-dynamical energy in the gas is transformed to heat and used.

Another way to deliver energy that can be seen in books are old systems of mechanical power transmission, widely used during the Industrial Revolution, which, although not widely used today as heating services, are often used as subsystems within other facilities. These single mechanic systems do not use fluids nor pipes but energy goes directly from generator nodes to consumer nodes through a system of shafts and pulleys.

These are probably the four kinds of energy most used in existing facilities. There are, of course, other kind of possible energy transmission, such as electromagnetic energy through air or special media, light energy (sun, laser), etc., but in this paper, we will use only those four.

Moreover, although it is not really an energy transmission in the usual sense, a further kind of energy, communication, has been added. It represents digital signals that flowing through some media serve to send messages - usually related to events- between the network nodes, and it is responsible to the event driven digital changes in the network.

In this way, five energy kinds will be considered, as Table 1 summarizes. This gives the network a layered structure, thinking each energy kind flows in a different layer, which is not far from reality.

Energy Hubs

An energy hub is a unit that provides the basic features of input and output, conversion, and storage for multiple energy carriers and represents a generalization or extension of the network node in an electrical system4. Each energy carrier introduces energy of a given type in the hub, where it can be transformed into energy of another type, but it can be also used and stored.

One can imagine five sockets into each hub to be used by the internal agents for communication, mechanical energy, electrical energy, chemical energy and thermal energy, respectively.

Suppose for example that a flow p_e of electric energy comes through the electrical socket into the hub, where a part p_em is converted into mechanical energy, a part p_ee is consumed, a part p_eg is converted into chemical energy, a part p_eh is converted into thermal energy, and the remaining power p_es is stored.

After the respective conversion c_em, c_ee, c_eg, c_eh, c_es and efficiency ?_em, ?_ee, ?_eg, ?_eh, ?_es, processes, the flows of mechanical l_em, chemical l_eg and thermal l_eh energies are given to their respective connected loads and the remainder is stored as electric energy e_e.

Also may be that the flows l_me, l_ge, l_he are fed form the mechanical, chemical and thermal conversion processes, giving an amount l_ee+l_me+l_ge+l_he of electric power flow, part of which, after the conversion r_es and efficiency ?_es processes, is stored as electric energy e_e, as Figure 2 shows.

From energy point of view only the four last of them are operative, so the energy conversion process at each hub can be represented as a block with four inputs p_m, p_e, p_g, p_h for input power flows, and four outputs l_m, l_e, l_g and l_ef or output load flows. The relationships between them are given by

or in matrix notation

L=EP

where P is the input power flow vector, L is the output load flow vector and E is the hub efficiency matrix.

The complete block diagram of a hub, for four energy carriers, including energy stores, is shown in Figure 3 results.

A much more simple and intuitive representation can be done using a graph like picture as the one that Figure 4 shows, where the dark zones represent energy storage elements, one near the power input an the other near the load, the clear zones represent loads, and the colored lines represent the conversion factors and efficiencies. This diagram is close to a System Dynamics representation.

As this figure shows, there is a network inside each hub, so really each hub is a network, and therefore a multi-carrier energy network can be considered as a network of networks. Even more, each vertex of this is again a network.

Each of the small pentagons of Figure 5 corresponds to a hub like Figure 4 shows. And also that if we were to look very closely, we would see that each of the small pentagons at the vertices of the Figure 4 is actually a new hub, and so on, so definitely we have a recursive structure of network of networks.

This is not surprising at all since other complex networks such as the Internet and the Smart Grid7 have already been named that way

Figure 4 shows a possible multi-carrier energy network with six nodes where each of them is a multi-carrier energy hub. Note that each of the small pentagons of Figure 5 corresponds to a hub like Figure 4 shows. And also that if we were to look very closely, we would see that each of the small pentagons at the vertices of the Figure 4 is actually a new hub, and so on, so definitely we have a recursive structure of network of networks.

In this way the model results as the superposition of a number of networks, one for each energy carrier, which one can imagine as if were “glued” at some nodes. Even more, if we refine the model we could see a new network inside each node, where the electric carriers interact. So in this way the model can be seen as a network of networks where the “big” network is the main network and each node is a “small” network, functioning as a conversion point, as it is explained below.

The power-flow algorithm, once adapted, remains valid to calculate magnitudes of non electric fluids, in fact it is easier because do not requires complex calculations.

Scenario

We have modeled the structure and power flow in a simple agent based multi-carrier energy network, which can be used to calculate potentials at nodes and flows through edges of the network, in terms of power generating devices and loads or energy consumers attached to each node

In order to model any operation of these networks for some special application area, the values of all energy generators and consumers must be given, so a model for each of them should be done.

Figure 7 shows the simulation window corresponding to very simple case study, with six agents, created only for trial purposes.

Co-evolution

The fact that Infrastructure Systems exhibit a co-evolutionary behavior has been related by certain authors some years ago9. In the book by 10, three fundamental needs of such systems were recognized. The first was the need for the introduction of novelty, meaning a mechanism must be in place whereby variants of the original structure can be created. Second, selection pressures had to operate, such as carbon emission targets which would make some conversion points ‘fitter’ than others. Finally, a retention mechanism was required, allowing structures to be transmitted from the present to the future8. Actually the three properties

had been borrowed from Biology and are also commonly used in the field of evolutionary algorithms. Figure 9 shows a typical diagram for co-evolution between individuals of two different species.

System transitions

Socio-technical systems are affected not only by physical laws but also by human behavior, regulatory agencies, government and private enterprises. In 9 the authors proposed a modelling framework for large-scale socio-technical systems (LSSTS) and defined system transitions, as a key aspect for evolution of these systems. A system transition is a “structural change in both technical and social subsystems”. Transitions emerge over time as a fundamental change of LSSTS. During transitions, the structure and the content of the physical subsystem change.

Scenarios for agent-based models

An agent-based model is “a collection of heterogeneous, intelligent, and interacting agents, which operate and exist in an environment, which in turn is made up of agents” 11.

Because the entire environment may be an extraordinarily complicated complex system, 9 recommended the use of scenarios.

For scenario working (1) we define parts of the system that are unaffected by other parts within the system, (2) we exclude them from the system, (3) everything outside the system boundary is, therefore, exogenous, (4) every thing relevant but exogenous makes up the scenario space. 12

The evolution of the system in one simulation is not a prediction of the future of that system. One needs an impact assessment by using different system evolutions at different scenarios.

Where do we start from?

Interesting is this system representation shown in 13, p.64, for energy transitions, where technological installations is an important part.

And also the observation by 14: “A complex system that works is invariably found to have evolved from a simple system that worked. The inverse proposition also appears to be true: A complex system designed from scratch never works and cannot be made to work. You have to start over, beginning with a working simple system.”

Conversion points

Transforming utilities conversion points (TUCP)enables us to represent critical infrastructure activities, using an ensemble with four elements: extract, transform, store and deliver, being each activity can further be configured in terms of its inputs, outputs, controls, and mechanisms as Figure 13 shows 8.

There is not a right way to get quantitative realizations, like simulation models, from TUCP. The reason is that TUCP include some arrows representing qualitative ideas (i.e. the technologies arrow), that must be instanced in actual quantitative descriptions before they can be represented using conventional modelling methods, always based on numerical methods. So each actual TUCP should be realized into a quantitative description for modelling, which eventually will result into a network, mathematically represented by weighted graph.

In this way, agent based modelling can be used for case studies, using environments where agents interact which each other using these TUCP networks.

In the author’s opinion, the Transforming Utilities Conversion Points conceptualization could serve to extend the role of the previously analyzed multi-carrier energy network. This extension would be done giving the network nodes (multi-carrier energy hubs in the energy network) the role of Transforming Utilities Conversion Points (TUCP), and to assign to the network edges (multi-carrier energy conductors in the energy network) the role of utilities in infrastructure networks.

So if for energy networks we used a certain number of carriers (4 types of energy and communications in our case, as Table 1 shows), now we should add more. We think that some of the flows, somehow comparable to energy flows, could be: money flow, cars flow, flow of goods by road, product flow, water flow (clean and dirty) and any other material flow imaginable.

Figure 14 shows a entirely imaginary representation of a possible scenario in which three TUCP nodes are connected using the same lines that in the previous energy network model, that is communications (yellow), mechanical energy (black), electrical energy (red), chemical energy (green) and thermal energy (blue) and, moreover, two further non-energy carriers: cash flow (magenta) and product flow (brown).