John spent many years working in the IT industry before returning to academia to gain an MSc in Applied Bioinformatics and to then undertake a PhD in Evolutionary Computing for Multi-Objective Optimisation.

Timos holds a first degree in Mechanical and Aeronautical Engineering from the University of Patras, Greece, and a PhD in Multi-Objective Aerodynamic Design Optimisation from the University of Cambridge, UK. He is a Research Fellow in the Propulsion Engineering Centre, School of Aerospace, Transport and Manufacturing, Cranfield University, and a Research Associate in the Engineering Design Centre, Department of Engineering, University of Cambridge.

Electrical power networks can be improved both technically and economically through the inclusion of distributed generator (DG) units, which may include renewable energy resources. This work uses multi-objective optimization by evolutionary computing, with power flow calculations and multi-dimensional results analysis, to investigate a method of defining optimal deployment of DG units. The results indicate that the method used is a feasible one for designing deployment of DG units in terms of type, number, and location.

Evolutionary computing in various forms has been used previously in complex systems research such as emergent computation

The method used here goes some way to answering questions such as how might a new infrastructure be composed in terms of DG units, how are its components geographically distributed, and how many of each type would be most appropriate given cost constraints.

One of the essential problems in electrical power networks is that of power flow and OPF calculations of alternating current (AC), and these calculations are at the center of Independent System Operator (ISO) power markets

A schematic diagram of a general large scale grid network

The power network, for example Figure 1, can be improved both technically and economically through the inclusion of distributed generation (DG) which may include renewable energy sources. DG units are lower output generators that provide incremental capacity at specific geographical locations, thus enhancing voltage support and improving network reliability while also acting economically as a hedge against a high price of centrally produced power, through locational marginal pricing (LMP). LMP creates prices at short intervals, such as five minutes, and causes the price to reflect the value of the energy at the specific location and time it is delivered, in terms of generation cost but also demand, and depends on how congested the transmission system is, since in a congested system the cheaper electricity may not be available in certain locations. The operation of grids by ISOs as unbundled auction wholesale spot power markets that support real-time pricing provides a further incentive to roll-out DG, thus arises the need to define the type, number and location of extra DG units

The work presented here addresses the composition of a DG AC electrical power network based upon the IEEE 30 Bus Test Case which represents a portion of the American Electric Power System (in the Midwestern US) in December 1961, and which was downloaded from

The aims of this work are two-fold: (a) To determine the composition of the power network in terms of the type, number and location of the non-central DG units, with the goal of finding the cheapest configuration (capital cost), of meeting demand for power while keeping over- and under-production of power as low as possible, and of minimizing the spot price and CO_{2} emissions, thus determining the best, or at least high performing candidate network solutions; (b) To analyse the multi-dimensional results of the evolutionary computation component in order to reveal relationships between the network's design vector elements, by means of most influential nodes and type of technology, as well as tipping points in the behaviour of the system.

The Plexos tool_{2} emissions. The volume of lost load (VoLL) is the threshold price above which loads prefer to switch off, while the dump energy price is that below which generators prefer to switch off, and these along with market auctions also contribute to the ratio of power generated to power consumed. Transmission losses are also taken into account within Plexos through sequential linear programming.

Plexos is integrated with a multi-objective optimizing evolutionary algorithm (MOOEA)

A MOOEA

MOO gives rise to a set of trade-off solution points

The IEEE 30-bus test system in single line diagram style

The evolutionary algorithm used here is a multi-objective optimizing genetic algorithm that self-adapts its control parameters, where the term self-adaptive is used in the sense of Eiben

The Plexos tool is used here as the source of the values of the objective functions that are evaluated and selected for, that is to say, the fitness indicators, by the MOOEA, as depicted in Figure 3.

The integration of Plexos with the self-adaptive multi-objective optimization algorithm.

The problem is defined as a set of potential DG units each of which may or may not be located at a given node (bus). The DG units are defined as (i) micro-gas turbine (ii) Wind turbine and (iii) Solar photovoltaic, where a unit of value 0 means the generator is not present at the location. The scenario allows for up to 5 units of each type to be located at any of the nodes defined as variable in the network diagram (Figure 2), which means that it is any except for the nodes 1, 2, 13, 22, 23 and 27, as these are the large fixed central OCGT power stations.

The labels shown as

There are 4 objective functions defined, all of which are to be minimised simultaneously and the values for all of which come from Plexos, these being:

Eq. 1

Eq. 2

Eq. 3

Eq. 4_{2}) = CO_{2}

in which the values represent respectively:

The generation cost (in currency, e.g. $)

The USE/DUMP energy (MWh)

Spot Price ($/MWh)

CO_{2} emissions (Kg)

Considering the values above, useDump, depending upon whether it is negative or positive, is respectively either the un-served amount of energy due to under-production or the dump energy due to over-production, relative to demand. By minimizing the absolute value of useDump, the optimization seeks to make this value approach zero, that is to say, to try to make the supply match the demand, thus obtaining the most efficient system. The spot price is the mean price achieved in the simulated market auctions over the course of the simulation, in Plexos.

A hard constraint,

Eq. 5

The hard constraint is increased in other runs to see what effect a larger number of allowed units may have, as shown in Equation 6:

Eq. 6

The candidate solutions chosen by the MOOEA, using the results from Plexos, are thus selected due to the effect their chosen DG units have on the electrical network due to their operating characteristics and where they feed into the network, defined in the topology as shown in Figure 2.

The MOOEA allows each new experiment, such as the one defined here, to override its default initializer which creates an initial population of candidate solutions by generating variables under a uniform random distribution regime within the ranges of the defined variables, in this case 0 <=

In subsequent generations, solutions will evolve that may break the hard constraint, due to mutation and recombination operators acting on ‘fit’ parent solutions selected for breeding, and in this case the solutions will be retained in the population but repaired. Repairing in this context means that a failing solution's vector of DG variables is changed until it falls within the constraint, by randomly choosing one of the variables, decrementing its DG unit count (when it has

The MOOEA is configured to have a mixed

The nodes, their generators and generator types.

Gas | Wind | Solar PV | ||||||

Node | DG | Var | Node | DG | Var | Node | DG | Var |

n03 | g02 | V01 | n03 | g09 | V02 | n03 | g10 | V03 |

n04 | g02 | V04 | n04 | g09 | V05 | n04 | g10 | V06 |

n05 | g02 | V07 | n05 | g09 | V08 | n05 | g10 | V09 |

n06 | g02 | V10 | n06 | g09 | V11 | n06 | g10 | V12 |

n07 | g02 | V13 | n07 | g09 | V14 | n07 | g10 | V15 |

n08 | g02 | V16 | n08 | g09 | V17 | n08 | g10 | V18 |

n09 | g02 | V19 | n09 | g09 | V20 | n09 | g10 | V21 |

n10 | g02 | V22 | n10 | g09 | V23 | n10 | g10 | V24 |

n11 | g02 | V25 | n11 | g09 | V26 | n11 | g10 | V27 |

n12 | g02 | V28 | n12 | g09 | V29 | n12 | g10 | V30 |

n14 | g02 | V31 | n14 | g09 | V32 | n14 | g10 | V33 |

n15 | g02 | V34 | n15 | g09 | V35 | n15 | g10 | V36 |

n16 | g02 | V37 | n16 | g09 | V38 | n16 | g10 | V39 |

n17 | g02 | V40 | n17 | g09 | V41 | n17 | g10 | V42 |

n18 | g02 | V43 | n18 | g09 | V44 | n18 | g10 | V45 |

n19 | g02 | V46 | n19 | g09 | V47 | n19 | g10 | V48 |

n20 | g02 | V49 | n20 | g09 | V50 | n20 | g10 | V51 |

n21 | g02 | V52 | n21 | g09 | V53 | n21 | g10 | V54 |

n24 | g02 | V55 | n24 | g09 | V56 | n24 | g10 | V57 |

n25 | g02 | V58 | n25 | g09 | V59 | n25 | g10 | V60 |

n26 | g02 | V61 | n26 | g09 | V62 | n26 | g10 | V63 |

n28 | g02 | V64 | n28 | g09 | V65 | n28 | g10 | V66 |

n29 | g02 | V67 | n29 | g09 | V68 | n29 | g10 | V69 |

n30 | g02 | V70 | n30 | g09 | V71 | n30 | g10 | V72 |

The results are given as 2D scatter plots and higher dimensional plots using the parallel coordinates (?-coords) technique

Scatter plots showing sumU on y-axis and (a) Top left: genCost (b) Top right: useDump (c) Bottom left: spotPrice (d) Bottom right: CO_{2}, and on the right a ?-coords plot showing a selected region of higher

Figure 4 concerns results obtained when the hard constraint of 70 was applied to

Also in Figure 4 in the ?-coords plot there is an indication that the system may have a tipping point (bifurcation) dependent upon the value of

The plots of Figure 6 and Figure 7 also related to the hard constraint of 70 units, and show the best performing solution found for the genCost objective. The latter figure makes it clear that it is the wind turbine DG units (indicated by W) that are the primary contributor to the performance of the best solution for genCost, with variable V32 having the most units allocated, and V11 being the most connected in the network (feeding into node n06).

Shows results when the hard constraint

The results of Figure 5 are presented similarly to those of Figure 4, but for the hard constraint of 200. The ?-coord plot shows the relationship between the number of DG units and best performing OFs more clearly (when in colour), in that the more DG units allocated, the better the OF performance. Clearly, without the constraint the system would attempt to allocate as many DG units as possible, so the constraint acts as a limit on the cost of DG deployment. The scatter plots of sumU against the OFs also show the clear trade-off trend.

It has been shown that this methodology can indicate not only the number of DG units, but also their type and their network location, in order to gain high performance when used with an appropriate OPF tool such as Plexos. Conversely, this approach could also be used to assist in the design of network topologies, working within the limitations of geography and socio-economic factors, by considering the connectedness of the network either by transmission line connection or by line capacity. For this network and the weather seen in the stated time period, it appears that wind-turbines may be the most important DG technology to deploy, although the other types are important too since all wind DG would be unlikely to equal the performance seen, due not least to its intermittency.

For HC=70, showing the 72 variables, the derived

For HC=70, showing the 72 variables, the derived