Análisis del tono

The microgrid unit commitment model presented in this chapter con- siders a day-ahead (24 hours) time frame with 96 (N ) snapshots or time steps each with a time span (Ts) of 15 minutes. For the demon-

stration, 5 controllable power generation units were considered, in- cluding two micro turbines, a fuel cell [95], a storage device and the utility grid. Furthermore, a controllable load including 4 electric vehicles is added to the microgrid set up. The cost and emission coefficients of three different thermal generation units are listed in Table 4.2, and are graphically presented in Fig. 4.5. Note that the

72 _{Chapter 4}

cost curve of the utility grid is not displayed in the upper graph of the figure since this cost varies in time.

CG(PG) a b c Micro Turbine 1 100 · 10−5.5 50 · 10−5.5 20 · 10−5.5 Micro Turbine 2 140 · 10−5.5 40 · 10−5.5 100 · 10−5.5 Fuel Cell 20 · 10−5.5 20 · 10−5.5 10 · 10−5.5 εG(PG) d e f Micro Turbine 1 4.09 · 10−3 −5.55 · 10−3 6.49 · 10−3 Micro Turbine 2 2.54 · 10−3 −6.05 · 10−3 _{5.64 · 10}−3 Fuel Cell 5.33 · 10−3 −3.55 · 10−3 _{3.38 · 10}−3

Table 4.2: Fuel cost and emission coefficients

Active output power (kW)

0 50 100 150

Fuel cost (Euro/h)

0 2 4 6 8 Micro turbine 1 Micro turbine 2 Fuel Cell

Active output power (kW)

0 50 100 150 Emission (kg/h) 0 50 100 150 Micro turbine 1 Micro turbine 2 Fuel Cell Slack Bus

Microgrid power system scheduling 73

A CO2 emission intensity of 381 · 10−3kg/kWh [99] is considered for

the power supply of the utility grid and is included in the lower graph of Fig. 4.5. Since a time horizon of 24 hours is considered in this model, the emission rate of the utility grid is regarded as a constant. As explained in section 4.3.4, the cost and emission coefficients of the storage unit and the controllable loads are set to zero. Additionally, the capacities of the microgrid generation units are listed in Table 4.3. For the storage unit, Emin is set to 0 kWh, Emax is set to 40

kWh, and EEVmax of each EV is set to 80 kWh. The charging rate of

each EV is limited between -19.2kW and -7.2kW, which results in a total (4 EVs) minimum and maximum charging rate of -28.8kW and -76.8kW respectively.

MT 1 MT 2 Fuel Cell Storage PGmax (kW) 160 240 260 ±50

Table 4.3: Microgrid generator capacities

The problem to be optimised includes multiple conflicting objective functions. In this work, a (hybrid) goal attainment method based genetic algorithm is applied to determine the global optimum. As explained in § 3.3, genetic algorithms are based on the process of natural selection which means they take the fundamental properties of natural selection and apply them to the problem to be solved. The genetic algorithm repeatedly modifies a population of individual so- lutions. At each step, the genetic algorithm selects individuals at random from the current population to be parents and uses them to produce the children for the next generation. Over successive gen- erations, the population proceeds toward an optimal solution. The outline and the operators of the genetic algorithm are described in ap- pendix A.1.2. Using the multi-objective genetic algorithm, the region near an optimal Pareto front can be determined relatively fast, but it can take many function evaluations to achieve convergence. There- fore, the goal attainment method is used as the hybrid solver together with a controlled elitist genetic algorithm. This hybrid technique solves the goal attainment problem, which is a formulation for min- imising a multi-objective optimisation problem. The hybrid method runs the genetic algorithm for a small number of generations to get near an optimum front. Subsequently, the solution (Pareto front) returned by the genetic algorithm is used as an initial point for the

74 _{Chapter 4}

hybrid goal attainment method which is faster and more efficient for a local search. The new individuals returned by the hybrid solver are combined with the existing population and a new Pareto front is obtained. Using this hybrid scheme results in the satisfaction of both objectives wherein the results can be calculated more accurately and more quickly.

Since we have multiple conflicting objective functions, the outcome will not give a single solution, but rather a set of solutions (Pareto optimal set). Without additional preference information (priorities), all solutions within this set are considered equally good. In this work, priority is given to the solution (extreme) with the lowest produced CO2, rather than considering the full range of solutions. A detailed

description and example of this hybrid method is presented in § 3.4.2. The model starts by initialising the different input characteristics, parameters and settings, including N , Ngen, CG(PG), εG(PG), PDa,

PGmin, PGmax, Estoragemin, Estoragemax, EEVmin, EEVmax, EEVTout and

EEV_Tin. Since the behaviour of the algorithm and the accuracy of

the result is dependent on the solver options and settings, it is im- portant to determine the parameters properly. The population size used to seed the genetic algorithm is set to 100 (candidate solutions). With a large population size, the genetic algorithm searches the so- lution space more thoroughly, thereby reducing the chance that the algorithm returns a local minimum that is not a global minimum. However, a large population size also causes the algorithm to run more slowly [70]. This value was chosen since a larger population size does not provide more accurate results. The iterations or gener- ations are set to (Nvar· 200). Nvar is the number of decision variables

which is equal to Ngen · N . The algorithm finds the minimum of

both objective or fitness functions. Here, a small function tolerance of 10−4 is set, which increases the accuracy of the calculated optimal value. The initial population, used to seed the genetic algorithm, is set to a 100-by-Ngen matrix whereby each entry is assigned with the

value 0.