Empirical results

The model structure is determined by the two main entities that are represented (cf. Figure 5.11): An aggregator who publishes electricity rates (pt) for each time slot (t) for the analysis period (time frame T, here one week), and several EVs which then individually decide when to charge. The EVs follow the individ-ual cost minimization approach presented in chapter 4.2. The simulation is per-formed in a similar way as for the benchmark model: a weekly optimization is repeated for 52 consecutive weeks, thus mapping an entire year of renewable energy oriented EV charging with data from 2009. As before, the model specifies similar starting and ending conditions for the relevant variables such as SOC, thus enabling this continuous analysis.

The Aggregator

The decision of the aggregator on how to set the value of the electricity rate pt is performed by a calibrated heuristic following the goal to match the demand of the EVs with the intermittent renewable generation as closely as possible, given individually optimizing price responsive EVs.

Two main variables are used by the aggregator to determine the electricity rate pt: First, the amount of the current renewable generation in relation to the renewable peak generation in the analysis time frame of one week (gt/gmax) is employed as an indicator for relative renewable generation scarcity, following the rationale applied in Chapter 4 to shift demand to the time slots with the highest renewable generation share in relation to total load. Second, the gen-eral availability of the EVs for charging at, i.e. the percentage of vehicles that is connected in a given time slot t, is considered. This variable serves as an in-dicator for potential demand, since it determines the upper bound of potential

Table 5.9: Uniform Pricing Model Parameters

Parameter Description Symbol Domain

Operational battery capacity C (kWh)

Min. number of time steps to fully charge ν^c (#)

Charging efficiency η^c (%)

Storage cost ψ (EUR/kWh)

Price per energy unit in time step t pt (EUR/kWh) Charge parameter for time step t ϕt (%)

Energy level of the battery at time t Lt (kWh) Energy consumption in time step t^a dt (kWh)

Location of the BEV zt (0: not at home

1: at home)

Total generation gt (kWh)

Intermittent generation g_t,I (kWh)

Maximum g_t,I, teT g_max,I (kWh)

Renewable generation and availability costs p_t,R (ct/kWh)

Conventional generation g_t,C (kWh)

Conventional generation costs p_t,C (ct/kWh)

Total load in time slot t lt (kWh)

a _d

t=kilometers driven in time step t (km) · power consumption per km (kWh/km)

demand in case that a considerable number of EV-owners decide to charge due to relatively low prices. This parameter was introduced as a measure to account for simultaneity effects of EV demand. The impact on the distribution of EV demand is analyzed within the context of the results obtained.

The overall simulation process and structure are depicted in Figure 5.11. The empirical driving profiles serve for the calculation of the EV charging availabil-ity at the home location and also as main constraints for the formulation of the individual cost minimization problem of the respective EVs. The aggregator in turn generates a price based on the scarcity of renewable energy and the overall availability at the home charging location. This price in turn serves as the main input for the individual EVs to make cost minimal charging decisions. All non-renewable demand resulting from these individual decisions it covered by the conventional generation.

While relative generation abundance (i.e. a high g_t,I/gmax∀t∈T,I) will result in a lower price, times of high potential demand (i.e. a high at) will in turn balance this effect and lead to higher total electricity prices. This relation which was described above is formalized in the following expression:

Figure 5.11: Simulation model structure and general interactions between the roles.

pt =











p_{t,C g}^gt,I

max,I ≤0.05 (1− ^gt,I

g_max,I) +wa· at

| {z }

p_t,R

else ,∀t∈ T (5.12)

For periods in which little or no renewable generation is available (i.e., if re-newable generation drops below 5 % of its weekly maximum) the price is set to the limit p_t,C, to further discourage charging. The level of 5 % is chosen in order to maximize the share of used renewable generation before relying on conven-tional generation and thus follows the same economic raconven-tionale as in Section 5.2, to minimize variable generation costs. Please observe that no further ramping or minimum run time constraints are imposed on the conventional generation in this particular case. This also supports a different economic evaluation approach in which the individual charging costs are assessed by the hourly prices from the European Energy Exchange (cf. Section 5.3.7).

The Individual Vehicles

The charging behavior of the vehicles is modeled using a linear optimization program that was introduced earlier in Section 4.2 thus incorporating the "Smart Charging Strategy" based on variable price incentives for every EV. The model

constraints are consistently formulated as above: The state of charge of the bat-tery needs to be in between 0 and the operational batbat-tery capacity at all times (Eq.

5.14). In addition the energy consumed corresponds to the energy that needs to be recharged during each optimization period of one week (Eq. 5.16. Further it is assumed that the battery of each EV is fully charged at the beginning of every week, and consequently needs to be fully charged at the end of the week in or-der to allow for a continuous evaluation over the course of 52 weeks of the year 2009. This potentially slightly reduces the flexibility of the vehicles to react to high renewable energy generation availability but provides a more conservative insight with respect to the mobility requirements of the EV-owners.

minϕt

→Cost=

∑

pt· ϕt

| {z }

Electricity Costs

(5.13)

C≥L_t−1+ ^C

ν^c· ϕt−dt

| {z }

SOCt

≥_0, ∀t∈ [_{2, T}]

(5.14)

C≥L1+ ^C

ν^c· ϕ1−d1

| {z }

SOC₁

≥0, t=1

(5.15)

∑

C ν^c· ϕt =

∑

dt, ∀t∈ [_{1, T}] _(5.16) The objective function of each vehicle is to minimize the incurred charging costs (Eq.5.13). These are determined by the amount of energy charged times the electricity rate pt. Additional degradation costs are not considered in this section, since the amount of energy charged by the vehicles is similar both for AFAP and smart charging. For V2G operation strategies storage costs need to be considered (cf. Section 4.3), for purely operational analyses this is not necessary if only the electricity costs are considered. As the focus of this section is on the price based charging coordination for renewable energy utilization the more detailed implication of storage costs was already performed in section 4.3 for the individual assessment.

ϕt=











1 : if SOCt+ ^C

ν^c ≤C and zt =1

C−SOC_t

C νc

: if SOCt+ ^C

ν^c >C and zt =1 0 : otherwise

(5.17)

As a reference case uncoordinated AFAP charging is again included in the analysis. Here it is assumed that vehicle owners charge as soon and as fast as it is possible after they arrive at the charging location, which is realistic, since this strategy minimizes the risk to have an empty or too little charged battery when the vehicle is needed. In the model notation this behavior translates to equation 5.17.