Based on the characteristics of two PEV charging modes illustrated in Section 2, the temporalspatial scheduling strategy separately schedules PEV normal charging demand and fast charging demand temporally and spatially.
Spatial scheduling strategy of fast charging
The spatial scheduling strategy aims to spatially schedule the PEVs with fast charging demand to get charged at optimal fast charging stations to consume the outputs of DGs with minimal cost. The strategy spatially schedules the PEV fast charging based on the fast charging requests R
_{
fch
} and the profiles of the DGs and the distribution network, as illustrated in Fig. 2. In this work, a set of assumptions are made as follows:

(1)
There assumes to be a geographical area with several PEV fast charging stations in the distribution network, and each charging station is assumed to be connected by a DG;

(2)
The whole day is divided into 48 time slots (i.e. 30 min per slot) [19, 20], and the output of DGs, the demand of baseload, and RTP are assumed to be detectable at the start of each time slot and remain unchanged during each time slot;

(3)
The PEVs are assumed to keep driving if the SoC is more than 0.3. When the SoC is lower than 0.3 when the current time slot ends, the PEV needs to get charged in fast charging mode in the next time slot;

(4)
There assumes to be an aggregation center with the access to the SoC and the location information of each PEV with the message format of R
_{
fch
} (SoC, location), to schedule the PEV fast charging behaviors at the start of each time slots.
The objective function F
_{
fch
} aims to improve the utilization efficiency of DGs, at the meanwhile reduce the cost of charging, as shown in (1):
$$ \min {F}_{fch}=\min \left({\omega}_1\sum_{i=1}^m\left{P}_{base}^i+{P}_{fch}^i{P}_{DG}^i\right+{\omega}_2\frac{\sum_{j1}^n{cost}^j}{n}\right) $$
(1)
where
$$ cost=\left(1{SoC}_0\right)\cdot {C}_{bat}\cdot RTP+ dis\cdot {E}_c\cdot RTP $$
(2)
ω
_{1} and ω
_{2} e assigned a value according to the different situation.
The first term in the objective function F
_{
fch
} represents the sum of the active power in each station, to make sure that the electric energy generated by DGs can be consumed spatially by PEVs as much as possible; the second term represents the average charging cost of each PEV. The total charging cost also consists of two parts, as shown in (2). The first part is the charging cost to fully charge the battery, and the second part represents the scheduling cost (i.e. the distance to the objective station). The variables in this objective function are the different charging places for each PEV with fast charging demand.
The objective function is subject to:
$$ \left\varDelta {U}^k\right<0.1\cdot {U}_0,\forall k=1,2,\cdots, l $$
(3)
$$ dis<\frac{SoC_0\cdot {C}_{bat}}{E_c} $$
(4)
where (3) means the voltage fluctuation on bus node k cannot exceed the upper and lower bounds of the node voltage; and (4) means that the PEVs cannot be scheduled to a charging station farther than the remaining mileage.
The proposed spatial scheduling strategy of PEV fast charging demand is carried out at the start of each time slot. Once the fast charging behaviors of all PEVs are determined by the scheduling strategy, the PEVs with fast charging demand will get charged in the assigned charging stations. Likely, in the next time slot, the DG output generation, the baseline demand, and RTP can be accurately detected again. Thus, the spatial scheduling strategy will repeat in every time slot with realtime information, which can ensure the realtime performance of the scheduling strategy.
Through the proposed spatial scheduling strategy of PEV fast charging demand, the electric power generated by DGs can be scheduled spatially to be consumed by PEV fast charging demand as much as possible with minimal cost. Moreover, the active power on every bus node in the distribution network will be more balanced.
Temporal scheduling strategy of normal charging
Unlike the PEV spatial scheduling, the temporal scheduling strategy aims to temporally schedule the PEVs with normal charging demand to get charged in optimal times to consume the distributed generation with minimal cost. The strategy schedules the PEV normal charging demand based on the normal charging requests R
_{
nch
}, the outputs of DGs, and the baseload profiles of the charging bus node, as illustrated in Fig. 3.
Here, the following assumptions are made:

(1)
The whole day is divided into 48 time slots (i.e. 30 min per slot), and the output of DGs, the demand of baseload, and RTP are assumed to be predictable dayahead and remain unchanged during each time slot;

(2)
There is assumed to be an aggregation center able to communicate with each PEV, schedule the normal charging behaviors and estimate PEV normal charging demand in the future;

(3)
When a PEV arrives at home, if the SoC is less than 0.8, it is assumed to have a normal charging request to get fully charged at night;

(4)
PEV sends a message to the aggregation center when it arrives at home, including the information of arrival time, current SoC, battery capacity, and leaving time, with the format of R
_{
nch
} (t
_{
a
}, SoC
_{0}, C
_{
bat
}, t
_{
end
}).
The objective function F
_{
nch
} also aims to improve the utilization efficiency of DGs, at the meanwhile reduce the cost of charging, as shown in (5):
$$ \min {F}_{nch}=\min \left({\omega}_1\sum_{t=1}^{48}\left(\left{P}_{base}^t+{P}_{nch}^t{P}_{DG}^t\right+{\omega}_2\sum_{j=1}^n{cost}_j^t\right)\right) $$
(5)
where
$$ \sum_{j=1}^n{cost}_j={P}_{nch}\cdot RTP\cdot T $$
(6)
ω
_{1}and ω
_{2} are coefficient factors, which can be assigned a value according to the different situation.
The first term in the objective function F
_{
nch
} represents the active power on a certain bus in 48 time slots to make sure that the electric energy generated by DGs can be consumed temporally by PEVs as much as possible; the second term represents the total charging cost in each time slot, as shown in (6). As the time slot is 30 min long, T equals 0.5. The variables in this objective function are the different charging time slots for the PEVs with normal charging demand.
The objective function is subject to:
$$ \left\varDelta {U}_t^k\right<0.1\cdot {U}_0,\forall t=1,2,\cdots, 48,\forall k=1,2,\cdots, l $$
(7)
$$ {SoC}^{t_{end}}=1 $$
(8)
where \( \left\varDelta {U}_t^k\right \) in (7) represents the voltage fluctuation on bus node k at time slot t, which means the voltage fluctuation of each bus node in each time slot cannot exceed the upper and lower bounds of the node voltage; and (8) means that the battery should be fully charged at the leaving time t
_{
end
}. It should be noticed about the constraint (7) that although the proposed temporal scheduling strategy of normal charging focuses on the fixed charging node, the influence on the distribution network still needs to be considered.
As the temporal profiles of distribution networks in the future are needed in the proposed temporal scheduling strategy, the outputs of DGs, the demand of baseload, and RTP should be predicted dayahead, and the predicting algorithm is available in [21]. Moreover, the temporal PEV normal charging demand in the future is also needed to be estimated, which can be obtained from the modeling approach in [19, 20] Once the normal charging behaviors in the current time slot of all PEVs are determined by the strategy, the SoC distribution (i.e. the expected charging duration) of PEVs with normal charging demand in the next time slot can be updated, and the realtime output of DGs, the baseload profiles and the RTP can also be detected to replace the predicted data. Thus, the temporal scheduling strategy will repeat in each time slot, which can ensure the realtime performance and the accuracy of the scheduling strategy.
Through the proposed temporal scheduling strategy of PEV normal charging, the electric power generated by DGs can get consumed by PEV normal charging demand as much as possible with minimal cost in every time slot. Moreover, the active power on the charging bus node in every time slot will also be more balanced.
In a word, based on the proposed temporalspatial scheduling strategy, the PEV charging demand can be separately scheduled to consume the electric power generated by DGs with minimal cost temporally and spatially, and the operation of the distribution networks can become more reliable and economical.