# An EV Charging Scheduling Mechanism Based on Price Negotiation
## 3 Price Negotiation Model
### Initial Price Model for Charging Station Operators and EV User
#### 3.1.2 Initial Price of Charging Station Operator  
Similarly, the charging station operator will also form an initial price that maximizes the interests after receiving the charging request. To form this initial price, the following factors should be mainly considered.  
(1) The current idle ratio \(IR_{j}\) of charging station \(CS_{j}\)  
For different time slots, the load of the charging station is different. Thus, the current idle ratio of the selected charging station is the key factor for pricing. \(IR_{j}\) is quantified by the Formulation (4).  
\[IR_{j}=\frac{DC_{c,j}}{CP_{idle,j}} \tag{4}\]  
where \(DC_{c,j}\) is the duty cycle of charging devices that are working in the charging station \(CS_{j}\), \(CP_{idle,j}\) is the total number of idle charging devices in \(CS_{j}\).  
(2) The current load \(L_{j}^{cs}(t)\) of charging station \(CS_{j}\)  
The current load of the charging station indicates the potential charging power supply for new arrival EVs. It is undoubtedly another key factor of pricing. \(L_{j}^{cs}(t)\) is calculated as follows at time slot \(t\).  
\[L_{j}^{cs}(t)=L_{j}^{cs,0}(t)-L_{j}^{res}(t) \tag{5}\]  
where \(L_{j}^{cs,0}(t)\) is the total actual load of \(CS_{j}\), \(L_{j}^{res}(t)\) is the total power generated by renewable energy resources of \(CS_{j}\) at time slot \(t\). \(L_{j}^{cs,0}(t)\) is calculated as follows.  
\[L_{j}^{cs,0}(t)=L_{j}(t)+\sum_{i\in N}P_{i} \tag{6}\]  
where \(L_{j}(t)\) is the load without any EVs charged, \(N\) is the total number of EVs that are charging in \(CS_{j}\), \(P_{i}\) is the charging power of \(ev_{i}\).  
\[P_{i}=\frac{(A_{i}-SOC_{i})\times Q_{i}}{t_{i}^{0}} \tag{7}\]  
where \(A_{i}\) is charging threshold of \(SOC_{i}\), \(Q_{i}\) is the battery capacity, \(t_{i}^{0}\) is the actual charging time of \(ev_{i}\). Generally, \(A_{i}\) is set as 0.95.  
The charging station needs to meet the following constraints when it allows EVs to be charged. The current load cannot exceed the maximum load \(L_{j,\max}^{cs}\) of \(CS_{j}\); the charging power of \(ev_{i}\) must be between the minimum charging power and the maximum charging power; and the actual charging time should not exceed the desired charging time \(t_{i}\) of the EV user. Generally, \(Q_{i}\), \(t_{i}\) and \(SOC_{i}\) are sent to the charging station operator together with the charging request.  
\[\left\{\begin{array}{l}0<L_{j}^{cs}(t)\leq L_{j,\max}^{cs}\\ P_{i,\min}\leq P_{i}\leq P_{i,\max}\\ t_{i}^{0}\leq t_{i}\end{array}\right. \tag{8}\]  
Thus, the initial charging price of the operator is formed as follows.  
\[p_{j,0}^{cs}=p_{0}\times(1+\delta)\times(\alpha_{1}\times IR_{j}+\alpha_{2} \times(L_{j}^{cs}(t)/EL_{j}^{cs})^{2}) \tag{9}\]where \(EL_{j}^{cs}\) is the daily average load of \(CS_{j}\), \(\delta\) is the expectation of profit of the charging station operator, \(\alpha_{1},\alpha_{2}\) indicate the influences of current idle ratio and current load of \(CS_{j}\), respectively. When the charging station is busy, the charging price will increase. When the current load of the charging station is higher than the daily average load, the charging price will also increase. In order to control the growth of the load of the power grid, the charging price increases with square; which will achieve peak shaving and valley filling.