## 4 A Pricing Strategy for EVs on Account of the Supply-Demand Relationship of the Micro-Grid
### Dynamic Time-Of-Use Pricing Strategy for EV Charging
#### 4.2.2 Calculation of the Dynamic Time-Of-Use Charging Price  
The peak-valley price is commonly formulated according to the electrical load of the grid. Since the output of distributed generators is unstable and the electrical load is fluctuating, the unbalanced power in the micro-grid is taken as the basis of formulating dynamic time-of-use price. Based on the load curve \(u_{1,load}\) and the output of renewable energy, the balance of supply and demand of the grid is taken  
Figure 4: The flow chart of dynamic time-of-use pricing strategy for EV charging. as the goal, to decide the dispatching demand for EV cluster in the time period \(k\), which is shown in Equation (16):  
\[\Delta P_{k\Delta T}=P_{w,k\Delta T}+P_{PV,k\Delta T}-P_{load,k\Delta T} \tag{16}\]  
where \(P_{w,k\Delta T}\) is the output of wind turbines in the time period \(k\), \(P_{PV,k\Delta T}\) is the output of photovoltaic in the time period \(k\), and \(P_{load,k\Delta T}\) is the electrical load in the time period \(k\) under peak-valley price of the micro-grid. Considering the generation and transmission costs of renewable energy and the peak-valley price in the micro-grid, the dynamic time-of-use price of EVs can only be adjusted within a certain range. On the one hand, the adjusted charging price in the time period \(k\) cannot be higher than the corresponding peak-valley price, otherwise the EV users will not be stimulated to participate in the load adjustment. On the other hand, the adjusted charging price should not be lower than the generation and transmission costs of renewable energy, in order not to reduce the operational economic efficiency of the entire micro-grid. Therefore, the peak-valley price \(p_{pv,k\Delta T}\) and the generation and transmission costs of renewable energy \(c_{d}\) are taken as the upper/lower limits of the charging price adjustment, respectively, and the dynamic time-of-use price in the time period \(k\) is updated within this range. This paper treats the peak-valley price as the initial charging price, to maximize the economic benefits of the micro-grid. When the number of EVs that can be dispatched under the updated time-of-use price \(p_{ch,k\Delta T}^{*}\) could meet the dispatching demand, the relevant number of EVs and the charging price \(p_{ch,k\Delta T}\) can be obtained. If the updated time-of-use price \(p_{ch,k\Delta T}^{*}\) is lower than the lower limit \(c_{d}\), even when the number of EVs responding to the grid still cannot reach the dispatching demand, the previous charging price and EV number will be the output. In addition, the EV users who do not respond to dispatching signals in the above process are charged according to the peak-valley price. The strategy proposed in this paper takes the balance of supply and demand of the micro-grid as the goal and fully considers the choice of EV users. The difference between the actual capacity of EVs responding to the grid and dispatching demand is set as the objective function as shown in Equation (17). \[\text{min}P=\text{min}\overset{NT}{\underset{k=1}{\sum}}(\overset{\Omega_{res} (k\Delta T)}{\sum}P_{ch,j}-\Delta P_{k\Delta T})^{2} \tag{17}\]  
where \(\Omega_{res}(k\Delta T)\) is the number of EVs responding to the grid in the time period \(k\). It can be seen from the formula that this paper solves the convex quadratic programming problem, i.e., the solution is the global optimal solution. The number of EVs responding to the dispatching periods is related to the users' driving demands, battery parameters, charging price, and user satisfaction degree. The constraint conditions are as follows:  
1. The battery constraint of EV charging  
In order to avoid overcharging resulting in the damage of battery lifetime, the battery of EV is assumed that can be charged within the maximum and minimum SOC. At the same time, the charging power is limited to the maximum and minimum values.