## 2 User-Side Energy Storage Economy Analysis
### Revenue Model  
**Delayed transformation income. ** With the rapid charge and discharge characteristic, energy storage can cut down peak load of the users to delay the cost of transformer upgrade. The delayed transformation benefit is shown as follows:  
\[S_{1}=C_{inv}[1-(\frac{1+ir}{1+id})^{n}]P_{N} \tag{4}\]  
\[n=\frac{\log_{10}(1+\lambda)}{\log_{10}(1+\tau)} \tag{5}\]  
where \(S_{1}\) is delayed transformation income (\(\gamma\)), \(C_{inv}\) is one-time investment cost coefficient required for electricity transformer upgrade (\(\gamma\)/kW), \(n\) is delay time of transformer upgrade after adding energy storage (year), \(\lambda\) is annual growth rate of load (%), \(\tau\) is peak clipping rate (%), respectively. **Direct income. ** Driven by the time-of-use price, energy storage charges when the electricity price is low and discharges when the electricity price is high. In this way, the revenue is seen as direct income. One day's direct income and the total direct income over life cycle are described in Equations (6) and (7), respectively. \[B_{2}=\sum_{t=1}^{T}m_{t}(t)[P_{dis}(t)U_{dis}(t)-P_{ch}(t)U_{ch}(t)]\Delta t \tag{6}\]  
\[S_{2}=\sum_{t_{s}=1}^{N_{s}}B_{2}D(\frac{1+ir}{1+id})^{t_{s}} \tag{7}\]  
where \(B_{2}\) is direct income of energy storage on a day, \(m_{t}(t)\) is time-of-use electricity price (\(\gamma\)/kWh). \(P_{dis}(t)\) and \(P_{ch}(t)\) are the charging power and discharging power at \(t\)th period (kW), respectively. \(U_{dis}(t)\) and \(U_{ch}(t)\) are the charging and discharging state of energy storage at \(t\)th period, respectively. \(T\) is total number of intervals in a day and its value is 96. \(\Delta t\) is the time interval and its value is 15 (min). \(S_{2}\) is total direct income in the full life cycle of energy storage (\(\gamma\)). \(D\) is annual running days of energy storage (day). **Government subsidies** To promote the development of energy storage, the government will subsidize the energy storage. The government subsidies in a day is described in Equation (8). Considering the discount rate and inflation rate, the total income of government subsidies over life cycle of energy storage is shown in Equation (9). \[B_{3}=\sum_{t=1}^{T}m_{e}P_{ch}(t)U_{ch}(t)\Delta t \tag{8}\]  
\[S_{3}=\sum_{t_{s}=1}^{N_{b}}B_{3}D(\frac{1+ir}{1+id})^{t_{s}} \tag{9}\]  
where \(B_{3}\) is government subsidies of energy storage on a day (\(\forall\)), \(m_{e}\) is government subsidized electricity price (\(\forall\)/kWh), and \(S_{3}\) is total income of government subsidies in full life cycle of energy storage (\(\forall\)). **Auxiliary service income**. Currently, the user-side energy storage providing auxiliary services can be mainly divided into three categories: peak shaving, demand response, and demand management. In the actual situation, users may select one or more services to participate in. As shown in Equation (10), peak shaving revenue is the income for the peak power reduction. The demand response revenue is the subsidy for users to reduce the peak power consumption in response to the grid command, which is shown in Equation (11). Demand management revenue is the monthly electrical capacity charge saved from replacing transformer capacity charge with demand charge after the installation of energy storage, which is shown in Equation (12). Demand charge is calculated based on the monthly maximum power, while the specific charging method is outlined in [20]. Total income of auxiliary service in the full life cycle of energy storage, which is shown in Equation (13):  
\[B_{ls}=\sum_{t=1}^{T}m_{ls}P_{dis}(t)U_{dis}(t)\Delta t \tag{10}\]  
\[B_{x}=\frac{1}{30}(S_{T}c_{dj}-\left\{ \begin{array}{cc}40a&b\leq 1.05a\\ 40a+80(b-1.05a)&b>1.05a\end{array} \right.)