The peak-to-valley difference of grid load is expanding day by day, and the system is under great pressure for peak regulation. The battery energy storage station is directly connected to the distribution network, which can store electric energy as a load when the electricity consumption is low, and release the electric energy as a power source when the electricity consumption is peak. With the gradual reduction of the cost of battery energy storage equipment and the further improvement of energy density, battery energy storage stations are expected to be popularized on a large scale. A large number of battery energy storage stations are distributed on the distribution network side, which can effectively reduce the load peak-to-valley difference, which is equivalent to improving the load characteristics for the power grid. The direct benefits brought by the improvement of load characteristics to the power grid include: reducing the demand for system reserve capacity, reducing the demand for peak regulation and frequency regulation units in the system; reducing the power flow of the transmission network during peak loads, reducing equipment investment in the transmission network, and improving transmission and distribution. utilization rate of electrical equipment; reduce the participation of thermal power units in peak shaving, and improve power generation efficiency.

**1. Economic model of Nas energy storage system**①The equipment fixed cost of NaS energy storage system

After the introduction of energy storage system and energy conversion control system into the power system, the capital cost of the entire power system has changed. The capital cost C

_{s}of energy storage is the sum of two parts of the cost, one part is related to the stored energy, the other part is related to the peak value when the energy is released, and is controlled by the transmission distance. That is, the capital cost is determined by the cost of the energy storage system, the power transmission system and the energy conversion control system, especially related to the installed power capacity and storage capacity:

C

_{S}=C

_{CS}+C

_{PTS}+C

_{CDCS}

It is convenient to express in terms of cost per unit of stored energy and installed electrical capacity:

C

_{CS}=C

_{e}E

_{S}

where C

_{e}– the cost of energy storage system per unit of stored energy [yuan/(kW·h)];

E

_{s }– Energy (kW·h) accumulated in the energy storage system.

C

_{PTS}+C

_{CDCS}=C

_{P}P

_{S}

In the formula, Cp – the cost of the power transmission system and the energy conversion control system combined (yuan/kW);

Ps – designed power capacity (kW).

Thus, the cost of energy storage is a function of two main storage characteristics:

C

_{S}=C

_{e}E

_{S}+C

_{P}P

_{S}

② Operation and maintenance cost of Nas energy storage system

After the energy storage equipment is used in the power system, it needs to pay a certain economic price for its operation every year, which includes the operation cost and maintenance cost of the equipment, the size of which depends on the initially designed power capacity, that is, the maximum energy storage capacity the size of;

C_{YW}=C_{y}P_{S}+C_{W}P_{S}

where C_{y} is the operating cost per unit of the energy storage system [yuan/(kW·year)];

C_{W} – maintenance cost per unit of energy storage system [yuan/(kW·year)].

The economic cost of Nas energy storage system is shown in Table 1.

Unit power construction cost Cp/(USD/kW) | 810~2 270 |

Unit energy storage cost Ce/[USD/kW.h] | 230~810 |

Unit operating cost Cy/[USD/(kW.year)] | 18~50 |

Unit maintenance cost Cw [USD/(kW.year)] | 3~9 |

**2. Equivalent annual value calculation of fixed cost of energy storage system**Capital investment is different from labor investment. After a capital investment, a return may be obtained soon or several years later. Therefore, after calculating the fixed cost of equipment, it must be converted into the corresponding equivalent annual value.

①Discounted present value of investment income

Discounted present value is the discount of a sum of money in the future to its present value at some interest rate. As we all know, compound interest calculation is the sum of the interest and principal in the first year as the principal in the second year, and then the interest is calculated repeatedly. The sum of the principal and interest at the end of the nth year is

A=A_{0}(1+r)^{n}

In the formula, A_{0}–principal;

r – annual interest rate;

n – the number of years;

A – Benefit and.

from the above formula

A_{0}=A/(1+r)n

The above formula is the calculation formula of the discounted value.

In the formula, A_{0}—discounted value;

A – an income in a future year;

n – the number of years;

r—the interest rate used for discounting;

(1+r)^{n}–multiple discount coefficient.

Using the above formula, the discounted value of the investor’s future investment income can be calculated.

② Equivalent annual value of investment income

Generally, after an investor engages in an investment, they do not obtain a one-time income in a certain year, but obtain an income every year in the following years. This is called the payment flow, and the payment flow is the present value of The calculation formula is

A_{0}=[A_{1}/(1+r)]+[A_{2}/(1+r)²]+…+[A_{n}/(1+r)^{n}]

In the formula, A_{i}/(1+r)^{i}[i=1,2,…,n]—the discounted value of the income obtained in the first year;

A_{0} – the present value of the payment stream.

If A_{1}=A_{2}=… A_{n}=A, it is called the present value of equal annual value, and its calculation formula is A_{0}=A/r[1-(1/1+r)^{n}]=A/r[1 -(1/1+r)^{-n}]

In the formula, A0 – the present value of the equivalent annual value;

A _{0}– annual income;

r discounted interest rate;

n—the number of years;

1/r[1-(1/1+r)^{-n}] – the present value coefficient of the equivalent annual value, the value of which is multiplied by A to obtain the present value of the equivalent annual value.

**3. Calculation of time-shifted electricity with energy storage system**Due to the current serious power shortage in China’s power grid, that is, the power generation is insufficient during the peak period of electricity consumption, and the peak-to-valley difference is increasing. Therefore, certain methods must be used to reduce the power generation during the peak period and increase the power generation during the valley period. And stored for use during peak hours, the specific method is described below.

Calculation of peak-shifting capacity: peak-shifting is to move the power-deficient capacity in the peak period to the trough period for storage, as shown in Figure 1.

Figure 1 shows the daily load curve of a certain system. It can be seen from the figure that the peak-to-valley difference of the daily load of the system is particularly significant, which may lead to insufficient power generation during the peak period of the system. Therefore, energy storage equipment is selected to shift the peak. For valley filling, assuming that the maximum power generation P_{0} of the power plant is known, the peak shifting capacity is shown in the shaded part of Figure 2.

Use the trapezoidal equal area rule to calculate the area of the shaded part to obtain the peak shift capacity, as follows:

A_{LD}=Σ[(P_{After}-P_{0})+(_{PBefore}-P_{0})/2]×5/60

In the formula, A_{LD} – power shortage capacity (kW`h);

P_{Before} – the amount of electricity generated at the previous moment (kW);

P_{After} – power generation (kW) at the next moment.

Due to the limitation of the maximum power generation capacity of the power plant, the additional power that can be generated during the low power generation cannot exceed its maximum power generation capacity, that is, P_{0}, so the shaded area in Figure 3 is the maximum allowable energy storage capacity.

Use the trapezoidal equal area rule to calculate the area of the shaded part to obtain the peak shift capacity, as shown in the formula:

A_{max}=Σ[(P_{after}-P_{0})+( P_{before}-P_{0})/2]×5/60

Where A_{max} – maximum allowable energy storage capacity.

After the above calculation, compare the size of A_{LD} and A_{max}. If A_{LD}<A_{max} is satisfied, it means that enough electric energy is allowed to be stored during the trough period of power generation and used in the peak period; otherwise, it means that the energy storage capacity of the power plant is insufficient during the trough period of power generation.