Day-ahead optimal dispatching of AC/DC hybrid system

In this paper, a distributed energy resource (DER) optimal scheduling method for AC/DC hybrid systems with power electronic transformer (PET) is proposed. Firstly, a PET scheduling model considering loss is established. Secondly, an optimal scheduling model of the AC/DC hybrid system with PET is established. Finally, the optimal scheduling model of the AC/DC system with PET is verified by a case and the effect of PET efficiency on the operating state of the system is discussed. The results show that using the power regulation ability of PET, the distributed generation can be fully absorbed and the operating cost of the system can be reduced.


Introduction
In recent years, with the continuous development of distributed generation technology, more and more clean energy has been applied in power system [1] . Distributed energy resources (DER) access to the power grid is divided into two types: AC access and DC access. Compared with AC access, DC access can save the commutation link and reduce the system loss. Therefore, the hybrid system with both AC and DC will be one of a dominant system structure in the furture [2] . As the distributed power generation device is constrained by various conditions of solar energy and wind energy, its power generation is intermittent, and a large amount of access will cause disturbance to the power grid.
In order to solve this problem, this paper applies power electronic transformer (PET) to AC/DC hybrid system. PET realizes its functions through the combination of power electronic devices and highfrequency transformers. Since the PET has the function of voltage transformation, isolation and energy transmission [3] . The structural topology of the AC/DC hybrid system with PET is shown in Figure 1.
In [4], the working principle, topological structure and control strategy of PET are elaborated in detail. In [5], the topological structure and control strategy of applying PET to distribution network are proposed. In [6], a unified reduced-order modeling method and a single-stage control strategy of PET for medium and high voltage power grid is proposed. For the day-ahead optimal dispatch of distributed energy in AC/DC hybrid system, an energy management and coordinated control method is proposed in [7] to realize the coordinated control of multisource AC/DC microgrid. In [8], an optimal operation model of AC/DC hybrid system is established and an improved black hole algorithm is proposed to optimize the operation of AC/DC hybrid system. In [9], a probabilistic economic dispatching method for the energy management of AC/DC hybrid system is proposed. In this paper, an optimal dispatching model is established to verify that the flexible port control ability of PET, which can realize the full absorption of distributed energy and reduce the operating cost of the system. Since the DER power is affected by weather factors, the energy fluctuations in the DC system and the AC system are frequent. PET can coordinate the power flow between the areas and control each port independently [11] . Using PET, the main grid can be directly connected to PET, which omits the transformation link between the main gird and the AC system. As the intermediate hub of energy transmission, PET has a certain power loss inside, and defines  as the power conversion coefficient of PET. This paper takes three-port PET to establish the scheduling model of PET, whose topology is shown in Figure 3. For the three-port PET, it has: indicating the sum of the total power of PET input from the main grid, the AC area, and the DC area at time t . Due to the loss of PET, the following equation holds: 1 in the two equations, and the optimal scheduling model of PET is obtained: The following power upper limit constraints for the interaction power of its three ports: Where M P is the maximum interaction power between PET and the main grid, AC P is the maximum interaction power between PET and AC system, and DC P is the maximum interaction power between PET and DC system.

Micro-turbine model
The power generation constraints of micro-turbine are as follows: turbine. Eq.(11) limits the power generation of the microturbine, and Eq. (12) and Eq.(13) control the ramp up and fall rates of the micro-turbine.

Battery model
The model of battery systems are expressed as follows: Where t B P is the stored energy of the battery storage system at time t , 1 t B P  is the stored energy of the battery storage system at time 1 t  , t BS P is the charge or discharge amount of the battery storage system at time t , and when it is positive, it means that the battery storage system is charged at time t ; when it is negative, it means that the battery storage system is discharged at time t .
is the upper limit of discharge per unit time of the battery storage system, and C max P is the upper limit of charge per unit time of the battery storage system, 1 B P is the stored energy of the battery storage system at the initial moment, and N B P is the stored energy of the battery storage system at the final moment.

Wind turbine model
This paper assumes that the wind speed satisfies the Weibull distribution, and its probability density function and mathematical expectation are as shown in Eq.(17) and Eq.(18).
Where ( ) f  is the probability density function; wind v is sample value of the wind speed; k is the shape parameter; c is the scale parameter, and ( ) E  is the mathematical expectation.
The output power of the wind turbine is calculated according to Eq.(19).
Where WT P is the output power of the wind turbine; in v , r v and out v are the cut-in wind speed, the rated wind speed and the cut-out wind speed of the wind turbine; wt P is the rated power of the wind turbine.

Photovoltaic model
The output power of photovoltaic satisfies the Beta distribution, and its probability density function and mathematical expectation are as shown in Eq.(20) and Eq.(21).
Where PV P and

Load model
The load in the system is divided into uncontrollable load and controllable load. For the controllable load, it refers to the load that can be reduced during a certain period of time, such as the air conditioning load, etc. is the controllable load before the load reduction of the DC system at time t , t DC  is the reduction load of the DC system at time t , and max DC  is the upper limit of the reduction load of the DC system.

Objective function
An optimal scheduling method of AC/DC hybrid system is proposed with minimum operating cost.

Equipment maintenance cost
In this paper, the maintenance cost of wind turbines and photovoltaics is considered, and the maintenance cost of the equipment is related to power. The maintenance cost of them is:

Micro-turbine power generation cost
The micro-turbine has a power generation cost, which can be expressed as: Where MT m is the power generation cost coefficient of the micro-turbine.

Purchase and sale of electricity cost
The AC/DC hybrid system is also connected to the main grid. When there is a surplus of power in AC/DC system, it can be profited by selling the surplus power to the main grid. When the power in AC/DC system is insufficient, the power shortage of the AC/DC system can be balanced by purchasing electricity from the main grid. The total cost of purchasing and selling electricity is the sum of the cost of purchasing electricity and the profit of selling electricity: Where buy C is the total electricity purchase cost, sell C represents the total electricity sales cost, buy C is a positive value, sell C is a negative value,

Battery storage loss cost
During the charging and discharging process of the battery storage system, there is a loss of electrical energy. The cost of battery storage loss is expressed as: Where B m is the loss cost coefficient of the battery storage system.

Controllable load reduction cost
The controllable load in the system can be reduced. This cost includes the cost of controllable AC load and DC load Where L m  is the unit cost of the controllable load at time t .
In summary, the objective function of the day-ahead optimal scheduling method is:

Constraints
The system should meet the power balance constraints during operation.  (7), and the power balance constraints of the system can be obtained:

Case study
A test case of AC/DC hybrid system with PET is shown in Figure 4. The system consists of an AC system and a DC system, which rely on PET for energy transmission.  The PET power conversion efficiency  =0.95. In order to ensure that the AC/DC hybrid system can achieve selfsufficiency as much as possible, and also consider the safety and stability of the AC/DC hybrid system, the maximum injection power of the main grid port is limited to 60 kW, and the active injection upper limit values AC P  Figure 5 shows the output power of AC port and DC port of PET within 24 hours. The positive value indicates that power is flowing from the AC/DC system, and the negative value indicates power is injected into the AC/DC system. Take 19-24h as an example, the DC system is in the power shortage state due to the decrease of the PV output. The AC system is in the power surplus state due to the increase of wind speed. At 19-21h, because MG is at the peak electricity price, the MT of the AC system is fully loaded at this time. The surplus power is transmitted to the DC system and sold to MG for maximum profit. At 22-24h, MG is at the valley electricity price, and the AC/DC systems can purchase electricity from MG at a lower cost. Therefore, the AC/DC systems purchases electricity from MG at the upper limit of the port at this time period.  Figure 6 shows the relationship between battery storage, main grid interaction power and main grid purchase cost. When the battery storage is positive, it indicates charging. When it is negative, it indicates discharge. When the main grid interaction power is positive, it indicates power flows from MG to AC/DC systems, and the negative power indicates that the power flows from AC/DC systems to MG. It can be clearly seen from Figure 6 that the behavior of the energy exchange between the battery storage and MG has a strong correlation with the main grid purchase cost.

Conclusion
In this paper, a day-ahead optimal dispatching method for AC/DC hybrid system with PET is proposed to realize the coordinated and optimal operation of "source-loadstorage". By analyzing the optimal dispatching results., it can be seen that the PET can flexibly transmit power in MG, AC system, and DC system through the power regulation capability of its port, thereby improving the absorption capacity of new energy, reducing the operating cost and improving the economy of the system.