Energy Balance Control of Energy Storage System Based on Improved Virtual DC Motor

Energy storage units have a big role in microgrids. To enhance the inertia of the DC microgrid while achieving energy balancing of each energy storage system, an energy balancing control of the energy storage system with virtual DC motor characteristics is proposed. By adding the VDCM technique to the traditional constant voltage control and adding the SoC information of the respective energy storage system to the virtual armature induction potential of the armature loop equation in the VDCM control, compared to existing controls, this control method can enhance DC microgrid inertia while balancing the SoC of the energy storage system, as well as charging and discharging mode switching without changing the control strategy. Finally, a multi-storage DC microgrid model is built in Matlab/Simulink, and the feasibility of the method is verified by simulation.


Introduction
DC microgrid has been widely used in our reality due to its simple structure, flexible control, and low input cost.DC microgrid is an ideal power distribution system that can fully use renewable energy sources [1].The power converter is the bridge between the individual units and the busbar.For the discontinuity and instability of renewable energy sources, energy storage technology can effectively splice these discontinuous renewable energy sources together and transform them into a continuous and stable energy supply [2].Energy storage systems can absorb grid energy and release energy at the same time, playing the role of peak and valley filling [3].Compared to generators that dominate conventional power systems, most of the energy storage system access is based on the power electronic converter interface, which itself does not have rotational inertia conducive to maintaining system voltage stability.Because of the apparent power random fluctuation of distributed energy and its load, the rapid change of transient power is likely to affect the voltage stability of the DC bus [4].
In recent years, China's inertia research on the DC microgrid mainly includes two aspects.The first way is to increase the capacity of the capacitor on the bus side or increase the capacity of the energy storage battery.The other way, the inclusion of virtual inertia in DC microgrids mainly includes virtual capacitance control and the inclusion of the motor's rotation equation in the control method to provide inertia [5].Droop control is a standard method to study the energy management of energy storage units [6].Because of the poor control accuracy and the inability to achieve the energy balance of each unit of energy storage, [7] proposes to add SoC averaging to the droop control to vary the droop coefficient and thus equalize the SoC.However, this method requires communication between the battery packs during calculating the average value of the SoC.[8] proposes weighting the virtual resistance to modify the charge/discharge rate of the energy storage system, but inertia is not taken into account.[9] proposes introducing virtual DC motor control in double closed-loop constant voltage control, which cannot satisfy the energy balance of the energy storage unit but provides damped inertia support for the system.
Virtual DC machine inertia control is proposed in [10], and SoC equalization control is introduced in its armature loop virtual armature resistance.However, this method requires frequent switching in charging and discharging, and communication between individual energy storage systems SoCs is required.
The virtual DC motor-based improved control proposed in this paper can show the superiority of this paper over [10] by comparing it with the traditional SoC equalization control.[10] can provide inertia to the DC microgrid and can realize the energy equalization of each energy storage unit, but the control strategy needs to be changed when switching between charge /discharge modes, and the communication between the energy storage SoCs is required, this paper enables the SoC equalization process without the need to change the control policy as well as the communication between SoCs.

DC microgrid topology and conventional droop control
2.1.DC microgrid topology DC microgrid has been widely used in our reality due to its simple structure, flexible control, and low input cost, a typical DC microgrid architecture is shown in Figure 1 below, which mainly consists of renewable generation units, energy storage units, bi-directional interface converters, and DC loads and AC load units.As some random factors can make the imbalance of energy in the network, affecting the bus voltage, the energy storage unit can output or absorb energy through the bus to achieve peak and valley reduction and stabilize the bus voltage; Meanwhile, at the same time, when the distributed generation unit fails to supply power, the system can be integrated into the larger grid thus making the micro-grid stable.The system often uses droop control when distributed generation units and energy storage units control the bus voltage.

Limitations of traditional droop control
In DC microgrids, droop control is often used between energy storage converters to equalize current between storage units, and regulation of current and output voltage is achieved by adding virtual resistors to the controller.
For the storage system, the conventional droop control expression is where v oi denotes the output voltage.v ref is the output voltage reference.R di is the droop factor, which is the virtual resistance in the controller.i oi is the output current.
. Output voltage and current curves at different reference voltages and dropout factors Equation 1shows that varying the virtual impedance can change the output current.Similarly, changing the value of the reference voltage, which is the intercept distance in the figure above, can also achieve this effect.Figure 2 shows the two-output voltage and current characteristics.Droop control can regulate the output current but it does not provide inertia nor does it equalize the SoC state.
A typical SoC equalization method with voltage compensation is shown in Figure 3 below.This control expression can be expressed as follows: Taking two power converter converters as an example, the following expressions are obtained: Further, the output current of each unit can be obtained as: It is known that the same virtual resistance R d1 = R d2 , if the compensation voltage is also the same and V (SoC), is taken as a monotonically increasing function, therefore, the above equation shows that the output current is proportional to the SoC.
Since the conventional droop control is inertia-free, the method is not conducive to improving the quality of the bus voltage, resulting in a more sensitive DC bus voltage with power.

VDCM Equivalent Model
An SoC equalization control strategy based on virtual DC motors is proposed for the limitation of the lack of inertia of droop control.Figure 4 shows the VDCM equivalent model.Bidirectional buck/boost has some equivalence with the VDCM model.The converter is equated to a two-port network with the front end and rear end connected to the energy storage unit and busbar respectively, and V bat is the battery output voltage.The front-end circuit of the VDCM equivalent is a dynamic armature induction with an electromotive force of E*, in which the battery charge state information is added for subsequent energy equalization of the energy storage unit, Ra is the virtual armature resistance, which acts as the droop factor, and Vout is the output voltage of the DC motor.
The Electro-mechanical equation and the armature circuit equation can describe the VDCM model: where J is the rotational inertia; T_m and T_e are mechanical torque and electromagnetic torque, ω is the actual angular velocity; D is the damping coefficient; ω 0 is the rated angular velocity.If operating under steady-state conditions, the control equation can be written as It is known that P_m -P_e = ∆P.The armature circuit equation is given by: _ ∆  ∅  ∅∆ (9) where E_ref is the armature voltage rating, ∆E is the armature voltage deviation, C T is the torque factor and ∅ is the magnetic flux.By analogizing with section 2.2 above, adding SoC to E gives the new armature-induced electric potential E*, E* = E_ref + ∆E + E (SoC).E_ref and ∆E represent V ref and ∆V in Equation (2) above respectively.R a corresponds to R d .Thus, the armature circuit equation of the modified virtual DC motor can be equated with Equation (2).

VDCM-based SoC equalization control
The VDCM-based SoC equalization control is shown in the following Figure 5. Compared to conventional control, the inclusion of a virtual DC motor can provide the system with inertia.In addition, by adding SoC information to the armature circuit to achieve SoC equalization and reasonable distribution of energy, the current regulation part is the conversion of I a through v ref /v bat as the reference value of the input for the energy storage battery, and finally, the control signal obtained through the PI regulator and the pwm link to control the bidirectional Buck/Boost variation.
This paper selects a function f (SoC) that is flexible and controllable for outputting current regulation: ⋅  (10) where k and n are droop curve adjustment factors, which can be selected according to different bus voltage ratings and power converter specifications, and the value of SoC is limited by SoCmin and SoCmax.

Simulation analysis
The simulation platform is built in Matlab, and the capacity of the energy storage unit is taken as 2.7 Ah and set 400 V as the bus voltage.The simulation time is set to 90 s so that the SoC can reach equalization smoothly.

Simulation analysis of VDCM control on voltage waveform and SoC equalization during discharge
Figure 6 (a) shows a comparison of the voltage regulation of the two control methods.The output current waveform of the energy storage unit with the SoC waveform under virtual DC motor control is shown in Figures 6 (b) and (c) where the initial value SoC of ESU#1 is taken as 75%, the value SoC of ESU#2 is taken as 67%, Ra is taken as 0.25, n is taken as 1, virtual inertia J is taken as 1/3, damping factor D is taken as 0.8, and the system works in the discharged state.As shown in Figure 6 (b) at the 20s and 40s, when the load throwing makes the absorbed power of the storage unit change, with virtual DC motor control, the bus voltage overshoot is smaller than with conventional sag control.In Figure 6 (c), the SoC equalization can be achieved by using the improved control method.

Simulation analysis of VDCM control on voltage waveform and SoC equalization during charging
Figure 7 (a) shows the comparison of voltage regulation of the two control methods.Figures 7 (b) and (c) show the output current waveform and SoC waveform of the energy storage device under improved control, where the value of SoC for ESU#1 is taken as 40%, the value of SoC for ESU#2 is taken as 33%, Ra is taken as 0.25, n is taken as 1, virtual inertia J is taken as 1/3, damping factor D is taken as 0.8, and the system works in the charging state.As shown in Figure 7 (b) for the 20 s and 40 s, when the load throwing makes the absorbed power of the storage unit change, the DC bus voltage overshoot with virtual DC motor control is smaller compared with the conventional droop control.In Figure 7 (c), the SoC equalization can be achieved by using the improved control method.

Simulation analysis of virtual DC motor control during charge/discharge switching
Figure 8 (a) shows a comparison of the voltage regulation of the two control methods.The output current waveform and SoC waveform of the energy storage unit under the improved control method is shown in Figure 8 (b) and (c), where the initial value SoC of ESU#1 is taken as 75%, the value SoC of ESU#2 is taken as 67%, Ra is taken as 0.25, n is taken as 1, virtual inertia J is taken as 1/3, damping factor D is taken as 0.8, and the system works in the charge/discharge state.As shown in Figure 8 (b) for the 20 s and 40 s, there is a sudden change in bus voltage when the energy storage unit operation mode is switched.Compared with the conventional droop control using virtual DC motor control still reduces the DC bus voltage overshoot, from Figure 8 (c), the improved control method allows the output current to be balanced with the SoC without switching the control strategy, the simulation experiments verifies the superiority of the improved control compared to [10] where the control strategy needs to be switched during charging and discharging and communication between SoCs is required.

Conclusion
An improved virtual DC motor control method is proposed for the problems of small inertia of the DC microgrid and uneven energy distribution of energy storage units.The traditional method and the improved method are compared by simulation.the simulation proves that the proposed improved control method can make the bus voltage less affected by the load change perturbation.In addition, the improved control method can achieve smooth switching of the two operation modes and energy balance without switching the control strategy as well as no communication between SoCs, which has some advantages compared with the control strategy in [10], this will be helpful for future research on the topic.

Figure 3 .
Figure 3. SoC balanced conventional droop control block diagram

Figure 4 .
Figure 4. Bidirectional DC/DC converter and VDCM equivalent circuit

Figure 6 .
Figure 6.Traditional control and improved control method voltage and SoC equalization diagram

Figure 7 .
Figure 7. Traditional control and improved control method voltage and SoC equalization diagram

Figure 8 .
Figure 8. Traditional control and improved control method voltage and SoC equalization diagram