An adaptive coordinated optimal control method for parallel bidirectional power converters in AC/DC hybrid microgrid

https://doi.org/10.1016/j.ijepes.2020.106596Get rights and content

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  • The economically optimal distribution scheme of BPCs is calculated.

  • A non-linear coordinated control method for BPCs is proposed.

  • A secondary voltage-regulated controller for BPCs is designed to control dc voltage.

Abstract

Parallel bidirectional power converters (BPCs) play an important role in achieving mutual support between the two grids and in improving the power quality. One of the difficulties of the study is how to coordinated control BPCs to simultaneously realize the dual goals of economically distribute transmission power among BPCs and the high dynamic quality. In view of this, this paper proposes an adaptive coordinated optimal control method for the parallel BPCs. First, taking the minimization of the sum of the power losses of BPCs as the objective, the economically optimal distribution scheme for power transmission among parallel BPCs is calculated. Second, a primary voltage-regulated controller is designed, outer loop of the primary voltage-regulated controller can distribute the dynamic transmission power among BPCs according to the power margin of each BPC, to avoid overloading BPCs, and inner loop of the primary voltage-regulated controller can realize the decoupling of the output variable and the interference variable, to improve the dynamic voltage quality. Third, a secondary voltage-regulated controller is designed, it can make the dc bus voltage restore to the rated value quickly after power disturbance occurs, and ensure the economically optimal distribution of the transmission power among BPCs after the system reaches the steady state. Finally, the stability of the proposed control method is illustrated and conclusions are verified.

Introduction

Smart distribution grids are profoundly changing the electric power generation, power transmission, power transformation, power distribution, and power utilization. And the biggest challenge for distribution grids comes from the massive use of distributed energy resources (such as distributed generation, distributed energy storage, and demand response). How to deal with many challenges, to make the smart grid maximize its potential and bring broader social and economic benefits, has become very urgent. The ac/dc hybrid microgrid can effectively integrate various ac and dc distributed energy resources and then gain access to smart distribution grids as an intelligent subsystem, which can not only provide a flexible and orderly way for renewable energy to distributed grid-connected power generation and large-scale accommodation, but also enhance the controllability and reliability of smart distribution grids, thereby improving the overall energy efficiency of the power system [1], [2], [3].

Compared with the pure ac microgrid and dc microgrid, the topological structure and operation mode of an ac/dc hybrid microgrid are more complicated and diverse, and the theoretical research difficulty of optimal operation and control is greatly increased. In order to facilitate research and to grasp the main contrasting technical issues, this paper focuses on the different characteristics of an ac system and a dc system in an ac/dc hybrid microgrid. The paper divides the ac/dc hybrid microgrid into three areas based on the physical characteristics of the ac and dc systems interconnected through parallel BPCs. They are the ac area, the dc area, and the ac/dc power interface area. The topology of ac/dc hybrid microgrid is shown in Fig. 1.

The parallel BPCs in ac/dc power interface area are the bridges between the dc area and the ac area and play an important role in maintaining the dynamic balance of the internal power of the ac/dc hybrid microgrid. They achieve mutual support between the ac and the dc areas, and improve the power quality of the ac/dc hybrid microgrid [4]. Meanwhile, since high-density DGs are adopted in the ac/dc hybrid microgrid, considering the volatility and uncertainty of the DGs’ output power, and the random nature of the ac and dc load, it is necessary to research into the flexible power control technology of the ac/dc power interface area [5], [6].

At present, the widely used control strategies for BPCs are PI control [7], [8], repetitive control [9], and deadbeat control [10]. However, PI control method is based on the idea of linearization at the operating point, so the control effect depends on the operating point, and PI control parameters are difficult to set. Deadbeat control and repetitive control can achieve indifference control, but it is sensitive to the control parameters, so it has a low robustness. In [11], the H robust control method was proposed, it could enhance the robustness of the system, but this control method was too complicated to use in the complex systems. In order to obtain better control effect and achieve a wide range stability, the nonlinear control method was proposed in [12], [13], [14], [15]. In [12], [13], a control method based on passive control theory was used in power system, which achieved a good control effects. In [15], a nonlinear controller was designed for the three-phase voltage PWM converter based on the exact linearization theory, and this paper dealt with the problem of first-order zero dynamics in the system, so the dynamic response characteristics of system was improved. However, there exist a host of converters operating in parallel in the ac/dc hybrid microgrid. They work together to expand the power capacity of inverter/rectifier and to improve the reliability of power interconnection support between the ac and dc areas. Therefore, it is necessary to study on the coordinated control method of parallel BPCs.

The key problems for the system with parallel BPCs are how to coordinate and distribute the power of each converter. The existing reference mainly starts from the perspective of the average distribution of power between parallel BPCs and focuses on how to improve the average distribution accuracy of the power. Traditional centralized control strategies, such as mean control [16] and master–slave current sharing control [17], can carry out the average distribution of power quickly and accurately, but require all BPCs to be interconnected. This requirement reduces the expandability of the system. On the contrary, the droop control does not require interconnection between various BPCs. This makes “plug and play” implementation easier, so it has received extensive attention [18], [19]. The main considerations for average power distribution control through parallel BPCs are as follows: 1) improve the power conversion efficiency of BPCs; 2) reduce circulating current; 3) avoid BPC overload caused by large power disturbances that occur when current sharing deviation is too large. However, because of the conversion efficiency of BPC is high-order nonlinear, when BPCs transmit a large power for a long time, optimizing the power of each BPC according to efficiency curve of each BPC rather than distributing the power evenly is more effective to reduce the power loss of each BPC and improve the economical operation of system. For 1), it is obvious that optimizing the power of each BPC according to efficiency curve of BPCs is more economical than the average distribution. Meanwhile, the trade-off between system efficiency and conversion quality should be taken into account in controlling BPC between the ac and dc areas [20]. For 2), the circulating current between parallel BPCs can be effectively reduced by the circulating current suppression method. The mechanism of generating the circulation current among parallel BPCs was proposed based on graphic analysis, and a simplified PWM strategy with switch state constraints was proposed to suppress the circulating current among parallel BPCs in [21], [22]. However, the graphic analysis cannot provide a detailed mathematical model or be used to conduct a strict quantitative analysis. In [23], a circulating current suppression method based on virtual impedance effectively suppressed the circulating current between BPCs. In [19], [24], the d-q-0 tri-axis control strategy is used to replace the traditional d-q two-axis control strategy, which effectively suppresses the circulating current among parallel BPCs. For 3), through a reasonable coordinated control method between parallel BPCs, the power disturbance can be effectively dealt with and BPC overload can be avoided.

In view of the above, this paper proposes an adaptive coordinated optimal control method for parallel BPCs when the hybrid ac/dc microgrid operates in grid-connected mode. The method draws on the idea of power system frequency modulation, and accordingly controls the dc bus voltage in two stages, the main contributions are as follows:

  • (1)

    The economically optimal distribution scheme of BPCs is calculated. According to the efficiency curve function, the economically optimal distribution scheme of the transmitted power among parallel BPCs can be obtained with the objective of minimizing the sum of BPCs, which can reduce the sum of the power losses of BPCs and improve the economy of system operation.

  • (2)

    A primary voltage regulation method for BPCs is proposed. The outer loop of primary voltage-regulated controller can adaptively distribute the dynamic transmission power appearing in the ac/dc hybrid microgrid, which can avoid overloading BPCs, and based on the differential geometry theory, the inner loop decouples the output variable from the interference variable, maintains the dc bus voltage stability and achieves the optimal dynamic response of power transmission.

  • (3)

    A secondary voltage regulating method based on the economically optimal distribution scheme of each BPC’s transmission power is proposed. It can quickly re-establish the dc bus voltage if a power disturbance occurs, and transmission power can be economically optimally distributed among the parallel BPCs after the system reaches the steady state, which achieves the purpose of optimal control.

Section snippets

Economically optimal distribution scheme for power transmission

According to the BPC efficiency data that were provided by the manufacturer [6], the efficiency curve function of a BPC can be obtained by fitting in Fig. 2.

Fig. 2(a) shows the efficiency curve of a BPC. The 11 black points in the figure are experimental measurement data provided by the manufacturer. Fig. 7(b) shows errors between the corresponding point of the fitted curve and experimental measurement data. According to Fig. 7(b), these errors are all<0.0005.

The efficiency curve function of a

Model of BPC

The topology of a BPC is shown in Fig. 4.

This paper set the d axis in the same direction as voltage vector of distribution network, according to the KCL and KVL, the differential equations of a BPC can be written by using orthogonal Parker transform as follow [25], [26]:diddt=ωiq-RLid+edL-1Luddiqdt=-ωid-RLiq+eqL-1Luqdudcdt=32edidCdcudc-3R2id2+iq2Cdcudc-ILCdcwhere L = Lj (j = a,b,c), R = Rj (j = a,b,c), then equation (3) can be written in the form of affine nonlinearity as follow:ẋ=f(x)+g(x)u+

Outer loop

The static transmission power reference value given by the ac/dc hybrid microgrid optimization operation unit may make the static power of each BPC different, which may cause the power margin of each BPC to be different. When a large power disturbance occurs, the dynamic power may cause BPCs with a small power margin overload. The outer loop of primary voltage-regulator controller is designed to assign each BPC with dynamic power according to its own power margin when power disturbance occurs.

Secondary voltage-regulated controller

After the primary voltage regulation of the system, if the deviation between the dc bus voltage and the rated value exceeds the threshold value or the dc bus voltage needs to be restored to the rated value, the microgrid energy management system (MEMS) issues an instruction to execute the secondary voltage regulation control based on the economically optimal distribution scheme of each BPC’s transmission power in this section.

According to the efficiency curve function of each BPC, the secondary

Stability analysis

Set the d-axis in the same direction as voltage vector of distribution network, it can be obtained P = 3/2*udid by orthogonal park transform. when voltage is the rated value, the per-unit of power and current can be obtained as i(p.u= 2/3*P(p.u). Coordinated control block diagram is shown in Fig. 9.

According to Fig. 9 (a) and (b), the characteristic polynomials of the control system are as follows:Ds=g1s5+g2s4+g3s3+g4s2+g5s+g6g1=0.5LT3g2=0.5RT3+2LT2g3=2RT2+2.5LTg4=2RT+L+LTk1KPWMg5=R+Lk1KPWMg6=

Simulation analysis

In this paper, based on an ac/dc hybrid microgrid demonstration project, the simulation model is built using MATLAB/Simulink according to Fig. 1. In this model, three BPCs run in parallel in the ac/dc power interface control area, parameters of the system are shown in Table 1.

Condition (1): The static power reference values (in per-unit quantities) of the three BPCs optimized according to the BPC efficiency curve were set to 0.8, 0.533 and 0.533, respectively. At 0.6 s and 0.85 s, loads of the

Conclusion

The coordinated control of BPCs in power interface of ac/dc hybrid microgrid is studied in this paper, and an adaptive coordinated optimal control method for parallel BPCs is proposed. Conclusions are summarized as follows:

  • (1)

    The economically optimal distribution scheme for transmission power is calculated. According to the fitting efficiency curve function of the BPC, the economically optimal distribution scheme for power transmission among parallel BPCs can be obtained with the objective of

CRediT authorship contribution statement

Peng Li: Conceptualization, Methodology, Supervision. Tianyu Guo: Methodology, Writing - original draft, Software, Validation, Writing - review & editing. Yuwei Li: Data curation, Validation, Software, Conceptualization. Xiaoqing Han: Conceptualization, Methodology. Peng Wang: Data curation, Resources. Xinming Li: Validation, Software. Zixuan Wang: Validation, Software.

Declaration of Competing Interest

The authors declared that there is no conflict of interest.

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 51577068, and in part by the National High Technology Research and Development Program of China (863 Program) under Grant 2015AA050104.

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