A coordination control strategy for parallel-connected boost converters in dc microgrid

Due to the constant power loads (CPLs), the system damping of the DC microgrid is reduced, which will lead to the collapse of bus voltage. In addition, the errors of current sharing amplify due to different line impedances. To address these issues, a hybrid coordination control strategy is proposed for parallel-connected boost converters, which realizes stable control and maintains the accuracy of the current distribution. Firstly, a passivity-based control (PBC) with a proportional-integral (PI) regulator is developed. The virtual damping-based PBC enhances the system damping and the PI regulator eliminates errors. On this basis, a secondary voltage control (SVC) featuring simplicity and weak dependence on communication is introduced to remove the errors of current distribution. Finally, the hybrid coordination control strategy is verified by RT-LAB-based hardware in the loop (HIL) experiment.


Introduction
Figure 1 shows a typical DC microgrid.Since CPL has negative impedance characteristics, the bus voltage is in danger of collapse due to the weak system damping [1].To eliminate the effects of CPL, several nonlinear control methods such as cooperative control, sliding-mode control, and nonlinear observers are developed [2].The nonlinear control can offset the influence of CPL, but its algorithm is complicated and it is easy to be affected by the converter parameters in the system [3][4][5].The passivitybased control (PBC) is applied with the resistive load [6].The PBC technique enables the better robustness of bus voltage.Nevertheless, the deviation from the operating point exists in the conventional control mode, especially when the loads are CPLs.
The advantage of droop control is the independence of communication [7], but there is an inherent conflict between the accuracy of current distribution and voltage regulation while the droop control is applied [8].In [9], the calculation of compensation signal in SVC requires the mean currents provided by all distributed generations (DGs), which will incur additional costs [10].
In this paper, a hybrid coordination control strategy is proposed for parallel-connected boost converters, which realizes stable control and maintains the accuracy of current distribution.In Section 2, the microgrid structure is introduced.In Section 3, a coordination control strategy based on composite PBC is presented.Experimental results are explained in Section 4. Finally, the conclusions of this paper are drawn in Section 5.

Parallel-connected boost converter system
To simplify the analysis, two boost converters are in parallel on the power side of the system, and CPL and resistive load are in parallel on the load side.In the Figure 2

Coordination control strategy based on composite PBC
The system is strictly passive only if the storage energy of the system is lower than the energy provided by the power supply.It means that there is dissipated energy in the system.When the resistive load of the system dominates, the system becomes stable, but it will lead to an increase in energy consumption at the output of the system.In order to eliminate energy consumption, the closed-loop feedback controller can be used to series virtual resistors in the inductive loop and parallel virtual resistors in the capacitive loop, which is the main idea of PBC.

PBC design
Inductance current and capacitance-voltage are selected.The circuit model of the state space averaging method for the converter system is: (1 ) (1 ) Where   represents input voltage;   and   represent inductance and capacitance;   represents inductance current;   represents the duty ratio.The equation can be written as: (1 ) The core purpose of the design for the passive controller is to make the inductive current and capacitor voltage reach the values of a steady state in a short time.Therefore, we suppose   =  −   and the energy error function of the system is ( ) To eliminate the effects of CPL and accelerate () → 0, damping   needs to be injected into the system.
  is taken.Figure 3 shows the structure of the parallel-connected boost converters with the injection of virtual damping.) Selecting and expanding the passivity-based controller yields: Where   is the reference voltage;   is the reference inductor current.The transformation of the reference value is zero, so   = 0 and   = 0. there is a zero-point problem in the right half-plane.The direct voltage control method cannot be used.The output voltage is indirectly controlled by controlling the output current.Reference current   selects the output current, i.e., ( )

Power Compensation of PBC
The PBC can ensure that the system reaches a steady state when system disturbances occur, but it will generate steady-state errors at the same time.The controller design is shown in Figure 4.In order to exclude the error   , a PI regulator is added to the original passivity-based controller as a feedback correction value for the variation of load.When the load changes, the compensated power ∆ is expressed as: P k e k e dt (7) The value of ∆ is limited by the power limiter, and its output ∆′ is used as the value of the compensation power for the passivity-based controller.In summary, the PBC with PI regulator ensures that each boost converter is passive and stable, and in turn, it ensures that the whole system is stable.

Secondary voltage control based on PBC with PI regulator
An inherent contradiction between voltage deviation and current-sharing accuracy exists in the conventional droop control.A secondary control design is shown in Figure 5.The secondary voltage control is realized by the feedback mechanism.A distributed secondary controller is designed for each local DG to achieve the recovery of bus voltage and accurate power sharing.The voltage signal is provided by secondary control and added to the droop control for voltage recovery, i.e., 11 Where  1 is the proportion coefficient;  1 is the integration coefficient;  1 is defined as:

Results
A HIL experimental platform based on RT-LAB is built.The RT-LAB-based HIL experimental platform is shown in Figure 6.The converters Parameters is shown in table 1.The current sharing accuracy is expressed by:   When the droop coefficient is set to 0.5, the voltage drops.The value of bus voltage is significantly lower than 750 V, and there is also a large error in current sharing.The error of current sharing is reduced.However, the hybrid coordination control strategy can maintain a stable DC bus voltage of 750 V while making the error of current sharing almost zero.
Meanwhile, the hybrid coordination control can also ensure that bus voltage is restored in a short time when there is a large disturbance.In Figure 7(b), the error of current sharing under the conventional droop is large, while the error under the hybrid coordination control strategy is almost zero.

CPL disturbance
A CPL disturbance is applied.The CPL increases to 18 kW at 0.5 s and recovers at 1 s.  8, after the CPL is disturbed, the hybrid coordination control strategy can restore bus voltage in a short time, and the error of current sharing is almost zero when the system reaches the new operating state.

Resistance disturbance
This subsection analyses the result under different control strategies when a resistive load disturbance occurs.A resistive load disturbance is applied to the system.The resistive load decreases from 50 Ω to 40 Ω at 0.5 s and recovers at 1 s.The waveforms under resistive load disturbance.From Figure 9, the hybrid coordination control strategy performs better than the conventional control strategy regardless of the resistive load variation, which is the same as the performance of the input voltage and CPL disturbances.

Conclusion
In this paper, the composite PBC for the parallel-connected boost converters is designed to ensure internal stability with CPL.When the line impedance is different, it will cause some effect.A hybrid coordination control strategy that takes the PBC with the PI regulator as the inner loop and the secondary voltage control as the outer loop is proposed based on the conventional droop control.The HIL experiment platform based on RT-LAB is built to verify the control strategy.The results of the experiment show that, regardless of whether the system is static or disturbed, the proposed strategy can ensure that the voltage maintains at reference and the error of current sharing is zero.

Figure 1 .
Figure 1.DC microgrid.Figure1shows a typical DC microgrid.Since CPL has negative impedance characteristics, the bus voltage is in danger of collapse due to the weak system damping[1].To eliminate the effects of CPL, several nonlinear control methods such as cooperative control, sliding-mode control, and nonlinear observers are developed[2].The nonlinear control can offset the influence of CPL, but its algorithm is complicated and it is easy to be affected by the converter parameters in the system[3][4][5].The passivitybased control (PBC) is applied with the resistive load[6].The PBC technique enables the better

Figure 4 .
Figure 4.The controller for the converters.In summary, the PBC with PI regulator ensures that each boost converter is passive and stable, and in turn, it ensures that the whole system is stable.

Figure 5 .
Figure 5.Control system of converters.A secondary control design is shown in Figure5.The secondary voltage control is realized by the feedback mechanism.A distributed secondary controller is designed for each local DG to achieve the recovery of bus voltage and accurate power sharing.The voltage signal is provided by secondary control and added to the droop control for voltage recovery, i.e.,

1 Figure 7 .
Figure 7.The waveforms under input voltage disturbance.When the droop coefficient is set to 0.5, the voltage drops.The value of bus voltage is significantly lower than 750 V, and there is also a large error in current sharing.The error of current sharing is reduced.However, the hybrid coordination control strategy can maintain a stable DC bus voltage of 750 V while making the error of current sharing almost zero.Meanwhile, the hybrid coordination control can also ensure that bus voltage is restored in a short time when there is a large disturbance.In Figure7(b), the error of current sharing under the conventional droop is large, while the error under the hybrid coordination control strategy is almost zero.

Figure 8 .
Figure 8.The waveforms under the CPL disturbance.From Figure8, after the CPL is disturbed, the hybrid coordination control strategy can restore bus voltage in a short time, and the error of current sharing is almost zero when the system reaches the new operating state.

Figure 9 .
Figure 9.The waveforms under resistive load disturbance.From Figure9, the hybrid coordination control strategy performs better than the conventional control strategy regardless of the resistive load variation, which is the same as the performance of the input voltage and CPL disturbances.
,  1 and  2 represent the input voltages;  1 and  2 represent the switches;  1 and  2 represent diodes;  1 and  2 represent energy storage inductors;  1 and  2 represent filter capacitances;  1 and  2 represent the line resistors;   represents the load resistance;  1 and  2 represent inductive currents;  1 and  2 represent the output currents;   represents the total output current;  1 and  2 represent the output voltages;   represents bus voltage; CPL is replaced by a current source;   represents the input voltage.