2.1. Control Strategies for HESSs and CPLs
Firstly, the control strategies for a HESS are described. There are n+1 parallel energy storge converters in a HESS, but the control strategies for the n parallel battery converters are very different from the control strategy for the SC converter. Bidirectional buck–boost converters are mostly used in HESSs to achieve the simplest structure. A number of n batteries cascaded with bidirectional buck–boost converters in parallel connections are utilized to sustainably provide or absorb energy and eventually to keep the DC bus voltage constant. A SC cascaded with a bidirectional buck–boost converter is adopted to quickly output or input high-frequency power.
For the DC microgrid model, a droop control strategy based on the DC bus voltage is adopted which utilizes the coupling relationship between the output voltage and the output current to generate a V–I droop characteristic and form V–I droop control. The V–I droop control of a bidirectional DC–DC converter is such that the output voltage and current are controlled according to a specific correspondence, and the control equation is shown below.
The V–I droop control adopted by n parallel battery converters is shown as follows:
In (1), vrefj is the reference DC bus voltage for the outer voltage loop of the j-th battery DC–DC converter. ibatj is the current of the j-th battery DC–DC converter, and kj is the droop coefficient of the j-th battery DC–DC converter.
Generally, the droop coefficient
kj satisfies
In (2), Δvdcmax and Δvdcmin are the maximum voltage sag and minimum voltage sag, respectively. ibatmax and ibatmin are maximum current and minimum current of the battery DC–DC converter, respectively.
The droop coefficients are usually related to the currents of battery DC–DC converters, and are shown as
In (3), ibatj is the current of the j-th battery DC–DC converter, and kj is the droop coefficient of the j-th battery DC–DC converter.
Based on (3), variable droop coefficients correspond to the variable currents of the battery DC–DC converters. Consequently, adjusting the droop coefficients allows one to obtain controllable currents for the battery DC–DC converters.
To eliminate the DC bus voltage sags introduced by the V–I droop control, voltage compensation Δ
vdc-ref is added to the conventional droop control equation in (1) and is shown as
According to (4), the reference DC bus voltage for the outer voltage loop of the j-th battery DC–DC converter is obtained. Similarly, the reference DC bus voltages of the n battery DC–DC converters are completely calculated. The n parallel battery converters are all controlled by inner current loops and outer voltage loops. The control strategies for n battery DC–DC converters are shown in
Figure 2.
The V–I droop characteristic of a battery DC–DC converter is shown in
Figure 3. According to the characteristic curve, the initial operation point is A; if the load power increases, the output current of the converter also increases, while the output voltage decreases, and finally, the operation point moves from A to B.
The objective of the n parallel battery converters is to keep the DC bus voltage constant, while the purpose of the SC converter is to absorb or supply high-frequency power.
Consequently, a low-pass filter (LPF) is utilized to obtain a high-frequency power difference between the microsources and CPLs, and the power is taken as the reference power
Psc-ref of the SC converter, as shown in
Figure 4. The power of the microsources is
PDG, and the power of the CPLs is
Pload. The filter time constant is
T.
The transfer function of the LPF is:
In (5), TS is the computational period, which is a fixed value during the filtering process.
According to
Figure 4, the reference power of the SC converter is deduced, and is shown as
After discretization, (6) is rewritten as follows:
Let
; thus, (7) is transferred into
Control strategies for the n battery buck–boost converters are shown in
Figure 2. V–I droop control is utilized to achieve controllable battery currents without communications. Different droop coefficients introduce different battery currents. To eliminate DC bus voltage sags caused by V–I droop control, voltage compensation Δ
vdc-ref is also added. Based on the current
ibatj of the j-th battery buck–boost converter, the droop coefficient
kj of the j-th battery buck–boost converter, and the provided constant value
vdc-ref of the DC bus voltage, the reference DC bus voltage
vrefj for the outer voltage loop of the j-th battery buck–boost converter is obtained. Then, based on the outer voltage PI controllers and the inner current PI controllers, PWM signals are produced for n battery buck–boost converters.
The control strategy for the SC buck–boost converter is also shown in
Figure 2. To absorb or supply high-frequency power, the LPF is utilized to obtain high-frequency power differences between the microsources and CPLs. The outer voltage PI controllers and inner current PI controllers are also utilized to generate PWM signals for the SC buck–boost converter.
The power characteristic of the CPLs is the most important parameter, and it can affect the stability of a DC microgrid. The buck converter and resistors controlled by the current control loop are used to represent typical CPLs. As the reference current varies, the power of the CPLs simultaneously changes. The CPL regulation feature is closely related to the proportional parameter of the current PI controller.
The control strategy for the CPLs is shown in
Figure 5.
vdc is the DC bus voltage, and
iref is the reference current of the CPLs. Based on the current PI controller, PWM signals are produced for the Buck converter.
2.2. Equivalent Model of DC Microgrids
In islanded DC microgrids, microsources are modeled as power sources, and the power and current are PDG and iDG, respectively. The power and current of the CPLs are Pload and idc, respectively. Modeling a HESS is very complex, and models of n batteries with cascaded converters are different from the model of one SC with one cascaded converter.
As shown in
Figure 6, when the battery is charging, the cascaded DC–DC converter operates in buck mode while
Q1 and
D2 are turned on, and the power flows from the DC bus to the battery. When the battery is discharging, the DC–DC converter operates in boost mode while
Q2 and
D1 are turned on, and the power flows from the battery to the DC bus.
The differential equation of the battery DC–DC converter is
In (9), vdc is the DC bus voltage, vbat is the battery voltage, iL is the inductor current, R is the equivalent internal resistance of the battery, and α is the charging and discharging factor of the battery.
Consequently, based on (9), the battery and the cascaded DC–DC converter are equivalently modeled as a generalized battery, resistor, and inductor in series, as shown in
Figure 7.
When n batteries and cascaded DC–DC converters are connected in parallel, the differential equations are
In (10), Rj is the equivalent internal resistance of the j-th battery.
Based on (10), the equivalent model of n batteries and cascaded DC–DC converters in parallel connections are derived and is shown in
Figure 8.
The SC cascaded DC–DC converter is controlled by the outer power loop, and the power relationship of the SC and the cascaded DC–DC converter is as follows:
In (11), isc is the output current of the SC’s DC–DC converter, vdc is the DC bus voltage, vSC and iSC are the voltage and current of the SC, respectively, and Psc is the power of the SC.
The equivalent model of the SC and the cascaded DC–DC converter is equivalent to a bidirectional power source and is shown in
Figure 9.
Based on the equivalent models of the microsources, CPLs, and HESS, an equivalent model of the DC microgrids is established and is shown in
Figure 10.
Rj is the equivalent internal resistance of the j-th battery,
α is the charging and discharging factor of the battery,
Lj is the inductance of the j-th DC–DC converter,
vbatj and
ibatj are the voltage and current of the j-th battery, and
PDG,
Psc, and
Pload are the power values of the microsources, the SC, and the CPLs, respectively.
iDG,
isc, and
idc are the currents of the microsources, the SC, and the CPLs, respectively.
vdc is the DC bus voltage, and
Cdc is the filter capacitor.