FIG. 7 illustrates a diagram of virtual power source equivalent models corresponding to the power supply network of FIG. 6, according to some aspects of the present disclosure.

FIG. 8 illustrates a diagram of virtual power source equivalent models corresponding to a power supply network with proportional current sharing among parallel-connected power supply units, according to some aspects of the present disclosure.

FIG. 9 illustrates a circuit diagram of a power supply network with proportional current sharing among parallel-connected power supply units, according to some aspects of the present disclosure.

FIG. 10 illustrates exemplary output characteristics of the virtual power source equivalent models of FIG. 8, according to some aspects of the present disclosure.

FIG. 11 illustrates a flowchart of a method for operating a power supply unit, according to some aspects of the present disclosure.

FIGS. 12A-12E illustrate simulation results of various power supply networks, according to some aspects of the present disclosure.

FIGS. 13A-13D illustrate various applications of a power supply network, according to some aspects of the present disclosure.

The present disclosure will be described with reference to the accompanying drawings.

DETAILED DESCRIPTION

Although specific configurations and arrangements are discussed, it should be understood that this is done for illustrative purposes only. As such, other configurations and arrangements can be used without departing from the scope of the present disclosure. Also, the present disclosure can also be employed in a variety of other applications. Functional and structural features as described in the present disclosures can be combined, adjusted, and modified with one another and in ways not specifically depicted in the drawings, such that these combinations, adjustments, and modifications are within the scope of the present disclosure.

In general, terminology may be understood at least in part from usage in context. For example, the term “one or more” as used herein, depending at least in part upon context, may be used to describe any feature, structure, or characteristic in a singular sense or may be used to describe combinations of features, structures or characteristics in a plural sense. Similarly, terms, such as “a,” “an,” or “the,” again, may be understood to convey a singular usage or to convey a plural usage, depending at least in part upon context. In addition, the term “based on” may be understood as not necessarily intended to convey an exclusive set of factors and may, instead, allow for existence of additional factors not necessarily expressly described, again, depending at least in part on context.

In practice, various approaches with varying degrees of complexity and current-sharing performance have been proposed for parallel-connected SMPS units. In general, methods for connecting SMPS units in parallel are characterized by connection styles, control configurations, and feedback functions, where each SMPS unit may include a DC to DC converter (DC/DC converter). As a power source can be either a voltage source or a current source, there are three fundamental structures (e.g., three types of structures) for connecting the SMPS units in parallel. Specifically, in a first type (Type 1), all SMPS units are voltage (Thévevin) sources. In a second type (Type 2), one or more SMPS units are voltage (Thévenin) sources, and other SMPS units are current (Norton) sources. In a third type (Type 3), all SMPS units are current (Norton) sources.

Some issues exist in the above three types of structures in terms of current-sharing accuracy, voltage regulation, dynamic performance, or other consideration factors. For example, Type 1 may have inaccurate current-sharing performance, poor dynamic response and suboptimal performance for large load ranges (low gain required for stability across a wide load range). Besides, Type 1 may lack robustness to variations in the current-sharing gain, and may have poor voltage regulation due to reliance on a large output resistance for the current sharing. In another example, with respect to Type 2, a precise current sensor and a current divider are needed on the load side. Accuracy in the current sharing is affected by variations in the master's current, resulting in poor noise immunity. Modularity is limited in Type 2 because the current divider is used on the load side. In still another example, with respect to Type 3, the accuracy of the current sharing depends greatly on the precise selection of current loop parameters. The control structure of Type 3 is complicated. Modularity is limited due to the requirement of interconnected current-sharing loops.

Further, some existing virtual impedance-based droop control methods for parallel-connected SMPS units may have the following issues. For example, with respect to complexity, implementations of the existing droop control methods can be complex, especially when dealing with high-order harmonics or unbalanced loads. In another example, with respect to sensitivity, the existing droop control methods are sensitive to the bandwidth of the current/voltage control loops, thereby limiting their effectiveness. In still another example, with respect to noise amplification, derivative controllers involved in the existing droop control methods can amplify the measurement noise, thereby requiring additional filters or methods to reduce or eliminate the measurement noise.

To address one or more of the aforementioned issues, the present disclosure introduces a virtual-model based control scheme for a power supply network which includes parallel-connected power supply units. The control scheme disclosed herein is based on a virtual power source equivalent model, and is a simple and efficient control scheme that can ensure equal current sharing among the parallel-connected power supply units (e.g., output currents of the power supply units being equal to one another) or proportional current sharing among the power supply units (e.g., output currents of the power supply units satisfying a proportional current sharing condition determined by a proportional current sharing coefficient, as described below in more detail). By emulating the virtual power source equivalent model, the control scheme disclosed herein can achieve droop control, which facilitates precise current sharing (e.g., equal or proportional current sharing) among the parallel-connected power supply units without the need of communicating signals between the power supply units. In the control scheme disclosed herein, the modularity and dynamic response of the power supply units can be enhanced, and stability of the power supply units across varying load ranges can also be enhanced, regardless of the type, capacity, topology, modulation, etc., of the power supply units. The control scheme disclosed herein can be easily implemented using digital circuits (e.g., a microcontroller (MCU) or digital signal processor (DSP)) or analog circuits (e.g., operational amplifiers, transistors, resistors, capacitors, etc.).

For example, the control scheme disclosed herein involves creating and emulating a one-port virtual power source equivalent model to control a DC power supply of a real power supply unit (e.g., an SMPS unit). The virtual power source equivalent model includes a DC Thévenin equivalent model in parallel connection with a DC current source. The DC Thévenin equivalent may include a desired DC voltage source V_sin series connection with a virtual impedance which has a finite resistance Ry and a finite inductance Ly. The DC current source maintains a constant offset current value Is.

At least a purpose of the control scheme disclosed herein is to mimic the behavior of the virtual power source equivalent model by measuring and regulating an output voltage and an output current of the real power supply unit. The emulation of the finite virtual impedance is achieved using a composite voltage-current controller. Instead of having a primary voltage control loop within a secondary current control loop (or vice versa), both the output voltage and the output current are simultaneously controlled by a single variable (e.g., a difference signal described below) to emulate the virtual impedance in the control scheme disclosed herein. Furthermore, by emulating a voltage source with a complex finite output impedance, voltage droop control can be achieved with a desirable dynamic performance. Consequently, when multiple power supply units each incorporating this control scheme are connected in parallel, identical or proportional current sharing is ensured among the power supply units by appropriately configuring virtual model parameters (e.g., V_s, R_v, and I_s) of the virtual power source equivalent models corresponding to the power supply units, respectively.

Consistent with some aspects of the present disclosure, the achievement of droop control may not only indicate that the output voltages of the parallel-connected power supply units are the same, but also indicate that the output currents of the parallel-connected power supply units satisfy a current sharing condition. For example, the output currents are equal to one another when equal current sharing is implemented, or the output currents satisfy a proportional current sharing condition determined based on a proportional current sharing coefficient, as described below in more detail.

FIG. 1 illustrates a block diagram of DC SMPS units that are connected in parallel, according to some examples of the present disclosure. In some examples, a DC SMPS unit may include a converter and can be equivalent to a Thévenin source (i.e., a dependent voltage source) with an output impedance. Multiple DC SMPS units may be connected to a load resistance (R_L) in parallel, and an equivalent structure 100 of the parallel-connected DC SMPS units is shown in FIG. 1. In FIG. 1, each DC SMPS unit can be considered as a branch 101, which includes a Thévenin source 102 and an output impedance 103. When connecting the multiple DC SMPS units in parallel without any active current-sharing control loop, each branch may need to be embedded with a respective droop control scheme to provide current sharing among the multiple DC SMPS units. Specifically, in the absence of an active current-sharing loop, each DC SMPS unit (each branch) may have a finite output resistance at a steady state.

Let I_i, V_i, and R_irepresent an output current, an equivalent Thévenin voltage, and an output resistance of the i^thDC SMPS unit (branch i), respectively. A common output voltage of each DC SMPS unit is denoted as V_o. FIG. 2A illustrates output characteristics of two DC SMPS units (e.g., a first branch “branch 1” and a second branch “branch 2”) connected in parallel without utilizing a current sharing loop. As shown in FIG. 2A, output curves of the two DC SMPS units are different (e.g., the output curves intersect with each other and are not identical). When the common output voltage of the first and second branches is V_o, the first branch may have a current I₁, and the second branch may have a current I₂. A current sharing error between the first branch and the second branch (e.g., a current difference between the first and second DC SMPS units) can be expressed as follows:

Δ
⁢
I

=

I
1

-

I
2

=

R
2

⁢

V
1

-

R
1

⁢

V
2

+

2
⁢

(

V
1

-

V
2

)

⁢

R
L

R
1

⁢

R
2

+

R
1

⁢

R
L

+

R
2

⁢

R
L

.

(
1
)

In the above equation (1), R_Lrepresents a load resistance. When equal (or identical) current sharing control is achieved between the first branch and the second branch, the current sharing error ΔI in the above equation (1) becomes zero, which can occur only if V₁=V₂and R₁=R₂. Therefore, in practice, equal current sharing can be accomplished among the parallel-connected DC SMPS units by setting all V_ito be identical and all R_ito be identical. FIG. 2B illustrates output characteristics of the two DC SMPS units of FIG. 2A when equal current sharing control is achieved. As shown in FIG. 2B, when V₁=V₂and R₁=R₂, the output curves of the two DC SMPS units are identical (e.g., the output curves are completely overlapped with each other). When the common output voltage of the first and second branches is V_o, the first branch and the second branch may have the same output current I_o=I₁=I₂.

Therefore, according to the one-port network theory, if each parallel-connected DC SMPS unit is contrived to behave as the same virtual Thévenin equivalent, it is easy to keep all V_ito be identical and all R_ito be identical. Then, droop control and equal current sharing are achieved among the parallel-connected DC SMPS units. Furthermore, to improve the performance of the virtual Thévenin equivalent, an offset DC current source is added to the Thévenin equivalent in parallel to offset the output voltage droop caused by the virtual impedance. For instance, with reference to FIG. 3B shown below, if only the Thévenin equivalent is used without an offset DC current source, the output voltage V_omay drop below V_swhen the output current I_oflows through a virtual impedance R_v, i.e., V_o=V_s−R_v*I_o. However, if an offset DC current source I_sis added in parallel and I_s=I_ocoincidently, in this case the output voltage V_obecomes V_o=V_s−R_vd*(I_o−I_s)=V_s.

Consistent with some aspects of the present disclosure, a virtual power source equivalent model is included in the control scheme disclosed herein to facilitate droop control and current sharing among the parallel-connected DC SMPS units. FIG. 3A illustrates a circuit diagram of a power supply circuit 300 in a power supply unit, according to some aspects of the present disclosure. FIG. 3A only shows an exemplary circuit structure of power supply circuit 300. It is contemplated that power supply circuit 300 may have a circuit structure different from that shown in FIG. 3A, which is not limited herein. FIG. 3B illustrates a diagram of a virtual power source equivalent model 350 which is equivalent to the power supply unit of FIG. 3A, according to some aspects of the present disclosure. Virtual power source equivalent model 350 provides an output voltage V_oand an output current I_oat its output port. The power supply unit of FIG. 3A is equivalent to virtual power source equivalent model 350 such that power supply circuit 300 also provides the output voltage V_oand the output current I_oat its output port like that of virtual power source equivalent model 350. In other words, the power supply unit of FIG. 3A is configured to mimic the behavior of virtual power source equivalent model 350 to output the same output voltage V_oand the same output current I_oas virtual power source equivalent model 350.

As shown in FIG. 3B, virtual power source equivalent model 350 may include a DC Thévenin equivalent model 352 and a DC current source 354 in parallel connection with DC Thévenin equivalent model 352. DC Thévenin equivalent model 352 may include an equivalent voltage source 356 and a virtual impedance Z_vin series connection with equivalent voltage source 356. Equivalent voltage source 356 may have a reference voltage value V_s, and DC current source 354 may have a reference current value Is. The virtual impedance Z_vmay have a resistance Ry and an inductance L_v, e.g., Z_v=R_v+jωL_v.

In some implementations, virtual power source equivalent model 350 can be a generalized power source, i.e., a combined voltage-current source model. The virtual impedance Z_vis equivalent to a series impedance of equivalent voltage source 356. L_vcan be used to remove noise and improve the dynamic response performance of the control scheme disclosed herein. A value of the virtual impedance may be selected as actually needed. For example, as described below in more detail, a zero virtual impedance may cause a virtual model emulator for virtual power source equivalent model 350 to be a pure DC voltage source; an infinite virtual impedance may cause the virtual model emulator to be a pure DC current source; and any non-zero finite virtual impedance may cause the virtual model emulator to be a composite voltage-current source which can be employed for droop control. Unlike a real impedance, this virtual impedance introduces no real power losses, which allows for the emulation of resistive behavior without compromising efficiency.

Referring to FIG. 2B again, when V₁=V₂and R₁=R₂are satisfied for the first and second branches discussed above, the following equations (2)-(3) can be obtained when each of the first and second branches is equivalent to the same virtual power source equivalent model 350 of FIG. 3B:

V
1

=

V
2

=

V
s

+

I
s

⁢

R
v

,

(
2
)

R
1

=

R
2

=

R
v

.

(
3
)

In other words, as long as each of the paralleled-connected SMPS units is implemented to emulate the same virtual power source equivalent model 350, the conditions for equal current sharing are satisfied (e.g., all V_iare identical and all R_iare identical). As a result, all the parallel-connected SMPS units may provide the same output current I_oand the same output voltage V_o.

The principle and method of implementing virtual power source equivalent model 350 in an individual SMPS unit are explained herein. Specifically, the reference voltage value V_sof equivalent voltage source 356 is set to be a constant, i.e., equal to a nominal output voltage value. The nominal output voltage value can be configured by a user or determined based on actual need. According to the Kirchhoff's current law, a current Iv that flows through the virtual impedance Z_vsatisfies the following equation (4):

I
v

=

V
s

-

V
o

R
v

+

s
⁢

L
v

=

I
o

-

I
s

.

(
4
)

The implementation of emulating virtual power source equivalent model 350 in a real SMPS unit can be obtained using a controller (also referred to as a virtual model emulator) in which both the output current and the output voltage are combined to form a single control variable (e.g., a difference signal, which can be used to regulate both the output voltage and the output current simultaneously as described below in more detail). The controller may emulate the virtual impedance in the above equation (4). The controller is described below in more detail with reference to FIGS. 4A and 4B. For example, virtual power source equivalent model 350 is incorporated into the control scheme disclosed herein using the following transfer function:

d
⁢

(
s
)

=

❘
"[LeftBracketingBar]"

Z
v

❘
"[RightBracketingBar]"

(

❘
"[LeftBracketingBar]"

Z
v

❘
"[RightBracketingBar]"

+
1

)

⁢

(

V
s

-

V
o

)

(

R
v

+

s
⁢

L
v

)

+

❘
"[LeftBracketingBar]"

Z
v

❘
"[RightBracketingBar]"

(

❘
"[LeftBracketingBar]"

Z
v

❘
"[RightBracketingBar]"

+
1

)

⁢

(

I
s

-

I
o

)

.

(
5
)

In the above equation (5), d(s) represents a difference signal, Z_vrepresents the virtual impedance which includes a resistance R_vand an inductance L_v. |Z_v| represents a modulus of Z_v. V_sand I_srepresent the reference voltage value and the reference current value of virtual power source equivalent model 350, respectively. V_oand I_orepresent the output voltage V_oand the output current I_o, respectively. An objective of the controller (or the virtual model emulator) is to regulate the output current I_oand the output voltage V_oto maintain d(s)=0. When the condition d(s)=0 is met, the above equation (4) is satisfied, and virtual power source equivalent model 350 is physically implemented in the real SMPS unit with the incorporation of the virtual impedance Z_v.

In the above transfer function (5),

(

V
s

-

V
o

)

(

R
v

+

s
⁢

L
v

)

and I_s−I_oare scaled by a normalization factor

❘
"[LeftBracketingBar]"

Z
v

❘
"[LeftBracketingBar]"

(

❘
"[LeftBracketingBar]"

Z
v

❘
"[RightBracketingBar]"

+
1

)

,

which allows the virtual impedance Z_vto have any value from zero to infinity. For example, a zero virtual impedance may cause the controller (or the virtual model emulator) to be a voltage controller, whereas an infinite virtual impedance may cause the controller (or the virtual model emulator) to be a current controller. Any finite non-zero virtual impedance may cause the controller (or the virtual model emulator) to be a composite voltage-current controller. Therefore, the controller (or the virtual model emulator) can be generalized into a unified voltage-current controller.

FIG. 4A illustrates a block diagram of a power supply unit 400, according to some aspects of the present disclosure. FIG. 4B illustrates a circuit diagram of power supply unit 400 of FIG. 4A, according to some aspects of the present disclosure. FIGS. 4A and 4B are described together. Referring to FIG. 4A, power supply unit 400 may be a DC SMPS unit, and may include a DC power supply circuit 402 and a regulation control circuit 410. DC power supply circuit 402 may provide an output voltage V_oand an output current I_oat an output port 430. Regulation control circuit 410 may be coupled to DC power supply circuit 402, and may generate a regulation control signal based at least in part on a measured voltage value of the output voltage V_oand a measured current value of the output current I_oat output port 430. Then, DC power supply circuit 402 may regulate, based on the regulation control signal, at least one of the output voltage V_oto have a target voltage value or the output current I_oto have a target current value.

In some implementations, the target voltage value of the output voltage V_ocan be a nominal voltage value set by a user or determined based on actual need. The target voltage value can be a voltage value that DC power supply circuit 402 aims to provide at output port 430. For example, by regulating the output voltage V_obased on the regulation control signal, the measured voltage value of the output voltage V_oat output port 430 may converge to the target voltage value and be stabilized at the target voltage value. As described below in more detail, when multiple power supply units 400 are connected in parallel, the output voltage V_oof each power supply unit 400 may have the same target voltage value. That is, each power supply unit 400 provides the output voltage V_ohaving the same target voltage value at its output port.

In some implementations, the target current value of the output current I_ocan be a current value that satisfies a current sharing condition (e.g., an equal current sharing condition or a proportional current sharing condition). For example, when multiple power supply units 400 are connected in parallel, the target current value of the output current I_oof each power supply unit 400 is identical such that the equal current sharing condition is satisfied. Alternatively, as described below in more detail, the target current value of the output current I_oof each power supply unit 400 can be determined based on a proportional current sharing coefficient such that the proportional current sharing condition is satisfied. Within each power supply unit 400, by regulating the output current I_obased on the regulation control signal, the measured current value of the output current I_omay converge to the target current value of the respective power supply unit 400 and be stabilized at the target current value of the respective power supply unit 400.

As shown in FIG. 4A, DC power supply circuit 402 may include a DC power source 404, a DC to DC (DC/DC) converter 406, and an output network 408. DC power source 404 may be configured to output a power supply signal. DC/DC converter 406 may be configured to convert the power supply signal received from DC power source 404 to a converted power supply signal. Output network 408 may include output port 430, and provide the output voltage V_oand the output current I_oat output port 430 based on the converted power supply signal.

For example, referring to FIG. 4B, DC power source 404 may be a DC voltage source having a voltage Vin. DC/DC converter 406 can be any type of converter, such as a flyback, forward, buck, boost, buck-boost, half bridge, or full bridge converter, which is not limited herein. DC/DC converter 406 may convert the voltage Vin provided by the DC voltage source to a converted power supply signal. Output network 408 can include at least one of an inductance or a capacitor. Output network 408 may have any suitable structure, which is not limited herein. Output network 408 receives the converted power supply signal as an input and outputs the output voltage V_oand the output current I_oat the output port. In FIG. 4B, the output port of output network 408 is connected to a rating load R_L. In some implementations, output network 408 may include an output filter circuit, which can be configured to suppress and remove output noise (e.g., to smooth out waveforms of the output voltage V_oand the output current I_o).

Consistent with some aspects of the present disclosure, virtual power source equivalent model 350 of FIG. 3B is designed to provide the output voltage V_ohaving the target voltage value and the output current I_ohaving the target current value at its output port. Power supply unit 400 can be equivalent to virtual power source equivalent model 350. That is, power supply unit 400 is configured to mimic the behavior of virtual power source equivalent model 350, such that DC power supply circuit 402 can be controlled (e.g., by the regulation control signal) to provide the output voltage V_ohaving the target voltage value and the output current I_ohaving the target current value at its output port, like that of virtual power source equivalent model 350. For example, based on the regulation control signal, DC power supply circuit 402 may be configured to regulate the output voltage V_oto have the target voltage value and the output current I_oto have the target current value at its output port. The regulation control signal can be generated based at least in part on model parameters of virtual power source equivalent model 350 (e.g., the virtual impedance Z_v, the reference voltage value V_s, the reference current value I_s), as described below in more detail.

As shown in FIG. 4A, regulation control circuit 410 may include a controller 412, a reference setting circuit 414, an impedance setting circuit 416, and a modulator 418. Although FIG. 4A shows that controller 412, reference setting circuit 414, and impedance setting circuit 416 are different components, reference setting circuit 414 and impedance setting circuit 416 can be integrated into controller 412 in some implementations.

Referring to FIG. 4B, reference setting circuit 414 may be configured to set the reference voltage value V_sand the reference current value I_s, and provide the reference voltage value V_sand the reference current value I_sto controller 412. For example, the reference voltage value V_sand the reference current value I_smay be determined based on a user input or based on an actual need. Impedance setting circuit 416 may be configured to set a resistance value R_vand an inductance value L_vfor the virtual impedance Z_v, and provide the resistance value R_vand the inductance value L_vto controller 412. For example, the resistance value Ry and the inductance value L_vmay be determined based on a user input or based on an actual need.

Referring to FIG. 4B, controller 412 may be coupled to DC power supply circuit 402. Controller 412 may be configured to measure the output voltage V_oof DC power supply circuit 402 through a voltage sensor, and measure the output current I_oof DC power supply circuit 402 through a current sensor. As a result, controller 412 can obtain a measured voltage value of the output voltage V_oand a measured current value of the output current I_o. Controller 412 may determine a difference signal based on (1) the virtual impedance Z_vof virtual power source equivalent model 350, (2) a voltage difference between the measured voltage value of the output voltage V_oand the reference voltage value V_s, and (3) a current difference between the measured current value of the output current I_oand the reference current value I_s. For example, the difference signal can be obtained using the following equation (6):

d
⁢

(
s
)

=

❘
"[LeftBracketingBar]"

Z
v

❘
"[RightBracketingBar]"

(

❘
"[LeftBracketingBar]"

Z
v

❘
"[RightBracketingBar]"

+
1

)

⁢

(

V
s

-

V
o
′

)

(

R
v

+

s
⁢

L
v

)

+

❘
"[LeftBracketingBar]"

Z
v

❘
"[RightBracketingBar]"

(

❘
"[LeftBracketingBar]"

Z
v

❘
"[RightBracketingBar]"

+
1

)

⁢

(

I
s

-

I
o
′

)

.

(
6
)

In the above equation (6), Z_vrepresents the virtual impedance which includes a resistance Ry and an inductance L_v. V_sand I_srepresent the reference voltage value and the reference current value of virtual power source equivalent model 350, respectively.

V
o
′

⁢

and
⁢

I
o
′

represent the measured voltage value of the output voltage V_oand the measured current value of the output current I_o, respectively. The equation (6) is similar to the equation (5), except that V_oand I_oin equation (5) are replaced by

V
o
′

⁢

and
⁢

I
o
′

in equation (6) to incorporate the measured voltage value of the output voltage V_oand the measured current value of the output current I_ointo the equation (6), respectively.

Next, controller 412 may generate a modulation reference signal based on the difference signal and send the modulation reference signal to modulator 418. In some implementations, controller 412 can include a proportional-integral (PI) controller, and the modulation reference signal can be an output signal generated by the PI controller using the difference signal as an input. It is contemplated that controller 412 can also be another suitable type of controller, which is not limited herein. In some implementations, controller 412 can be implemented using a microcontroller (MCU) or a digital signal processor (DSP) through firmware. Alternatively, controller 412 can be implemented using analog circuits such as operational amplifiers, transistors, resistors, capacitors, etc.

Modulator 418 may generate the regulation control signal (e.g., a modulated waveform) based on the modulation reference signal. The modulation reference signal may be used to adjust one or more modulation parameters of modulator 418. For example, the modulation reference signal may be used to adjust a frequency, a pulse phase, a pulse width, or a duty cycle of the modulated waveform output by modulator 418. Modulator 418 may send the regulation control signal to DC/DC converter 406 for the regulation of the output voltage V_oand the output current I_o. In some implementations, modulator 418 can be a pulse width modulator (PWM). The regulation control signal can be a pulse-width modulated waveform, which may act as a gate switching signal configured to drive DC/DC converter 406 to regulate the output voltage V_oand the output current I_o, such that the difference signal is reduced (e.g., the difference signal is driven to be zero). For example, the regulation control signal may change a frequency of DC/DC converter 406 to regulate the output voltage V_oand the output current I_o, such that the difference signal is driven to be zero.

FIG. 5 illustrates a block diagram of a power supply network 500, according to some aspects of the present disclosure. Power supply network 500 may include a plurality of power supply units 400 that are connected in parallel. For example, power supply network 500 may include a first power supply unit 400A and a second power supply unit 400B, which are connected in parallel. Output ports of first and second power supply units 400A and 400B are connected to a rating load R_L, respectively.

In some implementations, first power supply unit 400A may include a first DC power supply circuit 402A and a first regulation control circuit 410A coupled to first DC power supply circuit 402A. First DC power supply circuit 402A may include a first output port, and configured to provide an output voltage V_oand a first output current I_oat the first output port. First DC power supply circuit 402A may include a first DC power source 404A, a first DC/DC converter 406A, and a first output network 408A, as shown in FIGS. 6 and 10 below. First DC power source 404A, first DC/DC converter 406A, and first output network 408A may have functionalities like those of DC power source 404, DC/DC converter 406, and output network 408 of FIGS. 4A and 4B, and the similar description will not be repeated herein.

First power supply unit 400A may be equivalent to a first virtual power source equivalent model 350A (shown in FIG. 8). For example, first virtual power source equivalent model 350A is designed to provide an output voltage V_ohaving a target voltage value and a first output current I_o1having a first target current value at its output port. First power supply unit 400A is configured to mimic the behavior of first virtual power source equivalent model 350A, such that first DC power supply circuit 402A can be controlled (e.g., by a first regulation control signal) to provide the output voltage V_ohaving the target voltage value and the first output current I_o1having the first target current value at its output port, like that of first virtual power source equivalent model 350A.

First virtual power source equivalent model 350A may include a first DC Thévenin equivalent model and a first DC current source in parallel connection with the first DC Thévenin equivalent model. The DC Thévenin equivalent model may include a first equivalent voltage source and a first virtual impedance Z_v1in series connection with the first equivalent voltage source. The first equivalent voltage source may have a reference voltage value V_s, and the first DC current source may have a first reference current value I_s1. The first virtual impedance Z_v1may have a first resistance R_v1and a first inductance L_v1, e.g., Z_v1=R_v1+jωL_v1.

Referring to FIG. 5, first regulation control circuit 410A may generate a first regulation control signal based at least in part on a first measured voltage value of the output voltage V_oand a first measured current value of the first output current I_o1at the first output port. First regulation control circuit 410A may include a first controller 412A, a first reference setting circuit 414A, a first impedance setting circuit 416A, and a first modulator 418A.

First controller 412A may determine a first difference signal based on the first virtual impedance Z_v1of first virtual power source equivalent model 350A, a first voltage difference between the first measured voltage value of the output voltage V_oand the reference voltage value V_s, and a first current difference between the first measured current value of the first output current I_o1and the first reference current value I_s1. First controller 412A may generate a first modulation reference signal based on the first difference signal. First modulator 418A may generate the first regulation control signal based on the first modulation reference signal. Then, first DC power supply circuit 402A may regulate, based on the first regulation control signal, the output voltage V_oto have a target voltage value and the first output current L_o1to have a first target current value at the first output port.

First controller 412A, first reference setting circuit 414A, first impedance setting circuit 416A, and first modulator 418A may have functionalities like those of controller 412, reference setting circuit 414, impedance setting circuit 416, and modulator 418 of FIGS. 4A-4B, and the similar description will not be repeated herein.

In some implementations, second power supply unit 400B may include a second DC power supply circuit 402B and a second regulation control circuit 410B coupled to second DC power supply circuit 402B. Second DC power supply circuit 402B may include a second output port, and configured to provide the output voltage V_oand a second output current I_oat the second output port. Second DC power supply circuit 402B may include a second DC power source 404B, a second DC/DC converter 406B, and a second output network 408B, which are shown in FIGS. 6 and 10 below. Second DC power source 404B, second DC/DC converter 406B, and second output network 408B may have functionalities like those of DC power source 404, DC/DC converter 406, and output network 408 of FIGS. 4A and 4B, and the similar description will not be repeated herein.

Second power supply unit 400B may be equivalent to a second virtual power source equivalent model 350B (shown in FIG. 8). For example, second virtual power source equivalent model 350B is designed to provide the output voltage V_ohaving the target voltage value and a second output current I_o2having a second target current value at its output port. Second power supply unit 400B is configured to mimic the behavior of second virtual power source equivalent model 350B, such that second DC power supply circuit 402B can be controlled (e.g., by a second regulation control signal) to provide the output voltage V_ohaving the target voltage value and the second output current I_o2having the second target current value at its output port, like that of second virtual power source equivalent model 350B.

Second virtual power source equivalent model 305B may include a second DC Thévenin equivalent model and a second DC current source in parallel connection with the second DC Thévenin equivalent model. The DC Thévenin equivalent model may include a second equivalent voltage source and a second virtual impedance Z_vin series connection with the second equivalent voltage source. The second equivalent voltage source may have the same reference voltage value V_s, and the second DC current source may have a second reference current value I_s1. The second virtual impedance Z_v2may have a second resistance R_v2and a second inductance L_v2, e.g., Z_v2=R$2+jωL_v2.

Referring to FIG. 5, second regulation control circuit 410B may generate a second regulation control signal based at least in part on a second measured voltage value of the output voltage V_oand a second measured current value of the second output current I_o2at the second output port. Second regulation control circuit 410B may include a second controller 412B, a second reference setting circuit 414B, a second impedance setting circuit 416B, and a second modulator 418B.

Second controller 412B may determine a second difference signal based on the second virtual impedance Z_v2of second virtual power source equivalent model 350B, a second voltage difference between the second measured voltage value of the output voltage V_oand the reference voltage value V_s, and a second current difference between the second measured current value of the second output current I_o2and the second reference current value I_s2. Second controller 412B may generate a second modulation reference signal based on the second difference signal. Second modulator 418B may generate the second regulation control signal based on the second modulation reference signal. Then, second DC power supply circuit 402B may regulate, based on the second regulation control signal, the output voltage V_oto have the target voltage value and the second output current I_o2to have a second target current value at the second output port.

Second controller 412B, second reference setting circuit 414B, second impedance setting circuit 416B, and second modulator 418B may have functionalities like those of controller 412, reference setting circuit 414, impedance setting circuit 416, and modulator 418 of FIGS. 4A-4B, and the similar description will not be repeated herein.

Consistent with some aspects of the present disclosure, the first target current value of the first output current I_o1of first power supply unit 400A is equal to the second target current value of the second output current I_o2of second power supply unit 400B (e.g., I_o1=I_o2=I_o), such that equal current sharing is achieved in power supply network 500. FIG. 6 illustrates a circuit diagram 600 of power supply network 500 with equal current sharing among parallel-connected power supply units 400A and 400B, according to some aspects of the present disclosure. Each of power supply units 400A and 400B may have a structure like that of power supply unit 400 in FIG. 4B, and the similar description will not be repeated herein. FIG. 7 illustrates a diagram 700 of virtual power source equivalent models 350A and 350B with equal current sharing, according to some aspects of the present disclosure. Each of virtual power source equivalent models 350A and 350B may have a structure like that of virtual power source equivalent model 350 of FIG. 3B, and the similar description will not be repeated herein.

With reference to FIG. 7, second virtual power source equivalent model 350B is identical to first virtual power source equivalent model 350A. That is, first and second virtual power source equivalent models 350A and 350B are the same virtual power source equivalent model having the same model parameters, as shown in FIG. 7. For example, the first virtual impedance Z_v1is identical to the second virtual impedance Z_v2(e.g., R_v1=R_v2=R_v, L_v1=L_v2=L_v, Z_v1=Z_v2=Z_v), and the first reference current I_s1is identical to the second reference current I_s2(I_s1=I_s2=I_s). In this case, each of first and second virtual power source equivalent models 350A and 350B includes (a) the same DC Thévenin equivalent model and (b) the same DC current source having the reference current value I_sin parallel connection with the DC Thévenin equivalent model. The DC Thévenin equivalent model includes (a) the same equivalent voltage source having the reference voltage value V_sand (b) the first or second virtual impedance Z_v1or Z_v2(Z_v1=Z_v2=Z_v) in series connection with the equivalent voltage source.

With reference to FIG. 6, first reference setting circuit 414A of first power supply unit 400A or second reference setting circuit 414B of second power supply unit 400B may set the reference voltage value V_sand the reference current value I_s. For example, the reference voltage value V_sand the reference current value I_smay be set based on a user input or based on an actual need. First impedance setting circuit 416A of first power supply unit 400A or second impedance setting circuit 416B of second power supply unit 400B may set the resistance value and the inductance value of the virtual impedance Z_v. For example, the resistance value Ry and the inductance value L_vof the virtual impedance Z_vmay be set based on a user input or based on an actual need.

Consistent with some aspects of the present disclosure, referring to FIG. 5, the first target current value of the first output current I_o1of first power supply unit 400A is equal to the second target current value of the second output current I_o2of second power supply unit 400B multiplied by a proportional current sharing coefficient k (e.g., I_o1=k*I_o2), such that proportional current sharing is achieved in power supply network 500. In some implementations, the proportional current sharing coefficient k may be a ratio between a first rated capacity of first power supply unit 400A and a second rated capacity of second power supply unit 400B.

FIG. 8 illustrates a diagram 800 of virtual power source equivalent models 350A and 350B with proportional current sharing, according to some aspects of the present disclosure. Each of virtual power source equivalent models 350A and 350B may have a structure like that of virtual power source equivalent model 350 of FIG. 3B, and the similar description will not be repeated herein. FIG. 9 illustrates a circuit diagram 900 of power supply network 500 with proportional current sharing among power supply units 400A and 400B, according to some aspects of the present disclosure. Each of power supply units 400A and 400B may have a structure like that of power supply unit 400 in FIG. 4B, and the similar description will not be repeated herein.

If the proportional current sharing coefficient k is equal to 1, then the proportional current sharing scheme becomes the equal current sharing scheme. Then, second virtual power source equivalent model 350B is identical to first virtual power source equivalent model 350A, as shown in FIG. 7. On the other hand, if the proportional current sharing coefficient k is not equal to 1, then the proportional current sharing scheme is implemented. As shown in FIG. 8, second virtual power source equivalent model 350B have some parameters different from those of first virtual power source equivalent model 350A. That is, first and second virtual power source equivalent model 350A and 350B may have different virtual impedances and different reference current values, as shown in FIG. 8. For example, first virtual power source equivalent model 350A may have the first virtual impedance Z_v1(with the first resistance R_v1and the first inductance L_v1) and the first reference current value I_s1. Second virtual power source equivalent model 350B may have the second virtual impedance Z_v2(with the second resistance R_v2and the second inductance L_v2) and the second reference current value I_s2.

With reference to FIG. 9, first reference setting circuit 414A of first power supply unit 400A may set the reference voltage value V_sand the first reference current value I_s1. For example, the reference voltage value V_sand the first reference current value I_s1may be set based on a user input or based on an actual need. First impedance setting circuit 416A of first power supply unit 400A may set the first resistance value and the first inductance value of the first virtual impedance Z_v1. For example, the first resistance value R_v1and the first inductance value L_v1of the first virtual impedance Z_v1may be set based on a user input or based on an actual need. As described below in more detail, second reference setting circuit 414B of second power supply unit 400B may set the second reference current value I_s2based on the proportional current sharing coefficient k and the first reference current value I_s1. Second impedance setting circuit 416B of second power supply unit 400B may set the second resistance value R_v2and the second inductance value L_v2of the second virtual impedance Z_v2based on the proportional current sharing coefficient k and the first virtual impedance Z_v1.

It is understood that each power supply unit in power supply network 500 may have a respective controller (e.g., a respective virtual model emulator) which is independently implemented on the corresponding power supply unit. Theoretically, any number of power supply units, each of which can be equivalent to a respective virtual power source equivalent model, can be connected in parallel directly at their respective output ports with no communication among the power supply units. Droop control and current sharing control (e.g., equal or proportional current sharing) can be achieved among the power supply units through the emulation of the respective virtual power source equivalent models in the power supply units.

FIG. 10 illustrates exemplary output characteristics of virtual power source equivalent models 350A and 350B of FIG. 8, according to some aspects of the present disclosure. The configuration of model parameters (e.g., the second virtual impedance Z_v2and the second reference current I_s2) when the proportional current sharing scheme is implemented is provided herein with reference to FIG. 8 and FIG. 10. For example, with reference to FIG. 8, an output voltage V₁of first virtual power source equivalent model 350A and an output voltage V₂of second virtual power source equivalent model 350B at an open-circuit (OC) state satisfies the following equations:

{

V
1

=

V
s

+

R

v
⁢
1

⁢

I

s
⁢
1

V
2

=

V
s

+

R

v
⁢
2

⁢

I

s
⁢
2

,

(
7
)

V
1

=

V
2

.

(
8
)

Based on the equations (7) and (8), the following equation (9) can be obtained:

R

v
⁢
1

⁢

I

s
⁢
1

=

R

v
⁢
2

⁢

I

s
⁢
2

.

(
9
)

Then, based on the equation (9), a relationship between the first reference current value I_s1and the second reference current value I_s2can be shown by the following equation:

I

s
⁢
1

I

s
⁢
2

=

R

v
⁢
2

R

v
⁢
1

.

(
10
)

Also, a first output current I_o1of first virtual power source equivalent model 350A and a second output current I_o2of second virtual power source equivalent model 350B satisfy the following equations:

{

I

o
⁢
1

=

V
1

-

V
o

R

v
⁢
1

I

o
⁢
2

=

V
2

-

V
o

R

v
⁢
2

.

(
11
)

Based on the equations (8) and (11), the following equation (12) can be obtained:

I

o
⁢
1

I

o
⁢
2

=

R

v
⁢
2

R

v
⁢
1

.

(
12
)

The proportional current sharing coefficient k can be defined according to the following equation (13):

k
=

I

o
⁢
1

I

o
⁢
2

.

(
13
)

Then, by combing equations (10), (12) and (13), the following equation (14) can be obtained:

I

s
⁢
1

I

s
⁢
2

=

R

v
⁢
2

R

v
⁢
1

=

k
=

I

o
⁢
1

I

o
⁢
2

.

(
14
)

It is understood that a value of the proportional current sharing coefficient k can be selected arbitrarily or based on a user input or actual need. For example, the proportional current sharing coefficient k can be determined based on the rated capacities of the power supply units according to the following equation (15):

k
=

I

o
⁢
1

I

o
⁢
2

=

V
o

⁢

I

o
⁢
1

V
o

⁢

I

o
⁢
2

=

P
1

P
2

.

(
15
)

In the above equation (15), P_idenotes a rated power of the i^thpower supply unit, with i=1 or 2. That is, the contribution of each parallel-connected power supply unit to the power supply network depends on the capacity of the corresponding power supply unit. A power supply unit with a larger capacity may provide a larger current to the rating load, whereas a power supply unit with a smaller capacity may provide a smaller current to the rating load.

Based on the above equations (14) and (15), a process of configuring the model parameters of virtual power source equivalent models 350A and 350B when the proportional current sharing scheme is implemented is provided herein according to the following Steps 1-3. In Step 1, the proportional current sharing coefficient k can be determined based on the rated capacities of the power supply units according to the above equation (15). In Step 2, the reference voltage value V_s, the first resistance value R_v1, and the first reference current value I_s1can be set to be any suitable values, respectively, which is not limited herein. In Step 3, the second resistance value R_v2and the second reference current value I_s2can be set according to the above equation (14) (e.g., R_v2=k*R_v1, and I_s2=I_s1/k). It is contemplated that the above Steps 1-3 can be repeated for the configuration of any other power supply units in the power supply network. Once the model parameters for all virtual power supply equivalent models are set, each power supply unit incorporating a respective virtual power supply equivalent model may provide a respective current to the rating load according to its capacity. When the proportional current sharing coefficient k is equal to 1 (e.g., k=1), the proportional current sharing according to the proportional current sharing coefficient k becomes equal current sharing, as shown in FIGS. 6-7. As a result, power supply units of any type or any size can be connected in parallel directly for equal or proportional current sharing according to their capacities to avoid overload of each power supply unit.

FIG. 11 illustrates a flowchart of a method 1100 for operating a power supply unit, according to some aspects of the present disclosure. The power supply unit may include a DC power supply circuit and a regulation control circuit. For example, the power supply unit may be power supply unit 400 shown in FIGS. 4A-4B. It is understood that the operations shown in method 1100 may not be exhaustive and that other operations can be performed as well before, after, or between any of the illustrated operations. Further, some of the operations may be performed simultaneously, or in a different order than that shown in FIG. 11.

Method 1100 may begin with operation 1102 in which an output voltage V_oand an output current I_oare provided by the DC power supply circuit at an output port.

Method 1100 may proceed to operation 1104, in which a regulation control signal is generated by the regulation control circuit based at least in part on a measured voltage value of the output voltage V_oand a measured current value of the output current I_oat the output port. For example, operations like those described above with reference to FIGS. 4A-4B can be performed to generate the regulation control signal.

Method 1100 may proceed to operation 1106, in which at least one of the output voltage V_oor the output current I_omay be regulated, by the DC power supply circuit and based on the regulation control signal, to have a target voltage value or a target current value, respectively.

FIGS. 12A-12E illustrate simulation results of various power supply networks, according to some aspects of the present disclosure. In the virtual-model based control scheme disclosed herein, power supply units are connected in parallel to form a power supply network in which each power supply unit is equivalent to a respective virtual power source equivalent model. Droop control and equal or proportional current sharing can be achieved in the power supply network. FIGS. 12A-12C are simulation results related to the verification of the equal current sharing, FIG. 12D is a simulation result related to the verification of the proportional current sharing, and FIG. 12E is a simulation result related to the verification of a hybrid of the equal current sharing and the proportional current sharing.

With respect to the equal current sharing simulations in FIGS. 12A-12C, each power supply unit is a 12V/1100 W power supply unit and its dynamic response performance is also validated. The rated capacity of each power supply unit is set to be 1100 W. Each power supply unit is equivalent to the same virtual power source equivalent model 350 of FIG. 3B. The reference voltage value V_sin the Thevenin equivalent model is set to be 12V, and the reference current value I_sis set to be 90 A. Six power supply units (each incorporating the same virtual power source equivalent model 350 of FIG. 3B) are built in parallel to form the power supply network in the simulation. As discussed above, because the virtual-model based control scheme disclosed herein does not rely on the hardware implementation, topology and modulation selection of the power supply units, these power supply units can be modeled with different converter bridge structures, different component selections, and different PWM modes. It is contemplated that any number of power supply units (e.g., 2, 3, 4, 5, 6, 7, . . . ) can be included in the power supply network, which is not limited herein.

Referring to FIG. 12A, each power supply unit may be a first power supply model, and the resistance value Ry is set to be R_v=0.01Ω. The simulation result shown in FIG. 12A indicates that all the output currents I_oof the six parallel-connected power supply units are the same. The virtual model emulator exhibits fast dynamic response characteristics and optimal performance across large load ranges, due to the implementation of the composite voltage-current controller.

When I_od=OA which is equivalent to an open-circuit (OC) state, according to the virtual power source equivalent model, the OC output voltage is V_o=V_s+I_s×R_v=12V+90 A×0.01Ω=12.9V, which is identical to the simulated output voltage value “V_o=12.9V” shown in FIG. 12A. For example, the target current value of the output current I_ois OA. The target voltage value of the output voltage V_ois 12.9V, and a fluctuation 1202 in a voltage curve 1210 illustrates a process of regulating the output voltage V_oto have the target voltage value 12.9V.

When I_o=84 A, according to the virtual power source equivalent model, the output voltage is V_o=V_s+ (I_s−I_o)×R_v=12V+ (90 A−84 A)×0.01Ω=12.06V. This is also identical to the simulated output voltage value “V_o=12.06V” shown in FIG. 12A. For example, the target current value of the output current I_ois 84 A, and the target voltage value of the output voltage V_ois 12.9V. A fluctuation 1204 in voltage curve 1210 and a fluctuation 1206 in a current curve 1212 illustrate another process of regulating the output voltage V_oto have the target voltage value 12.06V and the output current I_oto have the target current value 84 A. This simulation result verifies that the control scheme disclosed herein ensures that all the power supply units behave as the same virtual power source equivalent model.

Referring to FIG. 12B, each power supply unit may also be the first power supply model, and the resistance value R_vis set to be R_v=0.001Ω. The simulation result shown in FIG. 12B indicates that all the output currents I_oof the six parallel-connected power supply units are the same. The composite voltage-current controller has a quick and stable response to sudden changes in loads, with a small overshoot and a short settling time. The simulation of FIG. 12B has a smaller resistance Ry than that of FIG. 12A. When the resistance R_vis smaller, the virtual power source equivalent model behaves more like an ideal voltage source, indicating that the output voltage V_oremains almost constant regardless of the load.

When I_o=OA which is equivalent to the open-circuit state, according to the virtual power source equivalent model, the OC output voltage is V_o=V_s+I_s×R_v=12V+90 A×0.001Ω≈12.1V. This is identical to the simulated output voltage value “V_o=12.1V” shown in FIG. 12B. When I_o=83.5 A, according to the virtual power source equivalent model, the output voltage is V_o=V_s+ (I_s−I_o)×R_v=12V+(90 A−83.5 A)×0.0010≈12.0V. This is also identical to the simulated output voltage value “V_o=12.0V” shown in FIG. 12B. This simulation result verifies that the control scheme disclosed herein ensures that all the power supply units behave as the same virtual power source equivalent model.

Referring to FIG. 12C, each power supply unit may be a second power supply model having a topology different from that of the first power supply model, and the resistance value R_vis set to be R_v=0.01Ω. The simulation result shown in FIG. 12C indicates that all the output currents I_oof the six parallel-connected power supply units are the same. The simulated power supply network shows a rapid and stable response to a step change in load.

When I_o=21 A, according to the virtual power source equivalent model, the output voltage is V_o=V_s+ (I_s−I_o)×R_v=12V+(90 A−21 A)×0.01Ω≈12.7V. This is identical to the simulated output voltage value “V_o=12.7V” shown in FIG. 12C. When I_o=76 A, according to the virtual power source equivalent model, the output voltage is V_o=V_s+(I_s−I_o)×R_v=12V+(90 A−76 A)×0.01Ω≈12.14V. This is also identical to the simulated output voltage value “V_o=12.14V” shown in FIG. 12C. This simulation result verifies that the control scheme disclosed herein ensures that all the power supply units behave as the same virtual power source equivalent model, regardless of the topology of the power supply model.

With respect to the proportional current sharing simulation shown in FIG. 12D, three different power supply units are employed in the power supply network to demonstrate the proportional current sharing, with a first power supply unit to be a 12V/1080 W unit, a second power supply unit to be a 12V/720 W unit, and a third power supply unit to be a 12V/360 W unit. Therefore, the proportional current sharing coefficient k can be set as 1080 W: 720 W: 360 W=3:2:1. For the first 12V/1800 W power supply unit, V_s=12V, R_v1=0.001Ω, and I_s1=90 A can be set based on an actual need. According to the above equation (14), V_s=12V, R_v2=0.001502, and I_s2=60 A can be set for the second 12V/720 W power supply unit, and V_s=12V, R_v3=0.0030, and I_s3=30 A can be set for the third 12V/360 W power supply unit. When these different power supply units are connected in parallel to form the power supply network, a simulation result of the power supply network is shown in FIG. 12D.

In FIG. 12D, in the steady state, the output currents of all the three different power supply units satisfy the proportional current sharing condition determined by the proportional current sharing coefficient k=3:2:1 (that is, I_o1:I_o2:I_o3=k=3:2:1), no matter how the load changes. Also, this simulation result shows the fast dynamic response performance of the control scheme disclosed herein regardless of the different implementations of the power supply units.

With respect to the hybrid simulation of the equal and proportional current sharing shown in FIG. 12E, three power supply units are employed to form a power supply network, with a first power supply unit to be a 12V/1080 W unit, a second power supply unit to be a 12V/1080 W unit, and a third power supply unit to be a 12V/360 W unit. Therefore, the proportional current sharing coefficient k can be set as 1080 W: 1080 W: 360 W=3:3:1. For the first 12V/1800 W power supply unit, V