An Improved Control and Energy Management Strategy of Three-Level NPC Converter Based DC Distribution Network

Abstract

To meet the challenge of large-scale renewable energy penetration and take full advantage of existing AC infrastructure, the bipolar DC distribution system is of interest. In this article, the system structure and characteristics of the bipolar DC distribution network are proposed. The three-level Neural Point Clamped Converter (NPC) is used in the proposed system to construct the bipolar DC system. To optimize the DC system performance, an improved cooperative control and energy management strategy is proposed mainly to mitigate DC voltage fluctuation and balance the positive and negative phase voltage. The improved strategy consists of (1) 2-degree of freedom (2DOF) PID controller in traditional voltage control loop; (2) cooperative controller to take full advantage of storage system; (3) voltage equalization controller to balance two-phase voltages; and (4) the energy management system to dispatch the response job to batteries and supercapacitors. Experiments and simulations are performed to validate the effectiveness of the proposed strategy.

1. Introduction

In recent years, due to the demand for clean and sustainable energy, the large-scale penetration of renewable energy has made it a challenge for the traditional distribution system. The control and energy management strategy of an AC distribution system with renewable energy is difficult to provide an efficient, flexible power grid with high power quality and enough stability margin [1]. Furthermore, the integration of most renewable energy sources in the AC distribution network needs additional power electronics devices to perform the power transformation, e.g., DC/DC, DC/AC converters for photovoltaic systems and AC/DC, DC/AC converters for wind power systems. In addition, the DC loads such as data centers, communication centers, electrical vehicles have similar integration problems with renewable sources.

Compared with AC distribution systems, DC distribution systems can easily integrate the renewable energy sources with improvements in dynamic performance, complication of control design, power quality, losses of transmission, and the cost of distribution network [2,3,4,5,6]. With the rapid development of power electronics devices, the distribution network introduces a lot of real-time automatic “controllable” features in different domains, such as the operational modes of power converters, the parameters of the digital controllers and the directions of power flow. In addition, the DC distribution network involves more power electronics devices and control algorithms. Thus, combined with the sensor and communication technology, the DC distribution system has tremendous potential to develop the smart grid. In fact, the proposed DC distribution network can be depicted as a cyber-physical intelligent system resulted from the fusion of power semi-conductors, communications, sensors, control and scientific computation.

As the bipolar DC distribution system is of interest to increase power supply capacity, operation reliability and reduce transmission losses, the bipolar DC system is discussed in this article. The DC bus voltage control is of great importance because the power flow and energy quality are mainly dominated by DC bus voltages in the DC distribution network [1,7,8,9,10,11].

The challenges and advantages of DC power systems for the future grid are discussed in [2]. Ref. [12] describes the implementation of a distributed coordinating control system for power electronic converters in a shipboard distribution system. The optimal power sharing for the converters is achieved, and the power sharing among different RESs and ESSs is not considered. In [13], the method to mitigate voltage unbalance is researched. It uses a static load transfer switch in the bipolar system to reduce unbalance. With this method, the VSC is not fully utilized and extra devices are required. In [14], a distributed control strategy for AC/DC hybrid micro grid is proposed. It considers the converters: RESs and EESs. However, the dynamic performances of different ESSs are not considered and the strategy is designed for the micro-grid instead of the distribution system. In [15], the power electronics-based DC distribution systems is focused, and a framework for the design of DC power systems is provided considering the interaction between various components. However, the detailed DGs and power electronics devices are not deeply considered and the system is thought to be unipolar. In [16], the charge sharing on energy storage devices in DC distribution systems is researched. However, the system is also thought to be unipolar. In [17], an enhanced droop-based DC-voltage control method is proposed for VSC based grids and the energy balance between AC and DC system is studied. Ref. [18] takes a systematic view on the control and protection of medium DC systems considering system control and fault current limiting. Many DC system technologies are researched in the DC micro-grid scenario. The DC micro-grid structure, bus voltage control, power management and bidirectional power flow problem are studied in [3,4,10,19,20]. The hybrid AC/DC micro-grid control is researched in [7,8,21]. The DC voltage control for DC micro-grid with multiple slack terminals is studied in [9]. The cooperative control with loads is discussed in [11]. The energy management of DC micro-grid is presented in [5,6,22]. The energy management with supervisory controller is also studied in [23]. The optimal control strategy is researched in [24]. The research on the DC micro-grid are beneficial to renewable sources integration and DC distribution network research; however, some new problems in DC distribution systems should be further researched.

In the article, the system structure of DC distribution network is proposed and the bipolar system is focused. The RESs and ESSs are considered in DC distribution system scenario. To achieve high power quality and balanced voltage, a three-level neural point clamped (NPC) converter is adopted to regulate the voltage of DC bus. The models of the three-level NPC converter and the DC distribution network are derived. In addition, the voltage equalization controller is adopted. In order to get better performance of DC bus voltage control, a 2DOF (2-degree of freedom) PID controller is adopted to get higher stability margin, better dynamic performance and reject the disturbance from renewable energy sources and the local loads. To fully utilize the storage system, including battery and supercapacitor, the cooperative control and energy management strategy of the DC distribution network is proposed. The experiment and simulation results are presented to demonstrate the effectiveness of the proposed strategy.

2. DC Distribution Network

2.1. Proposed DC Distribution Network

Although the DC distribution network has many advantages over the AC network, the infrastructure of the power grid nowadays has been constructed based on the AC network. Due to the tremendous cost of power grid construction, the AC/DC hybrid grid is necessary for the future distribution network. In addition, the interaction between AC and DC networks will have a deep impact on the performance and stability of the DC network. The schematic diagram of the proposed DC distribution network is shown in Figure 1a.

The system is composed of the traditional AC grid zone, DC distribution zone and control center zone. The support of the AC utility grid to the DC distribution network is necessary for a long time. The DC distribution network is connected to the 110 kV AC grid. Two VSCs convert AC power to ±1 kV bipolar DC power. It should be pointed out that an AC transformer is included in the VSC block to transfer AC voltage to the proper level. In this article, the VSCs are three-level NPC converters to get better power quality and construct the bipolar system. In the DC distribution zone, besides residential and industrial loads, several kinds of devices are integrated: renewable energy sources (such as photovoltaic system, wind turbine), storage devices, electrical vehicles, batteries and supercapacitors. Power converters have different control modes and control strategies that influence system performance and stability. In the control center zone, three control centers, namely energy management center, DG (Distributed Generator) dispatch center, and information analysis center perform the data processing, optimal control computation, monitoring, on-line parameter correction, energy management and dispatch tasks. Stable and reliable communication and sensor systems in DC distribution should be established, which are not shown in Figure 1a.

2.2. The Simplified DC Distribution Network

To simplify the analysis of the complicated DC distribution network, several assumptions are made as follows: (1) the capacitances of DC buses are relatively small compared with power inflowing into it; (2) the resistances of DC wires are very small (compared with the impedances of the same wires in the AC system); (3) only one VSC affords the responsibility to stabilize DC bus voltage, and other VSCs operate in constant power mode; and (4) every same kind of DG has the same control strategy.

The aforementioned assumptions are practical in small- or medium-scale DC distribution network. Based on these assumptions, all DC buses in the same DC distribution network can be equivalent to one DC bus. In addition, only one equivalent three-level NPC converter is reserved to control the voltage of DC bus in addition to merging all of the same kind of DGs into one equivalent DG. After the simplification, a schematic diagram of the simplified DC distribution network is presented in Figure 1b with all critical characters reserved.

3. Model of Three-Level NPC Converter

Figure 2 shows the typical schematic diagram of the three-level NPC converter. The three-level NPC converter consists of three identical half-bridge NPC converters. The DC side midpoint is set to the reference point. In the DC distribution network connected to the AC utility grid, the two-level VSC and the three-level NPC have identical DC-side current expression if capacitor voltages of three-level NPC and two-level VSC are equal and stable. It means that the dynamic behavior of two-level VSC is identical to three-level NPC. Nevertheless, three-level NPC still has advantages over two-level VSC in the DC distribution network. The three-level NPC provides an easy way to achieve bipolar DC voltage and has higher reliability, safety and lower rated voltage. The phase voltage balance can be achieved by proper three-level NPC control strategies. The three-level NPC is also suitable for relatively high voltage distribution systems. In addition, the three-level NPC has lower harmonic distortion on the AC-side.

3.1. Voltage of AC Side

The AC voltage of the three-level NPC converter can be expressed as

$$\left\{\begin{array}{c}{V}_{\mathrm{ta}}\left(t\right)=\frac{m_a\left(t\right)V_{\mathrm{DC}}}{2},\hfill \\ V_{\mathrm{tb}}\left(t\right)=\frac{m_b\left(t\right)V_{\mathrm{DC}}}{2},\hfill \\ V_{\mathrm{tc}}\left(t\right)=\frac{m_c\left(t\right)V_{\mathrm{DC}}}{2},\hfill \end{array}\right.$$

(1)

where $V_{\mathrm{DC}}$ is the DC-side terminal voltage of three-level NPC. As $V_{\mathrm{DC}}$ varies very slowly in a switch period, it is treated as a constant in aforementioned equations. $V_{\mathrm{ta}}\left(t\right),V_{\mathrm{tb}}\left(t\right),V_{\mathrm{tc}}\left(t\right)$ are the AC-side terminal voltage of phase A, phase B and phase C, respectively; $m_a\left(t\right),m_b\left(t\right),m_c\left(t\right)$ are modulating signals of phase A, phase B and phase C, respectively [25]. It should be pointed out that all functions are averaging functions.

$m_a\left(t\right),m_b\left(t\right),m_c\left(t\right)$ assumes the following form:

$$\left\{\begin{array}{c}{m}_a\left(t\right)=\widehat{m}\left(t\right)cos\left(\epsilon \left(t\right)\right),\hfill \\ m_b\left(t\right)=\widehat{m}\left(t\right)cos\left(\epsilon \left(t\right)-\frac{2\pi }{3}\right),\hfill \\ m_c\left(t\right)=\widehat{m}\left(t\right)cos\left(\epsilon \left(t\right)-\frac{4\pi }{3}\right),\hfill \end{array}\right.$$

(2)

where $\epsilon \left(t\right)$ contains all information about phase angle and frequency. In steady state, $\epsilon \left(t\right)$ satisfies

$$\epsilon \left(t\right)={\omega }_{0}t+{\theta }_0,$$

(3)

where ${\omega }_0,{\theta }_0$ are angular frequency and initial phase of utility AC grid.

The well-known dq-frame transformation is performed to simplify the analysis. The rotating reference frame is determined by the output of PLL (Phase Locked Loop). Denote the d-axis and q-axis components of AC-side voltage of NPC as $V_{\mathrm{td}}$ and $V_{\mathrm{tq}}$. Denote the d-axis and q-axis components of AC utility grid voltage as $V_{\mathrm{sd}}$ and $V_{\mathrm{sq}}$. If the PLL is connected to AC utility grid and operates in steady state, the real and reactive power delivered to the AC utility grid from the PCC (Point of Common Coupling) is

$$\left\{\begin{array}{c}{P}_s\left(t\right)=\frac{3}{2}{V}_{\mathrm{sd}}\left(t\right)i_d\left(t\right),\hfill \\ Q_s\left(t\right)=\frac{3}{2}{V}_{\mathrm{sq}}\left(t\right)i_d\left(t\right).\hfill \end{array}\right.$$

(4)

According to the topology of three-level VSC, the AC-side equations are

$$\left\{\begin{array}{c}{L}_1\frac{d{i}_d}{dt}=V_{\mathrm{td}}-V_{\mathrm{sd}}+L_1{\omega }_0{i}_q-R_1{i}_d,\hfill \\ L_1\frac{d{i}_q}{dt}=V_{\mathrm{tq}}-L_1{\omega }_0{i}_d-R_1{i}_q,\hfill \end{array}\right.$$

(5)

where $i_d,i_q$ are d-axis and q-axis components of AC-side currents, respectively. $\epsilon \left(t\right)$ is obtained from PLL connected to the AC utility grid.

3.2. Voltage of DC Side

According to Figure 1b, assuming balanced DC-side voltage, the DC-side equation of three-level NPC is

$$C\frac{d\left(V_{\mathrm{n}}+V_{\mathrm{p}}\right)}{\mathrm{dt}}=i_{\mathrm{EV}}+i_{\mathrm{RES}}+i_{DC}-i_{\mathrm{load}}+i_{\mathrm{stor}},$$

(6)

where $V_{\mathrm{p}}$ and $V_{\mathrm{n}}$ are the voltage of positive phase and negative phase, respectively. $i_{DC},i_{\mathrm{RES}},i_{\mathrm{EV}},i_{\mathrm{stor}},i_{\mathrm{load}}$ are equivalent DC side currents of three-level NPC, all renewable energy sources, electrical vehicles, storage systems and loads, respectively.

3.3. Voltage Equalization Problem of the DC Side

In ideal conditions, the positive phase voltage of three-level NPC should be equal to the negative phase. However, in practice, a lot of reasons can result in unbalance between positive and negative voltage of DC-side such as tolerances among components of three phases, sensor offsets, unbalanced loads, truncation errors from digital controller, and so on.

3.4. Structure of Control System

The traditional control of VSC uses dual loop control with two PI controllers. The inner loop is current loop and the outer loop is voltage loop. In this article, the control of VSC is improved with voltage equalization control, cooperative control, energy management and 2DOF controller. The system control block of proposed DC distribution network is shown in Figure 3. S1, S2P, S2N are voltage sensors of DC bus, positive phase and negative phase, respectively, and they are treated as ideal sensors in this article. In this section, the traditional control is briefly analyzed and the improved control will be presented in next section.

The transfer function of inner current loop is

$$\frac{k_{\mathrm{pi}}s+k_{\mathrm{ii}}}{L{s}^2+\left(R+k_{\mathrm{pi}}\right)s+k_{\mathrm{ii}}},$$

(7)

where $k_{\mathrm{pi}}$ and $k_{\mathrm{ii}}$ are the proportional and integrator gain of the PI controller in current loop, respectively; L and R are the inductance and resistance between the three-level NPC converter and AC grid, respectively.

The transfer function of traditional control can be derived as:

$$\frac{\left(K{k}_{\mathrm{pi}}{k}_{\mathrm{pv}}\right)s^2+\left(K{k}_{\mathrm{ii}}{k}_{\mathrm{pv}}+K{k}_{\mathrm{iv}}{k}_{\mathrm{pi}}\right)s+K{k}_{\mathrm{ii}}{k}_{\mathrm{iv}}}{\left(LC\right)s^4+\left(RC+C{k}_{\mathrm{pi}}\right)s^3+\left(C{k}_{\mathrm{ii}}+K{k}_{\mathrm{pi}}{k}_{\mathrm{pv}}\right)s^2+\left(K{k}_{\mathrm{ii}}{k}_{\mathrm{pv}}+K{k}_{\mathrm{iv}}{k}_{\mathrm{pi}}\right)s+K{k}_{\mathrm{ii}}{k}_{\mathrm{iv}}},$$

(8)

where $k_{\mathrm{pv}}$ and $k_{\mathrm{iv}}$ are the proportional and integrator gain of the PI controller in voltage loop, respectively; K is the gain of PWM and converter; C is the equivalent capacitance of DC bus between positive and negative phases.

The disturbance comes from loads and sources in the DC distribution network, and the transfer function of disturbance is:

$$\frac{L{s}^3+\left(R+k_{\mathrm{pi}}\right)s^2+k_{\mathrm{ii}}s}{\left(LC\right)s^4+\left(RC+C{k}_{\mathrm{pi}}\right)s^3+\left(C{k}_{\mathrm{ii}}+K{k}_{\mathrm{pi}}{k}_{\mathrm{pv}}\right)s^2+\left(K{k}_{\mathrm{ii}}{k}_{\mathrm{pv}}+K{k}_{\mathrm{iv}}{k}_{\mathrm{pi}}\right)s+K{k}_{\mathrm{ii}}{k}_{\mathrm{iv}}}.$$

(9)

4. Improved Strategy

4.1. Voltage Equalization Control

According to Section 3.3, the DC-side voltage equalization controller is necessary for the DC distribution network. In this article, the DC-side voltage unbalance is counteracted by intentional modulating signal asymmetry to the switching functions. A small direct component $m_0\left(t\right)$ is added to modulating signal as

$$\left\{\begin{array}{c}{m}_a\left(t\right)=m_0+\widehat{m}\left(t\right)cos\left(\epsilon \left(t\right)\right),\hfill \\ m_b\left(t\right)=m_0+cos\left(\frac{2\pi }{3}-\epsilon \left(t\right)\right)\widehat{m}\left(t\right),\hfill \\ m_c\left(t\right)=m_0+cos\left(\frac{4\pi }{3}-\epsilon \left(t\right)\right)\widehat{m}\left(t\right).\hfill \end{array}\right.$$

(10)

The impact of $m_0$ is shown in Figure 4.

It can be derived that the DC component of neural point current $i_{\mathrm{np}}\left(t\right)$ can be controlled by $m_0$ [25]:

$$i_{\mathrm{np}0}\left(t\right)=-\frac{6\widehat{i}cos\left(\gamma \right)}{\pi }{m}_0\left(t\right),$$

(11)

where $\widehat{i}$ is the current amplitude of the AC side, $\gamma$ is the power factor angle of three-level NPC, $i_{\mathrm{np}0}$ is the direct component of the current in the neural phase of the DC side. According to Equation (11) and the assumption that current amplitude and power factor vary slowly, the control transfer function is linear with variable gain.

It is easy to derive that the DC voltage unbalance component can be affected by $i_{\mathrm{np}0}$, namely:

$$\frac{d}{\mathrm{dt}}\left(V_{\mathrm{p}0}-V_{\mathrm{n}0}\right)=\frac{1}{2C}{i}_{\mathrm{np}0}.$$

(12)

From Figure 2, it is obvious that three AC phases are connected with Y-connection. Thus, only triple-n harmonic and DC components can exist in $i_{\mathrm{np}}$ (current of neural phase at the DC side). In addition, the unbalanced voltage between $Vp$ and $Vn$ can only have DC and triple-n harmonic components. In practice, harmonics higher than 3 oder can be ignored, and only three-order harmonics are considered in this article. In addition, we denote

$$\left\{\begin{array}{c}{V}_p=V_{\mathrm{p}0}-V_{\mathrm{r}3}sin\left(3\omega t-\zeta \right),\hfill \\ V_n=V_{\mathrm{n}0}+V_{\mathrm{r}3}sin\left(3\omega t-\zeta \right),\hfill \end{array}\right.$$

(13)

where $V_{\mathrm{r}3}$ is the amplitude of three-oder harmonic, $\zeta$ is initial phase of three-oder harmonic. According to Equation (13), we obtain

$$V_{\mathrm{p}0}-V_{\mathrm{n}0}=\left(V_p-V_n\right)-2V_{\mathrm{r}3}sin\left(3\omega t-\zeta \right).$$

(14)

The direct component $V_{\mathrm{p}0}-V_{\mathrm{n}0}$ cannot be measured by a sensor. Thus, to get a direct component, a low-pass filter is needed to extract $V_{\mathrm{p}0}-V_{\mathrm{n}0}$ from $V_p-V_n$. The control block diagram of voltage equalization can be depicted as Figure 5, where the disturbance comes from unbalanced DGs or loads between positive phase and negative phase, $K_s$ is the gain of sensor, and F(s) is the transfer function of a low-pass filter.

4.2. Cooperative Control with Storage System

In a future DC distribution network, reliable communication between a three-level NPC converter and a storage system with affordable time delay can be assured by advanced communication devices. Considering the short time constant of supercapacitors and the large capacity of batteries, the storage system can be controlled cooperatively with a three-level NPC converter to accelerate DC voltage response and mitigate fluctuation. The multi-agent system framework is adopted. Each battery or supercapacitor is designed as an agent. To maximize the system performance, global information should be used in normal communication circumstances. If the communication circumstances deteriorate, the agent should operate in another mode that only utilizes local information interacting with neighboring agents. Another important reason for cooperative control is the current limit of three-level NPC. Different from the VSC in the micro grid, the capacities of VSC and power disturbance can be very large. As a result, if a huge disturbance appears, the required current in a three-level NPC converter may exceed rated value. In this situation, cooperative control can mitigate this problem. It can be concluded that a new task of cooperative control in the DC distribution system (compared with widely researched DC micro grid scenarios) is to relieve the current of VSC in a heavy-load situation. In this article, only this task is focused on.

The reference DC bus voltage $V_{ref}$ and measured DC bus voltage $V_{DC}$ are used as inputs of the cooperative controller to estimate the power for the battery and supercapacitor. The output of the controller is the instantaneous reference power of the storage system. With $V_{ref}$ and $V_{DC}$, the energy deficiency of DC bus can be estimated by

$$\Delta E=\frac{C\left({V_{\mathrm{ref}}}^2-{V_{\mathrm{DC}}}^2\right)}{2}.$$

(15)

With cooperative controllers, some energy regulation tasks are dispatched to the storage system. The reference power of output can be determined by

$$P_{\mathrm{ref}}=\frac{\Delta E{K}_{\mathrm{t}2}}{K_{\mathrm{t}1}+K_{\mathrm{t}2}},$$

(16)

where $K_{\mathrm{t}1}$ and $K_{\mathrm{t}2}$ are dispatch coefficients of three-level NPC and storage system, respectively. The coefficients are determined by time constant and rated power of three-level NPC and storage system. Time constant and power are determined by equivalent parameters of the storage system, parameters of three-level NPC converter and the capacitance of an equivalent DC bus. As the parameters of the battery and the supercapacitor are equivalent in value to a cluster in the DC network, the parameters can vary when actual configuration of the storage system changes. In addition, the parameters of the three-level NPC converter and DC bus capacitance can also vary with time, temperature and operation state. Thus, the reliable performance of the cooperative controller needs the support of a reliable communication system. If a communication system deteriorates, the cooperative controller should be blocked.

4.3. Energy Management Strategy of the Storage System

In this article, the storage system consists of an equivalent battery and the supercapacitor. The battery has large storage capacity but low charge/discharge power, and the supercapacitor has inverse properties. The storage system is an auxiliary part and responses slower than the three-level NPC converter. It is also pointed out that the storage system in a DC distribution system needs to relieve the current of VSC during regulation. Considering the dynamic performance of VSC, battery and super capacitor, the components of different frequency disturbance should be dispatched to different devices. The high frequency components will be regulated by VSC. Thus, a low-pass filter is needed to isolate the high frequency component of $P_{\mathrm{ref}}$. The control block diagram of energy management is shown in Figure 6, where $P_b$ is the reference power of battery, and $P_s$ is the reference power of the supercapacitor.

The transfer function of low-pass filter is

$$F\left(s\right)=\frac{1}{T_{L}s+1},$$

(17)

where $T_L$ is the cut-off time of the low-pass filter. It is set to 0.025 s, which means that the disturbance components whose frequencies are lower than 40 Hz will be regulated by the storage system.

The transfer function of a battery is

$$F_B\left(s\right)=\frac{1}{T_{B}s+1},$$

(18)

where $T_B$ is the cut-off time of the battery.

The transfer function of a supercapacitor is

$$F_S\left(s\right)=\frac{1}{T_{S}s+1},$$

(19)

where $T_S$ is the cut-off time of supercapacitor.

The power controller 1 and power controller 2, which are actually bandwidth filters, apportion the high frequency component to a supercapacitor and the low frequency component to a battery. The transfer function of power controller 1 is

$$F_S\left(s\right)=\frac{1}{T_{H1}s+1}-\frac{1}{T_{L1}s+1}.$$

(20)

The transfer function of power controller 2 is

$$F_S\left(s\right)=\frac{1}{T_{H2}s+1}-\frac{1}{T_{L2}s+1}.$$

(21)

The $T_{H1}$, $T_{L1}$, $T_{H2}$, and $T_{L2}$ are set to 10 s, 0.1 s, 100 s, and 2 s, respectively. The Bode diagrams of low-pass filter, battery control and supercapacitor control are shown in Figure 7.

Considering the response speed of batteries, a rate limitation block is needed to limit the variation of a battery current. The speed advantage of a supercapacitor is taken to improve tracking performance. As for storage capacity, the supercapacitor is much smaller than the battery. Thus, if the current of the battery rises to a proper level, the battery should gradually charge a supercapacitor to avoid SOC (State of Charge) of the supercapacitor descending too much. It will be achieved by a SOC balancer. The input of an SOC balancer is the SOC of the supercapacitor and its output will increase with the SOC. It can be seen from Figure 6 that it will transfer the power regulation task of the supercapacitor to the battery when the SOC of the supercapacitor is high.

4.4. Two-Degree-of-Freedom Controllers

In the control system of three-level NPC converter based DC distribution networks, the part of three-level NPC converter control is the most important. Traditional control of this part adopts dual-loop control with two PI controllers. Thus, the fast response performance of PI controller always leads to an aggressive system with a large amount of overshoot. The desired system should respond quickly without sacrificing robustness. To achieve the propose, this article adopts a 2DOF controller to improve system performance. The schematic diagram of 2DOF controller is shown in Figure 8. The input step response, Bode diagram and output disturbance rejection response of traditional PI control are shown in Figure 9a–c, respectively.

It can be seen that 2DOF controller has two inputs (r and y) and one output (u). Where, r is the reference signal and y is the output of plant (In this section, the plant should include the DC bus, VSC and inner current loop). The transfer functions from both inputs r and y to the output u are PID controllers. The input y contributes to disturbance rejection without sacrifice of robustness. The transfer function of 2DOF controller is

$$u=K_p\left(br-y\right)+\frac{K_i}{s}\left(r-y\right)+\frac{K_{d}s}{\left(T_{f}s+1\right)}\left(cr-y\right).$$

(22)

To simplify analysis, the 2DOF controller is decoupled into two SISO (Single Input Single Output) PID controllers. Typical configurations of decoupled 2DOF controller include feedforward, feedback and filter. In proposed DC distribution network, the voltage of equivalent DC bus is mainly disturbed by renewable energy sources and loads. Thus, the equivalent feedback configuration is adopted. The configuration is shown in Figure 10.

The setpoint weights on the proportional and derivative terms need to be designated to 2DOF PID controllers. In addition, the parallel formula and equivalent parts T1, T2 are as follows:

$$\left\{\begin{array}{c}\mathrm{T}1\left(s\right)=b{K}_p+\frac{K_i}{s}+\frac{c{K}_{d}s}{T_{f}s+1},\hfill \\ \mathrm{T}2\left(s\right)=\left(1-b\right)K_p+\frac{\left(1-c\right)K_{d}s}{T_f,s+1},\hfill \end{array}\right.$$

(23)

where b and c are setpoint weights on proportional term and derivative term. $T_f$ is derivative filter time. The proper setpoint weights will balance the response speed and disturbance rejection.

To improve the control performance, the PI controller of voltage regulator is replaced by a 2DOF PID controller. The inputs of it are reference DC voltage and actual DC voltage. The T2 of the 2DOF controller can provide an equivalent fast feedforward compensation to disturbance current at the DC bus. Thus, the voltage fluctuation can be mitigated and the performance of the system is improved. With 2DOF controllers, the structure of the system is simplified and some mature tools can be used to tune the parameters of 2DOF controllers:

$$\left\{\begin{array}{c}b=1,\hfill \\ c=1,\hfill \\ K_p=356.1,\hfill \\ K_i=0.346,\hfill \\ K_d=0.08651.\hfill \end{array}\right.$$

(24)

We can get input step response, Bode diagram and output disturbance rejection response of 2DOF controllers, which are shown in Figure 11a–c, respectively. It can be seen that, compared with traditional PI control, all of the control performance including response time, overshoot and disturbance rejection are all dramatically improved.

5. Verification

In order to validate the proposed control and energy management strategy, all devices and controllers are developed in MATLAB/SIMULINK (R2016b, Mathworks, Natick, MA, USA). Some other important parameters of the system are shown in

Table 1. Parameters of control system.

Subsystem	Symbol	Value
Three-level NPC Control	L	0.0936 mH
	R	0.0042 $\mathsf{\Omega }$
	C	1 F
	$k_{\mathrm{pi}}$	1
	$k_{\mathrm{ii}}$	20
	$k_{\mathrm{pv}}$	2.5
	$k_{\mathrm{iv}}$	275
	Rated Voltage of DC side	1000 V
	Rated Voltage of DC side	700 V(rms)
	$f_c\left(carrierfrequency\right)$	1.65 KHz
Storage System	Initial Voltage of Battery	1000 V
	Initial Voltage of SC	1000 V
	Series resistance of SOC	0.0021 $\mathsf{\Omega }$
	Rated Capacitance of SOC	6 F
	Battery response time	29 s
	Maximum capacity of battery	1000 Ah
	Frequency of DC/DC converter	2.5 KHz

.

5.1. Test Scenario

To validate the effectiveness of DC bus voltage regulation and equalization, some severe loads/source changes are set. In the simulation model, power changes were simulated by two current sources connected to the DC bus. One simulated the change of balanced loads/sources and the other simulated the unbalanced loads/sources, which are shown in Figure 12a,b.

5.2. Three-Level NPC

To verify the effectiveness of proposed control and the energy management strategy, the three-level NPC converter hardware as illustrated in Figure 13 was built. The IGBTs of the three-level NPC converter were Infineon F3L100R07W2E3_B11 (Munich, Germany). The three-level NPC converter was controlled by a DSP processor (TI F28335, (Texas Instruments, Dallas, TX, USA)). The experimental profiles were observed by a ScopeCorder (Yokogawa DL850, Tokyo, Japan).

Some basic experiments’ verification results of three-level NPC converters were shown in Figure 14.

In the following subsection, the simulation and experiment verification were combined. The system-level properties of DC distribution networks including load variation, renewable energy output variation and storage system performance were verified by simulation. The three-level NPC converter and control strategy were performed in experiment hardware.

5.3. Traditional Control

The simulation results of traditional three-level NPC control (blue line) are shown in Figure 15. From 0.15 s to 11 s, the 600 kW step load was added to the DC distribution network, which resulted in fluctuation of DC voltage. The maximum deviation of DC voltage could be as much as 26 V. Before unbalanced loads were added, the voltages of negative and positive phase were nearly the same. However, at 5 s, the unbalanced loads were added, and the unbalance between positive voltage and negative voltage started to rise until the unbalanced load direction changed. The unbalance between positive and negative phase could be as much as 21 V. Before 11 s, the three-level NPC converter operated in rectifier mode and the power delivered from the AC grid also fluctuated under the regulation of the converter. The maximum power overshoot was about 80%. The waveform of converter AC side voltage between phase A and phase B is also displayed.

From 11 s to 20 s, the loads of DC distribution changed from about 600 kW to −600 kW, which meant the DGs in DC distribution produced more power than needed. In this period, the converter operated in inverter mode. Because of the larger step change, the fluctuation of voltage and power became more severe. The maximum voltage fluctuation was 68 V, and maximum voltage unbalance was 40 V. The maximum power overshoot was about 178.33%. In addition, the large power fluctuation made much higher requirements for a three-level NPC converter.

It can also be concluded that the balanced loads/sources have little impact on voltage equalization, and the impacts of unbalanced loads/sources on DC voltage are much smaller than voltage unbalance.

5.4. Voltage Equalization Controller

The simulation results of system with a voltage equalization controller (orange line) are also shown in Figure 15.

It can be seen that the adoption of the voltage equalization controller had little impact on fluctuation of DC voltage and NPC power. However, the voltage difference between the positive phase and negative phase became much smaller. On rectifier mode, the maximum unbalance was 10.87 V, which was just 41.81% of traditional control. On inverter mode, the maximum unbalance was 9.17 V, which was just 22.93% of traditional control.

It can be concluded that the voltage equalization control strategy can mitigate the voltage unbalance in the bipolar DC distribution network when unbalanced loads/sources exist.

5.5. Cooperative Control and Energy Management Strategy

The simulation results of systems with cooperative control and an energy management strategy are shown in Figure 16. The waveforms of simulation results with traditional control are reserved for comparison, which are still represented by blue lines.

The cooperative controller computes the power to compensate and sends the information to energy management systems. Due to the usage of a low-pass filter, the total power to be compensated is different from the output of the cooperative controller. Considering the response time of the storage system and the dynamic change of cooperative controller output, the actual output of storage system can be different from reference signals at the energy management output.

It can be seen from Figure 16 that the energy management strategy dispatched the fast change response job to supercapacitor and the the slow change response to battery. If the change rate of reference power is smaller than the rate limiter of battery, the supercapacitor will not work. In simulation results, it could be seen that fast changes in power were compensated by a supercapacitor, and the supercapacitor could be charged by a battery when there were no fast changes. The maximum power limitation of the battery was not considered.

It can be seen that, with cooperative control, the fluctuations of DC voltage and NPC converter power were mitigated dramatically, and the settling time became much smaller. On rectifier mode, the maximum voltage fluctuation was 7 V, which was only 26.92% of traditional control. On inverter mode, the maximum voltage fluctuation was 48 V, which was 70.59% of traditional control.

5.6. Synthetic Control Results

The simulation results of systems with 2DOF controller, cooperative control and voltage equalization control are shown in Figure 17. The waveforms of aforementioned simulation results were reserved for comparison. The corresponding colors are shown in the legend of Figure 17.

According to simulation results, it can be seen that the 2DOF PID controller could further improve the performance of system. The fluctuation of DC voltage and NPC converter were further mitigated. The performance of voltage equalization was close to system only with equalization controller, but the waveforms of negative phase and positive phase became much smoother.

6. Conclusions

The conceptions of the bipolar DC distribution network are proposed in this article. An improved control and energy management strategy based three-level NPC converter is analyzed, which includes the voltage equalization controller, 2DOF PID controller, cooperative controller and storage system energy management strategy. Experiment and simulation results validated the effectiveness of proposed strategy. Compared with traditional dual-loop PI control, the proposed strategies can reduce the voltage unbalance to 22.93% of traditional methods. The voltage fluctuation can be reduced to 26.92% of traditional methods. The current load of VSC is much relieved. In addition, the response speed and disturbance rejection performance are also much improved.