Sliding Mode Control of Ship DC Microgrid Based on an Improved Reaching Law

Abstract

The bus voltage of the ship DC microgrid is sensitive to the change of loads, which has an influence on the power supply quality. This paper introduces a hybrid energy storage system (HESS) that is composed of a battery set and a supercapacitor set, and further studied the control method of HESS. First of all, the topological structures of the ship DC microgrid and HESS are described. Second, combined with the frequency division droop control and voltage PI control, a sliding mode control (SMC) method is proposed to control the charge and discharge of HESS based on an improved reaching law. Finally, the simulation model of the ship DC microgrid is established for the verification of the control method. Simulation results show that: (1) HESS can overcome the shortage of the dynamic response ability of the diesel rectifier generator to the steep change of load power. The supercapacitor set and the battery set successfully respond to the high-frequency and low-frequency components of the differential power in the system, respectively. (2) Compared with the traditional PI control method, SMC can reduce the current chattering of HESS and the voltage fluctuation amplitude of the DC bus. The proposed SMC method can provide a reference for the stable and reliable operation of the ship DC microgrid.

1. Introduction

Due to outstanding advantages of fuel efficiency, system power density, and new energy utilization, the ship DC microgrid is gradually replacing the traditional AC power system and becoming the important development direction of the ship power system [1]. But compared with the onshore microgrid, the operation condition and working environment of the ship DC microgrid are more complex and serious. A great change in the external environment (wind, sea waves, ocean currents, etc.) or suddenly switching on or off the ship, will make a great impact on the stable operation of the ship DC microgrid. Especially for a warship DC microgrid, if high-energy pulse weapons are frequently used, the generator sets are easy to trip when they cannot quickly respond to the steep change of the high-energy load, which will result in a drastic fluctuation of the DC bus voltage and even lead to a power failure for the whole warship. The reliable and stable operation of the ship DC microgrid is seriously threatened [2,3]. Therefore, it is important to study how to ensure the stability and reliability of the ship DC microgrid.

In the operation process of a DC microgrid, the combination of different power supplies can theoretically support the stability and reliability of the microgrid. For renewable energy systems (RESs), there are many maximum power tracking technologies that have been used to obtain the maximum power output of photovoltaic (PV) and wind distributed generation (DG), such as perturbation and observation, incremental conductance, short-circuit current, and open-circuit voltage [4,5,6,7,8,9,10]. However, DG-generated current and power are limited by the meteorological conditions of the scenario application, and none of these methods could achieve the expected results. In order to eliminate the influence of the intermittent PV and wind DG on the stability and reliability of the microgrid, a hybrid energy storage system (HESS) consisting of high power density and high energy density storage units has been developed. High-power density storage units are used to compensate for the high-frequency components of the target power, whereas high-energy density storage units are used to compensate for the low-frequency components. Batteries with high-energy density and supercapacitors with high-power density are the most common energy storage units widely used in ships, automobiles, aerospace, and other industries [11,12,13,14]. If the HESS is applied in the ship DC microgrid, the supercapacitor will provide transient power response for short periods, and the battery will provide power quality support for long durations. Thus, the power fluctuation in the ship DC microgrid will be greatly reduced. Therefore, HESS provides an effective means and applicable scheme for balancing the contradiction between the output power of new energy power supplies and the load power, as well as for solving the flexible scheduling and distribution of electric power in the ship DC microgrid [15]. However, if there is only the hardware combination of DG units and HESS without a corresponding control method, power supplies of the ship DC microgrid will work separately, which is more likely to cause voltage fluctuation of the DC bus. Therefore, it is necessary to study the control method of HESS to appropriately distribute the power among the multiple power supplies.

In recent years, various online energy management systems (EMSs) have been presented to manage and control the nonlinear power converters of HESS [16,17]. Fuzzy logic control has been presented for the control of the battery, supercapacitor, and hydrogen storage system [18]. Filtration, state-machine, and rule-based systems for the battery and supercapacitor have also been implemented [19,20,21]. These online EMSs increase the complexity of power distribution and fail to estimate the system’s cost [22]. In addition, offline energy management algorithms based on genetic algorithms [23], droop control methods [24], and Pontryagin’s minimum principle have also been considered [25]. Furthermore, PID controller and one-point linearization have been applied by relevant scholars [26]. However, as these combinations of HESS to be used were designed according to typical applications such as electric vehicles and onshore microgrids, they are not fully suitable for the ship DC microgrid operating in island mode [27]. Due to the process of the interaction and cooperation of each part of the ship DC microgrid and HESS coupling being nonlinear, the linear control methods of HESS are not able to satisfy the requirements of ship operation under time-varying conditions. In addition, some studies focus on the linearized model of ship HESS but ignore the nonlinear model of RES, which hinders the better performance of the designed controller [28]. Because of the nonlinearity and uncertainty of the power converter model, robust nonlinear controllers have been presented to control the power supplies of microgrids [29]. Sliding mode control (SMC) is a robust and simple control technique used for accurate tracking under uncertain and disturbed situations [30]. It is an efficient and robust nonlinear controller due to its fast dynamics and simplicity [31]. However, in SMC, the system trajectory and the desired sliding surface cannot be completely coincident, which results in system chattering. Therefore, the SMC also needs to be improved to further reduce the chattering of the system, such as the second-order sliding mode approach [32], and the two-layers architecture controller, based on the theory of SMC and common Lyapunov functions [33].

The purpose of this paper is to propose an SMC method for the HESS of the ship DC microgrid based on an improved reaching law used to ensure the stability and reliability of the ship DC microgrid and reduce the current chattering of HESS. This paper is organized as follows. Section 2 introduces the topologies of ship DC microgrid and HESS. In Section 3, the proposed control method of HESS is described in detail, including a frequency division droop control loop, a voltage PI loop, and a current SMC loop. Next, the double closed loops of voltage and current of the diesel rectifier generator are described in Section 4. Section 5 analyzes the simulation results and verifies the effectiveness of the proposed method. Finally, conclusions are presented in Section 6.

2. Ship DC Microgrid

2.1. Ship DC Microgrid

The structure of the ship DC microgrid studied in this paper is illustrated in Figure 1. It is mainly composed of a diesel rectifier generator, a HESS, and loads. Each part connects to the DC bus. The diesel rectifier generator is the main power supply, which consists of a diesel generator and an AC-DC rectifier. The HESS is an auxiliary power supply used to compensate or absorb the differential power between the output power of the diesel rectifier generator and the required power of loads. It consists of a battery set with high energy density, a supercapacitor set with high power density, and two DC-DC converters. The loads are mainly composed of the propulsion load, the daily AC load, and two DC-AC converters.

The power balance in the ship DC microgrid can be expressed as

$$P_{\mathrm{gen}}+P_{\mathrm{hess}}=P_{\mathrm{load}}$$

(1)

where $P_{\mathrm{gen}}$ is the output power of the diesel rectifier generator, $P_{\mathrm{hess}}$ is the compensated or absorbed power by the HESS, and $P_{\mathrm{load}}$ is the total power of loads.

2.2. HESS Topology Structure

The HESS consists of a battery set, a supercapacitor set, and two standard bidirectional DC-DC converters. Its simplified circuit model is shown in Figure 2.

In Figure 2, $R_{\mathrm{bat}}$, $R_{\mathrm{sc}}$, $E_{\mathrm{bat}}$, and $E_{\mathrm{sc}}$ are internal series resistances and open circuit voltages of the battery set and supercapacitor set, respectively; $V_1$, $V_2$, $i_1$, and $i_2$ are output voltages and currents of the battery set and supercapacitor set, respectively; $R_1$, $R_2$, $L_1$, and $L_2$ are linear resistances and inductances of DC-DC converter 1 and 2, respectively; $R_{S_1}$, $R_{S_2}$, $R_{S_3}$, and $R_{S_4}$ are the on-resistances of the IGBT switch $S_1$, $S_2$, $S_3$, and $S_4$ in DC-DC converter 1 and 2, respectively; $S_1$ and $S_2$ are controlled by two complementary control signals, and $S_3$ and $S_4$ are also controlled by two complementary control signals; $V_{\mathrm{o}1}$, $V_{\mathrm{o}2}$, $i_{\mathrm{o}1}$, and $i_{\mathrm{o}2}$ are the output voltages and currents of DC-DC converter 1 and 2, respectively; $V_0$ is the DC bus voltage; and $i_{\mathrm{o}}$ is the load current.

According to Figure 2, the following state equation can be obtained [34]:

$$\{\begin{array}{l}{\dot{V}}_1=-\frac{V_1}{R_{\mathrm{bat}}{C}_1}-\frac{i_1}{C_1}+\frac{E_{\mathrm{bat}}}{R_{\mathrm{bat}}{C}_1},\\ {\dot{V}}_2=-\frac{V_2}{R_{\mathrm{sc}}{C}_2}-\frac{i_2}{C_2}+\frac{E_{\mathrm{sc}}}{R_{\mathrm{sc}}{C}_2},\\ {\dot{i}}_1=\frac{V_1}{L_1}-i_1\frac{R_1+R_{S_2}}{L_1}-\frac{V_0}{L_1}+D_1{i}_1\frac{R_{S_2}-R_{S_1}}{L_1}+V_0\frac{D_1}{L_1},\\ {\dot{i}}_2=\frac{V_2}{L_2}-i_2\frac{R_2+R_{S_4}}{L_2}-\frac{V_0}{L_2}+D_3{i}_2\frac{R_{S_4}-R_{S_3}}{L_2}+V_0\frac{D_3}{L_2},\\ {\dot{V}}_0=\frac{i_1+i_2}{C_0}-\frac{i_{\mathrm{load}}}{C_0}-D_1\frac{i_1}{C_0}-D_3\frac{i_2}{C_0}.\end{array}$$

(2)

where $D_1$ and $D_3$ are the duty factors of the input control signal of $S_1$ and $S_3$, respectively.

3. SMC Method for HESS

In Section 2, the simplified circuit and the state equation of HESS were introduced. In this section, the control method of HESS will be described in detail.

The schematic diagram of the control of HESS is shown in Figure 3. It mainly consists of a frequency division droop control loop, a voltage PI loop, and a current SMC loop.

First, the frequency division droop control is adopted for the reference voltage of the DC bus $V_{\mathrm{ref}}$ and the output currents of DC-DC converters 1 and 2. Its output voltages are used as the input reference voltages of the PI loop. Second, these input reference voltages and the output voltages of DC-DC converters 1 and 2 are controlled by a PI regulator. Its output currents are used as the input reference currents of the current SMC loop. Third, these input reference currents and output currents of HESS are controlled by SMC. Finally, the obtained outputs are used as the pulse control signals of DC-DC converters 1 and 2 after modulating by pulse width modulation (PWM).

3.1. Frequency Division Droop Control Method

As described in Section 2, HESS compensates for or absorbs the differential power $P_{\mathrm{hess}}$ between the diesel rectifier generator and the loads. In order to make full use of the best regulation performance of HESS for $P_{\mathrm{hess}}$, the supercapacitor set with high power density and the battery set with high energy density are usually used to respond to the high-frequency component and low-frequency component of $P_{\mathrm{hess}}$, respectively. Droop control is a decentralized control method widely used for power proportional distribution between multiple energy storage systems. This paper also adopts droop control methods based on virtual capacitance and virtual impedance to control the responses of the supercapacitor set and battery set to $P_{\mathrm{hess}}$, respectively [35]. The equivalent circuit of the frequency division droop control of the HESS for $P_{\mathrm{hess}}$ is illustrated in Figure 4.

From Figure 4, the basic circuit equation is obtained:

$$\left\{\begin{array}{l}{V}_{\mathrm{o}1}=V_{\mathrm{ref}}-i_{\mathrm{ol}}\cdot R_{\mathrm{v}1}\hfill \\ V_{\mathrm{o}2}=V_{\mathrm{ref}}-i_{\mathrm{ol}}\cdot \frac{1}{s{C}_{\mathrm{v}2}}\hfill \\ i_{\mathrm{ol}}+i_{\mathrm{o}2}=i_{\mathrm{o}}\hfill \end{array}\right.$$

(3)

where $R_{\mathrm{v}1}$ and $C_{\mathrm{v}2}$ are the droop coefficient and virtual capacitance, respectively.

The output voltages of DC-DC converters 1 and 2 are approximately equal to the DC bus voltage, i.e.,

$$V_{\mathrm{o}1}=V_{\mathrm{o}2}=V_{\mathrm{o}}$$

(4)

According to Equations (3) and (4), the distribution relationship of output current between the battery set and the supercapacitor set can be obtained:

$$\left\{\begin{array}{l}{i}_{\mathrm{o}1}=\frac{\frac{1}{R_{\mathrm{v}1}{C}_{\mathrm{v}2}}}{s+\frac{1}{R_{\mathrm{v}1}{C}_{\mathrm{v}2}}}\cdot i_{\mathrm{o}}=H_1(s)\cdot i_{\mathrm{o}}\hfill \\ i_{\mathrm{o}2}=\frac{s}{s+\frac{1}{R_{\mathrm{v}1}{C}_{\mathrm{v}2}}}\cdot i_{\mathrm{o}}=H_2(s)\cdot i_{\mathrm{o}}\hfill \end{array}\right.$$

(5)

From Equation (5), it can be seen that $H_1\left(s\right)$ and $H_2\left(s\right)$ are equivalent to a first-order low pass filter and a first-order high pass filter, respectively. It means that the load current $i_{\mathrm{o}}$ is decomposed into the low-frequency component and the high-frequency component, which are responded to by the battery set and the supercapacitor set, respectively. Therefore, the frequency division droop control of the HESS for $P_{\mathrm{hess}}$ is realized.

3.2. SMC Current Controller Design

The traditional exponential reaching law is

$$\dot{s}=-\epsilon \mathrm{sgn}(s)-ks$$

(6)

where $\epsilon$ and $k$ are the sliding mode gains, $\epsilon >0$, $k>0$, and $s$ is the switching function, which is derivable and crosses the origin.

Although the sliding mode gains $\epsilon$ and $k$ can be designed, they cannot be changed after design and changed with the system state. This will result in an overshoot. Therefore, an improved reaching law is proposed.

$$\dot{s}=-\epsilon {\left|s\right|}^{\alpha }\mathrm{sgn}(s)-ks{\left|s\right|}^{\beta }$$

(7)

where ${\left|s\right|}^{\alpha }$ and ${\left|s\right|}^{\beta }$ are the power terms, $0<\alpha <1$, $\beta >0$.

When $\left|s\right|$ is small, the control law makes the state variables in $\left|s\right|$ entering the sliding mode surface and move to the original point. Under the action of α and β, when $\left|s\right|$ gradually decreases, the variable speed term $\epsilon {\left|s\right|}^{\alpha }\mathrm{sgn}(s)$ also gradually decreases, but the exponential term $ks{\left|s\right|}^{\beta }$ quickly decreases to close to 0. In other words, the reaching rate decreases more slowly than the exponential reaching rate. Therefore, the improved reaching law can effectively reduce chattering.

First, we establish the sliding surface:

$$s=c_1{\int }_0^{t}edt+c_{2}e$$

(8)

The difference between the reference and actual output current of the energy storage units is a state variable:

$$\left\{\begin{array}{l}e=i_{\mathrm{ref}}-i\\ \dot{e}={\dot{i}}_{\mathrm{ref}}-\dot{i}\end{array}\right.$$

(9)

The first-order derivative of $s$ is

$$\dot{s}=c_{1}e+c_2\dot{e}$$

(10)

Based on the improved reaching law, combining Equations (2), (7), (9) and (10), the equivalent SMC control rate can be obtained:

$$\begin{array}{c}{D}_{1eq}=\frac{L_1{c}_1}{V_0{c}_2}(i_{\mathrm{batref}}-i_1)+c_2(-\frac{V_1}{V_0}+i_1\frac{R_1+R_{s_1}}{V_0}+1+\frac{L_1}{V_0}{\dot{i}}_{\mathrm{batref}})+\frac{{\epsilon }_1{L}_1}{V_0{c}_2}{\left|s\right|}^{{\alpha }_1}\mathrm{sgn}(s)+\frac{k_1{L}_1}{V_0{c}_2}s{\left|s\right|}^{{\beta }_1}\\ D_{3eq}=\frac{L_2{c}_1}{V_0{c}_2}(i_{\mathrm{scref}}-i_2)+c_2(-\frac{V_2}{V_0}+i_2\frac{R_2+R_{s_2}}{V_0}+1+\frac{L_1}{V_0}{\dot{i}}_{\mathrm{scref}})+\frac{{\epsilon }_2{L}_2}{V_0{c}_2}{\left|s\right|}^{{\alpha }_2}\mathrm{sgn}(s)+\frac{k_2{L}_2}{V_0{c}_2}s{\left|s\right|}^{{\beta }_2}\end{array}$$

(11)

Instead $\mathrm{sgn}(s)$ with a continuous function $\theta (s)$:

$$\theta (s)=\frac{s}{\left|s\right|+\delta }$$

(12)

where $\delta$ is an arbitrarily small positive number.

Define the Lyapunov function as

$$V=\frac{1}{2}{s}^2$$

(13)

Then, the following equation can be derived:

$$\dot{V}=s\dot{s}=-\epsilon {\left|s\right|}^{\alpha +1}-k{s}^2{\left|s\right|}^{\beta }$$

(14)

According to $0<\alpha <1$, $\beta >0$, the improved reaching law and the second Lyapunov method, $\dot{V}\le 0$ is permanently established. It proves that the inner current control loop is asymptotically stable.

4. Control Method for Diesel Rectifier Generator

The rectifier of the diesel generator adopts the control method of voltage/current double closed-loops, in which the outer feedback loop and the inner feedback loop are for DC output voltage and AC current, respectively. The rectifier works in the constant output voltage mode, and the constant reference voltage is the rated voltage of the DC bus. The d-axis and q-axis components of the input voltage $v_{\mathrm{d}}$ and $v_{\mathrm{q}}$ at the rectifier DC side are

$$\left\{\begin{array}{l}{v}_{\mathrm{d}}=-(K_{\mathrm{p}}+\frac{K_{\mathrm{i}}}{s})(i_{\mathrm{dref}}-i_{\mathrm{d}})+e_{\mathrm{d}}-\omega L{i}_{\mathrm{q}}\\ v_{\mathrm{q}}=-(K_{\mathrm{p}}+\frac{K_{\mathrm{i}}}{s})(i_{\mathrm{qref}}-i_{\mathrm{q}})+e_{\mathrm{q}}-\omega L{i}_{\mathrm{d}}\end{array}\right.$$

(15)

where $e_{\mathrm{d}}$ and $e_{\mathrm{q}}$ are the d-axis and q- axis components of the input three-phase voltage at the rectifier AC side in the two-phase rotating coordinate system, respectively; $K_{\mathrm{p}}$ and $K_{\mathrm{i}}$ are the proportional and integral coefficients of the PI controller in the inner current loop, respectively; $i_{\mathrm{d}}$ and $i_{\mathrm{q}}$ are the d-axis and q- axis components of the input current at the rectifier AC side in the two-phase rotating coordinate system, respectively; and $i_{\mathrm{dref}}$ and $i_{\mathrm{qref}}$ are the reference values of $i_{\mathrm{d}}$ and $i_{\mathrm{q}}$, respectively.

In general, the rectifier is controlled to operate with the maximum power factor. For $i_{\mathrm{qref}}$ equals 0, the rectifier only outputs active power at this time. Ignoring the power loss of the line, the output active power $P$ of the rectifier is

$$P=\frac{3}{2}{e}_{\mathrm{d}}{i}_{\mathrm{d}}$$

(16)

The active power at the DC side equals the output active power of the rectifier, thus

$$V_{\mathrm{o}}{I}_{\mathrm{dc}}=\frac{3}{2}{e}_{\mathrm{d}}{i}_{\mathrm{d}}$$

(17)

where $I_{\mathrm{dc}}$ is the output current of the rectifier.

Equation (17) shows the control principle of the voltage feedback loop of the rectifier. The $i_{\mathrm{d}}$ is adjusted by controlling $V_{\mathrm{o}}$. The DC bus voltage $V_{\mathrm{o}}$ is controlled with a PI controller to maintain its stability.

In summary, the schematic diagram of the double control loops of the generator rectifier is illustrated in Figure 5.

After obtaining the control parameters $v_{\mathrm{d}}$ and $v_{\mathrm{q}}$, the control pulse signal of the generator rectifier is generated by the traditional space vector pulse width modulation (SVPWM).

5. Simulation Results and Analysis

5.1. Simulation Conditions and Parameters

In this section, referring to the basic data of ‘Alsterwasser’ [36], a simulation model of the ship DC microgrid is built to verify the improved SMC control method. The load power of Alsterwasser varies from 0 kW to 110 kW during a certain period of operation. Such a wide fluctuation range of load power will pose a huge challenge to the stable operation of the ship DC microgrid. Referring to the power level of Alsterwasser, the daily AC load power, such as daily lighting and air conditioning, is set to 5 kW. There are three simulated operating conditions taken into account: (1) at t = 1 s, the propulsion load power steeply increases by 70 kW and then sharply drops to the daily AC load power 5 kW after 1.5 s; (2) at t = 4 s, the propulsion load power steeply increases by 80 kW and then sharply drops to the daily AC load power 5 kW after 1.5 s; (3) at t = 7 s, the propulsion load power steeply increases by 100 kW and then sharply drops to the daily AC load power 5 kW after 1.5 s. The parameters of the simulation model are listed in

Table 1. Simulation model parameters.

Parameters	Value
DC bus rated voltage/V	720
Rated capacity of rectifier generator/kW	135
Battery rated capacity/Ah	100
Supercapacitor rated capacitance/F	100
Supercapacitor rated voltage/V	500
Battery rated voltage/V	350
Simulation step/s	$2\times {10}^{-6}$

, and the parameters of the SMC controller are listed in

Table 2. SMC controller parameters.

Parameters	Value
${\epsilon }_1$	0.03
${\epsilon }_2$	0.05
$k_1$	0.015
$k_2$	0.1
${\alpha }_1$	0.99
${\alpha }_2$	0.98
${\beta }_1$	1
${\beta }_2$	1
$c_1$	3
$c_2$	8

.

5.2. Simulation Results

According to the three previously assumed operating conditions, the change of load power is illustrated in Figure 6. With the change of load power, the output power of the diesel rectifier generator is shown in Figure 7, and the exchange power of the HESS with the DC bus is shown in Figure 8.

It can be seen from Figure 6 and Figure 7 that the instantaneous output power of the diesel rectifier generator cannot quickly track or respond to steep increases (t = 1 s, 4 s, 7 s) or decreases (t = 2.5 s, 5.5 s, 8.5 s) in load power. As we can see from Figure 8, the supercapacitor set with high power density responds to the change of load power very quickly. It instantly releases or absorbs a large amount of electrical energy to quickly respond to the high-frequency component of $P_{\mathrm{hess}}$. However, due to the low energy density of the supercapacitor set, the power it absorbed or released decays rapidly. Subsequently, the battery set with high energy density mainly responds to the change of load power. It responds to the low-frequency component of $P_{\mathrm{hess}}$. Therefore, the HESS can overcome the shortage of the dynamic response ability of the diesel rectifier generator to the great change of load power.

Next, let us verify the SMC on the regulation of the HESS current. The current inner loops of DC/DC converters 1 and 2 are controlled by PI and SMC, respectively. Comparisons of the control effect of the discharge or charge current of the battery set and supercapacitor set are illustrated in Figure 9 and Figure 10, respectively.

As we can see from Figure 9, when the battery set is in the discharge state, from the partially enlarged drawings (for instance, t = 1.02~1.08 s, t = 4.04~4.08 s, and t = 7.06~7.08 s), the fluctuation chattering of the discharge current is about 1.1 A under the control of traditional PI, whereas it is only about 0.5 A under the SMC. We also can find that when the battery set is in charge state, from the partially enlarged drawings (such as t = 2.515~2.525 s and t = 8.52~8.56 s), the fluctuation chattering of charge current reduces from 1.75 A under the control of PI to only about 0.75 A under the SMC. Similarly, it can be seen from Figure 10 that, when the supercapacitor set is in the discharge state, compared with the PI control method, the fluctuation chattering of the discharge current of the supercapacitor set is reduced from 2 A to 0.5 A under the SMC during t = 1.06~1.1 s, t = 4.03~4.06 s, and t = 7.08~7.14 s; the reduction effect is especially obvious during t = 4.03~4.06 s. When the supercapacitor set is in the charge state, the SMC reduces the fluctuation chattering of charge current from 1.75 A to 0.75 A controlled by PI during t = 2.59~2.63 s and t = 5.63~5.66 s. Therefore, the proposed SMC method can effectively reduce the current fluctuation chattering of the battery set and the supercapacitor set.

The fluctuation of the DC bus voltage is shown in Figure 11. The fluctuation amplitude of the DC bus voltage caused by the change of loads under the SMC is less than that for the PI controller. Especially for voltage drops of the DC bus due to the increase of loads, the control effect is more obvious. SMC makes the fluctuation of the DC bus voltage far below the standard requirements. The effectiveness of the improved SMC method proposed in this paper is further verified.

6. Conclusions

The great change in load power seriously affects the stability of the DC bus voltage in ship DC microgrid. In this paper, HESS was introduced into the ship DC microgrid, and an SMC method based on an improved reaching law was proposed. The following conclusions can be drawn:

• The output power of the diesel rectifier generator cannot quickly track or respond to the steep change in load power.
• In HESS, the battery set can respond to the low-frequency component of the differential power in the system; at the same time, the supercapacitor set can respond to the high-frequency component.
• Compared with the traditional PI control, the proposed SMC method can reduce the current chattering of HESS and fluctuation amplitude of DC bus voltage and improve the stability of the ship DC microgrid.
• This research work provides a reference for the stable operation and control of ship DC microgrid.