Portal de Periódicos da CAPES

A flexible virtual inertial control algorithm for ship with propulsion load and pulse load

2021; Institution of Engineering and Technology; Volume: 15; Issue: 4 Linguagem: Inglês

10.1049/elp2.12039

1751-8679

Yunfeng Lin, Fu Lijun, Xiongbo Xiao,

Advanced Algorithms and Applications

IET Electric Power ApplicationsVolume 15, Issue 4 p. 453-462 ORIGINAL RESEARCH PAPEROpen Access A flexible virtual inertial control algorithm for ship with propulsion load and pulse load Lin Yunfeng, Lin Yunfeng orcid.org/0000-0003-0090-7051 National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan, ChinaSearch for more papers by this authorFu Lijun, Corresponding Author Fu Lijun lijunfu2006@sina.cn National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan, China Correspondence Lijun Fu, National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan, China. Email: lijunfu2006@sina.cn.Search for more papers by this authorXiao Xiongbo, Xiao Xiongbo National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan, ChinaSearch for more papers by this author Lin Yunfeng, Lin Yunfeng orcid.org/0000-0003-0090-7051 National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan, ChinaSearch for more papers by this authorFu Lijun, Corresponding Author Fu Lijun lijunfu2006@sina.cn National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan, China Correspondence Lijun Fu, National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan, China. Email: lijunfu2006@sina.cn.Search for more papers by this authorXiao Xiongbo, Xiao Xiongbo National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan, ChinaSearch for more papers by this author First published: 21 February 2021 https://doi.org/10.1049/elp2.12039AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The pulse load of an integrated power system (IPS) ship can produce very high power intermittently in a short period of time. Owing to the limited DC bus capacitance, the periodic pulse load charging and discharging process can make the IPS system state variables have a periodic alternating process during electromagnetic transients, especially at the bus voltage. In order to alleviate this problem, it is necessary to find a suitable control strategy. At first, this article establishes a mathematical model of DC bus voltage dynamics and propulsion motor load. Then, a flexible energy scheduling algorithm is proposed to coordinate the propulsion motor load and the pulse load based on the flexibility of IPS energy scheduling and the concept of virtual inertia. This algorithm can adaptively change the virtual inertia of the DC bus according to the pulse load power level and the propulsion motor load level to mitigate the impact of the pulse load on the IPS system. At the same time, the algorithm is also distributed and has little impact on the propulsion system. Finally, the effectiveness of the algorithm is verified through the mixed simulation of PSCAD and MATLAB and the hardware in the loop test. 1 INTRODUCTION The integrated power system (IPS) ship that combines the propulsion system and power system into one independent systems, serves the propulsion motor load (PML), pulse load (PL), hybrid energy storage system (HESS), communication and navigation equipment, and daily service load in the form of electric energy, thereby attaining the goal of comprehensively utilizing the energy sources of the whole ship. Among them, the distinguishing feature of IPS is that the power of the PML accounts for 80% of the total system power, and the instantaneous power of the PL charging unit is relatively large [1]. Using the transmission and distribution network structure of Medium-Voltage DC (MVDC) power supply and DC-zonal electric distribution system (DCZEDS), the second-generation IPS can significantly increase the power density and the torque density compared with the first-generation IPS [2]. The MVDC system of IPS has advantage over the Medium-Voltage AC system and high-frequency AC system, in power density and operational flexibility, which represents the direction of ship IPS development [3]. The advantage of using IPS is the flexible energy scheduling which can solve the power requirements of PL compared to traditional ships. Some loads such as laser beam weapon, electromagnetic gun, and electromagnetic launcher which need much power in a very short time are called PL. The PL is connected to the MVDC bus and release pulse energy intermittently with high energy density and power density. The general power requirements for PL vary in magnitude from a few hundred kilowatts to a few megawatts, and the intervals between iterative pulses vary from a few to couples of seconds [4]. PL devices may exceed the ships generators ability in terms of power ramp rate, which may drive the system to instability [5]. In addition, the constant power and negative impedance characteristics of the PML will also adversely affect the DC voltage stability. In order to reduce the influence of PL and constant power load (CPL) on the stability of IPS, three main technical solutions are proposed. The first technical framework is to use HESS with high energy and power density to coordinate with the generator control [6, 7]. The second technical framework is to improve the excitation control of the rectifier generator. The research in literature [8, 9] shows that the effect of PL on the MVDC voltage can be improved by introducing LQG and DC voltage feed forward control. The third technical framework is to coordinate the electricity demand between the PML and the PL. It has strong practicability but there is little research in this area currently [10]. The HESS generally adopts the form of parallel connection or cascade connection. It can be used as a power source for PL or can be connected in parallel to the DC bus to improve the bus voltage dynamics. Energy control algorithms for HESS can be divided into centralized control based on filtering and improved algorithms or distributed control that does not rely on communication [11]. The energy density and power density of energy storage batteries or capacitors are not high enough, especially in high-rate discharges [12]. The service life is limited, and the maintenance is complicated. In addition, the connection of energy storage equipment to the IPS requires the design of a bidirectional DC converter. This is subject to the constraints of IPS ships on equipment space [13]. The PML is connected to the MVDC bus as a rotating electrical machine through a multi-phase inverter. The mechanical part is decoupled from the electrical part of the grid. The speed of the PML is almost unresponsive to the changes of system power flow. Therefore, a large amount of inherent mechanical inertia is not fully obtained by the DC grid. Although there are many methods that can be used to improve the performance of electric propulsion systems [14], the task of ensuring the power supply of pulse weapon loads is higher than the maintenance of electric propulsion energy system performance under certain operating conditions such as battle circumstance. At present, when there is a power imbalance in the MCDC bus, the power difference of the system is usually balanced by charging and discharging the energy storage system paralleled on the DC side [15]. In the traditional speed closed-loop control mode, the power PML has negative impedance characteristics, which has a negative impact on the stability of the bus voltage [16]. If the inertia in the operation of the electric propulsion equipment is released by control algorithm, it is worth studying to compensate for the fluctuation of MVDC bus voltage in the transient process [17]. At the same time, the ship sailing in the ocean also has great inertia, and the effect of temporarily changing the electromagnetic torque on the ship's speed is almost negligible. Literature [18] proposed the idea that the energy in the rotating electrical machine can be used to support PL, but the focus of its research is second-level energy scheduling, which can only be adapted to specific working conditions, and the real-time and adaptability of energy scheduling is insufficient. The IPS model has characteristics of high dimensions, non-linearity, strong coupling, and multiple time scales. Time domain simulation is the main method to study the transient characteristics of IPS [19]. In order to improve the power quality of the DC bus and realize the flexible power adjustment between the power supply, the PML and the high-power PL, this article designs a control algorithm based on virtual inertia. Different from the idea of using energy storage to improve bus voltage transient process in reference [12-15], the innovation of this article is that only the control strategy of propulsion load needs to be improved, and it does not rely on additional energy storage and auxiliary converter. The proposed control strategy can coordinate different propulsion loads to participate in bus voltage regulation without relying on communication and save energy storage capacity configuration compared to [12]. By introducing multiple state feedbacks and fuzzy calculations, the propulsion load can participate in bus voltage regulation and load response to a certain extent without relying on communication. This article is composed of the following sections. Section 1 gives a background of the performance analysis of the IPS with PL and PML, and Section 2 presents a mathematical model of the system. Section 3 gives the algorithm of the virtual inertial control based on fuzzy logic. Section 4 gives the simulation analysis and experimental verification. Section 5 summarizes the conclusions. 2 MATHEMATICAL MODEL OF IPS WITH PML The structure of IPS is shown in Figure 1. The main turbine generator G1 and the auxiliary diesel generator G2 are connected in parallel to supply electricity to the MVDC bus. The rated powers of G1 and G2 are 20 and 5 MW, respectively, and the voltage of DC bus is 5 kV. The generators are connected to the MVDC through AC/DC converters. The energy storage system consists of a combination of batteries and supercapacitors that are connected and controlled using DC/DC converters. Compared with the AC system, there is no skin effect of current and no need to transmit reactive power, thus reducing the weight of the cable, and the loss of the transmission line can usually be controlled very small. The DC bus supplies power to the PML, the PL, and the DC/DC converter, their rated powers being 16, 4 and 4 MW, respectively. The DC/DC converter supplies power to the DCZEDS. FIGURE 1Open in figure viewerPowerPoint MVDC ship power system The propulsion motor model adopted in this article is the five-phase motor model of 15-phase induction motor after equivalent simplification. In the case of unsaturated magnetic flux of the motor, the main influencing factor of electromagnetic torque is the fundamental component of current, so the influence of the third harmonic can be ignored in the analysis of electromagnetic torque. The dq-axis decomposition method is used to control the torque and flux linkage independently. Since the fundamental current dominates the system dynamic process, the influence of the third harmonic current can be ignored when controlling and calculating the electromagnetic torque. To release the inertia of the PML, the load characteristics need to be analysed. The flux equations of the stator and rotor are: [ φ s d φ s q φ r d φ r q ] = [ L s 0 L m 0 0 L s 0 L m L m 0 L r 0 0 L m 0 L r ] [ i s d i s q i r d i r q ] (1) The voltage equations of the stator and rotor are: [ u s d u s q 0 0 ] = [ R s + L s p − ω s L s L m p − ω s L m ω s L s R s + L s p ω s L m L m p L m p 0 R r + L r p 0 ω s l L m 0 ω s l L r R r ] [ i s d i s q i r d i r q ] (2) According to Equation (1), the flux of the d-axis of the rotor is: φ r d = L m 1 + τ r p i s d (3)where Lm is the mutual inductance of the fixed rotor, Lr is the rotor leakage inductance. Ls is the stator leakage inductance, isd and isq are the excitation and torque components of the stator current, respectively, ird and irq the excitation and torque components of the rotor current, respectively, Rs is the stator resistance, Rr is the rotor equivalent resistance, φsd, φsq, φrd, φrq represent stator d-axis flux linkage, q-axis flux linkage, rotor d-axis flux linkage, q-axis flux linkage, respectively. τr is the rotor time constant, and τr = Lr/Rr, ωsl is the slip angular velocity, ωs is the synchronous angular velocity. p is differential operator. The electromagnetic torque equation is formulated below: T e = p n L m ( i r d i s q − i r q i s d ) = p n L m L r i s q φ r d (4) T e − T L = J p n d ω r d t (5)where Te is the electromagnetic torque of the motor, TL is the load torque, J is the equivalent inertia of the motor, propeller, and shaft system, the propulsion motor has a larger inertia, pn is the number of pole pairs of the motor, and ωr is the rotating angular velocity of the rotor. From Equations (3) and (4), we can know that the torque and magnetic field of the motor can be controlled separately. The block diagram of the electric propulsion control system is based on the closed-loop speed and the virtual capacitance control is shown in Figure 2. FIGURE 2Open in figure viewerPowerPoint Control diagram of propulsion system When the propeller rotates, it interacts with the water to generate thrust that moves the ship forward. Propeller load torque is expressed as follows: T L = K q ρ n 2 D 5 (6) where n is the propeller speed, the unit is r/s, D is the propeller diameter, the unit is m, ρ = 1025 kg/m3 is the seawater density, Kq is the torque coefficient of the propeller, generally obtained through open water experiments. The eighth-order Chebyshev polynomial fitting is used to obtain Kq. When the speed change is not large, the propeller load TL is basically unchanged. The DC voltage is determined by the unbalanced power of the system and the bus capacitance C which represents the inherent capacitance of the DC bus as shown in Equation (7). Δ P d c = C U d c d U d c d t (7) Δ P d c = Δ P H E S S + Δ P G + Δ P p + Δ P l o a d + Δ P l o s s (8) According to KCL law, the power of the DC bus power supply and load meets Equation (8),, where ΔPdc represents unbalanced power, PG, PHESS, Pp, Pload, and Ploss respectively represent generator set, HESS, PML PL, and transmission line loss power. Udc is the DC bus voltage. Transmission line loss is related to the real-time power flow of the power system. Because of the DC distribution network, the line loss can be controlled within a small range. Here 2% of the total power of a power system is used as a fixed transmission line loss. If the propulsion motor adopts the conventional speed control mode, the propulsion motor will exhibit negative impedance characteristics when the bus voltage changes, it will maintain the output power unchanged. In order to make the PML to participate in the regulation of the bus voltage, the bus capacitance can be equivalently increased by controlling the output power of the PML. The added capacitance is called a virtual capacitance Cv. The added virtual capacitance can slow down the bus voltage change rate. Δ P p = C v U d c d U d c d t = Δ T e ω s (9)where ωs is the synchronous angular velocity. According to the electromagnetic torque equation of the propulsion motor, the right of Equation (9) can be expressed as: Δ T e ω s = pn L m L r Δ i s q φ r d (10) For a given virtual capacitor Cv, the torque component of the stator current Δisq can be obtained by Equation (11), and k is a constant related to the system parameters. Δ i s q = C v U d c d U d c d t p n L m L r φ r d = k C v U d c d U d c d t (11) The Laplace transform of the above formula can obtain the torque component Δisq′ of the stator current. In order to avoid differential signal measurement noise, a low-pass filter is introduced, and ωg is the design corner frequency. Δ i s q ′ ( s ) = k C v U d c s U d c s + ω g (12) In order to avoid frequent adjustment of the electric propulsion system after the introduction of virtual capacitance, when the rate of change of the bus voltage is less than the set threshold m0, no virtual capacitance adjustment is introduced. C v = { 0 | d U d c d t | < m 0 C v 0 | d U d c d t | ≥ m 0 (13) According to Figure 2, keeping the outer loop of the rotation speed unchanged, the inner loop of the q-axis current control is modified according to the algorithm of this paper. In order to realize virtual inertial control, the current control loop needs to respond quickly to current commands. The transfer function of the multiphase inverter is represented as Equation (14), Kpwm and Ts represents the magnification and switch delay factor of the inverter, respectively. G p w m = K p w m T s s + 1 (14) Giu is the open loop transfer function for torque current control inner loop as shown in Equation (15). G i u = 1 L s s + R s (15) The current inner loop can suppress external disturbances and improve the dynamic response speed of the system. It is only related to the parameters of the motor. By simplifying, the transfer function block diagram shown in Figure 3 can be obtained. Among them, Giq is PI current controller, its expression is: G i q = K i p + K i i s = K i p ( τ i q s + 1 ) τ i q s (16) FIGURE 3Open in figure viewerPowerPoint q-Axis current closed-loop equivalent block diagram Here Kip and Kii are the proportional and integral coefficient, respectively, τiq is the integral time constant. PI controller parameter optimization is carried out according to the open loop transfer function of the system, which improves the crossing frequency from 16 Hz to 1.6 kHz as shown in Figure 4, and the phase margin is greater than 45°. FIGURE 4Open in figure viewerPowerPoint q-axis current control loop bode diagram The propulsion motor has a large mechanical inertia, and the response speed of the speed outer loop is slow. The effect of the virtual capacitance control on the speed outer loop is small. In addition, the algorithm does not depend on the central controller. So, it can be easily extended to include IPS with multiple sets of propulsion motors which will be verified in the following sections. 3 PROPOSED CONTROL ALGORITHM The mathematical model of the control algorithm based on fixed virtual capacitance was proposed. It can improve the transient process of DC voltage but cannot take into account the state of the PML and bus voltage. On this basis, this section proposes the use of fuzzy logic to achieve flexible adjustment of virtual inertia. The dynamic virtual inertia is mainly related to three factors, the load level of the PML ki1, the DC bus voltage change rate ki2, and the DC bus voltage deviation ki3. k i 1 = P P N , k i 2 = d U d c d t , k i 3 = U d c − U N (17) where P and PN represent the real-time power and rated power of each PML respectively, and UN represents the rated voltage of the DC bus. The calculation block diagram of dynamic virtual capacitance based on fuzzy logic is shown in Figure 5. FIGURE 5Open in figure viewerPowerPoint Proposed controller block diagram The next step is to determine the membership function. This article makes input ki1, ki2, ki3, and output ΔCv divided into five levels: Negative Big (NB), Negative Small (NS), Zero (ZE), Positive Small (PS), Positive Big (NB), each level membership functions adopts symmetric Gaussian function curve. Fuzzy membership functions as shown in Figure 6. FIGURE 6Open in figure viewerPowerPoint Fuzzy membership functions For the convenience of data processing, the input and output data of the fuzzy logic controller needs to be pre-processed. The variable ki1 data of the PML level is mapped to the interval 0 to 1, the variable ki2 and ki3 data of the voltage deviation and voltage change rate is mapped to the interval −1 to 1, and the dynamic virtual capacitance ΔCv is mapped to the interval 0 to 0.5. At the same time, in order to avoid the dynamic response of the bus voltage being too slow, the maximum value of the virtual capacitance should be limited. The improved virtual capacitor consists of two parts, a fixed value Cv0 and a dynamic virtual capacitor ΔCv with fuzzy logic output. The expressions of fixed value Cv0 and a dynamic virtual capacitor ΔCv with fuzzy logic are as follows: C v = { 0 | d U d c d t | < m 0 C v 0 + Δ C v | d U d c d t | ≥ m 0 (18) C v 0 = 0.2 i s q k U d c s U d c (19) Δ C v max = 0.5 i s q k U d c s U d c (20) Fuzzy rules are the key to dynamic virtual capacitor control. 3.1 Fuzzy rules between ΔCv and ki1, ki3 At a low or high PML level, the virtual capacitors that the propulsion system can provide are at a lower level (0.1–0.2). When the power propulsion system lacks sufficient inertia, the introduction of virtual capacitors can easily lead to the saturation limit of the current loop. The relationship between dynamic virtual capacitor and voltage deviation is relatively easy to understand, the virtual capacitor should be small or zero when the voltage deviation is close to zero, and when the voltage deviation is close to 1 or −1, a larger virtual capacitor is designed to make the voltage to normal values as soon as possible. The rule surface is shown in Figure 7a. FIGURE 7Open in figure viewerPowerPoint Fuzzy rule surface (in p.u.) 3.2 Fuzzy rules between ΔCv and ki2, ki3 The voltage change rate is also a reference factor for the dynamic adjustment of virtual capacitors, and when the voltage deviation is close to 0 and the voltage change rate is large (near 1 or −1), the dynamic virtual capacitor is designed to be 0.25, when the voltage change rate is near 0, the dynamic virtual capacitor is less than 0.25. When the voltage deviation is positive and the voltage change rate is positive, at this time the voltage is rising faster, a large virtual capacitor should be used to slow down this trend. Also, when the voltage deviation is positive and the voltage change rate is negative, the virtual capacitance is designed to be smaller, which can make the voltage recovery speed faster. A positive voltage deviation is similar to the above analysis. Figure 7b shows the rule surface. By designing fuzzy rules, the size of the virtual inertial response can be changed under different conditions. The fuzzy inference system uses the Mamdani-type fuzzy inference algorithm. By performing fuzzy inference calculation according to the set period, the dynamic virtual capacitance ΔCv of the fuzzy control output can be obtained. The bandwidth of the virtual capacitor control outer loop should be much smaller than the bandwidth of the propulsion motor current control inner loop, the calling period of fuzzy logic is set to 300 Hz. 4 RESULTS 4.1 Simulation validation In order to verify the proposed control algorithm, a joint simulation scheme of PSCAD/EMTDC and MATLAB is used. PSCAD packs the data of bus voltage, voltage change rate and PML level (ki1, ki2, ki3) to MATLAB by calling the data interface. After performing fuzzy rule calculation and deblurring in MATLAB, the dynamic virtual capacitance data is transmitted to PSCAD. Among them, the simulation step is controlled by PSCAD and set to 20 us. The main simulation parameters are shown in Table 1 according to [20]. TABLE 1. MVDC and control system parameters Item Value Item Value L 150.1 ωg 700 Hz τiq 0.1905 s m0 0.2 TS 1e−3 s Pg 20 MW C 0.1 F Pn 2 Ls 0.0119 (p.u.) UN 5000 V Rs 0.0609 (p.u.) Pload 16 MW 4.1.1 Constant virtual inertial control under PL Set the simulation conditions as follows: free navigation starts from 0 s, and accelerates to the set speed of 120 r/min within 60 s 4 MW PL connected at 60 s and disconnected at 62 s. The transient response of the system state with and without virtual capacitor control can be seen from Figure 8a. Bus voltage fluctuations severely affected by the PL with no virtual capacitor, the minimum and maximum value of DC bus voltage are 4930 and 5065 V, respectively. As the virtual capacitor increases, the amplitude of the bus voltage change becomes smaller which indicating that the virtual inertial control has an obvious effect of suppressing the bus voltage fluctuation. From the speed curve of the propulsion motor shown in Figure 8b, the larger the virtual capacitance, the more obvious the speed change, but still around 120 r/min. The response time scale of the state variable of speed is greater than the electromagnetic transient, which belongs to electromechanical transient. The change of the electromagnetic power of the propulsion motor increases with the increase of the virtual capacitance as shown in Figure 8c. When Cv is set to 1, the maximum change of the electromagnetic power of the propulsion motor is 1.5 MW. From the ship speed curve in Figure 8d, virtual capacitor control has almost no effect on the ship propeller rotate speed, because the time scale of the ship's speed response is much larger than the electromagnetic transient process. This also shows the superiority of the control strategy proposed in this article. FIGURE 8Open in figure viewerPowerPoint (a) DC bus voltage with constant Cv (b) Propeller speed (c) Propulsion load power (d) Propeller rotate speed 4.1.2 Dynamic virtual inertial control under PL After the system reaches the steady state, fixed virtual capacitance control and dynamic virtual capacitance control are added, respectively. The fixed virtual capacitance is 0.46 and the dynamic virtual capacitance is obtained by fuzzy logic defuzzification algorithm. Comparing the MVDC bus voltage curves shown in Figure 9a, it is obvious that the local minimum and maxima values of the bus voltage drop and rise are basically the same, which are 4950 and 5050 V, respectively, and the bus voltage recovery speed is faster when the dynamic virtual capacitor is adopted which verifies the effectiveness of the proposed fuzzy control algorithm. The change curve of the dynamic virtual capacitance is consistent with the designed fuzzy rules, and the virtual capacitance output by the fuzzy algorithm during voltage recovery process is significantly lower than the fixed virtual capacitance as shown in Figure 9b. FIGURE 9Open in figure viewerPowerPoint (a) DC bus voltage (b) Constant and dynamic Cv 4.1.3 Dynamic virtual inertial control under different PML levels Keep other conditions unchanged and investigate the response of the PML at different load levels. The simulation results are shown in Figure 10. When the load level is 0.5, the PML has the largest margin for virtual inertia adjustment. In the transient process of load input and removal, when the load level is 0.5, the dynamic virtual capacitance of the propulsion motor is approximately 22.2% higher than when the load level at 0.3, and the power response of PML is 17.2% larger than the load level of 0.3. This corresponds to the actual working conditions and the designed fuzzy rules, which verifies the correctness of the designed fuzzy rules. It is further proved that the load level of the PML is not conducive to the improvement of virtual inertia when the load level is too low or too high. The maintenance of PML level at a reasonable moderate level under the cruise conditions of the ship will help to suppress the bus voltage fluctuation caused by PL. FIGURE 10Open in figure viewerPowerPoint (a) PML power (b) Dynamic Cv under different PML level 4.1.4 Dynamic virtual inertial control under different PL levels Keep the remaining parameters of the system unchanged, the load level of the PML is 0.3, and the response curve of the main state variables of the system when the value of the PL is set to 4 and 2 MW is shown in Figure 11. The difference in PL power mainly affects the change rate of the MVDC bus voltage. According to the designed fuzzy rules, the greater the voltage change rate and the same sign as the voltage deviation, the larger the fuzzy logic dynamic virtual capacitance. As can be seen from Figure 11, the greater the PL, the greater the power response of the PML. When the PL power is 4 MW, the power response of the PML can reach 2 MW. When the PL power is 2 MW, the power response of the PML can reach 1 MW. After adding the virtual capacitor control, the bus voltage drop change amplitude is under 2% of rated bus voltage. At the same time, the maximum value of the dynamic virtual capacitance does not exceed the upper limit of 0.6, which is consistent with the fuzzy rules of the design. FIGURE 11Open in figure viewerPowerPoint (a) DC bus voltage under different disturbance (b) PML power under different disturbance (c) Dynamic Cv under different disturbance 4.1.5 Dynamic virtual inertial control with different PML Ships with IPS generally contain two or more main propulsion motors and two auxiliary propulsion motors as shown in Figure 1. The control algorithm designed in this article can achieve distributed control functions without communication. Each propulsion motor can participate in the bus voltage regulation according to its own capacity and on-grid power. Figure 12 shows the simulation results when take two propulsion motors of the same capacity and different load rates. It can be seen that the two propulsion motors participate in the bus voltage regulation according to their respective capacities and load levels. Among them, the load rate of 1# propulsion motor is close to half of rated power. Therefore, the response of dynamic virtual capacitance and transient power is more obvious than that of 2# propulsion motor. It is verified that the control algorithm proposed has distributed coordination of multiple propulsion motors features. In addition to the coordination between the propulsion motors, the flexible virtual inertial control of the propulsion motors can also cooperate with the HESS to enhance the inertia of the bus voltage. In Figure 12c, when multiple propulsion loads work at the same time, the power quality improvement effect of bus voltage is better than that of single propulsion load. At the same time, the improvement effect of bus voltage is also related to the capacity and load rate of propulsion load. FIGURE 12Open in figure viewerPowerPoint (a) Dynamic Cv with two propulsion in different load level (b) Two PML power under the same load disturbance (c) DC bus voltage under signal and multi-PML 4.2 Experimental validation The proposed controller is validated using the processor in the loop (PIL) technique by embedding the algorithm on DSP TMS320F28335 board shown in Figure 13. The control algorithm for the virtual inertial control based on fuzzy logic and calculation of voltage change rate is converted to a binary file and is embedded on the TMS320F28335 board [21]. The fuzzy reasoning and calculation process in fuzzy logic control is done offline, and by making fuzzy query table, fuzzy reasoning can be realized in the microcontroller quickly. In order to be more consistent with the actual system, we added measurement noise in the simulation to verify that the fuzzy logic-based distributed virtual inertial control meets the requirements of real-time, accuracy and correctness. The experimental verification system we built is shown in Figure 13. FIGURE 13Open in figure viewerPowerPoint Experimental verification platform Taking PL continuous operation as an example, hardware-in-the-loop verification is performed. In order to verify the correctness and robustness of fuzzy logic operation in dynamic virtual inertial control algorithm, the period of the periodic PL is set to 4 s, and the duty cycle is 50%. The simulation results are shown in Figure 14. The red curve represents the system voltage, dynamic virtual capacitance Cv and PML power obtained by off-line simulation, and the blue curve represents the data obtained by the controller hardware in the loop experiment. From Figure 14a, it can be seen that the controller operation results are basically consistent with the simulation results after adding virtual measurement noise, which verifies that the algorithm run in microcontroller is correct and robust. It can be clearly seen from Figure 14b,c that the offline simulation results of DC bus voltage and PML power are basically consistent with the hardware-in-the-loop simulation results, and the error is within the allowable range, which lays the foundation for the next physical verification and application. FIGURE 14Open in figure viewerPowerPoint (a) Dynamic Cv (b) DC bus voltage (c) PML power 5 CONCLUSION Without adjusting the propulsion load power, the switching of the PL can cause the MVDC bus voltage with small capacitance to change rapidly. This articel proposes an adaptive virtual inertia control strategy to increase the equivalent inertia of the MVDC bus by introducing virtual inertia to the propulsion load. It can not only mitigate the mutation rate and fluctuations of the DC voltage and improve the power supply quality but also has the following advantages: (1) By simply improving the current control loop of the existing propulsion load controller, the electric propulsion load can simulate a given virtual capacitance without adding additional controllers. Through the introduction of fuzzy logic, variable virtual inertia can be adjusted flexibly according to the system states to meet the requirements of power quality. The dynamic virtual capacitance control algorithm based on fuzzy logic considers the voltage and voltage change rate of the MVDC bus and the load rate of the PML. (2) The propulsion load has a large capacity, and the ship has a large inertia. The proposed virtual inertial control has little effect on the speed regulation performance of the electric propulsion system. It only changes the transient power of the propulsion load and does not affect the steady-state power. Multiple propulsion loads can adaptively respond to virtual inertia adjustment without communication. (3) It can reduce the capacity configuration of energy storage, thereby saving cost and space. In addition, it can be combined with the control of the energy storage system to improve the DC bus voltage stability which will be studied in the future. ACKNOWLEDGEMENTS This work was supported in part by the Major Program of National Natural Science Foundation of China under Grant 51522706 and Grant 51607187 and in part by the National Key Basic Research Program 973 Project of China under Grant 613294. REFERENCES 1Weiming, M.: A survey of the second-generation vessel integrated power system. APAP 2011 – Proceedings: 2011 International Conference on Advanced Power System Automation and Protection. 2, 1293– 1302 (2011) 2Weiming, M.: Development of vessel integrated power system. In: 2011 International Conference on Electrical Machines and Systems, ICEMS, pp. 1– 12 (2011) 3Doerry, N.: Next generation integrated power systems NGIPS technology development Roadmap, pp. 120 (2007) https://www.researchgate.net/publication/235029761_Next_Generation_Integrated_Power_System_NGIPS_Technology_Development_Roadmap 4Steurer, M., et al.: Investigating the impact of pulsed power charging demands on shipboard power quality. IEEE Electric Ship Technologies Symposium, ESTS, 315– 321 (2007) 5Wang, G., et al.: Stability analysis of integrated power system with pulse load. Int. J. Electr. Power Energy Syst., 105462 (2020) 6Vu, T.V., et al.: Predictive control for energy management in ship power systems under high power ramp rate loads. IEEE Trans. Energy Convers. 32(2), 788– 797 (2017) 7Liu, S., Su, P., Zhang, L.: A nonlinear disturbance observer based virtual negative inductor stabilizing strategy for DC microgrid with constant power loads. Energies. 11(11), 59728– 59741 (2018) 8Zhu, L., et al.: Decentralized linear quadratic Gaussian control of multi-generator MVDC shipboard power system with constant power loads. 2013 IEEE Electric Ship Technologies Symposium, ESTS, 308– 313 (2013) 9Zhai, X., et al.: Application of feed forward control in the excitation system of pulse rectified generator. Trans. China Electrotech. Soc. 28(7), 151– 156 (2013) 10Alafnan, H., et al.: Stability improvement of DC power systems in an all-electric ship using hybrid SMES/battery. IEEE Trans. Appl. Supercond. 28(3), 1– 6 (2018) 11Wang, Y., et al.: Adjustable inertial response from the converter with adaptive droop control in DC grids. IEEE Trans. Smart Grid. 10(3), 3198– 3209 (2019) 12Faddel, S., et al.: Coordination of hybrid energy storage for ship power systems with pulsed loads. IEEE Trans. Ind. Appl. 56(2), 1136– 1145 (2020) 13Liu, S., et al.: A virtual negative inductor stabilizing strategy for DC microgrid with constant power loads. IEEE Access. 6, 59728– 59741 (2018) 14Soliman, H.M.: Improve the performance characteristics of the IPMSM under the effect of the varying loads. IET Electr. Power Appl. 13(12), 1935– 1945 (2019) 15Fu, Y., et al.: Controllable inertial control strategy of rotating motor in DC distribution network. Electric Power Automat. Equip. 38(10), 32– 38 (2018) 16Du, W., et al.: Stability criterion for cascaded system with constant power load. IEEE Trans. Power Electron. 28(4), 1843– 1851 (2013) 17Liu, X., Forsyth, A.J., Cross, A.M.: Negative input-resistance compensator for a constant power load. IEEE Trans. Ind. Electron. 54(6), 3188– 3196 (2007) 18Domaschk1, L.N., et al.: Coordination of large pulsed loads on future electric ships. IEEE Trans. Magn. 43(1), 450– 455 (2007) 19Shi, J., Amgai, R., Abdelwahed, S.: Modelling of shipboard medium-voltage direct current system for system level dynamic analysis. IET Electr. Syst. Transp. 5(4), 156– 165 (2015) 20Wang, G., Xiao, R., Wu, X.: Analysis of integrated power system with pulse load by periodic orbit. IEEE Trans. Plasma Sci. 47(2), 1345– 1351 (2019) 21Cheng, S., et al.: Control strategy for permanent magnet synchronous motor with contra-rotating rotors under unbalanced loads condition. IET Electr. Power Appl. 9(1), 71– 79 (2015) Volume15, Issue4April 2021Pages 453-462 FiguresReferencesRelatedInformation