Available online at www.sciencedirect.com
ScienceDirect
Energy Reports 8 (2022) 130–137
www.elsevier.com/locate/egyr
2021 7th International Conference on Advances in Energy Resources and Environment
Engineering (ICAESEE 2021), November 19–21, 2021, Guangzhou, China
Modular modeling method and power supply capability evaluation for
integrated hydrogen production stations of DC systems
Qi Wua,c , Qiang Yaob , Li Dinga,c , Wei Peia,c , Wei Denga,c ,∗
a
Institute of Electrical Engineering Chinese Academy of Sciences, No. 6, Zhongguancun North 2nd Road, Haidian District, Beijing 100190, China
State Grid Inner Mongolia East Electric Power Integrated Energy Service Co., Ltd, Erdos East Street, Saihan District, Hohhot, Inner Mongolia
Autonomous Region 010010, China
c University of Chinese Academy of Sciences, No. 19, Yuquan Road, Shijingshan District, Beijing 100049, China
b
Received 9 February 2022; accepted 8 March 2022
Available online 24 March 2022
Abstract
Low-voltage DC distribution system has many advantages, such as facilitating the access of DC loads and distributed
energies and improving the network’s stability. It has become a new idea for integrated hydrogen production stations. Power
supply capacity and small-signal stability are important indexes to evaluate a low-voltage DC integrated system. Based on the
master–slave control mode, this paper selects the typical star structure as the research object, constructs the system transfer
function through the scalable modular modeling method, and further evaluates the impact of the high-order DC hydrogen
production station integrated system on the hydrogen production capacity under the changes of the line length and master
station position. The results show that the hydrogen production capacity of the system decreases gradually with the main
station moving from side to inside. Finally, a practical example is analyzed by MATLAB/Simulink simulation to verify the
accuracy of the theory. This study can provide an effective theoretical method for the structure optimization and integrated
parameter design of low-voltage DC system.
© 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the scientific committee of the International Conference on Advances in Energy Resources and Environment
Engineering, ICAESEE, 2021.
Keywords: Low-voltage DC system; Master–slave control; Small-signal stability; Power supply capacity; Constant power characteristics; Transfer
function
1. Introduction
The world is currently in an important stage of the energy transition. Hydrogen production from renewable energy
can promote the development of the existing energy system to a greener and more optimized direction and is an
effective means to solve prominent problems such as energy shortage and serious environmental pollution [1]. To
∗ Corresponding author at: Institute of Electrical Engineering Chinese Academy of Sciences, No. 6, Zhongguancun North 2nd Road, Haidian
District, Beijing 100190, China.
E-mail address: dengwei@mail.iee.ac.cn (W. Deng).
https://doi.org/10.1016/j.egyr.2022.03.073
2352-4847/© 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http:
//creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the scientific committee of the International Conference on Advances in Energy Resources and Environment
Engineering, ICAESEE, 2021.
Q. Wu, Q. Yao, L. Ding et al.
Energy Reports 8 (2022) 130–137
reduce conversion energy consumption, the integration of multiple hydrogen production stations through DC system
will become the development trend of the future power grid.
Although the DC system has obvious advantages in integrated hydrogen production stations, the characteristics of
weak damping and low inertia are particularly prominent because the DC system contains a large number of voltage
source PWM converters (Voltage Source Converter, VSC) and hydrogen production power DC/DC converters [2].
When the system adopts master–slave control mode, the hydrogen production station under constant power control
mode presents negative impedance characteristics [3], which worsens the problem of voltage fluctuation and even
leads to the instability of the system [4,5]. The above problems not only limit the efficient utilization of hydrogen
energy, but also limit the safe and stable operation of the system. Therefore, many scholars have conducted in-depth
research on the stability of DC system integration in renewable energy/ hydrogen energy.
Ref. [6] establishes the small-signal model of the system under typical grid structures, and studied the influence
of system parameters on system stability under different grid structures based on the changes of participation factors
and system characteristic roots. Ref. [7] analyzes the influence of controller parameters on the stability of isolated
DC microgrid. Starting from the linearized Thevenin equivalent model of the converter station, Ref. [8] studies the
resonance characteristics and stability of the DC grid, and designs the parameters of the outer power loop damping
controller by feeding back the DC current output by the converter. Ref. [9] proposes three different topologies for
DC microgrid, and carries out modeling and stability analysis, focusing on the influence of the line impedance.
Ref. [10] reveals that the low damping LC link composed of the equivalent reactance of the line and the voltage
stabilizing capacitor of the converter in the DC microgrid will interact with the output impedance of the VSC,
resulting in system oscillation instability.
Generally speaking, the existing research focuses on the modeling method, stability judgment method and
topology of multi-terminal DC system. However, with the continuous increase of the scale of hydrogen production
station, the traditional small-signal modeling method for stability analysis will face a series of bottleneck problems
such as high order of system state matrix and difficult to expand, resulting in huge computational workload for
system stability analysis. Therefore, the stability analysis method and scene expansion need to be further deepened.
In view of the above problems, this paper uses transfer function to study the stability characteristics of the star
system under the master–slave control mode. It mainly includes: the second part introduces the system structure,
equivalent circuit, and master–slave control strategy; the third part presents the method of modular construction of
the transfer function of the system based on the master–slave control strategy; the fourth part sets up several typical
integration scenarios, and analyzes the stability differences of different integration scenarios under the star system;
the fifth part designs the most stable integration scenario for the case, and verify the accuracy of theoretical analysis
through Simulink simulation; the sixth part is the conclusion of this article.
2. System description
Fig. 1(a) shows the schematic diagram of star low-voltage multi-terminal DC system, in which the AC system is
connected to the DC network through VSC N , and the hydrogen production station 1 to hydrogen production station
N-1 are interconnected through DC bus. In addition, the DC bus can be connected to renewable energy such as
photovoltaic and wind power, energy storage devices and various DC loads.
The AC system is set as an ideal three-phase symmetrical power grid. VSC is the main device to control DC
voltage in multi-terminal DC system, and its control characteristics play a leading role in the stability of the system.
For VSC, hydrogen production stations and the DC network, the corresponding equivalent circuit is constructed by
ignoring the power loss, as shown in Fig. 2.
Among them, VSC N represents the master station VSC, ia N , ibN , icN , Ua N , UbN , UcN respectively represent the
AC side A, B, C phase current of the main station VSC, and the grid voltage of A, B, C phase. Rs N , Ls N , Ps N , Qs N
respectively represent the equivalent resistance, equivalent inductance, active power, and reactive power of the AC
side of the master station VSC, while Uoa N , UobN , UocN represent the A, B and C phase bridge voltage of the AC
side of the master station VSC; PdcN , idcN , UdcN , C N respectively represent the DC power, output current, output
voltage and DC side capacitance of VSC. Pn , Udcn , Cn respectively represent the integration power, input voltage
and DC side capacitance of the nth hydrogen production station. Rn , Ln , in respectively represent the line resistance,
line inductance, DC line current of the nth hydrogen production station.
The system control strategy adopted in this paper is shown in Fig. 3. Among them, UdcN,ref represents the
reference value of the output voltage on the DC side of the master station VSC. Ud N represents the d-axis component
131
Q. Wu, Q. Yao, L. Ding et al.
Energy Reports 8 (2022) 130–137
Fig. 1. Schematic diagram of low voltage multi-terminal DC integrated system.
Fig. 2. Schematic diagram of system equivalent circuit. (a) the equivalent circuit of master station; (b) the equivalent circuit of hydrogen
production station interconnected to DC grid.
Fig. 3. VSC control strategy.
of UaN , UbN , UcN (when the AC system is an ideal power grid, Ud N is regarded as a constant value); id N represents
the d-axis component of iaN , ibN , icN ; Uod N represents the d-axis component of UoaN , UobN , UocN ; id N ,ref represents
the reference value of id N ; kpvN , kivN represent the outer loop PI parameters of the master station VSC, and kpiN , kiiN
represent the inner loop PI parameters of the master station VSC respectively. Uq N represents the q-axis component
of UaN , UbN , UcN (when the AC system is an ideal power grid, Uq N is 0); iq N represents the q-axis component of
iaN , ibN , icN ; Uoq N represents the q-axis component of UoaN , UobN , UocN ; iq N ,ref represents the reference value of
iq N . Because active power is mainly transmitted in DC systems, iq N ,ref is usually set to 0. The master station VSC
adopts DC voltage control strategy to keep the voltage of DC network constant; each hydrogen production station
adopts constant power control, so it does not directly participate in the regulation of DC voltage, and shows constant
power characteristics when working, which can be equivalent to constant power load (Constant Power Load, CPL).
3. Modular modeling method
In order to facilitate the analysis, VSC N is set as the master station, for low-voltage multi-terminal DC systems,
the process of modularizing the transfer function model of N-terminal system is proposed, as shown in Fig. 4.
132
Q. Wu, Q. Yao, L. Ding et al.
Energy Reports 8 (2022) 130–137
Fig. 4. Flow chart of modular modeling..
3.1. Modeling of master station and single hydrogen production station
The transfer function of the DC voltage control loop of the master station VSC N satisfies [11]:
(
)
k pv N s + kiv N (1 − τ0 s)
G master (s) = K
s (τi s + 1)
(1)
2
N −4Rs N Ps N 0
s N Ps N 0
, K = 3Ud 2U
, τi is the setting coefficient of the inner current loop.
Among τ0 = 3U 2L2 −4R
d N UdcN
dN
s N Ps N 0
Considering the constant power control of hydrogen production station, a single hydrogen production station is
equivalent to CPL model. Req,n is the equivalent constant power impedance of hydrogen production station n, which
satisfies:
(Udcn )2
Req,n = −
(2)
Pn
3.2. Modular splicing
The module of hydrogen production station n satisfies KCL equation:
(
)
dUdcn
Udcn
1
i n = Cn
+
= Cn s +
Udcn
dt
Req,n
Req,n
Bring the Eq. (3) into the KVL equation can get:
di n
UdcN = L n
+ i n Rn + Udcn
dt
(
)
1
= L n si n + i n Rn + 1/ Cn s +
in
Req,n
Zn is the equivalent impedance of hydrogen production station n, which satisfies:
(
)
UdcN
1
Zn =
= L n s + Rn + 1/ Cn s +
in
Req,n
133
(3)
(4)
(5)
Q. Wu, Q. Yao, L. Ding et al.
Energy Reports 8 (2022) 130–137
Conducting overall equivalence of 1 to N − 1 modules of each parallel hydrogen production station, the overall
equivalent impedance Zall is obtained, which meets the requirements:
(
)
1
1
1
1
Z all = 1/
+
+ ··· +
+ ··· +
(6)
Z1
Z2
Zn
Z N −1
Connecting the overall equivalent impedance Zall of the hydrogen production stations to the DC line at the
master station side, the next level equivalent impedance Z can be obtained by connected Zall in parallel with the
DC capacitor C N of the master station, and then connecting Z in series with Gmaster (s), the overall transfer function
of the system can be obtained (see Fig. 5):
(
)
k pv N s + kiv N (1 − τ0 s)
1
G system (s) = K
(7)
s (τi s + 1)
C N + 1/Z all
Fig. 5. Modular splicing diagram of star structure.
4. Comparative analysis of power supply capacity in different integration scenarios
This paper selects a typical six-terminal DC system with five hydrogen production stations as the research object.
The hydrogen production stations are numbered 1 to 5, and VSC6 is the master station. The system transfer functions
corresponding to the typical structures of the low-voltage multi-terminal DC system in Fig. 1 are established by
using the modular splicing method in Section 3, and the bode diagrams are drawn respectively. In order to compare
and analyze the systems, the parameters and changing trends of each hydrogen production station are set to be
consistent. There are three main integration scenarios, as shown in Figs. 6–8. Where, l1 , l2 , l3 , l4 , l5 are the DC side
lines of each hydrogen production station, respectively. The length can be calculated from the distance l between
hydrogen production stations. The benchmark parameters of converter stations and hydrogen production stations
are shown in Table 1.
Considering the symmetry, Fig. 9 only describes the characteristics of the multi-terminal DC system corresponding to the three integration scenarios, and the remaining three scenarios are similar, and will not be repeated. It
can be seen from Fig. 9 that as the transmission power of a single hydrogen production station P H continues to
increase, the high frequency gain of the system continues to increase, and the phase angle margin and amplitude
margin continue to decrease. When P H reaches the upper limit, the phase angle margin Pm is close to 0◦ , and the
amplitude margin Gm is close to 1, and the system reaches the stable operation boundary. According to Fig. 9, the
upper limit of the integrated power for different integration scenarios can be obtained, as shown in Table 2.
The changes in the integration scenario are mainly reflected in the length of the DC side line of each hydrogen
production station, and the length of the transmission line is an important parameter that affects the stability of the
system and the power regulation capability. By comparing and analyzing the data of each scenario in Table 2, it can
be found that as the length of the DC side line of the hydrogen production station tends to be balanced (the main
station changes from side to inner), the power supply capacity of the system gradually decreases. It can be seen
from Fig. 9 that, except for the resonance peak, the overall shape of the bode diagram does not change significantly
in different scenarios.
134
Q. Wu, Q. Yao, L. Ding et al.
Energy Reports 8 (2022) 130–137
Fig. 6. Integration scene 1.
Fig. 7. Integration scene 2.
Fig. 8. Integration scene 3.
Fig. 9. Comparison of system characteristics of different integration scenes. (a) scene 1; (b) scene 2; (c) scene 3.
Table 1. Parameters of VSC, hydrogen production station and DC network.
Parameter
Value
Parameter
Value
Parameter
Value
P1,2,3
Rs6
L4,5
R4,5
C4,5
k pv6
l
250 kW
0.1 m
0.05 mH
0.018 
800 µF
1.51
0.2 km
P4,5
Ls6
L6
R6
C6
kiv6
250 kW
0.35 mH
0.005 mH
0.0018 
3500 µF
25
P6
L1,2,3
R1,2,3
C1,2,3
τi
Udc6
1.25 MW
0.05 mH
0.018 
800 µF
1.67 × 10−4
750 V
Table 2. Upper limit of power regulation for different integration
scenes.
Integration scenes
Parameter
Value
Scene
Scene
Scene
Scene
Scene
Scene
PH
PH
PH
PH
PH
PH
240
217
195
195
217
240
1
2
3
4
5
6
135
kW
kW
kW
kW
kW
kW
Q. Wu, Q. Yao, L. Ding et al.
Energy Reports 8 (2022) 130–137
5. Simulation and verification
5.1. Case 1
The integration scene 3 with the weakest transmission capability is performed simulation on the MATLAB/Simulink platform to obtain the power and voltage waveforms, as shown in Fig. 10. It can be seen that the
total upper limit of the integrated power of the five hydrogen production stations is 980 kW, which is basically the
same as the result of scene 3 in Table 2. The modular modeling method and stability analysis have been verified
accordingly.
Fig. 10. Simulation waveform of integration scene 3.
5.2. Case 2
The integration scene 1 with the best transmission capability is performed simulation on the MATLAB/Simulink
platform to obtain the power and voltage waveforms, as shown in Fig. 11. It can be seen that the total integrated
power upper limit of the five hydrogen production stations is 1200 kW, which is basically consistent with the results
of scene 1 in Table 2. The modular modeling method and stability analysis have been verified accordingly.
6. Conclusions
Based on the master–slave control strategy, this paper uses the modular modeling method to build the
system transfer function of the multi-terminal DC system integrating hydrogen production stations under the star
structure. Compared with the eigenvalue analysis method [12,13], this method can conveniently reflect the stability
characteristics of high-order system, avoiding the construction of high-order matrix, and expand flexibly to adapt to
the change of the number of system terminals. So the effects of different integration scenes (different master station
location and line length) on system stability are conveniently studied. The specific conclusions are as follows:
(1) As the position of the master station moves from the side to the inner, the upper limit of the system power
transmission capacity is significantly reduced. As the lengths of parallel lines gradually approach, the decreasing
trend becomes more obvious;
(2) The influence of the above arrangement and line parameter changes on the system is mainly reflected in the
reshaping of the system impedance, the resonance points and the resonance peak of the Bode diagram.
On the one hand, the control method also includes various droop control strategies and the topological structure
of the multi-terminal DC system is diverse. On the other hand, the distributed energy and energy storage devices in
the DC system can participate in coordinated control, which will significantly affect the operating characteristics of
the system. Therefore, in the next research, different types of control strategies, topological structures, and converter
equipment will be considered to the stability analysis of hydrogen production stations integrated low-voltage
multi-terminal DC system.
136
Q. Wu, Q. Yao, L. Ding et al.
Energy Reports 8 (2022) 130–137
Fig. 11. Simulation waveform of integration scene 1.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could
have appeared to influence the work reported in this paper.
Acknowledgments
This research was supported by Major science and technology projects in Inner Mongolia Autonomous Region,
China (2021ZD0040).
References
[1] Macias Fernandez A, Kandidayeni M, Boulon L, et al. An adaptive state machine based energy management strategy for a multi-stack
fuel cell hybrid electric vehicle. IEEE Trans Veh Technol 2020;69.1(2020):220–34.
[2] Lin P, Zhang C, Wang J, et al. On autonomous large-signal stabilization for islanded multibus DC microgrids: A uniform nonsmooth
control scheme. IEEE Trans Ind Electron 2020;67.6(2020):4600–12.
[3] Rahimi AM, Emadi A. Active damping in DC/DC power electronic converters: a novel method to overcome the problems of constant
power loads. IEEE Trans Ind Electron 2009;56.5(2009):1428–39.
[4] Kongpan A, Theppanom S, Serhiy B, et al. Adaptive stabilization of uncontrolled rectifier based AC–DC power systems feeding
constant power loads. IEEE Trans Power Electron 2018;33.10(2018):8927–35.
[5] Ali E, Alireza K, Claudio H, et al. Constant power loads and negative impedance instability in automotive systems: definition, modeling,
stability, and control of power electronic converters and motor drives. IEEE Trans Vehicular Technol 2006;55.4(2006):1112–25.
[6] Xiaorong Zhu, Zheng Li, Fanqi Meng. Stability analysis of DC microgrid based on different grid structures. Trans China Electrotechn
Soc 2021;36.1(2021):166–78.
[7] Kotra S, Mishra MK. Design and stability analysis of DC microgrid with hybrid energy storage system. IEEE Trans Sustain Energy
2019;10.3(2019):1603–12.
[8] Li Y, Tang G, Wu Y, et al. Modeling, analysis and damping control of DC grid. Proc CSEE 2017;37.12:3372–82.
[9] Pang SZ, Nahid-Mobarakeh B, Pierfederici S, et al. DC microgrid topologies and stability analysis for electrified transportation systems.
In: IEEE 18th International Power Electronics and Motion Control Conference (PEMC). 2018, p. 1055–60.
[10] Guo L, Feng Y, Li X, et al. Stability analysis and research of active damping method for DC microgrids. Proc CSEE
2016;36.4(2016):927–36.
[11] Deng W, Pei W, Wu Q, et al. Analysis of interactive behavior and stability of low voltage multi-terminal DC system under droop
control modes. IEEE Trans Ind Electron 2021. http://dx.doi.org/10.1109/TIE.2021.3095803.
[12] Eskandari M, Li L, Moradi MH, et al. A control system for stable operation of autonomous networked microgrids. IEEE Trans Power
Deliv 2020;35.4(2020):1633–47.
[13] Sharma RK, Mishra S, Pullaguram D. A robust H∞ multivariable stabilizer design for droop based autonomous AC microgrid. IEEE
Trans Power Syst 2020;35.6(2020):4369–82.
137