Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid

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Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid Yong Zhang, Wei Wei* College of Electrical Engineering, Zhejiang University, Hangzhou, 310027, China

highlights We mainly developed a decentralized coordination control strategy among the generation, storage, hydrogen production unit, fuel cell in the island dc microgrid. The main highlights are listed as follows.
Energy conversion efficiency of HPU is derived.
Efficiency adaptive control strategy for HPU is designed.
SoC and the instantaneous charging or discharging powers for battery are considered.
PeV droop control strategy of PV generators is designed.

article info

abstract

Article history:

Renewable energy sources (RESs) have been limited to connect to main grid because of

Received 23 November 2019

their inherent disadvantages such as the fluctuation and intermittence of the output

Received in revised form

power, the inconsistency with load curve and the impact on the relay protection. Hydrogen

5 January 2020

production unit (HPU) can address the above issues because it can achieve large-capacity

Accepted 8 January 2020

and long-term power absorption, and requires not much of the RESs. In this paper, an

Available online xxx

adaptive coordination control strategy is proposed in the islanded DC microgrid containing PV generators, storage battery, fuel cell and HPU. As for HPU, the energy conversion effi-

Keywords:

ciency from electric energy to hydrogen energy of HPU is derived and it reveals that there

PV generator

exists a peak value in the efficiency curve. Then an efficiency adaptive control is proposed

Storage battery

to adjust the power absorption by regulating the efficiency point based on the dc bus

Fuel cell

voltage. As for storage battery, the state of charge (SoC) and the instantaneous charging

Hydrogen production unit

and discharging power of the battery are considered, which can avoid the battery being

Energy conversion efficiency

overused or damaged. As for PV generator, the designed PV controller can adaptively

Adaptive coordination control

regulate its output power from the maximum power point to the reference power point. As for fuel cell, it is designed that the fuel cell starts to supply power in low-SoC condition with constant power control strategy. Finally, the stability of the coordination control strategy is analyzed based on Nyquist stability criterion and the control effectiveness is verified with simulation and experimental results. © 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

* Corresponding author. E-mail address: [email protected] (W. Wei). https://doi.org/10.1016/j.ijhydene.2020.01.058 0360-3199/© 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Zhang Y, Wei W, Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.058

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Introduction Since the traditional thermal power plants consume a lot of unsustainable and limited coal and produce a great number of harmful gas that would pollute the air and damage the living environment, the renewable energy sources such as solar energy, wind energy, tidal energy have been explored for decades [1e4]. Especially, photovoltaic (PV) generation has been expanded rapidly because of the advantages of flexibility and scalability, the breakthrough of the solar energy conversion technology, and the government's science and technology incentive policy [5e7]. It is reported by the Polaris Solar Photovoltaic website that the total installed PV capacity is about 500 GW around the world in 2018. However, there are some inherent shortcomings such as fluctuation and intermittence of the output power, the inconsistency between power characteristics and load characteristics, the impact of the complex power flow on the reliability of the relay protection, which will limit its connection to the main grid and lead to serious photovoltaic curtailment phenomenon [8e10]. The curtailment rate of the PV generators in northwest China is more than 10% in 2018, which has caused lots of economic losses. Storage technologies can effectively solve the problem of the PV power curtailment. There are various kinds of energy storage methods, such as mechanical energy storages including pumping water and compressing air as well as rotating flywheels [11e13], electrical energy storages including supercapacitors and superconductive materials [14,15], thermal energy storage including phase-change materials [16], electrochemical energy storages including leadacid battery and lithium-ion battery [17,18] and so on. Generally, the abovementioned methods have both advantages and disadvantages. For example, the pumped-storage method can absorb large electric power, but it is difficult to select a suitable location, besides, the long investment cycle and great evaporation losses should be considered. Take another example, the lead-acid battery is the most widely used storage method nowadays with the advantage of high efficiency. But it has the disadvantages of short life span and its available capacity will degrade gradually. In summary, the abovementioned methods intend to store electricity or convert electrical energy into other kinds of energy. They can solve the electricity storage problems to some extent and have been applied in practical engineering, but there also exist some unsatisfying shortcomings. Hence, it is necessary to develop the new energy storage technique. Hydrogen energy technology is regarded as an important support for the large-scale development of smart grid and renewable energy generation, and hydrogen gas is increasingly becoming the hub of multiple energy connection and obtaining the focus of energy departments in many countries [19,20]. For one reason, hydrogen production unit (HPU) can achieve large-capacity and long-term consumption of the electric energy produced by the renewable energy sources. For another reason, HPU does not require very much about the power quality and can tolerate the disadvantages of the renewable energy sources. In addition, hydrogen can be applied in many aspects such as hydrogen metallurgy, hydrogen irrigation, rocket fuel, hydrogen treatment, and fuel

cell as shown in Fig. 1 [21e24], which can replace traditional fossil fuels and reduce environmental pollution. Therefore, the application of HPU in the distributed microgrid can effectively compensate the defects of renewable energy sources. The electrolysis techniques mainly include the high temperature solid oxide electrolyser and the alkaline electrolyser [25,26]. The former owns the advantage of high energy conversion efficiency, but it cannot be widely applied because of the strict working condition. By contrast, the efficiency of the alkaline electrolyser technology is slightly lower, but it has been deeply researched and widely applied because of the easy implementation. Øystein [27] analyzed the influence of the temperature and the cathode plate area on the terminal voltage based on the experimental data. Moreover, the empirical equation was constructed based on the thermodynamics, electrochemical knowledge and heat transfer theory. The model of this kind of HPU has been applied in the distributed generation system to help absorb the wind and solar energy ever since, which can effectively provide a junction between the electricity energy and chemical energy and promote the development of integrated energy internet [28,29]. It is significant to provide a well-designed coordination control strategy among the integrated energy units in the islanded dc microgrid. When only the storage battery is used to absorb the surplus power generation of PV generator, the state-of-art literatures have been investigated as follows. Based on the dc bus level, Sun et al. [30] proposed a distributed control strategy for modular PV generators and battery storage. But the control strategy for the PV generators must be switched at different dc bus voltage levels, which may cause power fluctuation. Similarly, a mode-adaptive decentralized control strategy for the multiple renewable distributed generators and storage is proposed in Ref. [31], which means the generation and battery storage can support each other by selecting different modes according to the dc bus voltage level. But the SoC of the storage battery is not considered in this paper. As for the SoC, Lu et al. [32,33] proposed an adaptive droop method for the multiple storages in order to balance the SoCs of different batteries. But the instantaneous charging or discharging power are not considered in these papers. Xia et al. [34] proposed SoC-based droop control to balance different SoCs and the voltage-current droop control in the outer loop can limit the instantaneous power magnitude. But the linear relationship between dv and SoC limits the PV output power even though the SoC locates in the healthy condition. In summary, on the one hand, the storage battery plays the key role to support the dc bus voltage and balance the dc bus power, and the abovementioned references contribute to coordination control among different units. But on the other hand, the high price of the storage battery will limit its absorbing power capacity, and will also limit the development of distributed renewable energy generation. The cooperative application of the short-time scale battery storage and long-time scale load can avoid the battery overused, meanwhile, the PV generator can be made full use of and can avoid frequent power curtailment. Wu et al. [35] proposed a generation-storage-load coordinated control strategy based on the dc bus voltage level. The load controller can perceive the variation of the dc bus voltage and change the power

Please cite this article as: Zhang Y, Wei W, Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.058

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Fig. 1 e Hydrogen production plant in the renewable energy system. consumption with hysteresis control strategy accordingly. But the authors did not discuss the load characteristics in detail, and just cut it off manually. Zhou et al. [36] constructed the model among the hydrogen production unit, fuel cell and wind generator, and demonstrated the simulation results among different physical quantities. It is praiseworthy that the authors considered the electrical and gas flow characteristics in a complex system, but they did not pay attention to the coordination control strategy among the different units in detail. Bornapour et al. [37] presented the optimal stochastic coordinated scheduling among the hydrogen storage, wind, photovoltaic and other units in a long-time scale. Based on the model predictive power and voltage control method, Hu et al. [38] proposed a coordinated control strategy for the hydrogen storage and the renewable energy sources to achieve smooth grid synchronization and connection. But they didn't consider the energy conversion efficiency of HPU, which is an important factor in determining its wide application. In summary, this paper applies HPU in the dc microgrid dominated by PV generators and proposes an adaptive coordination control among the PV generator, battery storage, fuel cell and HPU. The innovations of this paper compared with the existing methods are shown in Table 1, which can be concluded that this paper has considered the multiple PV generators, SoC protection, over power protection, decentralized control, large energy density and HPU efficiency. Specifically, by analysing the operation mechanism of HPU,

it is found that there exists a peak value in the energy conversion efficiency curve. Then an efficiency adaptive control based on the dc bus voltage signal is proposed. When the output power of PV generators is increased because of the strong irradiance, or the battery is almost getting full charged, or some loads are cut out, the dc bus voltage will rise. HPU can perceive the variation of the bus voltage in this case and regulate its power consumption at the cost of some efficiency. Furthermore, the control strategy of the battery storage is designed with consideration of the SoC and the instantaneous charging as well as discharging power. In addition, when there is not much surplus PV power in the sunset situation, HPU will decrease its power consumption adaptively. Finally, if the dc bus voltage decreases under the setting value, fuel cell needs to supply power to the local loads.

Energy conversion efficiency analysis of HPU HPU generally consists of many alkaline electrolyser cells. The extra heating source is necessary to keep the temperature for the chemical reaction. The water is electrolyzed to produce hydrogen and oxygen, and the electric energy can be transformed into chemical energy in this way. There exist reversible and irreversible reactions in the alkaline electrolyzer. The irreversible reaction includes ohmic polarization and

Table 1 e Comparison with existing methods. Existing methods Multiple PVs SoC protection Over power protection Decentralization Large energy density HPU efficiency Ref. [30] Ref. [32] Ref. [34] Refs. [36e38] This paper

✓ 7 ✓ ✓ ✓

✓ ✓ ✓ 7 ✓

7 7 ✓ 7 ✓

7 7 ✓ 7 ✓

7 7 7 ✓ ✓

7 7 7 7 ✓

Please cite this article as: Zhang Y, Wei W, Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.058

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concentration polarization reactions. The terminal voltage of HPU can be obtained as


Vele ¼ Vrev þ Vohm þ Vcon Vo ¼ NVele

(1)

where Vele is the terminal voltage of the single electrolyzer unit, Vrev is the reversible voltage, Vohm is the overvoltage caused by the ohmic polarization, Vcon is the overvoltage caused by concentration polarization, N is the number of the electrolyzer, Vo is the terminal voltage of HPU. The reversible voltage, ohmic polarization voltage and the concentration polarization voltage can be obtained as [27].   8 5 Vohm ¼ r1 þ r2 T=Aele I > < Vrev ¼ 1:253  2:4516e T;       > : Vcon ¼ s1 þ s2 T þ s3 T2 log t1 þ t2= þ t3 2 þ a= I þ 1 T A T ele

(2) where T is the working temperature, I is the operating current, Aele is the cathode plate area, r1, r2, s1, s2, s3, t1, t2, t3, a are the correlation coefficients.

h% ¼

Qh ,ð1  bTÞ ,100% ¼ Qheat þ Qpower

KRh ð1  bTÞ

2

(3)

where vh is the hydrogen production rate, n is the Mole number, K is electrochemical equivalent coefficient, F is the Faraday coefficient, s is the chemical valence variation of the reactant. According to the calorific value coefficient of hydrogen, the chemical heat energy of the produced hydrogen in unit time can be calculated as NI Rh sF

(5)

The ohmic polarization process and concentration polarization process of HPU will generate extra heat energy Qextra, which can be calculated as Qextra ¼ NðVohm þ Vcon ÞI

(6)

To maintain the temperature of the reaction process, the external heat source is necessary to compensate the lost heat for HPU, and it can be written as Qheat ¼ TS  lQextra ¼ ðTS  lNðVohm þ Vcon ÞIÞ

(7)

Frature T, and l is the thermal dissipation coefficient. Based on equation (1) ~ (7) and the specified parameters in Table 2, the energy conversion efficiency is calculated as

13

0

  B 6 2FVrev þ 2Fð1  lÞ4r1Aþrele2 T І þ s1 þ s2 T þ s3 T2 log@

dn NI ¼K dt sF

Qh ¼ K

Qpower ¼ Vo I ¼ NðVrev þ Vohm þ Vcon ÞI

t t t1 þ T2 þ 32 þa T

According to Faraday's law of electrolysis, the molar flow rate of the produced hydrogen can be calculated according to the rate of the input charge as vh ¼

The input energy of HPU consist the input electric energy Qpower and the heat energy Qheat from the extra heat source. According to equation (1), the input power can be obtained as

Aele

,100%

(8)

C7 І þ 1A5 þ 2FTS NІ

According to equation (8) and the parameters in Table 2, the relationship among the efficiency, the input current and the temperature of HPU can be drawn in Fig. 2. It can be seen that the energy conversion efficiency increases first and then decreases with the increase of the input current. The reasons are presented as follows. The additional heat energy needs to be added to maintain the temperature in the reaction process. Hence, the power consumption of HPU is limited when the input current is very small, thus the

(4)

where Rh is the calorific value coefficient of hydrogen.

Table 2 e Parameters of the model of HPU. Variable r1 r2 s1 s2 s3 t1 t2 t3 a T

Value

Variable

Value

2.3e-3 Um2 1.107e-7 Um2 C1 1.286e-1V 2.378e-3 V C 0.606e-5 V C2 3.559e-2 m2A1 1.3029e-2 m2 CA1 2.513e-3 m2 C2A1 3 m2 75  C

F s K Aele N b Rh S l

96485 Cmol-1 2 1300 0.25 m2 100 2.98e-3 284.7 kJmol-1 90 Jmol1K1 0.3

Fig. 2 e Relationship among the efficiency, current and temperature of HPU.

Please cite this article as: Zhang Y, Wei W, Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.058

international journal of hydrogen energy xxx (xxxx) xxx

efficiency of the system is very low in this situation. With the increase of the input current, the absorbed power is increased and the compensated thermal energy is relatively small, therefore the efficiency of the system gets improved. When the input current increases to a certain value, the concentration polarization and ohmic polarization will consume lots of electric energy. This part of energy cannot be transformed into chemical energy, which reduces the efficiency of the system. The concentration polarization and ohmic polarization process will produce much heat, which can compensate some of the heat provided by the external thermal source. Hence, the efficiency will decrease slowly.

Proposed decentralized coordination control strategy The operation modes of the islanded dc microgrid system is shown in Fig. 3. If the bus voltage vbus equals to the rated value Vn, the battery gets charged slowly and HPU works at the maximum efficiency point. If vbus rises over Vn, it means there is much surplus PV output power and HPU needs to degrade its efficiency to absorb much more power. When HPU operates at the allowable maximum power point, the corresponding bus voltage is V1. If vbus rises over V1, it means the battery is almost getting full charged and HPU cannot consume the surplus PV power totally. In this case, the PV generators need to limit its output power. When vbus rises about to the allowable maximum value V2, the PV generators will only supply the local loads and HPU. Similarly, when the instantaneous power P of the battery is positive, it means the battery is getting discharged. If vbus is smaller than Vn, HPU needs to degrade its consumed power by decreasing the energy efficiency. The voltage at the allowable minimum power consumption is V3. If vbus decreases under V3, HPU needs to be cut out and the battery continues to supply the local loads. If vbus decreases under V4, it means the SoC of the battery is very limited and the fuel cell will be put into operation to supply the local loads. PV generators begin to work in the next day,

5

and HPU will be put into operation again when the bus voltage increases to the rated value. The fuel cell is used as the backup power supply, it is necessary to shut down fuel cell at this time.

Efficiency adaptive control of HPU The efficiency adaptive control is shown in Fig. 4. When the required power of the local loads is satisfied, and there still exists surplus PV power, HPU and the battery will share the surplus power. HPU operates at the maximum efficiency point with two advantages. The large instantaneous charging power of the battery can be avoided, which will benefit its life span. Besides, the maximum energy conversion efficiency indicates that HPU is in optimal utilization condition. When the produced power is larger than the consumed power, the dc bus voltage will rise because of the high SoC or the large charging power. When the produced power is smaller than the consumed power, the dc bus voltage will drop because of the low SoC or large discharging power. The main control circuit is shown in Fig. 4(a). The reference efficiency value can be written as 8 < hr ¼ hmax  rr ,ðvbus  Vn Þ h  hr : rr ¼ max V1  Vn

&

8 < hl ¼ hmax  rl ,ðvbus  V3 Þ h  hl : rl ¼ max Vn  V3 (9)

where rr and rl are the decreasing slopes, hmax is the maximum efficiency value, hr and hl are the allowable efficiency values. The efficiency adaptive control algorithm is shown in Fig. 4(b). The dc bus voltage is compared with the rated value after passing through the low-pass filter. If the dc bus voltage vbus is at the rated value Vn, HPU will work at the maximum efficiency point. In this case, h(n) will be always smaller than the reference value hmax, hence only the algorithm in the right green part in Fig. 4(b) is operated. If vbus is between Vn and V1, or between V3 and Vn, the reference efficiency value will be reduced adaptively. Therefore, the whole algorithm in Fig. 4(b) will be executed.

Fig. 3 e Operation modes of the dc microgrid system. Please cite this article as: Zhang Y, Wei W, Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.058

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Fig. 4 e Main circuit and the adaptive control algorithm.

Control strategy of storage battery Storage battery plays an important role in the PV dominated microgrid system. Generally, the battery with a large capacity is relatively expensive, thus it is cost-efficient to configure a battery with a suitable capacity to coordinately operate with HPU. The existing control methods mostly consider the SoC, which can make the SoC of the battery operate in a safe range. In fact, when the SoC is in the safe range, the large instantaneous charging or discharging power will also damage the battery. The SoC and the instantaneous charging or discharging power of the battery are considered in Fig. 5. When the SoC of the battery locates in the safe range between SoCl and SoCu, the output result is zero. When the SoC of the battery is larger than SoCu, the output result of the function should increase with increase of SoC. Then the dc bus voltage will increase. When the SoC of the battery is lower than SoCl, the output result of the function should decrease with decrease of SoC. Then the dc bus voltage will decrease. Therefore, the SoC function can be expressed as 8 < rsoc ðSoC  SoCu Þ; f ðSoCÞ ¼ 0; : rsoc ðSoC  SoCl Þ;

if SoC  SoCu if SoCl < SoC < SoCu if SoC  SoCl

(10)

where rsoc is the coefficient, SoCu and SoCl are the upper and lower setting values respectively. If the charging power amplitude is smaller than the reference, it means the charging power is in the safe range and the output result will be zero as shown in equation (11a). If the charging power amplitude is greater than that of the reference power, it means the large charging power may do harm to the battery. Besides, it is designed that the output result of the function (11a) is related to the SoC of the battery which can be expressed as
f ðPch Þ ¼

0; if Pch >  P* rp ð100  SoCÞð  Pch  P* Þ;


f ðPdisch Þ ¼

0; if Pdisch < P* rp SoCðP*  Pdisch Þ;

if Pch  P*

if Pdisch  P*

(11a)

(11b)

where rp is the coefficient, Pch and Pdisch are the charging and discharging powers respectively, P* is the allowable maximum power amplitude value. Similarly, the output value is zero when the discharging power is smaller than the reference power. When the discharging power is larger than the reference power, the output result of the function will be positively related to the SoC with the similar analysis. Thus, the information of the discharging power can be transformed to other units in the microgrid system. There are two advantages of the proposed approach. Generally, the SoC should be very low after discharging for a night, and the PV generator starts to work in the morning. Although the SoC is very low, the dc bus voltage will rise in a short time because of the large instantaneous charging power according to equation (11). Then HPU will perceive the dc bus voltage and degrade its efficiency to absorb more power. Thus, the battery can avoid bearing a large instantaneous charging power. Similarly, the SoC should be very high after charging for a daytime, and the PV generators are stopped in the late afternoon. Although the SoC is very high, the dc bus voltage will drop in a short time because of the large discharging power. Then HPU will consume less power. Therefore, the battery can avoid bearing a large instantaneous discharging power.

Fig. 5 e Control strategy of the battery. Please cite this article as: Zhang Y, Wei W, Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.058

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Fig. 6 e (a) Control strategy of the PV generator. (b) Control strategy of the fuel cell.

Control strategy of PV generator

Stability analysis of the control strategy

According to the characteristic of the PV generator, the MPPT algorithm is commonly used to take full advantages of the solar energy. The whole control strategy of PV system is shown in Fig. 6(a). As mentioned above, when the dc bus voltage rises over the rated reference Vn, HPU will perceive the dc bus voltage and degrade its efficiency to absorb much more power. But there is an allowable maximum absorbed power for HPU, and the corresponding voltage threshold is V1. Therefore, the PV generator will operate at the MPPT mode if the dc bus voltage is lower than the voltage threshold V1. If the dc bus voltage rises over the voltage threshold V1, which means all the loads cannot absorb the PV output power totally, then the output power of PV generators should be limited. The reference value of the generated power is expressed as 8 > < Pref ¼ Pm  rpv ðvbus  V1 Þ Pm > : rpv ¼ V2  V1

(12)

where rpv is decreasing slope of the reference power, Pm is the maximum output power of the PV generator, V2 is the allowable maximum dc bus voltage.

Control strategy of fuel cell Fuel cell behaves as a backup power and its model is wellresearched, and the control strategy is shown in Fig. 6 (b). Fuel cell is put into operation with the constant power control strategy if the bus voltage is smaller than V4, and it will share the loads or charge the battery until the next day. When the dc bus voltage rises to the rated value, HPU will be put into operation. Meanwhile, since the whole efficiency is low when HPU and fuel cell work at the same time, fuel cell needs to be shut down when the dc bus voltage rises to the rated value. In summary, as for HPU, the efficiency adaptive control strategy is proposed, which means HPU can adjust its absorbed power by regulating the reference efficiency value according to the dc bus voltage. As for battery, both the SoC and the instantaneous charging and discharging power are considered. As for PV generator, the P-V droop control strategy can make PV generators work off from the MPPT mode seamlessly. As for fuel cell, the constant power control and voltage hysteresis control are well-designed.

It is very important to measure the suitability and stability of the coordination control strategy. Normally, a state space model is established, which contains lots of control parameters and droop coefficients. The small interference is added in, then the small-signal model of the whole control system can be constructed by ignoring high-order terms. According to the Nyquist stability criterion, if the eigenvalues of the coefficient matrix are all located on the left side of the imaginary axis, it means the system is convergent and the control strategy is stable. If there is one eigenvalue located on the right side of the imaginary axis, it means the system is divergent and the control strategy is unstable [39,40]. If we only change one parameter, then the eigenvalues of the coefficient matrix will change correspondingly. It can reflect the influence of a certain parameter on the stability of the whole control system. If all the eigenvalues of the coefficient matrix are on the left side of the imaginary axis even though a parameter changes largely, it means the control system has a high redundancy for this parameter. If the eigenvalues of the coefficient matrix cross the imaginary axis with the increase of a certain parameter, it means the control system has a low redundancy for this parameter and it should be designed very small. According to the abovementioned design guidelines, some explanations are given first. Second, the state space equation of the whole control strategy is established. Third, the smallsignal model including many control parameters is derived. Finally, the influence of a certain parameter on the stability of the control system is analyzed. Fig. 7 shows the power flow among different units. Because the fuel cell and HPU are not operated at the same time and

Fig. 7 e Simplified structure of the dc microgrid system.

Please cite this article as: Zhang Y, Wei W, Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.058

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the stability analysis results of different mode are similar, the stability of the proposed coordination control strategy in the discharging condition among the PV generators, storage battery, local loads and HPU is analyzed. Similarly, the other operation modes such as charging mode or fuel cell supplying-

current, kh is the approximate decreasing slope of the efficiency curve. According to the above equations, some state variables are defined as follows, x1 ¼ 1/(Tbsþ1)ib, x2 ¼ SoC, x3 ¼ Ppv, x4 ¼ ih. Then the state-space model of the system can be derived as

8 rp P* þ rsoc rp Vb 1 Vb  rsoc SoCl > > Tb · x1 ¼ x1 þ x2  x3 þ x4  x1 x2 þ > > v r r rload > load bus load > > > > * < rp P þ rsoc rp Vb 1 Vb  rsoc SoCl Cb · x2 ¼ x2  x3 þ x4   x1 x2 þ vbus rload rload rload > > >  *  > > · > T x ¼ rpv rp P þ rsoc x2  x3 þ rpv rp Vb x1 x2 þ Vb  rsoc SoCl þ rpv V2 > > pv 3 >   : Th · x4 ¼ kh rh rp P* þ rsoc x2  x4 þ kh rh rp Vb x1 x2 þ Vb  rsoc SoCl þ kh rh V2 power mode can be also analyzed with the small-signal model but not presented here. The power interconnection among the generation, storage and HPU is mainly focused, thus the line resistances are omitted to simplify the analysis. In addition, because the time scale of the inner loop is much smaller than the outer loop, the inner loop can be considered unchanged in

Based on equation (13) ~ (17), the small-signal model of the control strategy is constructed to analyse the stability of the system. By linearizing equation (17) and neglecting the second order, the small-signal model is derived as

! ! rp P* þ rsoc  rp Vb x1s rp P* þ rsoc  rp Vb x1s 1 rp Vb x2s x3s rp Vb x2s 1 1 8 · D x ¼  þ þ þ þ Dx3 þ Dx4 Dx Dx2  1 1 > 2 2 > T T T T r T r V T V T V b b load b load b bus b > b b bus bus > > > > ! ! > > > > rp Vb x2s x3s rp Vb x2s rp P*  rsoc rp P* þ rsoc  rp Vb x1s 1 1 > > · Dx1 þ Dx2  þ þ Dx3 þ x4 > 2 2 < D x2 ¼  Cb Vbus Cb Cb rload Cb rload Cb Vbus Cb Vbus >   > > > rpv  rp P*  rsoc þ rpv rp Vb x1s rpv rp Vb x2s 1 > > · x ¼ D Dx þ Dx2  Dx3 > 3 1 > > T T T pv pv pv > > > >   > : kh rh  rp P*  rsoc þ kh rh rp Vb x1s kh rh rp Vb x2s 1 D· x4 ¼ Dx1 þ Dx2  Dx4 Th Th Th the analysis. The dc bus voltage supported by the storage battery is vbus ¼ Vref þ dP þ dSoC ¼ Vref

 þ rp SoC P* 

þ rsoc ðSoC  SoCl Þ

Vb ib Tb s þ 1

1 Cb

(13)

Z ib dt

(14)

where Cb is the capacity of the battery, and ib is the operating current. The filtered output power of the PV source is obtained as Ppv ¼ 

rpv ðvbus  V1 Þ Tpv s þ 1

(15)

where Tpv is the time constant value of the filter of the PV. Similarly, the filtered operating current of HPU is approximately expressed as the following equation to simplify the analysis. ih y  kh

rh ðvbus  Vn Þ Th s þ 1

(18)

where Vbus, x1s, x2s, x3s, x4s are the steady values, and can be expressed as the following equations.



where Tb is the time constant value of the filter of the battery. The SoC can be written as SoC ¼ SoC0 

(17)

(16)

where Th is the time constant value of the filter of the HPU

8 Vbus ¼ Vref  rp x2s ðVb x1s  P* Þ þ rsoc ðx2s  SoC*Þ > > > > < x1s ¼ V 1 Þ  rpv ðVbus  V2 Þ Vbus  ref rload þ rh ðVbus  V  x2s ¼ Vbus  Vref þ rsoc SoC* rsoc  rp ðVb x1s  P* Þ > > > > x3s ¼ rpv ðV2  Vbus Þ : x4s ¼ kh rh ðV1  Vbus Þ

(19)

The parameters of the whole system are listed in Section Control effectiveness presentation. According to Nyquist stability criterion and the small-signal model of equation (18), the influence of the parameters on the stability of the system is discussed and the stability analysis results are shown in Fig. 8. Because there are lots of parameters in the abovementioned equation and the length of this paper is limited, the droop control parameters and time delay parameters of different units are selected for analysis. For example, Fig. 8 (a) shows the movement tendency of the system eigenvalues when the power droop coefficient rp of the storage battery changes from 0 to 100e-4. It can be seen that there are two symmetrical poles moving rapidly toward to the imaginary axis. Its physical meaning can be explained as that the large droop coefficient rp will own a fast adjustment speed, but it is at the expense of the stability of the system. Finally, the droop coefficient rp of the storage battery is selected as 1e-4 to ensure enough stability

Please cite this article as: Zhang Y, Wei W, Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.058

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Fig. 8 e Dominant poles of the control system.

margin. Similarly, Fig. 8(b) and (c) demonstrate the trajectory of the system eigenvalues when the power droop coefficient rpv of the PV generators changes from 0 to 300, and the power droop coefficient rh of the HPU changes from 0 to 0.1. It can be found that almost all the dominant poles move on the left part of the imaginary axis, which means that the system has high redundancy for these parameters and the requirement for these parameters are not very strict. Finally, the power droop coefficients rpv and rh are selected as 180 and 0.02 respectively. Fig. 8(d), (e) and (f) show the influence of the filtering parameters on the stability of the system. It can be seen that the dominant poles will move toward the imaginary axis with the

Table 3 e Parameters of the system.

PV generators

Storage battery

HPU

Fuel cell

Else

Variable

Value

Variable

Value

L C kvi rpv P1# Vin L kvp kip rp L rh kip hr L kpp kip PL Vbus V2 V4

2 mH 1000uF 200 180 15 kW 200V 2 mH 1 0.01 1e-4 6 mH 0.02 1 0.56 1.5 mH 2 10 25 kW 500V 550V 460V

Cpv kvp kip Tpv P2# Vbus C kvi Tb rsoc C Th kii hl C kpi

500uF 5 0.01 0.01 30 kW 500V 2000uF 100 0.01 2 2000uF 0.01 100 0.45 1000uF 100

f V1 V3

5 kHz 540V 470V

increase of the time constant values. Finally, the filtering parameters are all selected as a small value 0.01. Other parameters can be analyzed in the same way, and the parameters can be determined finally.

Control effectiveness presentation Simulation results presentation The parameters are shown in Table 3. The simulation results in MATLAB/Simulink circumstance are presented to intuitively and clearly show the control effectiveness. The variables in Fig. 9 and Fig. 10 are the dc bus voltage vbus, battery SoC, the output result dP of equation (11), battery power Pb, energy conversion efficiency h% of HPU, absorbed power Ph of HPU, output powers Ppv1 and Ppv2 of PV generators respectively. Fig. 9 discusses the charging situation of the battery. Firstly, when there is not much surplus PV power, HPU works at the maximum efficient point, and the battery is getting charged slowly in stage I. The irradiance is increased at 10s, and both the output powers of the PV1# and PV2# are increased. The increased dP is superimposed to the voltage reference value, which will lead to the growth of the dc bus voltage. HPU can degrade its energy conversion efficient to absorb much more power in stage II. At about 18s, HPU works at the allowable maximum power point, and the dc bus voltage continues to rise. Hence, the PV generators limit their output power seamlessly according to the dc bus voltage in stage III. Finally, the charging power of the battery is almost zero, and the dc bus voltage is stable. PV generators only supply the local loads and HPU. Fig. 10 discusses the discharging situation of the battery. When the irradiance is not sufficient, the PV output power is

Please cite this article as: Zhang Y, Wei W, Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.058

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Fig. 9 e The charging mode of the battery.

not enough. The battery discharges to supply the local loads and HPU, and the dc bus voltage maintains at the rated value if the SoC is in the setting range in stage I. During stage II, the dc bus voltage begins to drop because the SoC degrades under the setting value. HPU will work on the left part of the maximum efficiency point, which means HPU can reduce its power consumption by decreasing the efficiency. During stage III, HPU is adaptively shut down because the bus voltage decreases to the setting value. During stage IV, the PV generators are shut down in the evening, and the battery supplies the local loads. During stage V, since the storage battery continuously discharges to supply the local loads, the bus voltage drops gradually. The fuel cell is put into operation when the dc bus voltage decreases to the setting value. During stage VI, since the fuel cell supplies the local loads and charges the battery for a long time, the dc bus voltage rises gradually. When the dc bus voltage increases to the rated value, HPU will be put into operation and the fuel cell is shut down, which can simulate the working condition in the early morning. During stage VII, PV generators start to work, which will charge the storage battery and supply the local loads and HPU. Then the system returns to the first case.

Experimental results presentation The model of the islanded DC microgrid including PV generators, storage battery, HPU, fuel cell and local load is constructed, compiled and downloaded in RTLAB version 11.2.2.108 platform to verify the practicability of the proposed control strategy. RTLAB is an industrial real-time platform whose ultra-high-speed performance model (XHP) can greatly reduce the system management consumption to less than 1 ms. Hence, the system can be made full use of to calculate the high dynamic and real-time model, especially for the complex problems that require high fidelity response and high accuracy. The method can compensate the limitations of the hardware setup platform, and has been widely used in the electronic systems, such as power electronic converter and the control strategy, power system and so on. Generally, it needs many hours for the battery charging or discharging over the safe range in practice. But a small capacity battery is configured to observe the control effectiveness during the mode switching condition. The experimental results in charging condition is presented as follows. In order to clearly elaborate the control

Please cite this article as: Zhang Y, Wei W, Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.058

international journal of hydrogen energy xxx (xxxx) xxx

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Fig. 10 e The discharging mode of the battery.

effectiveness in the charging condition, the waveforms are approximately divided into three stages as shown in Fig. 11. During stage I, the PV output power supplies the local loads and the surplus power is shared by HPU and the battery. HPU works at the maximum efficiency point, and the battery gets charged slowly. During stage II, the PV output power is increased with the increase of the irradiance. The extra instantaneous power generated by PV sources will flow into the battery. Then the control strategy of the battery outputs a large value dP, which will be superimposed in the voltage reference. Hence, the dc bus voltage rises rapidly, and HPU can perceive the variation of the dc bus voltage and degrade its energy conversion efficiency to absorb much more power. It should be pointed out that the dc bus voltage waveform offsets downward 450V to observe the detail, and the efficiency curve offsets downward 0.5. During stage III, the PV generators limit their output power to balance the dc bus voltage. Finally, the battery gets floating charged and the PV generator will only supply the local loads and HPU. The analysis results in charging condition are demonstrated as follows. Normally, this situation happens in a sunny day. Firstly, the irradiance is not very strong in the early morning, the PV generators mainly support the local loads. The surplus power will be consumed by the storage battery and HPU. It is designed that HPU works at the maximum

efficiency point, which means it only absorbs a small part of PV power generation. The configuration capacity of the battery determines the duration time of this process. Secondly, when the SoC of the storage battery is charged to the setting value, HPU needs to increase its power absorption at some cost of energy conversion efficiency. Thirdly, when HPU works at its maximum allowable power consumption, it means all the local loads, storage battery, HPU cannot consume the PV power generation. Then PV generators need to limit their output power. Finally, the storage battery is in float-charging condition, HPU is operated at the maximum allowable power point. The whole process is adaptively and automatically adjusted. The experimental results in discharging condition is presented as follows. The waveforms of the discharging situation are divided into seven parts as shown in Fig. 12. The working condition in the afternoon is shown in stage I. There is not much surplus PV power and the battery discharges to share some of the loads. The dc bus voltage can keep at the rated value because the SoC is still in the safe range. The working condition in the late afternoon is shown in stage II. The SoC decreases under the setting value, and the dc bus voltage begins to drop. HPU works at the left side, which means it can decrease its consumed power by decreasing its energy conversion efficiency. The working condition in the sunset time is

Please cite this article as: Zhang Y, Wei W, Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.058

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Fig. 11 e The charging situation of the battery.

Fig. 12 e The discharging situation of the battery.

Please cite this article as: Zhang Y, Wei W, Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.058

international journal of hydrogen energy xxx (xxxx) xxx

shown in stage III. HPU is cut out because the dc bus voltage drops under the setting value. Meanwhile, the PV generators begin to stop operation in the evening as shown in stage IV. The working condition in the dark night is shown in stage V. The fuel cell starts to supply the local loads and charges the battery. The working condition in the early morning of the next day is shown in the stage VI. When the dc bus voltage rises to the rated value, HPU will be put into operation again, and the fuel cell will be shut down. The working condition in the late morning of the next day is shown in the stage VII. The PV generators begin to supply the local loads and HPU, meanwhile, the battery gets charged gradually. Since the SoC of the battery is low, there is a long time for the charging process. The dc bus voltage will operate stably and HPU will work at a certain efficiency point. The analysis results in discharging condition are demonstrated as follows. The waveform in Fig. 12 is not as intuitive as the simulation results, but the transition process can be also reflected. The discharging condition usually happens in the evening or in the rainy weather. First, when SoC of the storage battery is very high, it will supply local load and HPU. The configuration capacity of the battery determines the duration time of this process. Secondly, when the SoC decreases to the setting value, HPU needs to decrease its power consumption. This process is designed to verify the compatibility of the coordination control strategy. Thirdly, when the SoC decreases to a lower setting value, HPU needs to be cut out. Then the storage will supply the local loads only. Fourthly, if the configuration capacity of the battery is limited, then the fuel cell needs to start to help supply the local loads until the PV generators are put into operation again. In summary, this section mainly demonstrates the coordination control effectiveness of the overcharging and over discharging situations with simulation and experimental results. The two kinds of the results are basically coincided, which can verify the effectiveness of the proposed decentralized coordination control strategy.

Conclusions In this paper, a decentralized coordination control strategy among the PV generators, battery storage, HPU and fuel cell is designed in the islanded dc microgrid. Firstly, the efficiency adaptive control strategy for HPU is designed, which means that HPU can adaptively regulate its absorbed power by adjusting the energy conversion efficiency according to the dc bus voltage. Secondly, both the SoC and the instantaneous charging or discharging power are considered in the control strategy of the battery, which can avoid the battery being overused or damaged. Thirdly, the P-V droop control strategy can make the PV generator work from the MPPT mode to the limited power mode seamlessly. Fourthly, fuel cell works as a backup power and is controlled at the constant power mode. Finally, the simulation and experimental results are demonstrated to verify the effectiveness of the proposed control strategy. Besides, the proposed coordination control needs no communication lines, and can make full use of the PV sources.

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Acknowledgements This work was supported by the State Grid Science and Technology Program (SGBJDK00D WJS1700158) and Key Research and Development Plan of Zhejiang Province (2017C01039).

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Please cite this article as: Zhang Y, Wei W, Decentralized coordination control of PV generators, storage battery, hydrogen production unit and fuel cell in islanded DC microgrid, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.01.058