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A generalized droop control approach for islanded DC microgrids hosting parallel-connected DERs
Sustainable Cities and Society 36 (2018) 237–245
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Sustainable Cities and Society journal homepage: www.elsevier.com/locate/scs
A generalized droop control approach for islanded DC microgrids hosting parallel-connected DERs
MARK
⁎
Sajjad Golshannavaza, , Vahid Mortezapourb a b
Electrical Engineering Department, Urmia University, Urmia, Iran School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran
A R T I C L E I N F O
A B S T R A C T
Keywords: DC microgrids (MGs) Islanded operation Load current and power sharing Voltage regulation Generalized droop control strategy
A great attention is dedicated to design a generalized droop control approach contributing to proper load current sharing and voltage regulation in DC microgrids (MGs). The established approach is based on fundamental principles of parallel-connected distributed energy resources (DERs) equivalent circuit ending in a general method effective for different interconnection schemes. Accordingly, proper load sharing and voltage regulation are pursued in DERs with different power ratings and different cable impedances. Moreover, the proposed approach is apt to be operated in both load current and power sharing modes. Comparative studies are conducted to evaluate performance of the proposed approach regarding these two control strategies and highlighting the possible differences. Accordingly, the desired control and technical requirements could be accommodated, effectively. Detailed simulation studies are conducted and compared with each other to interrogate performance of the proposed approach. Results are discussed in depth.
1. Introduction The concept of microgrid (MG) is an expediting factor in swift deployment of small-scale distributed energy resources (DERs), more specifically in islanded and remote areas (Hatziargyriou, Asano, Iravani, & Marnay, 2007). Besides the traditional power resources, renewable-based DERs are one of the main elements of MGs and are widely deployed in cities and rural environments. For instance, rooftype PVs are now a common seen at these areas (Sasidharan & Singh, 2017). By developing a suitable and well-defined control system, these resources could be easily integrated into the energy grid and contributing to reduce emissions and environmental pollutions (Ahmad & Alam, 2017). Besides, the energy grid of sustainable cities mainly depends on MG concept which outlines the great importance of this notion to be explored more (Chan, Cameron, & Yoon, 2017; Wouters, 2015). On the other hand, if different types of consumers in a particular boundary interact with each other, they could attain further mutual benefits. This notice also adds to the merits of MG concept in real-case applications (Reynolds, Rezgui, & Hippolyte, 2017). As clarified, all of these features enable the swift progress and the final transition towards the sustainable cities through MG implementations (Hussain, Muhammad Arif, Aslam, & Danial Ali Shah, 2017). Technically speaking, MG is defined as a single entity accommodating a cluster of loads and generating units inside a particular
⁎
boundaries being operated in a grid-connected or an autonomous mode. It also provides seamless transitions between grid-connected and islanded modes of operation. MGs fall in two main categories including alternative current (AC) and direct current (DC) types. The latter type manifests competitive features over the former (Planas et al., 2015; John Justo, Mwasilu, Lee, & Jung, 2013). Annihilating the skin effect and power quality issues, absence of frequency control, and an easy power flow are some of the main features of DC MGs over their AC counterparts. Accordingly, DC MGs offer higher figures of merit say as efficiency, reliability, safety, redundancy, and reduced cost (Chehardeh, Lesani, Zadeh, & Siavashi, 2009; Jian, He, Jia, & Xie, 2013). Taking a look from consumption requirements, many of the loads in MG premises demand a DC power emphasizing the superiority of DC electrification (Boeke & Wendt, 2015; Fregosi et al., 2015). Computers and data centers, variable-speed drives, and light emitting diodes are to be named, but a few. Dealing with generation shape of DERs in DC MGs, they produce power inherently in DC form or it is converted to DC through power electronics converters. Photovoltaics (PVs), fuel cells (FCs), and energy storage systems (ESSs) are in touch with DC power. In contradiction, wind turbines (WTs) and the main grid provide an AC power being converted to an equivalent DC. In recent attempts, DC and AC MGs are coupled together through an interfacing converter introducing the concept of hybrid MGs (Mortezapour & Lesani, 2017). This type of MG provokes opportunities
Corresponding author. E-mail address: [email protected] (S. Golshannavaz).
http://dx.doi.org/10.1016/j.scs.2017.09.038 Received 13 June 2017; Received in revised form 29 August 2017; Accepted 30 September 2017 2210-6707/ © 2017 Elsevier Ltd. All rights reserved.
Sustainable Cities and Society 36 (2018) 237–245
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Fig. 1. (a) Two parallel-connected DC/DC converters, (b) equivalent circuit.
parallel-connected DERs. The proposed approach is a generalized one established based on fundamental principles of DERs equivalent circuit which could contribute to proper load current sharing and a proper power sharing among them. Moreover, the proposed droop strategy demonstrates satisfactory results in DERs with different rated powers and different interconnection cable impedance. Detailed simulation studies are evolved to assess performance of the proposed approach and come into a comparison platform. The remainder of this manuscript is organized as follows: Section 2 addresses the principle formulation of the proposed approach. Based on these equations, Section 3 extends V–I droop characteristics to achieve two individual objectives say as proper sharing of load current and proper power sharing. Some technical considerations regarding the proposed approach are discussed in Section 4. Simulation studies are provided in Section 5 and detailed comparative studies are conducted to portray the merits of the proposed approach. Concluding remarks and general discussions are unveiled in the last section.
of both AC and DC MGs. However, it is not the main focus of the present study and accordingly is not tailored here. On the main side, the ongoing study looks into the efficient DC MGs. Considering data exchange between the embedded elements, DC MGs could be operated in two main configurations. In one type, there are communication links to establish bilateral data transfers between specific DERs and the control center. Centralized control approaches (Yang, Paire, Gao, Miraoui, & Liu, 2015; Farhadi & Mohammed, 2015) and master/slave methods (Mazumder, Tahir, & Acharya, 2008; Ferreira, Braga, Ferreira, & Barbosa, 2012) require such connections. Although beneficial for small-scale MGs, communication links are not judged as economic and reliable solutions for real-scale MGs. The second scheme excludes the need for high bandwidth communication links wherein each DER deploys its local variables for control purposes. Accordingly, DERs are operated in a decentralized manner without any data transfer. Droop control method is a popular decentralized approach which controls the converter output voltage based on its output current (Bouzid et al., 2015). Different droop control strategies have been proposed for DC MGs. In (Gu, Xiang, Li, & He, 2014), considering the presence of ESSs, the droop control strategy is evaluated in three different modes. Based on the output power level, one of the three modes is selected for droop strategy. Proper responses are attained based on the proposed strategy; however, it does not accommodate parallel operation of DERs and the cable impedance is not considered in the proposed approach. Authors in (Augustine, Mishra, & Lakshminarasamma, 2015) have developed a figure of merit called as droop index to assign the minimum power losses and circulating current between the parallel-connected DERs converters. To this end, droop resistance is determined and then based on V–I droop mechanism, proper load current sharing is performed. A similar approach is adopted in (Niyitegeka, Choi, & Ok, 2016) which deploys a different form of droop index. Targeting the minimization of generation cost, appropriate droop gains are determined in (Moayedi & Davoudi, 2017). The proposed approach improves load current sharing of parallel converters. A variable droop gain is developed in (Lu et al., 2014) in which by increasing the droop gain, load current sharing gets better. On the other side, any decrement in droop gain ameliorates the voltage regulation with reduced voltage deviations. A variable droop gain is also established in (Tahim, Pagano, Lenz, & Stramosk, 2015) which hinges on ESS state of charge. A virtual capacitance is deployed in (Xu et al., 2017) to improve dynamic response of voltage and current signals. Evidently, significant attempts have been made to design efficient droop strategies for proper control requirements of DC MGs. Meanwhile, some influencing issues such as load current sharing in DERs with different rated powers, appropriate power sharing instead of current sharing, and the effect of cable resistance are still under question. This manuscript establishes an efficient droop control strategy for DC MGs which affords a proper load current and power sharing in
2. Proposed load sharing approach The proposed approach for a proper load sharing in an islanded DC MG is developed in this section. The investigated test system is shown in Fig. 1(a) whereas its equivalent circuit is illustrated in Fig. 1(b). In this figure, VDC1, VDC2, I1, I2, and R1, R2 signify the output voltages and the output currents of converters 1 and 2, respectively. The cables resistance is also denoted by R. To establish the load voltage (VL) expression, kirchoff’s voltage law (KVL) is applied in Fig. 1(b). The compact representation of this parameter is as follows.
VL =
RL (R2 VDC1 + R1 VDC2) R1 RL + R2 RL + R1 R2
(1)
In this equation, RL models the load resistance. Solving the equivalent circuit for converters currents, I1 and I2 are expressed based on (2) and (3).
I1 =
R2 VDC1 + (VDC1 − VDC2) RL R1 RL + R2 RL + R1 R2
(2)
I2 =
R1 VDC2 − (VDC1 − VDC2) RL R1 RL + R2 RL + R1 R2
(3)
Two different outlooks could be applied in load sharing. In the first view, load current sharing is the aim of the implemented droop strategy. This notion is the running trend in majority of the conducted studies. The second one fulfills this mission by a proper power sharing among the DERs converters. The proposed approach is explored on the basis of these two notions and a thorough comparison is performed. It is worth mentioning that in both of the cases; the converters power ratings could be equal or unequal with each other. Dealing with the 238
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If (6) is satisfied, the load power is equally shared between the parallel converters. As can be seen, in both (4) and (6), the cable resistances are in general form which could attain different values. If the resistances are equal, the voltages would be equal to yield in an equal load current and power sharing among the converters.
proposed approach, it is worth-mentioning that as a technical principle, one of the resources should be treated with a constant reference voltage and the reference voltages of the remaining DERs converters would be determined based on this reference voltage and also the control objective (an equal load current sharing or an equal load power sharing). In order to keep the proposed approach a general one, in both of these cases, the transmission line or cable resistances are assumed to be different. In order to provide an easy understanding of the proposed approach, at the initial, a system with two parallel-connected DERs is formulated and then, the obtained results are extended for “n” parallelconnected DERs.
2.2. Parallel converters with unequal rated powers (P1 = KP2) 2.2.1. First view: load current sharing In this case, the rated powers of parallel-connected converters are assumed to follow P1 = KP2. Accordingly, the currents should be shared exactly with the same ratio (I1 = KI2). By substituting (2) and (3) in this statement, the following expression is obtained.
2.1. Parallel converters with equal rated powers (P1 = P2) 2.1.1. First view: load current sharing As the parallel-connected converters are assumed to be of the same size, an equal load current sharing would be desired for the converters. In this case, the desired ratio of converters output voltages is determined by making (2) and (3) equal with each other. By this way, (4) is obtained.
VDC1 =
R1 + 2RL VDC2 R2 + 2RL
VDC1 =
If (4) is valid, the load current is divided equally between the converters. In the case of the data provided for the investigated two parallel-connected DERs in Table 1, the second resource is designated as a constant voltage reference; however, the first resource determines its voltage reference with respect to the constant reference voltage and the control target. Note that the load resistance, namely RL, is an unknown parameter from the DERs viewpoint. This unknown parameter needs to be signified in terms of local signals including voltage and current to end in a practical control system.
2.2.2. Second View: power Sharing In this case, the load power is divided based on the main ratio (P1 = KP2). Accordingly, (8) should be satisfied.
By substituting (2) and (3) in (8), the desired ratio of the output voltages is obtained by (9).
2.1.2. Second View: Power Sharing In this case, it is assumed that the control strategy pursues an equal power sharing task among the converters rather than an equal current sharing. To this end, (5) should be satisfied.
(6)
Table 1 The investigated test system parameters.
Vmin , Vrated, Vmax , Vcv Cable resistance (R1)
(1 + K )2RL2 + 4K (R1 RL + R2 RL + R1 R2) 2(R2 + RL)
VDC2 (9)
By substituting (2) and (3) in (5), the desired ratio of voltages is obtained based on (6).
Parameter
RL (1 − K ) +
Expectedly, if K = 1, (9) reduces to (6). In Fig. 2, the solid line corresponds to the second view which pursues a proper load power sharing. With respect to subfigure (a), it can be seen that at higher values of load resistances (smaller load currents), both the current and power sharing approaches yield in similar results with negligible differences. Meanwhile, subfigure (b) depicts the percentage error of these two approaches against the load resistance. As can be seen, how much the load resistance decreases (at higher load currents), a relatively huge difference is captured based on these two control approaches. For instance, at RL = 0.15Ω, nearly there is 10% difference between the recorded ratios.
(5)
R1 + RL VDC2 R2 + RL
(8)
VDC1 I1 = KVDC2 I2
VDC1 =
VDC1 =
(7)
Seemingly, if K = 1, (7) reduces to (4). Fig. 2 depicts the changes in ratio of converters output voltages due to changes in load resistance. This figure is obtained based on the data provided in Table 1 which includes the investigated test system information. In this figure, the dashed line corresponds to the first view which pursues a proper load current sharing.
(4)
VDC1 I1 = VDC2 I2
KR1 + RL (1 + K ) VDC2 R2 + RL (1 + K )
Value
3. Proposed V–I droop strategy
95V , 100V , 105V , 105V
In conventional approaches, droop strategy is represented based on V–I characteristics with a constant droop gain. These methods are mainly based on (10).
0.1Ω
Vi = Vref − Di Ii
0.2Ω
Here, Vrefrepresents the desired output voltage and Vi, Ii denote the output voltage and current of i-th converter. Di is the droop gain of i-th converter. In general, the main purpose is to establish a meaningful dependency between the voltage and current signals to approach a specific control objective. The established framework is not necessarily to be in the form of (10) and it could be stated in a different manner. In the proposed approach, considering one of the converters, its output voltage is assumed to be kept constant and hence, the other converter (in “two” parallel-connected DERs system) experiences a varying output voltage to control the load current or power between the converters. Let assume that VDC2 is kept constant and VDC1 is adjusted. The established
Cable resistance (R2) Cable resistance (R3)
0.1Ω Load resistance (RL)
5Ω → 2.5Ω PEMFC-1
6kW , 45V PEMFC-2
12kW , 45V PEMFC-3
9kW , 45V
239
(10)
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1 0.9 0.8
0.93
0.7
0.92
Difference (%)
P1=0.5*P2 I1=0.5*I2
0.94
0.91 0.6 0.5
1 0
20
1.5
10
5
2
40 60 Load Resistance (Ohm)
80
0 0
100
2
4 6 8 Load resistance (Ohm)
10
Fig. 2. Comparison of the proposed load current and load power sharing approaches, (a): ratio of the converters output voltages against the changes in load resistance, (b): the percentage error in the obtained ratios against the load resistance.
2 AP VDC1 + BP VDC1 + CP = 0
approach is explored for both of the aforementioned cases, namely load current and load power sharing developed in (7) and (9). In these sentences, the load resistance RL is an unknown parameter on the DERs viewpoint and hence, they are not applicable in practice. Accordingly, with respect to (1) and also the circuit representation, RL is represented in the term of voltage and current signals of parallel DERs.
RL =
R2 VDC1 − R1 R2 I1 (R1 + R2) I1 + VDC2 − VDC1
such that AP = R22 I1 + R2 VDC2 K BP = VDC2 (KVDC2 (R1 − R2) − R1 R2 I1 (K − 1)) 2 CP = −KVDC2 R1 (R1 I1 + VDC2)
Solving (14) for VDC1, yields in the following expression. (11)
VDC1 = VDC2 K
To follow the desired voltage ratios obtained in the preceding section in (7) and (9), the V–I characteristics is developed. It should be mentioned that with the aim of achieving a more generalized approach, the conducted analysis is established on the converters with unequal rated powers (P1 = KP2).
This section deals with “n” parallel-connected DERs and extends the general representation of the proposed approach. Similarly, one of the converters is treated as constant voltage and is abbreviated by subscript “cv”. The output voltages of the other converters are adjusted with reference to this constant voltage. Let assume that the desired output voltage of i-th converter is to be determined. By applying mathematical simplifications, the following expressions are represented in a summarized manner. In the case of load current sharing, i.e. (Ii = KiIcv), the following equation is valid for the output voltage of i-th converter.
2 AI VDC1 + BI VDC1 + CI = 0 such that AI = R2 K BI = R2 I1 (R2 − KR1) − KVDC2 (R2 − R1)
R VDCi = Vcv − ⎛ cv − Ri ⎞ Ii ⎝ Ki ⎠
(12)
⎜
Solving (12) for VDC1, yields in the following expression.
(R2 − KR1) I1 − KVDC2 K
(15)
3.3. Extending the proposed approach for “n” parallel-connected DERs
In this case, the purpose is to find the relationship between the voltage and current signals of converter-1 (VDC1 and I1) such that the load current is properly shared between the converters. In general form, I1 = KI2. By substituting (11) in (7), a quadratic relationship is formed between the voltage and current variables denoted in (12).
VDC1 = −
VDC2 + R1 I1 KVDC2 + R2 I1
A fine attention on (15) reveals a non-linear V–I droop characteristic desired for converter-1 to contribute to a proper power sharing between the parallel-connected converters. In a similar manner, here, the parameters are known and through the current measurement, the voltage reference value is calculated to attain a proper load power sharing.
3.1. V–I droop control for proper load current sharing in two parallelconnected DERs
2 CI = R1 VDC2 I1 (R2 − KR1) − KR1 VDC2
(14)
⎟
(16)
If the objective is to attain a proper load power sharing, i.e. (Pi= KiPcv), the following equation speaks for the i-th converter output voltage.
(13)
Note that (13) represents the desired V–I droop characteristic for converter-1 to contribute to a proper load current sharing between the parallel-connected converters. Here, VDC2 and R2 have certain values. Moreover,K and R1 are also known parameters. Therefore, by measuring only the current magnitude, the desired voltage reference could be attained for a proper load current sharing.
VDCi = Vcv
Vcv + Ri Ii Vcv +
R cv I Ki i
(17)
Excluding the converter with constant reference voltage and in the case of remaining converters, as the constant reference voltage and the cable resistance are known, it is only required to attain the load current magnitude. Accordingly, based on the load current measurement and the control objective, the reference voltage of each converter is computed by (17).
3.2. V–I droop control for proper power sharing in two parallel-connected DERs In this case, the main attempt is to find the relationship between the voltage and current signals of converter-1 (VDC1 and I1) such that the demanded power is properly shared between the converters. Similarly, it is assumed that P1 = KP2. By substituting (11) in (9), a quadratic relationship is formed between the voltage and current variables denoted in (14).
4. Technical considerations of the proposed approach This section explores the droop gain variations obtained based on the proposed approach in both the load current and power sharing outlooks. Then, an approach is developed to determine the converter which is assigned to be operated with a constant output voltage. As 240
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magnitude. The statements in (18) and (19) necessitate that for a negative droop gain value, the following expression should be satisfied.
Power Sharing Current Sharing
104
R cv − Ri > 0 Ki
102 100
As Pi = KiPcv, (20) is rewritten as follows.
98 96
0
5
10
15
20
Accordingly, the converter which contributes to a greater R × P is assigned to be treated with a constant output voltage. By this way, the remaining converters would be adjusted at lower output voltages without any overvoltage risk. As mentioned earlier, in the investigated test system and based on the data provided in Table 1, converter-2 demonstrates a greater R × P and hence is adjusted with a constant voltage. Meanwhile, the negative droop gain values of converter-1 are seen in Fig. 4. This issue underlines the preceding remarks. Let assume that the cable resistances are based on the values in Table 1. Then, if the voltage of the second converter namelyVDC2 is considered as the constant output voltage, the droop characteristic of the first converter is demonstrated in Fig. 5. As R2 = 2R1, then P1 = 2P2 results inR1P1 = R2P2. Accordingly, as Fig. 5 demonstrates, the reference voltage of first DER would be equal with the constant reference voltage. However, if R2P2 > R1P1 and the first converter is decided as the constant reference voltage, then (21) is not satisfied and the droop characteristic would see a positive gain, as seen in Fig. 5. It is clear that this case could instigate unacceptable overvoltage magnitude.
25
well, the variations of load bus voltage are addressed in more details. 4.1. Droop gain analysis With respect to (16) and (17), the slope of VDCi − Iicurve determines the droop gain value. At the investigated load current and power sharing strategies, (18) and (19) represent the droop gain expressions.
Current sharing
= −(
R cv − Ri ) Ki
(18)
R
∂VDCi ∂Ii
Power sharing
(21)
R cv Pcv > Ri Pi
Fig. 3. V–I droop curves for load current and power sharing strategies.
∂VDCi ∂Ii
(20)
= −Vcv2
( Kcv − Ri ) i
(Vcv +
R cv 2 I) Ki i
(19)
The following analysis is based on the data provided in Table 1 adopted for the numerical studies. With respect to the parameter values in this table, the output voltage of converter-2 is selected to have a constant value and the output voltage of converter-1 is to be determined (Further explanations on selecting the converter with constant output voltage are provided in the subsequent section). Accordingly, the droop curve of VDC1 − I1 is tailored in Fig. 3. The corresponding droop gain is also explored in Fig. 4. Evidently, in the case of load current sharing, the droop gain value remains constant which is represented by a dashed line. In contradiction, in the case of power sharing strategy, the droop gain follows a non-linear manner depicted by a solid line. It can be seen that how much the load current increases, a greater difference is noticed between the load current and power sharing strategies.
4.3. Bus voltage variation Performance of the proposed approach is also tailored on bus voltage variations. To this end, Ii = KiIcv is substituted in (16) and thus, (22) is attained. It should be mentioned that substituting Pi = KiPcv in (17) also ends in the following expression. (22)
Vcv − R cv Icv = VDCi − Ri Ii
Note that this equation represents the load bus voltage and hence all of the resources end in similar results. It is worthy to mention that although the overall treat of resources is such to attain an equal load bus voltage, (21) demonstrates that the largest voltage drop relates to the DER with constant reference voltage. Regarding this converter, the interconnection cable size is such determined that at the maximum load current, the voltage drop is curbed in less than the maximum permissible amount. This feature is a remarkable merit of the proposed approach which contributes to a better voltage response compared to the recently proposed approaches in DC MG control. In these approaches, by increasing the load current, the droop gain reduces the bus voltage magnitude and a greater voltage drop is noticed.
4.2. Determination of the converter with constant voltage As clarified, in the proposed approach, one of the converters is treated with a constant voltage at its output terminal and the output voltages of the remaining converters are determined with respect to this converter. This section develops an analysis to determine the converter with constant output voltage. For a successful performance of the proposed approach, the output voltage of a particular converter is kept constant at the rated/no-load value and the droop gains of the other converters are adjusted in negative values. Accordingly, the output voltage of the remaining converters would be less than the rated voltage
5. Simulation studies Detailed simulation studies are conducted to evaluate performance of the proposed droop strategies in different conditions and also to establish a comparison platform. To this end, a DC MG, shown in Fig. 6, is modeled in MATLAB/Simulink platform. As can be seen,
-0.13
105 Power Sharing Current Sharing
-0.14
P1=0.5*P2 P1=2P2 P1=4*P2
100
-0.15 0
5
10
15
20
95
25
0
20
40
60
Fig. 5. V–I droop characteristic of the first DER.
Fig. 4. Droop gain variations for load current and power sharing strategies.
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Fig. 6. System representation of the proposed droop strategy on a typical DC MG.
proportional-integral (PI) controllers are deployed in current and voltage control processes. The inner loop (PIi) affords the current control which is mainly considered to improve the dynamic response of the investigated system. The outer loop handles the voltage control (PIv) and is mainly to remove the steady-state error and attain better tracking performance. It should be mentioned that the duty-cycle of the pulse width-modulation (PWM) signal hinges on the magnitude of voltage signal and speaks for the ratio of the time that the switching element is turned on. By this way, the output voltage is controlled. This MG contains two Proton Exchange Membrane Fuel Cell (PEMFC) stack models feeding a boost DC/DC converter. DGs are modeled with PEMFCs with the ratings of 6 kW and 45 V DC. The converters are connected to load through cables with resistances R1 and R2. The load is represented in a pure resistive form with resistance of RL. The remaining data regarding the MG could be found in Table 1. In simulation studies, it is assumed that at t = 10 s, RL is decreased from 5 Ω to 2.5 Ω. Accordingly, the output current would vary. To evaluate load sharing capability of the proposed approach, three different scenarios are assessed. Moreover, performance of the proposed control approach is also tailored in the case of a constant-power load considering both load current and power sharing objectives. Each of these scenarios is investigated as follows.
I1
20
X: 13.15 Y: 16.66
X: 7.977 Y: 11.79
15 X: 5.77 Y: 8.577
10 5
X: 10.9 Y : 22.9
I2
5
10 Time (Sec.)
(a) 105
100
95
V1 V2 VL
5
X: 8 Y: 101.9 X: 13 Y: 98.89
10 Time (Sec.)
(b) 2000
5.1. Conventional droop control applied on converters with equal rated power
X: 12 Y: 2317
P1 P2 X: 8 Y: 1215
1500
In this scenario, two converters with rated power of 6 kW are considered. As the conventional droop mechanism is applied, droop gain is obtained by Di = (Vmax − Vmin)/Imax,i, where Imax,iis the maximum current of i-th converter. In response to the changes in loading of the MG, the output current and the output voltage of converters, load voltage, and power generation of each converter is shown in Fig. 7. As can be seen, due to differences in cables resistance (R1≠ R2), the load current and power are not properly shared between the converters and there exists about 15% deviation between the converters contributions.
X: 13 Y: 1703
X: 6 Y: 888.4
1000 5
10 Time (Sec.)
Fig. 7. Performance of the conventional droop mechanism, (a): output current of converters, (b): output voltage of converters and load voltage, (c): output power of each converter.
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I1 I2
I1 I2
20
X: 12 Y: 20.19
Current (A)
20
15 X: 6 Y: 10.29
20.5
10.35 X: 7 Y: 10.35
10.3
15
X: 12 Y: 20.39
10.25
X: 13 Y: 20.01
20 7
10
X: 8 Y: 10.25
7.5
8
12
12.5
13
10 5
10 Time (Sec.)
5
15
10 Time (Sec.)
(a1)
(a2)
105
Voltage (V)
105 X: 6 Y: 102.9
100
X: 14 Y: 101
V1 V2 VL
95
5
10 Time (Sec.)
X: 6 Y: 103
100
95
15
5
10 Time (Sec.)
(b1)
Power (W)
X: 7 Y: 1081
1500 1075
X: 8 Y: 1070
X: 12 Y: 2120
2100
X: 13 Y: 2079
2080
1070 7
7.5
P1 P2
2000 2120
1080
1000
(b2)
P1 P2
2000
X: 14 Y: 101
V1 V2 VL
8
12
12.5
X: 12 Y: 2101
1500 X: 6 Y: 1076
13
1000 5
10 Time (Sec.)
15
5
10 Time (Sec.)
Fig. 8. Performance of the proposed droop mechanism on converters with equal rated power, (a): output current of converters, (b): output voltage of converters and load voltage, (c): output power of each converter.
output current of converter-2 is exactly twice the output current of converter-1. This notice is due to the fact that P2 = 2P1. However, with respect to subfigure (c1), the output powers of converters do not follow each other by a factor of two. At the initial seconds, there exists 1.3% error and following t = 10 s, it reaches to 2.5%. In the case of a proper power sharing task, subfigure (a2) demonstrates that the load current is not shared by a factor of two. Initially, 1.3% error is captured and following t = 10 s, the current error reaches to 2.5%. However, subfigure (c2) displays that the output power is divided between the converters exactly by a factor of two. Shedding more lights on the obtained results speaks for a smaller voltage deviation in power sharing strategy rather than the load current sharing approach. As can be seen, the proposed approach satisfactorily shares the output current and power among the converters.
Due to improper load current and power sharing, the output voltages of the converters are not the same. 5.2. Proposed droop control applied on converters with equal rated power Similar to the previous scenario, two converters with rated power of 6 kW are considered and the proposed droop control approach is deployed. Both of the load current and power sharing strategies are investigated. Results are demonstrated in Fig. 8. In the case of load current sharing, subfigure (a1) demonstrates that the load current is equally shared between the converters; subfigure (b1) depicts the output voltages being approached to each other; and subfigure (c1) illustrates the power sharing task between the converters which are not exactly equal. At the initial seconds, there exists 0.48% error and following t = 10 s, it reaches to 0.94%. In the case of a proper power sharing task, subfigure (a2) demonstrates that the load current is not equally shared. Initially, 0.51% error is seen and following t = 10 s, the current error is 0.97%. However, subfigure (c2) displays that the output power is equally divided between the converters. Besides the negligible differences, these remarks certify outperformance of the proposed droop control approach.
5.4. Proposed droop control applied on three parallel converters with constant-power load In this scenario, the proposed droop control approach is tested on three parallel-connected DERs connected to a constant-power load, rather than a constant resistance. The detailed data in regard of these three DERs have been previously provided in Table 1. As the second DER renders the largestR × P, it is designated as the DER with constant output voltage reference and the reference voltage of the remaining converters is determined with respect to this converter. In simulation studies, the constant-power load is 2 kW which is increased to constant 6 kW at t = 10 s. The obtained results are demonstrated in Fig. 10. With respect to the obtained results, it can be seen that the proposed droop control approach performs well considering both the load current and load power sharing. In order to accurately compare the obtained
5.3. Proposed droop control applied on converters with unequal rated power In contradiction to the previous scenarios, the converters are not equally rated. Converter-1 is rated at 6 kW and converter-2 is rated at 12 kW. The proposed droop control approach is tailored in these conditions. Both of the load current and power sharing strategies are investigated and the results are demonstrated in Fig. 9. In the case of load current sharing, subfigure (a1) demonstrates that the magnitude of 243
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30 X: 12 Y: 26.58
X: 6 Y: 13.64
15
X: 8 Y: 6.818
10 5
Current (A)
20
I1 I2
25
I1 I2
25
X: 14 Y: 13.29
20
10 Time (Sec.)
X: 6 Y: 13.55
15
X: 8 Y: 6.908
10 5
5
15
X: 12 Y: 26.26
5
10 Time (Sec.)
(a1)
(a2 )
105
Voltage (V)
105
X: 6 Y: 102.3
100
95
X: 14 Y: 13.64
X: 14 Y: 99.68
V1 V2 VL
5
10 Time (Sec.)
X: 6 Y: 102.3
100
95
15
X: 14 Y: 99.75
V1 V2 VL
5
10 Time (Sec.)
(b1)
(b2)
3000
3000 P1 P2
2000
X: 12 Y: 2791
X: 6 Y: 1432
1500 X: 8 Y: 702
1000 500
5
P1
2500 Power (W)
2500
X: 14 Y: 1343
P2
2000
X: 6 Y: 1423
1500 X: 8 Y: 711.4
1000
10 Time (Sec.)
X: 12 Y: 2758
500
15
5
X: 14 Y: 1379
10 Time (Sec.)
Fig. 9. Performance of the proposed droop mechanism on converters with unequal rated power (P2 = 2P1), (a): output current of converters, (b): output voltage of converters and load voltage, (c): output power of each converter.
Comparing the obtained results certifies the corresponding ratios and confirms the outperformance of the proposed control approach. It can be seen that both of the load current and load power sharing end in similar results with low differences. Besides, it can be deduced that the
result before and after the load change, Table 2 gathers the numerical results. With respect to the data in Tables 1 and 2, in the case of load current sharing I1 = 0.5I2 and I3 = 0.75I2. Moreover, it can be seen that in the case of load power sharing, P1 = 0.5P2 and P3 = 0.75P2.
30 IL1 IL2 IL3
20
Current (A)
Current (A)
30
10
0
5
10 Time (Sec.)
10
0
15
IL1 IL2 IL3
20
5
10 Time (Sec.)
(a1)
(a2)
3000
3000
Power (W)
P1 P2 P3
2000
1000
0
5
10 Time (Sec.)
1000
0
15
P1 P2 P3
2000
5
10 Time (Sec.)
Fig. 10. Performance of the proposed droop mechanism on 3 parallel converters with unequal rated power, (a): output current of converters, (b): output power of each converter.
244
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Table 2 Power and current values in the investigated constant-power load. Converters
Current Sharing Strategy Current (A)
Converter 1 Converter 2 Converter 3 Total
Power Sharing Strategy Power (W)
Current (A)
Power (W)
Before t = 10 s
After t = 10 s
Before t = 10 s
After t = 10s
Before t = 10s
After t = 10s
Before t = 10s
After t = 10s
4.303 8.606 6.455 19.364
13.38 26.76 20.07 60.21
446.29 903.7 670.83 2020.8
1351.24 2809.90 2040.28 6201.42
4.3293 8.5533 6.4805 19.363
13.62 26.23 20.296 60.148
449.04 898.091 673.57 2020.7
1377.19 2754.39 2065.79 6197.37
Chehardeh, M. I., Lesani, H., Zadeh, M. K., & Siavashi, E. M. (2009). An optimal control strategy to alleviate sub-synchronous resonance in VSC-HVDC systems. Power electronicsand intelligent transportation system (PEITS). 2nd International Conferenceon: Shenzhen250–255. Farhadi, M., & Mohammed, O. A. (2015). Performance enhancement of actively controlled hybrid DC microgrid incorporating pulsed load. IEEE Transactions on Industry Applications, 51(September–October (5)), 3570–3578. Ferreira, R. A. F., Braga, H. A. C., Ferreira, A. A., & Barbosa, P. G. (2012). Analysis of voltage droop control method for dc microgrids with Simulink: modeling and simulation. 10th IEEE/IAS international conference on industry applications (pp. 1–6). Fregosi, D., et al. (2015). A comparative study of DC and AC microgrids in commercial buildings across different climates and operating profiles. IEEE first international conference on DC microgrids (ICDCM) (pp. 159–164). Gu, Y., Xiang, X., Li, W., & He, X. (2014). Mode-Adaptive decentralized control for renewable DC microgrid with enhanced reliability and flexibility. IEEE Transactions on Power Electronics, 29(September (9)), 5072–5080. Hatziargyriou, N., Asano, H., Iravani, R., & Marnay, C. (2007). Microgrids. IEEE Power and Energy Magazine, 5(July-August no. 4), 78–94. Hussain, A., Muhammad Arif, S., Aslam, M., & Danial Ali Shah, S. (2017). Optimal siting and sizing of tri-generation equipment for developing an autonomous community microgrid considering uncertainties. Sustainable Cities and Society, 32, 318–330. Jian, Z. H., He, Z. Y., Jia, J., & Xie, Y. (2013). A review of control strategies for DC microgrid. Fourth international conference on intelligent control and information processing, 666–671. John Justo, J., Mwasilu, F., Lee, J., & Jung, J.-W. (2013). AC-microgrids versus DC-microgrids with distributed energy resources: A review. Renewable and Sustainable Energy Reviews, 24(August), 387–405. Lu, X., Sun, K., Huang, L., Guerrero, J. M., Vasquez, J. C., & Xing, Y. (2014). Virtual impedance based stability improvement for DC microgrids with constant power loads. IEEE energy conversion congress and exposition (ECCE) (pp. 2670–2675). Mazumder, S. K., Tahir, M., & Acharya, K. (2008). Master–Slave current-Sharing control of a parallel DC–DC converter system over an RF communication interface. IEEE Transactions on Industrial Electronics, 55(no. 1), 59–66. Moayedi, S., & Davoudi, A. (2017). Unifying distributed dynamic optimization and control of islanded DC microgrids. IEEE Transactions on Power Electronics, 32(no. 3), 2329–2346. Mortezapour, V., & Lesani, H. (2017). Hybrid AC/DC microgrids: A generalized approach for autonomous droop-based primary control in islanded operations. International Journal of Electrical Power & Energy Systems, 93, 109–118. Niyitegeka, G., Choi, J., & Ok, Y. (2016). Improved droop control for effective load sharing and voltage regulation in DC microgrids. Electric power quality and supply reliability (PQ) (pp. 125–132). Planas, E., Andreu, J., Ignacio, J., Gárate, I., de Alegría, M., & Ibarra, E. (2015). AC and DC technology in microgrids: A review. Renewable and Sustainable Energy Reviews, 43, 726–749. Reynolds, J., Rezgui, Y., & Hippolyte, J.-L. (2017). Upscaling energy control from building to districts: Current limitations and future perspectives. Sustainable Cities and Society. Sasidharan, N., & Singh, J. G. (2017). A resilient DC community grid with real time ancillary services management. Sustainable Cities and Society, 28, 367–386. Tahim, A. P. N., Pagano, D. J., Lenz, E., & Stramosk, V. (2015). Modeling and stability analysis of islanded DC microgrids under droop control. IEEE Transactions on Power Electronics, 30(no. 8), 4597–4607. Wouters, C. (2015). Towards a regulatory framework for microgrids—The Singapore experience. Sustainable Cities and Society, 15, 22–32. Xu, Q., Hu, X., Wang, P., Xiao, J., Tu, P., Wen, C., et al. (2017). A decentralized dynamic power sharing strategy for hybrid energy storage system in autonomous DC microgrid. IEEE Transactions on Industrial Electronics, PP(no. 99), 1. Yang, N., Paire, D., Gao, F., Miraoui, A., & Liu, W. (2015). Compensation of droop control using common load condition in DC microgrids to improve voltage regulation and load sharing. International Journal of Electrical Power & Energy Systems, 64, 752–760.
total generated power of DERs is a bit greater than the load power which is due to the power losses in cable resistances. Note that the load power sharing results in lower dissipated power against the load current sharing approach. Let call back the numeric example. To feed the 6 kW load, 6197.3 W is generated based on load power sharing and 6201.42 W is generated based on load current sharing. Although there is not a huge difference, but as mentioned earlier, at the higher load power values, the differences would get larger. For instance, by increasing the load power from 2 kW to 6 kW, the percentage error increases from 0.0049% to 0.0653%. 6. Conclusion A generalized droop control approach for DC MGs was developed in this manuscript. The proposed approach was formulated based on fundamental principles of equivalent circuit adopted for two main objectives say as proper load current sharing and proper power sharing tasks. The investigated analysis demonstrated that increasing load current, i.e. decreasing load resistance, ends in larger deviations of these two control targets. Similarly, in the case of larger differences in cable resistances and the converters rated powers, larger differences were noticed in regards of current sharing and power sharing processes. Based on the conducted simulations, it was seen that the conventional droop mechanism does not contribute to a proper load sharing between the converters which provoked a larger error between the converters voltages. This is while; outperformance of the proposed approach on both load current and power sharing were noticed. Small errors were reflected on the output currents and output powers of the converters. It was inferred that in both of the current sharing and power sharing strategies, output voltages of the converters are similar with small differences. However, the power sharing approach contributes to smaller deviations in output voltages. The adopted droop control approach could be readily deployed for an effective and precise load sharing task in DC MGs with parallel-connected DERs. References Ahmad, F., & Alam, M. S. (2017). Feasibility study, design and implementation of smart polygeneration microgrid at AMU. Sustainable Cities and Society, 14 [Available online]. Augustine, S., Mishra, M. K., & Lakshminarasamma, N. (2015). Adaptive droop control strategy for load sharing and circulating current minimization in low-Voltage standalone DC microgrid. IEEE Transactions on Sustainable Energy, 6(no. 1), 132–141. Boeke, U., & Wendt, M. (2015). DC power grids for buildings, in DC Microgrids (ICDCM). IEEE first int. conf. (pp. 210–214). Bouzid, A. M., Guerrero, J. M., Cheriti, A., Bouhamida, M., Sicard, P., & Benghanem, M. (2015). A survey on control of electric power distributed generation systems for microgrid applications. Renewable and Sustainable Energy Reviews, 44, 751–766. Chan, D., Cameron, M., & Yoon, Y. (2017). Key success factors for global application of micro energy grid model. Sustainable Cities and Society, 28, 209–224.
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Contents lists available at ScienceDirect
Sustainable Cities and Society journal homepage: www.elsevier.com/locate/scs
A generalized droop control approach for islanded DC microgrids hosting parallel-connected DERs
MARK
⁎
Sajjad Golshannavaza, , Vahid Mortezapourb a b
Electrical Engineering Department, Urmia University, Urmia, Iran School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran
A R T I C L E I N F O
A B S T R A C T
Keywords: DC microgrids (MGs) Islanded operation Load current and power sharing Voltage regulation Generalized droop control strategy
A great attention is dedicated to design a generalized droop control approach contributing to proper load current sharing and voltage regulation in DC microgrids (MGs). The established approach is based on fundamental principles of parallel-connected distributed energy resources (DERs) equivalent circuit ending in a general method effective for different interconnection schemes. Accordingly, proper load sharing and voltage regulation are pursued in DERs with different power ratings and different cable impedances. Moreover, the proposed approach is apt to be operated in both load current and power sharing modes. Comparative studies are conducted to evaluate performance of the proposed approach regarding these two control strategies and highlighting the possible differences. Accordingly, the desired control and technical requirements could be accommodated, effectively. Detailed simulation studies are conducted and compared with each other to interrogate performance of the proposed approach. Results are discussed in depth.
1. Introduction The concept of microgrid (MG) is an expediting factor in swift deployment of small-scale distributed energy resources (DERs), more specifically in islanded and remote areas (Hatziargyriou, Asano, Iravani, & Marnay, 2007). Besides the traditional power resources, renewable-based DERs are one of the main elements of MGs and are widely deployed in cities and rural environments. For instance, rooftype PVs are now a common seen at these areas (Sasidharan & Singh, 2017). By developing a suitable and well-defined control system, these resources could be easily integrated into the energy grid and contributing to reduce emissions and environmental pollutions (Ahmad & Alam, 2017). Besides, the energy grid of sustainable cities mainly depends on MG concept which outlines the great importance of this notion to be explored more (Chan, Cameron, & Yoon, 2017; Wouters, 2015). On the other hand, if different types of consumers in a particular boundary interact with each other, they could attain further mutual benefits. This notice also adds to the merits of MG concept in real-case applications (Reynolds, Rezgui, & Hippolyte, 2017). As clarified, all of these features enable the swift progress and the final transition towards the sustainable cities through MG implementations (Hussain, Muhammad Arif, Aslam, & Danial Ali Shah, 2017). Technically speaking, MG is defined as a single entity accommodating a cluster of loads and generating units inside a particular
⁎
boundaries being operated in a grid-connected or an autonomous mode. It also provides seamless transitions between grid-connected and islanded modes of operation. MGs fall in two main categories including alternative current (AC) and direct current (DC) types. The latter type manifests competitive features over the former (Planas et al., 2015; John Justo, Mwasilu, Lee, & Jung, 2013). Annihilating the skin effect and power quality issues, absence of frequency control, and an easy power flow are some of the main features of DC MGs over their AC counterparts. Accordingly, DC MGs offer higher figures of merit say as efficiency, reliability, safety, redundancy, and reduced cost (Chehardeh, Lesani, Zadeh, & Siavashi, 2009; Jian, He, Jia, & Xie, 2013). Taking a look from consumption requirements, many of the loads in MG premises demand a DC power emphasizing the superiority of DC electrification (Boeke & Wendt, 2015; Fregosi et al., 2015). Computers and data centers, variable-speed drives, and light emitting diodes are to be named, but a few. Dealing with generation shape of DERs in DC MGs, they produce power inherently in DC form or it is converted to DC through power electronics converters. Photovoltaics (PVs), fuel cells (FCs), and energy storage systems (ESSs) are in touch with DC power. In contradiction, wind turbines (WTs) and the main grid provide an AC power being converted to an equivalent DC. In recent attempts, DC and AC MGs are coupled together through an interfacing converter introducing the concept of hybrid MGs (Mortezapour & Lesani, 2017). This type of MG provokes opportunities
Corresponding author. E-mail address: [email protected] (S. Golshannavaz).
http://dx.doi.org/10.1016/j.scs.2017.09.038 Received 13 June 2017; Received in revised form 29 August 2017; Accepted 30 September 2017 2210-6707/ © 2017 Elsevier Ltd. All rights reserved.
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Fig. 1. (a) Two parallel-connected DC/DC converters, (b) equivalent circuit.
parallel-connected DERs. The proposed approach is a generalized one established based on fundamental principles of DERs equivalent circuit which could contribute to proper load current sharing and a proper power sharing among them. Moreover, the proposed droop strategy demonstrates satisfactory results in DERs with different rated powers and different interconnection cable impedance. Detailed simulation studies are evolved to assess performance of the proposed approach and come into a comparison platform. The remainder of this manuscript is organized as follows: Section 2 addresses the principle formulation of the proposed approach. Based on these equations, Section 3 extends V–I droop characteristics to achieve two individual objectives say as proper sharing of load current and proper power sharing. Some technical considerations regarding the proposed approach are discussed in Section 4. Simulation studies are provided in Section 5 and detailed comparative studies are conducted to portray the merits of the proposed approach. Concluding remarks and general discussions are unveiled in the last section.
of both AC and DC MGs. However, it is not the main focus of the present study and accordingly is not tailored here. On the main side, the ongoing study looks into the efficient DC MGs. Considering data exchange between the embedded elements, DC MGs could be operated in two main configurations. In one type, there are communication links to establish bilateral data transfers between specific DERs and the control center. Centralized control approaches (Yang, Paire, Gao, Miraoui, & Liu, 2015; Farhadi & Mohammed, 2015) and master/slave methods (Mazumder, Tahir, & Acharya, 2008; Ferreira, Braga, Ferreira, & Barbosa, 2012) require such connections. Although beneficial for small-scale MGs, communication links are not judged as economic and reliable solutions for real-scale MGs. The second scheme excludes the need for high bandwidth communication links wherein each DER deploys its local variables for control purposes. Accordingly, DERs are operated in a decentralized manner without any data transfer. Droop control method is a popular decentralized approach which controls the converter output voltage based on its output current (Bouzid et al., 2015). Different droop control strategies have been proposed for DC MGs. In (Gu, Xiang, Li, & He, 2014), considering the presence of ESSs, the droop control strategy is evaluated in three different modes. Based on the output power level, one of the three modes is selected for droop strategy. Proper responses are attained based on the proposed strategy; however, it does not accommodate parallel operation of DERs and the cable impedance is not considered in the proposed approach. Authors in (Augustine, Mishra, & Lakshminarasamma, 2015) have developed a figure of merit called as droop index to assign the minimum power losses and circulating current between the parallel-connected DERs converters. To this end, droop resistance is determined and then based on V–I droop mechanism, proper load current sharing is performed. A similar approach is adopted in (Niyitegeka, Choi, & Ok, 2016) which deploys a different form of droop index. Targeting the minimization of generation cost, appropriate droop gains are determined in (Moayedi & Davoudi, 2017). The proposed approach improves load current sharing of parallel converters. A variable droop gain is developed in (Lu et al., 2014) in which by increasing the droop gain, load current sharing gets better. On the other side, any decrement in droop gain ameliorates the voltage regulation with reduced voltage deviations. A variable droop gain is also established in (Tahim, Pagano, Lenz, & Stramosk, 2015) which hinges on ESS state of charge. A virtual capacitance is deployed in (Xu et al., 2017) to improve dynamic response of voltage and current signals. Evidently, significant attempts have been made to design efficient droop strategies for proper control requirements of DC MGs. Meanwhile, some influencing issues such as load current sharing in DERs with different rated powers, appropriate power sharing instead of current sharing, and the effect of cable resistance are still under question. This manuscript establishes an efficient droop control strategy for DC MGs which affords a proper load current and power sharing in
2. Proposed load sharing approach The proposed approach for a proper load sharing in an islanded DC MG is developed in this section. The investigated test system is shown in Fig. 1(a) whereas its equivalent circuit is illustrated in Fig. 1(b). In this figure, VDC1, VDC2, I1, I2, and R1, R2 signify the output voltages and the output currents of converters 1 and 2, respectively. The cables resistance is also denoted by R. To establish the load voltage (VL) expression, kirchoff’s voltage law (KVL) is applied in Fig. 1(b). The compact representation of this parameter is as follows.
VL =
RL (R2 VDC1 + R1 VDC2) R1 RL + R2 RL + R1 R2
(1)
In this equation, RL models the load resistance. Solving the equivalent circuit for converters currents, I1 and I2 are expressed based on (2) and (3).
I1 =
R2 VDC1 + (VDC1 − VDC2) RL R1 RL + R2 RL + R1 R2
(2)
I2 =
R1 VDC2 − (VDC1 − VDC2) RL R1 RL + R2 RL + R1 R2
(3)
Two different outlooks could be applied in load sharing. In the first view, load current sharing is the aim of the implemented droop strategy. This notion is the running trend in majority of the conducted studies. The second one fulfills this mission by a proper power sharing among the DERs converters. The proposed approach is explored on the basis of these two notions and a thorough comparison is performed. It is worth mentioning that in both of the cases; the converters power ratings could be equal or unequal with each other. Dealing with the 238
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If (6) is satisfied, the load power is equally shared between the parallel converters. As can be seen, in both (4) and (6), the cable resistances are in general form which could attain different values. If the resistances are equal, the voltages would be equal to yield in an equal load current and power sharing among the converters.
proposed approach, it is worth-mentioning that as a technical principle, one of the resources should be treated with a constant reference voltage and the reference voltages of the remaining DERs converters would be determined based on this reference voltage and also the control objective (an equal load current sharing or an equal load power sharing). In order to keep the proposed approach a general one, in both of these cases, the transmission line or cable resistances are assumed to be different. In order to provide an easy understanding of the proposed approach, at the initial, a system with two parallel-connected DERs is formulated and then, the obtained results are extended for “n” parallelconnected DERs.
2.2. Parallel converters with unequal rated powers (P1 = KP2) 2.2.1. First view: load current sharing In this case, the rated powers of parallel-connected converters are assumed to follow P1 = KP2. Accordingly, the currents should be shared exactly with the same ratio (I1 = KI2). By substituting (2) and (3) in this statement, the following expression is obtained.
2.1. Parallel converters with equal rated powers (P1 = P2) 2.1.1. First view: load current sharing As the parallel-connected converters are assumed to be of the same size, an equal load current sharing would be desired for the converters. In this case, the desired ratio of converters output voltages is determined by making (2) and (3) equal with each other. By this way, (4) is obtained.
VDC1 =
R1 + 2RL VDC2 R2 + 2RL
VDC1 =
If (4) is valid, the load current is divided equally between the converters. In the case of the data provided for the investigated two parallel-connected DERs in Table 1, the second resource is designated as a constant voltage reference; however, the first resource determines its voltage reference with respect to the constant reference voltage and the control target. Note that the load resistance, namely RL, is an unknown parameter from the DERs viewpoint. This unknown parameter needs to be signified in terms of local signals including voltage and current to end in a practical control system.
2.2.2. Second View: power Sharing In this case, the load power is divided based on the main ratio (P1 = KP2). Accordingly, (8) should be satisfied.
By substituting (2) and (3) in (8), the desired ratio of the output voltages is obtained by (9).
2.1.2. Second View: Power Sharing In this case, it is assumed that the control strategy pursues an equal power sharing task among the converters rather than an equal current sharing. To this end, (5) should be satisfied.
(6)
Table 1 The investigated test system parameters.
Vmin , Vrated, Vmax , Vcv Cable resistance (R1)
(1 + K )2RL2 + 4K (R1 RL + R2 RL + R1 R2) 2(R2 + RL)
VDC2 (9)
By substituting (2) and (3) in (5), the desired ratio of voltages is obtained based on (6).
Parameter
RL (1 − K ) +
Expectedly, if K = 1, (9) reduces to (6). In Fig. 2, the solid line corresponds to the second view which pursues a proper load power sharing. With respect to subfigure (a), it can be seen that at higher values of load resistances (smaller load currents), both the current and power sharing approaches yield in similar results with negligible differences. Meanwhile, subfigure (b) depicts the percentage error of these two approaches against the load resistance. As can be seen, how much the load resistance decreases (at higher load currents), a relatively huge difference is captured based on these two control approaches. For instance, at RL = 0.15Ω, nearly there is 10% difference between the recorded ratios.
(5)
R1 + RL VDC2 R2 + RL
(8)
VDC1 I1 = KVDC2 I2
VDC1 =
VDC1 =
(7)
Seemingly, if K = 1, (7) reduces to (4). Fig. 2 depicts the changes in ratio of converters output voltages due to changes in load resistance. This figure is obtained based on the data provided in Table 1 which includes the investigated test system information. In this figure, the dashed line corresponds to the first view which pursues a proper load current sharing.
(4)
VDC1 I1 = VDC2 I2
KR1 + RL (1 + K ) VDC2 R2 + RL (1 + K )
Value
3. Proposed V–I droop strategy
95V , 100V , 105V , 105V
In conventional approaches, droop strategy is represented based on V–I characteristics with a constant droop gain. These methods are mainly based on (10).
0.1Ω
Vi = Vref − Di Ii
0.2Ω
Here, Vrefrepresents the desired output voltage and Vi, Ii denote the output voltage and current of i-th converter. Di is the droop gain of i-th converter. In general, the main purpose is to establish a meaningful dependency between the voltage and current signals to approach a specific control objective. The established framework is not necessarily to be in the form of (10) and it could be stated in a different manner. In the proposed approach, considering one of the converters, its output voltage is assumed to be kept constant and hence, the other converter (in “two” parallel-connected DERs system) experiences a varying output voltage to control the load current or power between the converters. Let assume that VDC2 is kept constant and VDC1 is adjusted. The established
Cable resistance (R2) Cable resistance (R3)
0.1Ω Load resistance (RL)
5Ω → 2.5Ω PEMFC-1
6kW , 45V PEMFC-2
12kW , 45V PEMFC-3
9kW , 45V
239
(10)
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1 0.9 0.8
0.93
0.7
0.92
Difference (%)
P1=0.5*P2 I1=0.5*I2
0.94
0.91 0.6 0.5
1 0
20
1.5
10
5
2
40 60 Load Resistance (Ohm)
80
0 0
100
2
4 6 8 Load resistance (Ohm)
10
Fig. 2. Comparison of the proposed load current and load power sharing approaches, (a): ratio of the converters output voltages against the changes in load resistance, (b): the percentage error in the obtained ratios against the load resistance.
2 AP VDC1 + BP VDC1 + CP = 0
approach is explored for both of the aforementioned cases, namely load current and load power sharing developed in (7) and (9). In these sentences, the load resistance RL is an unknown parameter on the DERs viewpoint and hence, they are not applicable in practice. Accordingly, with respect to (1) and also the circuit representation, RL is represented in the term of voltage and current signals of parallel DERs.
RL =
R2 VDC1 − R1 R2 I1 (R1 + R2) I1 + VDC2 − VDC1
such that AP = R22 I1 + R2 VDC2 K BP = VDC2 (KVDC2 (R1 − R2) − R1 R2 I1 (K − 1)) 2 CP = −KVDC2 R1 (R1 I1 + VDC2)
Solving (14) for VDC1, yields in the following expression. (11)
VDC1 = VDC2 K
To follow the desired voltage ratios obtained in the preceding section in (7) and (9), the V–I characteristics is developed. It should be mentioned that with the aim of achieving a more generalized approach, the conducted analysis is established on the converters with unequal rated powers (P1 = KP2).
This section deals with “n” parallel-connected DERs and extends the general representation of the proposed approach. Similarly, one of the converters is treated as constant voltage and is abbreviated by subscript “cv”. The output voltages of the other converters are adjusted with reference to this constant voltage. Let assume that the desired output voltage of i-th converter is to be determined. By applying mathematical simplifications, the following expressions are represented in a summarized manner. In the case of load current sharing, i.e. (Ii = KiIcv), the following equation is valid for the output voltage of i-th converter.
2 AI VDC1 + BI VDC1 + CI = 0 such that AI = R2 K BI = R2 I1 (R2 − KR1) − KVDC2 (R2 − R1)
R VDCi = Vcv − ⎛ cv − Ri ⎞ Ii ⎝ Ki ⎠
(12)
⎜
Solving (12) for VDC1, yields in the following expression.
(R2 − KR1) I1 − KVDC2 K
(15)
3.3. Extending the proposed approach for “n” parallel-connected DERs
In this case, the purpose is to find the relationship between the voltage and current signals of converter-1 (VDC1 and I1) such that the load current is properly shared between the converters. In general form, I1 = KI2. By substituting (11) in (7), a quadratic relationship is formed between the voltage and current variables denoted in (12).
VDC1 = −
VDC2 + R1 I1 KVDC2 + R2 I1
A fine attention on (15) reveals a non-linear V–I droop characteristic desired for converter-1 to contribute to a proper power sharing between the parallel-connected converters. In a similar manner, here, the parameters are known and through the current measurement, the voltage reference value is calculated to attain a proper load power sharing.
3.1. V–I droop control for proper load current sharing in two parallelconnected DERs
2 CI = R1 VDC2 I1 (R2 − KR1) − KR1 VDC2
(14)
⎟
(16)
If the objective is to attain a proper load power sharing, i.e. (Pi= KiPcv), the following equation speaks for the i-th converter output voltage.
(13)
Note that (13) represents the desired V–I droop characteristic for converter-1 to contribute to a proper load current sharing between the parallel-connected converters. Here, VDC2 and R2 have certain values. Moreover,K and R1 are also known parameters. Therefore, by measuring only the current magnitude, the desired voltage reference could be attained for a proper load current sharing.
VDCi = Vcv
Vcv + Ri Ii Vcv +
R cv I Ki i
(17)
Excluding the converter with constant reference voltage and in the case of remaining converters, as the constant reference voltage and the cable resistance are known, it is only required to attain the load current magnitude. Accordingly, based on the load current measurement and the control objective, the reference voltage of each converter is computed by (17).
3.2. V–I droop control for proper power sharing in two parallel-connected DERs In this case, the main attempt is to find the relationship between the voltage and current signals of converter-1 (VDC1 and I1) such that the demanded power is properly shared between the converters. Similarly, it is assumed that P1 = KP2. By substituting (11) in (9), a quadratic relationship is formed between the voltage and current variables denoted in (14).
4. Technical considerations of the proposed approach This section explores the droop gain variations obtained based on the proposed approach in both the load current and power sharing outlooks. Then, an approach is developed to determine the converter which is assigned to be operated with a constant output voltage. As 240
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magnitude. The statements in (18) and (19) necessitate that for a negative droop gain value, the following expression should be satisfied.
Power Sharing Current Sharing
104
R cv − Ri > 0 Ki
102 100
As Pi = KiPcv, (20) is rewritten as follows.
98 96
0
5
10
15
20
Accordingly, the converter which contributes to a greater R × P is assigned to be treated with a constant output voltage. By this way, the remaining converters would be adjusted at lower output voltages without any overvoltage risk. As mentioned earlier, in the investigated test system and based on the data provided in Table 1, converter-2 demonstrates a greater R × P and hence is adjusted with a constant voltage. Meanwhile, the negative droop gain values of converter-1 are seen in Fig. 4. This issue underlines the preceding remarks. Let assume that the cable resistances are based on the values in Table 1. Then, if the voltage of the second converter namelyVDC2 is considered as the constant output voltage, the droop characteristic of the first converter is demonstrated in Fig. 5. As R2 = 2R1, then P1 = 2P2 results inR1P1 = R2P2. Accordingly, as Fig. 5 demonstrates, the reference voltage of first DER would be equal with the constant reference voltage. However, if R2P2 > R1P1 and the first converter is decided as the constant reference voltage, then (21) is not satisfied and the droop characteristic would see a positive gain, as seen in Fig. 5. It is clear that this case could instigate unacceptable overvoltage magnitude.
25
well, the variations of load bus voltage are addressed in more details. 4.1. Droop gain analysis With respect to (16) and (17), the slope of VDCi − Iicurve determines the droop gain value. At the investigated load current and power sharing strategies, (18) and (19) represent the droop gain expressions.
Current sharing
= −(
R cv − Ri ) Ki
(18)
R
∂VDCi ∂Ii
Power sharing
(21)
R cv Pcv > Ri Pi
Fig. 3. V–I droop curves for load current and power sharing strategies.
∂VDCi ∂Ii
(20)
= −Vcv2
( Kcv − Ri ) i
(Vcv +
R cv 2 I) Ki i
(19)
The following analysis is based on the data provided in Table 1 adopted for the numerical studies. With respect to the parameter values in this table, the output voltage of converter-2 is selected to have a constant value and the output voltage of converter-1 is to be determined (Further explanations on selecting the converter with constant output voltage are provided in the subsequent section). Accordingly, the droop curve of VDC1 − I1 is tailored in Fig. 3. The corresponding droop gain is also explored in Fig. 4. Evidently, in the case of load current sharing, the droop gain value remains constant which is represented by a dashed line. In contradiction, in the case of power sharing strategy, the droop gain follows a non-linear manner depicted by a solid line. It can be seen that how much the load current increases, a greater difference is noticed between the load current and power sharing strategies.
4.3. Bus voltage variation Performance of the proposed approach is also tailored on bus voltage variations. To this end, Ii = KiIcv is substituted in (16) and thus, (22) is attained. It should be mentioned that substituting Pi = KiPcv in (17) also ends in the following expression. (22)
Vcv − R cv Icv = VDCi − Ri Ii
Note that this equation represents the load bus voltage and hence all of the resources end in similar results. It is worthy to mention that although the overall treat of resources is such to attain an equal load bus voltage, (21) demonstrates that the largest voltage drop relates to the DER with constant reference voltage. Regarding this converter, the interconnection cable size is such determined that at the maximum load current, the voltage drop is curbed in less than the maximum permissible amount. This feature is a remarkable merit of the proposed approach which contributes to a better voltage response compared to the recently proposed approaches in DC MG control. In these approaches, by increasing the load current, the droop gain reduces the bus voltage magnitude and a greater voltage drop is noticed.
4.2. Determination of the converter with constant voltage As clarified, in the proposed approach, one of the converters is treated with a constant voltage at its output terminal and the output voltages of the remaining converters are determined with respect to this converter. This section develops an analysis to determine the converter with constant output voltage. For a successful performance of the proposed approach, the output voltage of a particular converter is kept constant at the rated/no-load value and the droop gains of the other converters are adjusted in negative values. Accordingly, the output voltage of the remaining converters would be less than the rated voltage
5. Simulation studies Detailed simulation studies are conducted to evaluate performance of the proposed droop strategies in different conditions and also to establish a comparison platform. To this end, a DC MG, shown in Fig. 6, is modeled in MATLAB/Simulink platform. As can be seen,
-0.13
105 Power Sharing Current Sharing
-0.14
P1=0.5*P2 P1=2P2 P1=4*P2
100
-0.15 0
5
10
15
20
95
25
0
20
40
60
Fig. 5. V–I droop characteristic of the first DER.
Fig. 4. Droop gain variations for load current and power sharing strategies.
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Fig. 6. System representation of the proposed droop strategy on a typical DC MG.
proportional-integral (PI) controllers are deployed in current and voltage control processes. The inner loop (PIi) affords the current control which is mainly considered to improve the dynamic response of the investigated system. The outer loop handles the voltage control (PIv) and is mainly to remove the steady-state error and attain better tracking performance. It should be mentioned that the duty-cycle of the pulse width-modulation (PWM) signal hinges on the magnitude of voltage signal and speaks for the ratio of the time that the switching element is turned on. By this way, the output voltage is controlled. This MG contains two Proton Exchange Membrane Fuel Cell (PEMFC) stack models feeding a boost DC/DC converter. DGs are modeled with PEMFCs with the ratings of 6 kW and 45 V DC. The converters are connected to load through cables with resistances R1 and R2. The load is represented in a pure resistive form with resistance of RL. The remaining data regarding the MG could be found in Table 1. In simulation studies, it is assumed that at t = 10 s, RL is decreased from 5 Ω to 2.5 Ω. Accordingly, the output current would vary. To evaluate load sharing capability of the proposed approach, three different scenarios are assessed. Moreover, performance of the proposed control approach is also tailored in the case of a constant-power load considering both load current and power sharing objectives. Each of these scenarios is investigated as follows.
I1
20
X: 13.15 Y: 16.66
X: 7.977 Y: 11.79
15 X: 5.77 Y: 8.577
10 5
X: 10.9 Y : 22.9
I2
5
10 Time (Sec.)
(a) 105
100
95
V1 V2 VL
5
X: 8 Y: 101.9 X: 13 Y: 98.89
10 Time (Sec.)
(b) 2000
5.1. Conventional droop control applied on converters with equal rated power
X: 12 Y: 2317
P1 P2 X: 8 Y: 1215
1500
In this scenario, two converters with rated power of 6 kW are considered. As the conventional droop mechanism is applied, droop gain is obtained by Di = (Vmax − Vmin)/Imax,i, where Imax,iis the maximum current of i-th converter. In response to the changes in loading of the MG, the output current and the output voltage of converters, load voltage, and power generation of each converter is shown in Fig. 7. As can be seen, due to differences in cables resistance (R1≠ R2), the load current and power are not properly shared between the converters and there exists about 15% deviation between the converters contributions.
X: 13 Y: 1703
X: 6 Y: 888.4
1000 5
10 Time (Sec.)
Fig. 7. Performance of the conventional droop mechanism, (a): output current of converters, (b): output voltage of converters and load voltage, (c): output power of each converter.
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I1 I2
I1 I2
20
X: 12 Y: 20.19
Current (A)
20
15 X: 6 Y: 10.29
20.5
10.35 X: 7 Y: 10.35
10.3
15
X: 12 Y: 20.39
10.25
X: 13 Y: 20.01
20 7
10
X: 8 Y: 10.25
7.5
8
12
12.5
13
10 5
10 Time (Sec.)
5
15
10 Time (Sec.)
(a1)
(a2)
105
Voltage (V)
105 X: 6 Y: 102.9
100
X: 14 Y: 101
V1 V2 VL
95
5
10 Time (Sec.)
X: 6 Y: 103
100
95
15
5
10 Time (Sec.)
(b1)
Power (W)
X: 7 Y: 1081
1500 1075
X: 8 Y: 1070
X: 12 Y: 2120
2100
X: 13 Y: 2079
2080
1070 7
7.5
P1 P2
2000 2120
1080
1000
(b2)
P1 P2
2000
X: 14 Y: 101
V1 V2 VL
8
12
12.5
X: 12 Y: 2101
1500 X: 6 Y: 1076
13
1000 5
10 Time (Sec.)
15
5
10 Time (Sec.)
Fig. 8. Performance of the proposed droop mechanism on converters with equal rated power, (a): output current of converters, (b): output voltage of converters and load voltage, (c): output power of each converter.
output current of converter-2 is exactly twice the output current of converter-1. This notice is due to the fact that P2 = 2P1. However, with respect to subfigure (c1), the output powers of converters do not follow each other by a factor of two. At the initial seconds, there exists 1.3% error and following t = 10 s, it reaches to 2.5%. In the case of a proper power sharing task, subfigure (a2) demonstrates that the load current is not shared by a factor of two. Initially, 1.3% error is captured and following t = 10 s, the current error reaches to 2.5%. However, subfigure (c2) displays that the output power is divided between the converters exactly by a factor of two. Shedding more lights on the obtained results speaks for a smaller voltage deviation in power sharing strategy rather than the load current sharing approach. As can be seen, the proposed approach satisfactorily shares the output current and power among the converters.
Due to improper load current and power sharing, the output voltages of the converters are not the same. 5.2. Proposed droop control applied on converters with equal rated power Similar to the previous scenario, two converters with rated power of 6 kW are considered and the proposed droop control approach is deployed. Both of the load current and power sharing strategies are investigated. Results are demonstrated in Fig. 8. In the case of load current sharing, subfigure (a1) demonstrates that the load current is equally shared between the converters; subfigure (b1) depicts the output voltages being approached to each other; and subfigure (c1) illustrates the power sharing task between the converters which are not exactly equal. At the initial seconds, there exists 0.48% error and following t = 10 s, it reaches to 0.94%. In the case of a proper power sharing task, subfigure (a2) demonstrates that the load current is not equally shared. Initially, 0.51% error is seen and following t = 10 s, the current error is 0.97%. However, subfigure (c2) displays that the output power is equally divided between the converters. Besides the negligible differences, these remarks certify outperformance of the proposed droop control approach.
5.4. Proposed droop control applied on three parallel converters with constant-power load In this scenario, the proposed droop control approach is tested on three parallel-connected DERs connected to a constant-power load, rather than a constant resistance. The detailed data in regard of these three DERs have been previously provided in Table 1. As the second DER renders the largestR × P, it is designated as the DER with constant output voltage reference and the reference voltage of the remaining converters is determined with respect to this converter. In simulation studies, the constant-power load is 2 kW which is increased to constant 6 kW at t = 10 s. The obtained results are demonstrated in Fig. 10. With respect to the obtained results, it can be seen that the proposed droop control approach performs well considering both the load current and load power sharing. In order to accurately compare the obtained
5.3. Proposed droop control applied on converters with unequal rated power In contradiction to the previous scenarios, the converters are not equally rated. Converter-1 is rated at 6 kW and converter-2 is rated at 12 kW. The proposed droop control approach is tailored in these conditions. Both of the load current and power sharing strategies are investigated and the results are demonstrated in Fig. 9. In the case of load current sharing, subfigure (a1) demonstrates that the magnitude of 243
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30 X: 12 Y: 26.58
X: 6 Y: 13.64
15
X: 8 Y: 6.818
10 5
Current (A)
20
I1 I2
25
I1 I2
25
X: 14 Y: 13.29
20
10 Time (Sec.)
X: 6 Y: 13.55
15
X: 8 Y: 6.908
10 5
5
15
X: 12 Y: 26.26
5
10 Time (Sec.)
(a1)
(a2 )
105
Voltage (V)
105
X: 6 Y: 102.3
100
95
X: 14 Y: 13.64
X: 14 Y: 99.68
V1 V2 VL
5
10 Time (Sec.)
X: 6 Y: 102.3
100
95
15
X: 14 Y: 99.75
V1 V2 VL
5
10 Time (Sec.)
(b1)
(b2)
3000
3000 P1 P2
2000
X: 12 Y: 2791
X: 6 Y: 1432
1500 X: 8 Y: 702
1000 500
5
P1
2500 Power (W)
2500
X: 14 Y: 1343
P2
2000
X: 6 Y: 1423
1500 X: 8 Y: 711.4
1000
10 Time (Sec.)
X: 12 Y: 2758
500
15
5
X: 14 Y: 1379
10 Time (Sec.)
Fig. 9. Performance of the proposed droop mechanism on converters with unequal rated power (P2 = 2P1), (a): output current of converters, (b): output voltage of converters and load voltage, (c): output power of each converter.
Comparing the obtained results certifies the corresponding ratios and confirms the outperformance of the proposed control approach. It can be seen that both of the load current and load power sharing end in similar results with low differences. Besides, it can be deduced that the
result before and after the load change, Table 2 gathers the numerical results. With respect to the data in Tables 1 and 2, in the case of load current sharing I1 = 0.5I2 and I3 = 0.75I2. Moreover, it can be seen that in the case of load power sharing, P1 = 0.5P2 and P3 = 0.75P2.
30 IL1 IL2 IL3
20
Current (A)
Current (A)
30
10
0
5
10 Time (Sec.)
10
0
15
IL1 IL2 IL3
20
5
10 Time (Sec.)
(a1)
(a2)
3000
3000
Power (W)
P1 P2 P3
2000
1000
0
5
10 Time (Sec.)
1000
0
15
P1 P2 P3
2000
5
10 Time (Sec.)
Fig. 10. Performance of the proposed droop mechanism on 3 parallel converters with unequal rated power, (a): output current of converters, (b): output power of each converter.
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Table 2 Power and current values in the investigated constant-power load. Converters
Current Sharing Strategy Current (A)
Converter 1 Converter 2 Converter 3 Total
Power Sharing Strategy Power (W)
Current (A)
Power (W)
Before t = 10 s
After t = 10 s
Before t = 10 s
After t = 10s
Before t = 10s
After t = 10s
Before t = 10s
After t = 10s
4.303 8.606 6.455 19.364
13.38 26.76 20.07 60.21
446.29 903.7 670.83 2020.8
1351.24 2809.90 2040.28 6201.42
4.3293 8.5533 6.4805 19.363
13.62 26.23 20.296 60.148
449.04 898.091 673.57 2020.7
1377.19 2754.39 2065.79 6197.37
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total generated power of DERs is a bit greater than the load power which is due to the power losses in cable resistances. Note that the load power sharing results in lower dissipated power against the load current sharing approach. Let call back the numeric example. To feed the 6 kW load, 6197.3 W is generated based on load power sharing and 6201.42 W is generated based on load current sharing. Although there is not a huge difference, but as mentioned earlier, at the higher load power values, the differences would get larger. For instance, by increasing the load power from 2 kW to 6 kW, the percentage error increases from 0.0049% to 0.0653%. 6. Conclusion A generalized droop control approach for DC MGs was developed in this manuscript. The proposed approach was formulated based on fundamental principles of equivalent circuit adopted for two main objectives say as proper load current sharing and proper power sharing tasks. The investigated analysis demonstrated that increasing load current, i.e. decreasing load resistance, ends in larger deviations of these two control targets. Similarly, in the case of larger differences in cable resistances and the converters rated powers, larger differences were noticed in regards of current sharing and power sharing processes. Based on the conducted simulations, it was seen that the conventional droop mechanism does not contribute to a proper load sharing between the converters which provoked a larger error between the converters voltages. This is while; outperformance of the proposed approach on both load current and power sharing were noticed. Small errors were reflected on the output currents and output powers of the converters. It was inferred that in both of the current sharing and power sharing strategies, output voltages of the converters are similar with small differences. However, the power sharing approach contributes to smaller deviations in output voltages. The adopted droop control approach could be readily deployed for an effective and precise load sharing task in DC MGs with parallel-connected DERs. References Ahmad, F., & Alam, M. S. (2017). Feasibility study, design and implementation of smart polygeneration microgrid at AMU. Sustainable Cities and Society, 14 [Available online]. Augustine, S., Mishra, M. K., & Lakshminarasamma, N. (2015). Adaptive droop control strategy for load sharing and circulating current minimization in low-Voltage standalone DC microgrid. IEEE Transactions on Sustainable Energy, 6(no. 1), 132–141. Boeke, U., & Wendt, M. (2015). DC power grids for buildings, in DC Microgrids (ICDCM). IEEE first int. conf. (pp. 210–214). Bouzid, A. M., Guerrero, J. M., Cheriti, A., Bouhamida, M., Sicard, P., & Benghanem, M. (2015). A survey on control of electric power distributed generation systems for microgrid applications. Renewable and Sustainable Energy Reviews, 44, 751–766. Chan, D., Cameron, M., & Yoon, Y. (2017). Key success factors for global application of micro energy grid model. Sustainable Cities and Society, 28, 209–224.
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