energies Article
Improving Transient Response of Power Converter in a Stand-Alone Microgrid Using Virtual Synchronous Generator Cao-Khang Nguyen 1 , Thai-Thanh Nguyen 1 1
2
*
ID
, Hyeong-Jun Yoo 1 and Hak-Man Kim 1,2, *
Department of Electrical Engineering, Incheon National University, Songdo-dong, 119 Academy-ro, Yeonsu-gu, Incheon 22012, Korea;
[email protected] (C.-K.N.);
[email protected] (T.-T.N.);
[email protected] (H.-J.Y.) Research Institute for Northeast Asian Super Grid, Incheon National University, 119 Academy-ro, Yeonsu-gu, Incheon 22012, Korea Correspondence:
[email protected]; Tel.: +82-32-835-8769; Fax: +82-32-835-0773
Received: 31 October 2017; Accepted: 21 December 2017; Published: 23 December 2017
Abstract: Multiple power converters based on the droop controllers have been used widely in the microgrid (MG) system. However, owing to the different response time among several types of power converters such as grid-feeding and grid-forming converters, low frequency oscillation occurs with high overshoot in the transient state. This paper proposes a novel control strategy based on the virtual synchronous generator (VSG) for improving transient response of parallel power converters during large disturbance in the stand-alone microgrid. The proposed VSG control, which inherits the transient state characteristic of the synchronous generator, can provide inertia virtually to the system. The transient response of voltage and frequency is improved, while the total system inertia response is compensated. Thus, the system stability can be enhanced by using the proposed VSG control. Additionally, the small signal analysis of the conventional VSG controller and the proposed VSG controller are carried out to show the effectiveness of the proposed VSG controller. The derivation of frequency, which is used to evaluate the inertia support of the VSG controller to the MG system, is discussed. The simulation result demonstrates that the overshoot of the transient response can be reduced, and the system stability is improved when the proposed VSG controller is applied. The MG system based on the real-time simulator OP5600 (OPAL-RT Technologies, Montreal, QC, Canada) is carried out to verify the feasibility of the proposed VSG controller. Keywords: microgrid control; virtual synchronous generator; power converter; power conversion
1. Introduction In recent years, distributed generations based on renewable energy sources (RESs) such as photovoltaics and wind generations have been paid more attention from researchers in many parts of the world [1]. In order to improve the integration of distributed generations (DGs) into the distributed network, the MG system that is composed of different DGs, energy storage systems, and controllable loads was developed [2]. The DGs are interfaced with the MG bus using two types of power converters, namely the grid-feeding converter and the grid-forming converter [3]. Whereas the grid-feeding converter is used to regulate the power exchange with the MG system, the grid-forming converter controls the system voltage and frequency in the stand-alone mode [4]. In order to exchange power among DGs, the droop controller that imitates the steady state characteristic of a synchronous generator is usually considered as a practical method without the need of communication link. Thus, managing the power delivery of the system is costly. The droop control strategy was originally proposed for the uninterruptible power supply (UPS) system that Energies 2018, 11, 27; doi:10.3390/en11010027
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contains several grid-forming units [5–7]. The UPS system is usually supplied for local loads, where the line impedances are similar. In the islanded microgrid with multiple power converters connected in parallel with loads, the line impedances are much different and dominantly resistive, which affects to the performance of voltage and frequency of the system. The P-ω droop control was extended to the parallel inverters based DGs in the stand-alone MG [8]. However, in comparison with the conventional power system where line impedances are mainly inductive, the line impedances in MG are dominantly resistive, causing several problems in the operation [9]. Consequently, several studies have been proposed for improving droop controller in the parallel stand-alone MG. Instead of using a conventional P-ω droop controller, the P-V droop controller was proposed to deal with the inaccurate reactive power sharing problem [10]. In addition, a virtual impedance was introduced to imitate a virtual inductor for the impedance line [11]. On the other hand, the author in [12] proposed a virtual frame transformation to decouple the relationship between the active and reactive power and enhance the performance of the system. The adaptive decentralized droop controller was introduced to preserve power sharing stability and reduce power oscillation [13]. Furthermore, a detailed analysis of the droop controller applied in the parallel operation of DGs was discussed. The droop coefficient was also optimized by using particle swarm optimization (PSO) to improve the performance and stability of the distributed system [14]. Although the droop controller has been widely adopted in the stand-alone MG, it still has several drawbacks. In a conventional power system with massive rotating generators, the inertia stored in the rotor of synchronous generator plays an important role to maintain the system stability. However, an MG system, which is a small-scale power system, already has a relatively small inertia response [15]. In addition, the RESs are interfaced with the AC bus by the power converters based on the droop controllers, which contributes small inertia response to the MG system. After large disturbance such as generator tripping, system fault, or significant load changes in the MG system with low inertia response, the system voltage and frequency might fluctuate significantly, which may trip the generator or sensitive load [16,17]. Low inertia response of the MG system might pose challenges to the operator for maintaining the system stability [18,19]. In order to tackle the problem, virtual synchronous generator (VSG) control, which provides virtual inertia to the MG system, was first introduced in [20]. By imitating the steady state and the transient behavior of the synchronous generator, the total inertia of the MG system can be increased [21]. The detailed analysis of VSG control and droop control was studied in [22], showing the effectiveness of the VSG control over droop controller in term of the stability field. Various studies have proposed, taking the advantage of VSG controller for the MG in both grid-feeding converter and grid-forming converter [23,24]. The author in [25] introduced a VSG-based grid-feeding converter for a short-term energy buffer to smooth the power fluctuation of DGs. Besides, a modification of VSG with frequency deviation for the grid-forming converter was proposed to improve the transient response of the MG system [26]. Additionally, the parameters of the VSG controller are designed and analyzed in [27,28]. However, comparing to the MG system with only grid-forming or grid-feeding converters, the overshoot of the transient response in the MG system with both power converters is much higher due to the different response time of two converters [29]. In previous studies, the transient response of the power converters was not considered in both the droop controller and the conventional VSG controller. In order to address this gap, the major contribution of this study is to propose a VSG control for reducing the transient response of the power converters in the MG system. The output power derivation of power converters is added in the VSG controller to improve the primary response of active power and frequency under the load transient. The small signal analysis of the conventional VSG controller and proposed VSG controller is carried out to show the improvement of the transient response in the case of using the proposed VSG controller. The root locus of the systems is obtained from the mathematical model of both methods to evaluate the effectiveness of the proposed VSG controller. An analysis of virtual inertia and virtual damping
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factor of the VSG controller is studied to demonstrate that the system stability can be improved by changing the of virtual damping factor and inertia factor. The rest this paper is organized asvirtual follows: Section 2 briefly presents the structure of inverterrest of this paper in is the organized as follows: Section3,2the briefly presents structure of basedThe distributed generator stand-alone MG. In Section principle of thethe proposed VSG inverter-based distributed generator in the stand-alone MG.results In Section 3, the principle of controller the proposed controller is discussed. System parameters and simulation of the proposed VSG are VSG controller is discussed. System parameters results of the proposed VSG controller analyzed in Section 4. Finally, the conclusion ofand the simulation paper is given in Section 5. are analyzed in Section 4. Finally, the conclusion of the paper is given in Section 5. 2. Inverter-Based Distributed Generation 2. Inverter-Based Distributed Generation The structure of an inverter-based DG is illustrated in Figure 1. In this structure, a DG, which Thea structure of an ainverter-based DG illustrated in Figuresystem, 1. In this DG, which can can be photovoltaic, wind turbine, orisan energy storage is structure, connecteda to the AC bus be a photovoltaic, a wind turbine, or an energy storage system, connected the AC busconverter through through the converter. Inverter-based DG can be classified into is two types: a to grid-feeding the Inverter-based be classified into twocan types: a grid-feeding and a andconverter. a grid-forming converter.DG Thecan grid-feeding converter be considered as aconverter current source grid-forming converter. The grid-feeding considered as between a currentMG source connected with high impedance in parallelconverter to controlcan the be power exchange andconnected the utility with high impedance in parallel to control the power exchange between MG and the utility grid. grid. Nevertheless, it has no ability to control the system frequency and voltage. Thus, the gridNevertheless, it has no ability to control the system frequency and voltage. Thus, the grid-feeding feeding converter cannot operate individually without any support from a synchronous generator or converter cannotofoperate individually without anythe support from a synchronous generator as or athe other the other types converter. On the other hand, grid-forming converter is designed voltage types of converter. On the other hand, the grid-forming converter is designed as a voltage source source connected with low impedance in series. It plays an important role in regulating the voltage connected withoflow in series. Itoperation. plays an Therefore, important the roleAC in regulating thegrid-forming voltage and and frequency the impedance system in stand-alone voltage of the frequency of the in stand-alone operation. Therefore, the AC voltage ofconverters. the grid-forming converter can be system considered as the reference of voltage for other grid-feeding In this converter can be considered as the reference of voltage for other grid-feeding converters. In this study, study, a combination of DGs based on the grid-feeding converter and the grid-forming converter is afocused. combination of DGscontrol based on the grid-feeding and the grid-forming converter focused. The detail scheme for each converter type of converters is presented in the is following The detail control scheme for each type of converters is presented in the following subsections. subsections. L1
-
-
Voltage Controller
+
Power Controller
L2
+
DG1
R1
PWM
PWM
Current Controller
Current Controller
R2
DG2
Load
Power Controller
Figure 1. Structure of inverter based distributed generation in MG system. Figure 1. Structure of inverter based distributed generation in MG system.
2.1. Grid-Forming Converter 2.1. Grid-Forming Converter The control scheme for the grid-forming converter can be divided into three cascaded The control scheme for the grid-forming converter can be divided into three cascaded controllers, controllers, including power controller, voltage controller, and current controller, as described in including power controller, voltage controller, and current controller, as described in Figure 2. The outer Figure 2. The outer control loop consists of active and reactive power controller, which generates the control loop consists of active and reactive power controller, which generates the reference angle θ and reference angle θ and the amplitude E* for the reference output voltage. Whereas the VSG controller the amplitude E* for the reference output voltage. Whereas the VSG controller is applied to the active is applied to the active power controller to generate the reference angle θ, the droop controller is power controller to generate the reference angle θ, the droop controller* is employed in the reactive employed in the reactive power controller to regulate the amplitude E for the reference of output power controller to regulate the amplitude∗ E* for the reference of output voltage. The reference of voltage. The reference of output voltage 𝑣𝑎𝑏𝑐 regulated from the power controller is calculated by output voltage v∗abc regulated from the power controller is calculated by the following equations: the following equations: ∗ v𝑣∗a𝑎∗ = (θ ) =E 𝐸 ∗ cos cos(𝜃) 2𝜋 ∗ ∗ ∗ 𝑐𝑜𝑠(𝜃 +2π ) v∗b𝑣𝑏==E𝐸 cos θ + 3 3 2𝜋 ∗ ∗ 𝑣 = 𝐸 𝑐𝑜𝑠(𝜃 − 2π ) v∗c 𝑐= E∗ cos θ − 3 3
(1) (1)
(2) (2) (3) (3)
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DC source
VSC Lf
+ -
AC Bus
ilabc θ
abc
θ
PWM
ma
mb
dq
ilq
vod
ω
voq
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Q
P
VSC
abc
+ -
ild
mc
ioabc
Power calculation
PLL
dq
DC source
θ
abc
θ
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uoabc
uoabc
uoabc
Cf
Lf
dq md
mq
D
ild
ilq
iod
ioq
ilabc
ild* θ
θ
ma
mb
control
mc
Voltage control
ilq*
abc
abc
vabc* dq
vildoq* ilq dq
θ
uoabc
Cf
vod*
PWM Current
mq
dq md ild
1/s
od
ω
oq
iod
θ
ioq
ild*
vod*
E 1/s
ωN
+ ω*
- + P* -
1/Js
ω
Kp
Q
Kq
D
+ P
Q
P
E* + +
+
Power calculation
PLL
θ ilq
1/Js
abc
θ
ioabc- +
uoabc
uoabc
Equation dq (1) v v
abc
θ
AC Bus P*
θ
Q* +
+
abc
+ P
Kp
ω + ω*
ω Figure 2. Control scheme of the virtual synchronous converter. v * generator control–based grid-forming Equation Current Voltagesynchronous generator Figure 2. Control scheme of the virtual control–based grid-forming converter. N
abc
control
ilq*
control
(1)
voq*
dq
E* Q The output voltage reference is transferred from 𝑎𝑏𝑐 reference frame to 𝑑𝑞 reference frame K + + -to + The output voltage reference is transferred from abc reference frame dq reference framenamely before before sending to the inner controllers. The inner control Eloop contains two controllers, Q* sending to the inner controllers. The inner control loop contains two controllers, namely current current controller voltage controller. Whereas the voltage controller regulates the amplitude of Figure 2. and Control scheme of the virtual synchronous generator control–based grid-forming converter. controller and voltage controller. Whereas the voltage controller regulates the amplitude of voltage voltage determined by the VSG controller, the currents controller conducts the current supplied by determined byto the VSGvoltage controller, thevalue. currents conducts the frame current by the The output reference is transferred 𝑎𝑏𝑐 reference to supplied 𝑑𝑞 reference frame the converter match its reference In controller otherfrom words, the current flowing through theconverter inductor to match its reference In controllers. other flowing through the filter L f is sending tovalue. the inner The the inner control loop contains two namely filter 𝐿𝑓before is conducted to regulate thewords, voltage oncurrent the capacitor filter 𝐶𝑓 .controllers, Theinductor structure of inner current controller and voltage controller. Whereas the voltage controller regulates the amplitude of conducted to depicted regulate the voltage3.on thereference capacitorvalue filter C Thecurrent structure of inner 𝑖controller is depicted ∗ controller is in Figure The off .the controller is compared with 𝑙𝑑 supplied voltage determined by the VSG controller, the currents controller conductswith the current by ∗ is compared in Figure 3. The reference value of the current controller i the measured current iPI ld ld the measured current 𝑖 flowing through the inductor filter. Then, the error signal is input to the 𝑙𝑑 its reference value. In other words, the current flowing through the inductor the converter to match flowing through the inductor filter. Then, the error signal is input to the PI controller. The output of controller. of thetocurrent is on thethe modulating signal, is utilized to compare filterThe 𝐿𝑓 output is conducted regulatecontroller the voltage capacitor filter 𝐶𝑓 . which The structure of inner the current controller is to thedetermine which is to controller compare the transistor carrier signals to ∗ is depicted inmodulating Figure 3. The reference value ofutilized thethe current is compared with with thecontroller carrier signals thesignal, switching time of insulated gate𝑖with bipolar (IGBT) 𝑙𝑑 determine the switching time of the insulated gate bipolar transistor (IGBT) switches. The output of theThe measured current flowingcontroller through theisinductor filter.in Then, error signal is input to the PI switches. output of the𝑖𝑙𝑑current calculated the the following equations: controller. The output of the current controller is theequations: modulating signal, which is utilized to compare the current controller is calculated in the following with the carrier signals switching ∗time of the insulated∗gate bipolar transistor (IGBT) 𝑚𝑑to=determine 𝑣𝑜𝑑 − 𝜔𝑖the (4) 𝑙𝑞 𝐿𝑓 + 𝑘𝑝𝑐 (𝑖𝑙𝑑 − 𝑖𝑙𝑑 ) + 𝑘𝑖𝑐Z∫(𝑖𝑙𝑑 − 𝑖𝑙𝑑 )𝑑𝑡 switches. The output of the current controller is calculated ∗ ∗ md = vod − ωilq L f + k pc (ild − ild ) in + the k ic following − iequations: dt (4) (ild ) ld q
∗ − 𝑖 ) + 𝑘 ∫(𝑖 ∗ −∗ 𝑖 )𝑑𝑡 (𝑖 ∗𝑙𝑞 − 𝜔𝑖 𝑚𝑞 𝑚 =𝑑𝑣=𝑜𝑞𝑣+ 𝐿𝑓𝐿𝑓++𝑘𝑘𝑝𝑐 − 𝑙𝑑 𝑖𝑙𝑞) +𝑖𝑐𝑘𝑖𝑐Z∫(𝑖 𝑜𝑑 𝜔𝑖 𝑝𝑐(𝑖 𝑙𝑑 𝑙𝑞 𝑙𝑑 𝑙𝑑 𝑙𝑞 𝑙𝑑 − 𝑖𝑙𝑞)𝑑𝑡
∗ voq + ωild L f + k pc ilq ∗
(5)
(4)
∗ ilq
mq = − ilq + k ic ∗ − ilq dt (5) 𝑚𝑞 = 𝑣𝑜𝑞 + 𝜔𝑖𝑙𝑑and 𝐿𝑓 + integral 𝑘𝑝𝑐 (𝑖𝑙𝑞 − 𝑖components )𝑑𝑡 (5) 𝑚𝑑 and where 𝑘𝑖𝑣 and 𝑘𝑖𝑐 are the proportional of𝑖𝑙𝑞current controller and 𝑙𝑞 ) + 𝑘𝑖𝑐 ∫(𝑖𝑙𝑞 − 𝑚𝑞 arek iv the modulating in the 𝑑𝑞 frame. where and k ic are thesignals proportional andreference integral components of current controller and md and mq where 𝑘𝑖𝑣 and 𝑘𝑖𝑐 are the proportional and integral components of current controller and 𝑚𝑑 and are the modulating signals in the dq reference frame. 𝑚 are the modulating signals in the 𝑑𝑞 reference frame. 𝑞
Voltage Controller
Current Controller
Voltage Controller
vod*
+
voq*
kpv+kiv/s
vod*
- + -
kpv+kiv/s
Current Controller
ild*
ild*
+
kpc+kic/s
+-
kpc+kic/s
vod
vod
iildld
ωlfωlf
voq
voq
iilqlq
ωlfωlf
voq*- +
+
kpv+kiv/s
kpv+kiv/s
ilq* -
ilq*++ -
kpc+kic/s
kpc+kic/s
vod + +-
+
Figure 3. Control scheme of inner controller.
+-
+
+
+
+ voq
Figure 3. Control scheme of inner controller. Figure 3. Control scheme of inner controller.
vod +
+ voq
md
mq
md
mq
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Regarding the voltage controller, it is employed to control the output voltage of the MG. Similar the voltage is employed to control the voltage of thethe MG. Similar to theRegarding current controller, thecontroller, set value ofit the voltage controller v∗od is output also compared with measured ∗ to the current controller, the set controller 𝑣𝑜𝑑(PI) is also compared with the voltage vod of the AC bus and thenvalue inputoftothe the voltage proportional-integral controller. However, the ∗ ∗ measured voltage 𝑣 of the AC bus and then input to the proportional-integral (PI) controller. 𝑜𝑑 controller i and i are the reference values of current controller, as shown in output signals of voltage ld lq ∗ ∗ However, thecurrent outputreference signals of voltage controller 𝑖𝑙𝑑 and 𝑖𝑙𝑞 are the reference values of current Figure 3. The can be treated in (6) and (7). controller, as shown in Figure 3. The current reference can be treated in (6) and (7). Z ∗ i∗ld = k pv (v∗∗od − vod ) + k pc (v∗od ∗ − v od ) dt 𝑖𝑙𝑑 = 𝑘𝑝𝑣 (𝑣𝑜𝑑 − 𝑣𝑜𝑑 ) + 𝑘𝑝𝑐 ∫(𝑣𝑜𝑑 − 𝑣𝑜𝑑 )𝑑𝑡 Z ∗ ∗ ∗ = k pv v oq i𝑖lq v∗∗oq − voq )𝑑𝑡 dt ∗ − v oq + k pc = 𝑘 (𝑣 − 𝑣 ) + 𝑘 ∫(𝑣 − 𝑣 𝑝𝑣 𝑜𝑞 𝑜𝑞 𝑝𝑐 𝑜𝑞 𝑜𝑞 𝑙𝑞
(6) (6) (7) (7)
where k pv and k pc is the proportional and integral components of voltage controller. where 𝑘𝑝𝑣 and 𝑘𝑝𝑐 is the proportional and integral components of voltage controller. The conventional droop controller is applied to the reactive power controller in order to determine The conventional droop controller is applied to the reactive power controller in order to the amount of reactive power that can be transferred through the AC bus, based on the fluctuation of determine the amount of reactive power that can be transferred through the AC bus, based on the AC voltage. Figure 4 shows the control scheme of reactive power controller. The output of reactive fluctuation of AC voltage. Figure 4 shows the control scheme of reactive power controller. The output power controller is the voltage reference which input to the voltage controller. It is given as follows: of reactive power controller is the voltage reference which input to the voltage controller. It is given as follows: E∗ = E − k q ( Q∗ − Q) (8) 𝐸 ∗ = 𝐸 − 𝑘𝑞 (𝑄 ∗ − 𝑄) (8) The relation between reactive power and AC voltage is described through a droop coefficient, The between reactive(9). power and AC voltage is described through a droop coefficient, which canrelation be defined by Equation which can be defined by Equation (9). Vmax − Vmin k𝑘q == 𝑉𝑚𝑎𝑥 − 𝑉𝑚𝑖𝑛 (9) (9) Q − Q 𝑞 min 𝑄max − 𝑄 𝑚𝑎𝑥 𝑚𝑖𝑛 where V𝑣max and Vmin are the maximum and minimum AC voltage that can be allowed and Qmax𝑄and 𝑚𝑎𝑥 and 𝑣 𝑚𝑖𝑛 are the maximum and minimum AC voltage that can be allowed and 𝑚𝑎𝑥 Qmin𝑄are the maximum and minimum reactive power transferred through the AC and are the maximum and minimum reactive power transferred through thebus. AC bus. 𝑚𝑖𝑛
D ω -
+ ω*
kp
-
Pm
+ + P*
+ P
1/Js
ʃ
θ
ωN (a)
Q* -
kq
+ Q
E*
+ + E
(b)
Figure 4. Control scheme: (a) virtual synchronous generator (VSG) controller; (b) 𝑄 ‐ 𝑉 droop Figure 4. Control scheme: (a) virtual synchronous generator (VSG) controller; (b) Q − V droop controller. controller.
Regarding the active power controller, the control scheme of conventional virtual synchronous Regarding the active power controller, the control scheme of conventional virtual synchronous generator control method applying to the grid forming converter is described in Figure 4. The main generator control method applying to the grid forming converter is described in Figure 4. The main component which can be used to distinguish the VSG controller and droop controller is the swing component which can be used to distinguish the VSG controller and droop controller is the swing equation. It can be described as follows: equation. It can be described as follows: dω 𝑑𝜔 Pm + −𝜔ω𝑁N)) (ω − 𝑃𝑚==P𝑃++Jω 𝐽𝜔N𝑁 + Dω 𝐷𝜔𝑁N(𝜔 dt 𝑑𝑡 𝑑𝜃 dθ =𝜔 𝑑𝑡 = ω dt
(10) (10)
(11) (11)
where P𝑃m𝑚the themechanical mechanical power generated from the governor, 𝑃 measured active of power of the power generated from the governor, P measured active power the inverter, inverter, 𝐽 the virtualDinertia, 𝐷 is the damping 𝜔 is the frequency, angular frequency, rated J the virtual inertia, is the damping factor, ωfactor, is the angular ω N is the𝜔rated angular 𝑁 is the angular frequency of the and system, andelectrical 𝜃 is the angle. electrical angle. frequency of the system, θ is the The mechanical power Pm m generated generated from from the the governor governor is is described as (𝜔∗ − 𝜔) = −𝑘𝑝 (𝑃∗ − 𝑃𝑚 ) (ω ∗ − ω ) = −k p ( P∗ − Pm )
(12) (12)
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2.2. Grid-Feeding Converter 2.2. Grid-Feeding Converter The grid-feeding converter can be controlled as a current source, connecting with the AC bus through high parallelconverter impedance. the grid-forming converter maintainwith the the voltage and The grid-feeding canWhile be controlled as a current source,can connecting AC bus frequency of the MG, the grid-feeding converter regulates power sharingcan with other DGs. structure through high parallel impedance. While the grid-forming converter maintain the The voltage and of the controller grid-feeding converter is shown inregulates Figure 5. The grid-feeding converter consists frequency of theofMG, the grid-feeding converter power sharing with otheralso DGs. The of three cascaded control loops: droop controller, power controller, and current controller. Whereas structure of the controller of grid-feeding converter is shown in Figure 5. The grid-feeding converter the current grid-feeding converter similar controller, to that of grid-forming converter, power also consistscontroller of threeofcascaded control loops:is droop power controller, andthecurrent control is used to control the power exchange with anotherconverter distributed generator, which is determined controller. Whereas the current controller of grid-feeding is similar to that of grid-forming by the droop The equation controllers for active power-frequency reactive converter, thecontroller. power control is used oftodroop control the power exchange with another and distributed power-voltage are as follows: generator, which is given determined by the droop controller. The equation of droop controllers for active power-frequency and reactive power-voltage are given as follows: (13) (ω ∗∗ − ω ) = −k p ( P∗∗ − P) (𝜔 − 𝜔) = −𝑘𝑝 (𝑃 − 𝑃) (13) V ∗∗ − = −𝑘 −k q(𝑄 Q) ((𝑉 ( Q∗∗−−𝑄) −V 𝑉)) = 𝑞
(14) (14)
where 𝑘 k p and k q are droop coefficients of P − ω droop controller and Q − V droop controller. where 𝑝 and 𝑘𝑞 are droop coefficients of 𝑃‐ 𝜔 droop controller and 𝑄‐ 𝑉 droop controller. Power controller
Frequency droop controller
Current controller vod
ω* kp
+ω
E*
+
+
+ P*
E +
Q* + +
kq
-
+
ild*
kpp+kip/s
+
P
Q +
+-
-
ild
ωlf
ilq
ωlf
ilq*+ -
kpp+kip/s
md
kpc+kic/s
+
kpc+kic/s
+
mq +
voq
Figure 5. Control scheme of grid-feeding converter. Figure 5. Control scheme of grid-feeding converter.
3. Proposed Virtual Synchronous Generator Control 3. Proposed Virtual Synchronous Generator Control The control scheme of proposed VSG controller is illustrated in Figure 6. The derivative The control scheme of proposed VSG controller is illustrated in Figure 6. The derivative component is added to the governor block before going to the swing equation. In the steady state, the component is added to the governor block before going to the swing equation. In the steady state, the active power derivation is equaled to zero because the mechanical power generated from the active power derivation is equaled to zero because the mechanical power generated from the governor governor is unchanged. Therefore, the dynamic response of active power is not affected. However, is unchanged. Therefore, the dynamic response of active power is not affected. However, during the during the transient state, the active power is fluctuated, which makes the derivative component of transient state, the active power is fluctuated, which makes the derivative component of active power active power varied proportionally. Hence, the overshoot of active power can be reduced by varied proportionally. Hence, the overshoot of active power can be reduced by subtracting the active subtracting the active power derivation. In addition, a rating coefficient is multiplied with the active power derivation. In addition, a rating coefficient is multiplied with the active power derivation to power derivation to improve the efficiency of power derivation. The swing equation of the proposed improve the efficiency of power derivation. The swing equation of the proposed VSG controller is VSG controller is modified as follows: modified as follows: dP dω 𝑑𝑃 𝑑𝜔 P𝑃m𝑚− + Dω (ω − ω ) ) (15) (15) − P𝑃 = = k𝑘d𝑑 dt + + Jω 𝐽𝜔N 𝑁 dt + 𝐷𝜔𝑁N(𝜔 − 𝜔𝑁N 𝑑𝑡 𝑑𝑡 dP where 𝑑𝑃 is the the active active power power derivation; derivation; k𝑘d isisthe where thederivative derivativecoefficient. coefficient. dt is 𝑑 𝑑𝑡
P*
kd
d/dt
D -
ω
kp
+ ω*
+
+ +
+ P*
1/Js
P
ωN
Figure 6. Control scheme of VSG controller.
ʃ
θ
subtracting the active power derivation. In addition, a rating coefficient is multiplied with the active power derivation to improve the efficiency of power derivation. The swing equation of the proposed VSG controller is modified as follows: 𝑃𝑚 − 𝑃 = 𝑘𝑑 Energies 2018, 11, 27
where
𝑑𝑃 𝑑𝑡
𝑑𝑃 𝑑𝜔 + 𝐽𝜔𝑁 + 𝐷𝜔𝑁 (𝜔 − 𝜔𝑁 ) 𝑑𝑡 𝑑𝑡
(15) 7 of 17
is the active power derivation; 𝑘𝑑 is the derivative coefficient. P*
kd
d/dt
D -
ω
kp
+
+
+
+ +
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ʃ
1/Js
-
P*
ω*
-
θ
ωN
P
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Figure 6. Control scheme of VSG controller. Figure 6. Control scheme of VSG controller.
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The modification of swing equation presented in (15) can be transferred to the Laplace domain The modificationofofswing swingequation equationpresented presented in domain The modification in (15) (15) can canbe betransferred transferredtotothe theLaplace Laplace domain as follows: as follows: as follows: 𝐾 111 ∗∗ 𝐾K = = 𝛥𝑃 ∆P (16) − ∆P −−k𝑘𝑘d𝑑s∆P (∆P ) (𝛥𝑃 𝑠𝛥𝑃) (16) (𝛥𝑃∗−−𝛥𝑃 𝛥𝑃 − 𝑠𝛥𝑃) (16) ω Js + D (𝐽𝑠 ( ) 𝑑 𝜔N𝑁(𝐽𝑠 + +𝐷) 𝐷)𝑠𝑠s = 𝛥𝑃 𝜔 𝑁 where ω is the nominal nominal angular angular frequency frequency of the MG system and K is the rating coefficient of active where ωNωis the where N is the nominal angular frequency of the MG system and K is the rating coefficient of active power and frequency. frequency. power and frequency. From (16), the transfer VSG controller controllercan canbe bedescribed describedinin (17) and From (16), the transferfunction functionof ofthe the proposed proposed VSG (17) and thethe small signal model is obtained from the transfer function is illustrated in Figure 7: from the transfer function is illustrated in Figure 7: small signal model is obtained from the transfer function is illustrated in Figure 7: 𝛥𝑃 𝛥𝑃 𝐾 ∆P K == ∗∗= 𝜔 (𝐽𝑠 (𝐽𝑠 𝛥𝑃 𝜔 𝛥𝑃 + 𝐷) 𝐾(𝑘 1) ∗ ∆P ω𝑁N𝑁 ( Js + D )++𝐾(𝑘 K (k𝑑𝑑d𝑠𝑠s++ +1) 1)
kkdd
ss
ΔP* ΔP* + + -
1
1
Δω Δω + ++
1 1
ωN
Js+D
ωN
(17) (17) (17)
ΔP
1
1 s s
+
Js+D
K
ΔP
K
Figure 7. Small signal model of active power of proposed VSG controller. Figure 7. 7. Small Small signal signal model model of of active active power power of of proposed proposed VSG Figure VSG controller. controller.
Similarly, the small signal model of the conventional VSG controller described in Figure 8 is also Similarly, the signal the conventional VSG Similarly, the small signal model of of conventional VSG controller controller described described in Figure Figure 8 is also obtained from itssmall closed loop model transfer function below: obtained from its closed closed loop loop transfer transfer function function below: below: 𝛥𝑃 𝐾 = (18) ∗ 𝛥𝑃 𝛥𝑃 𝜔𝑁 (𝐽𝑠 +𝐾 ∆P K𝐷) + 𝐾 = (18) (18) 𝛥𝑃∗ ∗= ω 𝜔𝑁 (𝐽𝑠 + 𝐷) + 𝐾 ∆P N ( Js + D ) + K ΔP* +
ΔP* +
-
-
1
1
1ωN
Js+D 1
ωN
Js+D
Δω + Δω + +
+
1
s1
s
ΔP
K
K
ΔP
Figure 8. Small signal model of active power of the VSG controller.
Figure 8. Small signal model of active power of the VSG controller.
8. Small signal model of signal active power VSGin controller. The root locusFigure plot obtained from the small modelof is the shown Figure 9. In this figure, the system poles of the conventional VSG controller and the proposed VSG controller are compared in The root locus plot obtained from the small signal model is shown in Figure 9. In this figure, the The locus plot obtained inertia. from the small signalthat model is the shown in is Figure 9. Infrom this figure, case of root increasing the rotational It is observed when inertia increased J = 10 tothe system poles of the conventional VSG controller and the proposed VSG controller are compared in J = 2000, theof system poles of the conventional VSGand controller and the VSG proposed VSG controller move in system poles the conventional VSG controller the proposed controller are compared case of increasing the rotational inertia. It is observed that when the inertia is increased from J = 10 to farofaway from the axis, which illustrates the improvement of the overshoot in the from transient case increasing thereal rotational inertia. It is observed that when the inertia is increased J = 10 J = 2000, the system poles of the conventional VSG controller and the proposed VSG controller move stability poles margin theconventional MG system. VSG controller and the proposed VSG controller to response J = 2000, and the system ofofthe far away from the real axis, which illustrates the improvement of the overshoot in the transient move far away from the real axis, which illustrates the improvement of the overshoot in the transient response and stability margin of the MG system. response and stability margin of the MG system.
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Figure 9. Root locus plot of the converters with conventional and proposed VSG control. Figure 9. Root locus plot of the converters with conventional and proposed VSG control. Figure 9. Root locus plot of the converters with conventional and proposed VSG control.
In addition,Figure it can be seen 10 that the derivative 9. Root locus from plot of Figure the converters withwhen conventional and proposedcoefficient VSG control. 𝑘𝑑 is increased, In addition, itbe canseen be seen from Figure 10 thatwhen when the the derivative coefficient 𝑘𝑑 kisd increased, In addition, it can from Figure 10 that derivative coefficient increased, the the proposed VSG controller have smaller oscillation and the settling time of theissystem is also theVSG proposed VSG controller have smaller oscillation and the settling time of system the𝑘system is also proposed controller have smaller oscillation and the settling time of the is also increased In addition, it can be seen from Figure 10 that when the derivative coefficient is increased, 𝑑 increased compared to that of the conventional droop controller. Furthermore, similar with the rating increased compared to that of the conventional droop controller. similar with theisrating the VSG controller have smaller oscillation and the Furthermore, settling time of the system also compared toproposed thatsettling of the conventional droop controller. Furthermore, similar with the rating coefficient, the coefficient, the time of the system is also increased by increasing the damping factor coefficient,compared the settling timeofofthe the system is also increased by increasing the similar damping factor 𝐷, as 𝐷, as increased to that conventional droop controller. Furthermore, with the rating settling time the system is also increased by increasing the damping factor D, as described in Figure 11. described in of Figure 11. described inthe Figure 11. time of the system is also increased by increasing the damping factor 𝐷, as coefficient, settling described in Figure 11. 200 150
200 200 150 150 100
Imaginary axis axis Imaginary
Imaginary axis
100
100 50
50
50 0
0
0 -50
-50 -50 -100
-100
-100 -150 -150 -200 -5 -200 -5
-2.5 -2 -1.5 -1 -0.5 0 Real axis -2.5 -2 -1.5 -1 -0.5 0 -200 axis Figure 10. Root locus plot of the convertersReal when increasing the derivative coefficient.
-150
-4.5
-4
-3.5
-3
-4.5
-4
-3.5
-3
-4 of the -3.5 -3 -2.5 increasing -2 -1.5 -1 -0.5 0 Figure 10.-5Root -4.5 locus plot converters when the derivative coefficient. Figure 10. Root locus plot of the convertersReal when increasing the derivative coefficient. axis 200
Conventional VSG control
Proposed VSG control
Figure 10. Root locus plot of Conventional the converters increasing the derivative coefficient. VSG controlwhenProposed VSG control 200
100 Imaginary axis axis Imaginary
200
Imaginary axis
100
D=500 D=500 VSG control Conventional
D=200
D=100
D=200 VSG control Proposed D=100
100 0
D=500
D=200
D=100
0 -100
0 -100 -200 -25 -20 -15 -10 -5 0 -200 Real axis -25 -20 -15 -10 -5 0 -100 Realwhen axis increasing the damping factor. Figure 11. Root locus plot of the converters
Figure 11. Root locus plot of the converters when increasing the damping factor.
Figure 11. Root locus plot of the converters when increasing the damping factor. -200 -25 -20 -15 -10 -5 0 Real axis
Figure 11. Root locus plot of the converters when increasing the damping factor.
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A detailed simulation is executed using SimPowerSystems toolbox of Matlab/Simulink (version 4. Simulation Results R2011b, MathWorks, Natick, MA. USA) environment in order to verify the effectiveness of the proposed A detailed is executed using MG, SimPowerSystems toolbox Matlab/Simulink (version VSG control. In thissimulation simulation, a low voltage which consists of twoofinverter-based DGs and load, R2011b, MathWorks, Natick, MA. USA) environment in order to verify the effectiveness of the is studied. The electrical load is connected in parallel with two DGs through impedance lines, which proposed VSG control. In this simulation, a low voltage MG, which consists of two inverter-based comprises both resistive and inductive components, as shown in Figure 1. The impedance lines are DGs and load, is studied. The electrical load is connected in parallel with two DGs through considered as mainly resistive. The droop coefficients of active power and voltage are designed to impedance lines, which comprises both resistive and inductive components, as shown in Figure 1. ensure that the frequency of the system is fluctuated from 59.8 Hz to 60.2 Hz. The MG is designed The impedance lines are considered as mainly resistive. The droop coefficients of active power and to operate kHz oftoswitching frequency to avoid high frequencyfrom oscillation. voltage at are10 designed ensure that the frequency of the the system is fluctuated 59.8 Hz toThe 60.2detailed Hz. parameters MG aretolisted in Table The MGofisthe designed operate at 10 1.kHz of switching frequency to avoid the high frequency The simulation is divided to several time Initially, oscillation. The detailed parameters of the MGintervals. are listed in Table 1.the MG operates with a small load (load 1). The After that, a big load change (load 2) intervals. is connected to the 8 s before simulation is divided to several time Initially, theMG MGat operates withcutting a small off loadfrom (load 1).at After a big loadthe change (load 2) is connectedof tothe the active MG at power 8 s before cutting off from the system 14 s.that, To evaluate dynamic performance and frequency under the system at 14 s. To the VSG dynamic performance power and frequencyand under the loading transition, theevaluate proposed control is appliedoftothe theactive grid-forming converter then is the loading proposedand VSG control is applied the grid-forming converter and then is compared withtransition, the droopthe controller conventional VSGto controller. compared with the droop controller and conventional VSG controller. Table 1. System parameters. Table 1. System parameters. Parameters Parameters
Values Values
DC-linkDC-link voltage voltage 380 V380 V AC bus AC voltage bus voltage 220 V220 V System frequency 60 Hz System frequency 60 Hz Frequency deviation ±0.2 Hz Frequency ±0.2 Hz Switching frequencydeviation10 kHz Switching Virtual inertia frequency 32 kg·10 m2kHz
Virtual inertia
32 kg.m2
Parameters Parameters Load 11 Load Load 22 Load Resistive impedance Resistive impedance Inductive impedance Inductive Frequency impedance droop gain Frequency droop gain Voltage droop gain Voltage droop gain
Values Values 5 kW 5 kW 10 kW 10 kW 0.355 Ohm 0.355 Ohm 0.15 mH 0.15 mH 4.189 × 10−4 −4−2 4.1893××1010 3 × 10−2
It can be observed from Figure 1212 that after s, the the active activepower powerinincase case of It can be observed from Figure that afterthe thelarge largeload loadchange change at at 88 s, using conventional VSG control, and proposed VSG control differs significantly. ofdroop using control, droop control, conventional VSG control, and proposed VSGmethods control methods differs When droop controller is applied, the transient response of active power has low inertia. In addition, significantly. When droop controller is applied, the transient response of active power has low inertia. due In toaddition, the different inertia between two types of converter, oscillation occurs. Thus, this results due to the different inertia between two types of converter, oscillation occurs. Thus, this in a in a high overshoot the dynamic response of active power. of The inertia of the can be by highresults overshoot of the dynamicofresponse of active power. The inertia the system cansystem be supported supported by applying VSG the conventional VSG controller it has the ability provide to inertia applying the conventional controller because it has thebecause ability to provide inertiatovirtually the MG. virtually to the MG. However, although the lack of inertia can be solved in this case, the overshoot is to However, although the lack of inertia can be solved in this case, the overshoot is still larger compared still larger compared to that of the droop controller. By using the proposed VSG controller, the inertia that of the droop controller. By using the proposed VSG controller, the inertia support feature inherited feature inherited from the conventional VSG controller is remained. Moreover, the overshoot fromsupport the conventional VSG controller is remained. Moreover, the overshoot of the proposed method is of the proposed method is considerably reduced compared to that of the droop controller and considerably reduced compared to that of the droop controller and conventional VSG controller. When conventional VSG controller. When load 2 is cut off from the MG at 14 s, the proposed VSG method load 2 is cut off from the MG at 14 s, the proposed VSG method shows a better performance compared shows a better performance compared to that of other methods. The active power has higher inertia to that of othertomethods. active power higher inertia compared to thecompared droop controller, compared the droopThe controller, and thehas overshoot is reduced significantly to that ofand the the overshoot is reduced conventional VSGsignificantly controller. compared to that of the conventional VSG controller.
Figure 12. Active power of grid-forming converter.
Figure 12. Active power of grid-forming converter.
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With regard to the grid feeding converter, it can be seen from Figure 13 that there is a trade-off With regard to the grid feeding converter, it can be seen from Figure 13 that there is a trade-off of active power between the two converters. Whereas the dynamic response of the grid-feeding and of Energies active 2017, power between the two converters. Whereas the dynamic response of the grid-feeding and 11, 27 10 of 17 grid-forming converter looks similar to high overshoot and oscillation when the droop controller grid-forming converter looks similar to high overshoot and oscillation when the droop controller is is applied, there is no overshoot in theconverter, active power in seen case of applying the VSG and With regard the grid feeding it can be from Figure thatconventional there is aVSG trade-off applied, there is notoovershoot in the active power in case of applying the13 conventional and the theproposed proposed VSG controller. Besides that, although VSG control is not applied to the grid-feeding of activeVSG power between the two converters. Whereas thecontrol dynamicisresponse of theto grid-feeding and controller. Besides that, although VSG not applied the grid-feeding converter, the inertia of active power is also improved because the total inertia of the system is increased grid-forming converter looks similar to high overshoot and oscillation when the droop controller is is converter, the inertia of active power is also improved because the total inertia of the system applied, there is no overshoot in the active power in case of applying the conventional VSG and the when VSG control is applied to the grid-forming converter [24]. increased when VSG control is applied to the grid-forming converter [24]. proposed VSG controller. Besides that, although VSG control is not applied to the grid-feeding converter, the inertia of active power is also improved because the total inertia of the system is increased when VSG control is applied to the grid-forming converter [24].
Figure 13. Active power of grid-feeding converter. Figure 13. Active power of grid-feeding converter. Active can power grid-feeding converter. Additionally, the inertiaFigure of the13. system beofobserved clearly in the frequency response, which Additionally, the inertia of the system can be observed clearly in grid-forming the frequencyconverter, response,inwhich is depicted in Figure 14. When the droop controller is utilized for the the Additionally, the inertia of the system can be observed clearly in the frequency response, which is depicted in Figure 14. When the droop within controller utilized for which the grid-forming converter, steady state, the frequency is fluctuated the is limited range is allowed from 59.8 Hzintothe is depicted in Figure 14. When the droop controller is utilized for the grid-forming converter, in the steady state, the frequency is fluctuated the limited range which isover allowed from 59.8 Hz1 to 60.2 Hz. However, in the transient state, within the frequency response fluctuated 59.8 Hz when load steady state, the frequency is fluctuated within the limited range which is allowed from 59.8 Hz to 60.2isHz. However, transient state, the frequency overtends 59.8 Hz when load 1 is connected at in 8 the s. Therefore, the system stabilityresponse can be fluctuated affected and to be unstable. 60.2 Hz. However, in the transient state, the frequency response fluctuated over 59.8 Hz when load 1 Nonetheless, thethe conventional VSG controller and proposed controller increase connected at 8 s.applying Therefore, system stability can be affected and tendsVSG to be unstable.can Nonetheless, is connected at 8 s. Therefore, the system stability can be affected and tends to be unstable. theNonetheless, totalthe inertia and reduce overshoot and low frequency oscillation of the system. applying conventional VSG controller and proposed VSG controller can increase the total inertia applying the conventional VSG controller and proposed VSG controller can increase and reduce lowovershoot frequency oscillation of theoscillation system. of the system. the totalovershoot inertia andand reduce and low frequency
Figure 14. System frequency. Figure 14. System frequency. Figure 14. System frequency.
On the other hand, virtual inertia and the virtual damping factor play an important role in On the other hand, virtual inertia and the virtual damping factor play an important role in improving the ofofthe to fully fully understand understand theirimpacts impacts on MG, the in On the other hand, inertia and the to virtual damping factor play anonimportant role improving thestability stabilityvirtual thesystem. system. In In order order their thethe MG, the analysis ofofthese isis investigated. The MG firstsimulated simulatedwith with𝐽 = 𝐽= 𝐷 50. = 50. analysis thesecomponents components investigated. first 3232 and 𝐷= improving the stability of the system. In orderThe to MG fullyisisunderstand their impacts onand the MG, the After that, whereas the damping factor is remained unchanged, the virtual inertia is increased to = After whereas the damping factor is remained unchanged, the virtual inertia to 50. 𝐽 =𝐽After analysis ofthat, these components is investigated. The MG is first simulated with J =is32increased and D = 4040 and 48, respectively. Figure 15 the active activepower powerperformance performanceofof grid-forming and𝐽 = 𝐽 the = 48, respectively. 15 describes describes the thethe grid-forming that, whereas damping factorFigure is remained unchanged, the virtual inertia is increased to J = 40 and converter at various inertia values. It can be seen that even though the overshoot of the grid-forming converter at various inertia values. It can be seen that even though the overshoot of the grid-forming J = 48, respectively. Figure 15 describes the active power performance of the grid-forming converter
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at various inertia Energies 2017, 11, 27values. It can be seen that even though the overshoot of the grid-forming converter 11 of 17 is slightly increased, the system is provided more inertia during the transient time. It is also converter is slightly increased, the system is provided more inertia during the transient time. It istrue alsofor converter is slightly increased, the system is provided more inertia during the transient time. It is also the true dynamic response of the grid-feeding converter, as shown Figure 16. The16.inertia of theofsystem for the response of the grid-feeding converter, as in shown in Figure The inertia Energies 2017,dynamic 11, 27 11 of 17the true for the dynamic response of the grid-feeding converter, as shown in Figure 16. The inertia of the is observed through frequency response, as described in Figure 17. An17. increase of virtual system isclearly observed clearlythe through the frequency response, as described in Figure An increase of system is observed through the frequency response, as described in Figure 17. An increase of inertia value leads to clearly the growth ofgrowth total system inertia. virtual inertia value leads to thethe ofistotal system inertia. converter is slightly increased, system provided more inertia during the transient time. It is also virtual inertia value leads to the growth of total system inertia. true for the dynamic response of the grid-feeding converter, as shown in Figure 16. The inertia of the system is observed clearly through the frequency response, as described in Figure 17. An increase of virtual inertia value leads to the growth of total system inertia.
Figure 15. Active power of grid-forming converter with different virtual inertia.
Figure 15. converter with withdifferent differentvirtual virtualinertia. inertia. Figure 15.Active Activepower powerof ofgrid-forming grid-forming converter Figure 15. Active power of grid-forming converter with different virtual inertia.
Figure 16. Active power of grid-feeding converter with different virtual inertia. Figure 16. Active power of grid-feeding converter with different virtual inertia. Figure 16. 16. Active power converterwith withdifferent different virtual inertia. Figure Active powerofofgrid-feeding grid-feeding converter virtual inertia.
Figure 17. System frequency with different virtual inertia. Figure17. 17.System Systemfrequency frequency with virtual inertia. Figure with different different Figure 17. System frequency with differentvirtual virtualinertia. inertia.
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the virtual damping factor, as can be observed in Figures 18 and 19, a With regard to the virtual damping factor, as can be observed in Figures 18 and 19, there is a trade-off between the two DGs. In this case, the virtual damping factor is increased from D = 50 to Withbetween regard to virtual factor, as can damping be observed in Figures 18 and 19,𝐷there a trade-off thethe two DGs. damping In this case, the virtual factor is increased from = 50isto With regard to the virtual damping factor, as can be observed in Figures 18 and 19,𝐷 there istoa D= 500 and D = 1000, respectively. While the active power of the grid-forming converter is increased, trade-off between the two DGs. In this case, the virtual damping factor is increased from = 50 𝐷 = 500 and 𝐷 = 1000 , respectively. While the active power of the grid-forming converter is trade-off between the two DGs. In this case, theThe virtual damping factor increased from 𝐷avoids = 50 to 𝐷 = 500 and 1000 , respectively. While the active power of the grid-forming converter isthe that of the grid-feeding converter isconverter decreased. system frequency isisdecreased, which increased, that 𝐷 of=the grid-feeding is decreased. The system frequency is decreased, which 𝐷 = 500 and 𝐷 = 1000 , respectively. While the active power of the grid-forming converter is increased, that of the grid-feeding converter is decreased. The system frequency is decreased, which system to be unstable because the frequency derivation is limited, as shown in Figure 20. avoids the system to be unstable because the frequency derivation is limited, as shown in Figure 20. increased, of the grid-feeding converter decreased. The system frequency is decreased, which avoids the that system to be unstable because the is frequency derivation is limited, as shown in Figure 20. avoids the system to be unstable because the frequency derivation is limited, as shown in Figure 20.
Figure 18. Active power of grid-forming converter with different virtual damping factors. Figure 18.18.Active with different differentvirtual virtualdamping dampingfactors. factors. Figure Activepower powerofofgrid-forming grid-forming converter converter with Figure 18. Active power of grid-forming converter with different virtual damping factors.
Figure 19. Active power of grid-feeding converter with different virtual damping factors. Figure 19. Active power of grid-feeding converter with different virtual damping factors. Figure 19. Active power of grid-feeding converter with different virtual damping factors. Figure 19. Active power of grid-feeding converter with different virtual damping factors.
Figure 20. System frequency with different virtual damping factors. Figure 20. System frequency with different virtual damping factors. Figure 20. System frequency with different virtual damping factors. Figure 20. System frequency with different virtual damping factors.
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The inertia clearly in theinderivation of frequency d f /dt, which inertiaresponse responseis observed is observed clearly the derivation of frequency 𝑑𝑓/𝑑𝑡is, illustrated which is in Figure 21. can be that the during transient at 8 sstates and 14 frequency illustrated in It Figure 21.seen It can beduring seen that thestates transient at s, 8 sthe and 14 s, the derivation frequency of droop controller the highest when the conventional controllerVSG and derivation of droophas controller hasovershoot. the highestHowever, overshoot. However, when theVSG conventional proposed controller are the are derivation frequency varies slower than that of the droop controller VSG and proposed VSGapplied, controller applied,ofthe derivation of frequency varies slower than controller, its controller, overshoot and is slightly decreased. that of the and droop its overshoot is slightly decreased.
Figure 21. Derivative component of system frequency. Figure 21. Derivative component of system frequency.
5. Experimental Results 5. Experimental Results The complete MG system with the proposed VSG controller is built and tested experimentally The complete MG system with the proposed VSG controller is built and tested experimentally using real time simulation system (OPAL-RT). The structure of the MG performed in the experiment using real time simulation system (OPAL-RT). The structure of the MG performed in the experiment is is similar with that of the simulation. Due to the mismatch of line impedances, the inaccurate reactive similar with that of the simulation. Due to the mismatch of line impedances, the inaccurate reactive power sharing occurs as a serious problem in the MG system. In order to deal with this problem, the power sharing occurs as a serious problem in the MG system. In order to deal with this problem, the virtual impedance method is applied for the grid-forming converter. The detail of virtual impedance virtual impedance method is applied for the grid-forming converter. The detail of virtual impedance is is introduced, following the equation below. introduced, following the equation below. ∗ 𝑣𝑟𝑒𝑓 = 𝑣𝑎𝑏𝑐 − 𝑍𝑣𝑖𝑟 (𝑠)𝑖𝑜 (19) ∗ vre f = v abc − Zvir (s)io (19) where 𝑍𝑣𝑖𝑟 is the virtual output impedance, 𝑣𝑟𝑒𝑓 is the reference of output voltage obtained by the ∗ using virtual 𝑣𝑎𝑏𝑐 isimpedance, the output voltage reference achieved by conventional 𝑃‐ 𝜔 by droop where Zvir is impedance, the virtual output vre f is the reference of output voltage obtained the controller, and 𝑖 is the output current of the grid-forming converter. ∗ 𝑜 using virtual impedance, v abc is the output voltage reference achieved by conventional P − ω droop If the and virtual component is included toconverter. the virtual impedance, as presented. 𝑣𝑖𝑟 grid-forming controller, i isinductive the output current of 𝐿the o
If the virtual inductive component Lvir is𝑍𝑣𝑖𝑟 included = 𝑠𝐿𝑣𝑖𝑟to the virtual impedance, as presented. (20)
It can be seen from Equation (20) that the reference Zvir = sLvir of output voltage is proportionally changed (20) depending on the derivation of output current. Thus, the effect of the resistive component on the output voltage can from be reduced, and(20) thethat active can of be output shared voltage equally.isInproportionally this part, a comparison It can be seen Equation thepower reference changed between the proposed VSG controller and the droop controller considering virtual impedance depending on the derivation of output current. Thus, the effect of the resistive component control on the is presented. output voltage can be reduced, and the active power can be shared equally. In this part, a comparison It is the obviously seen from Figuresand 22 and 23 thatcontroller when theconsidering transient response of reactive control power between proposed VSG controller the droop virtual impedance when the proposed VSG controller is applied, the transient response of power is reduced in is presented. comparison with that of the droop controller. It is obviously seen from Figures 22 and 23 that when the transient response of reactive power when the proposed VSG controller is applied, the transient response of power is reduced in comparison with that of the droop controller.
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Figure 22. Reactive power of the proposed VSG control with virtual impedance. Figure 22. 22. Reactive Reactive power power of of the the proposed proposed VSG VSG control control with virtual impedance. Figure with virtual impedance. Figure 22. Reactive power of the proposed VSG control with virtual impedance.
Figure 23. Reactive power of the droop control considering virtual impedance. Figure 23. Reactive power of the droop control considering virtual impedance. Figure 23. Reactive power of the droop control considering virtual impedance. Figure 23. Reactive power of the droop control considering virtual impedance.
With regard to the active power, Figure 24 shows that after a load change at 15 s, the transient With regard to the active power, Figure 24 shows that after a load change at 15 s, the transient response of activetopower of grid forming converter is slightly reduced whenatthe proposed VSG With regard the power, Figure 24 after 15 s, Withof regard the active active power, Figure 24 shows showsisthat that after areduced a load load change change 15 proposed s, the the transient transient response activetopower of grid forming converter slightly whenatthe VSG control is applied. By contrast, the transient response of grid-feeding converter presents much better response of power of forming slightly when the VSG response of active activeBy power of grid grid forming converter converterofis isgrid-feeding slightly reduced reduced when the proposed proposed VSG control is applied. contrast, the transient response converter presents much better improvement in case of adopting the proposed VSG controller, as shown in Figure 25. control is applied. By contrast, the transient response of grid-feeding converter presents much better control is applied. By contrast, the transient response of grid-feeding converter presents much better improvement in case of adopting the proposed VSG controller, as shown in Figure 25. improvement improvement in in case case of of adopting adopting the the proposed proposed VSG VSGcontroller, controller,as asshown shownin inFigure Figure25. 25.
Figure 24. Active power of the grid-forming converter. Figure 24. Active power of the grid-forming converter. Figure 24. 24. Active Active power power of of the the grid-forming grid-forming converter. converter. Figure
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Figure 25. Active power of the grid-feeding converter. Figure 25. Active power of the grid-feeding converter. Figure 25. Active power of the grid-feeding converter.
Regarding frequency response, it can be seen from Figure 26 that the by applying the proposed Regarding frequency response, can from 26 by applying the proposed Regarding frequency response, it system can be be seen seen from Figure Figure 26 that thattothe the byof applying thecontrol proposed VSG control, the total inertia of theit is enhanced compared that the droop with VSG control, the total inertia of the system is enhanced compared to that of the droop control with VSG control, the total In inertia of thethe system compared to that of the droopiscontrol with virtual impedance. addition, peakisofenhanced overshoot in the frequency response significantly virtual impedance. InIn addition, peak ofmaximum overshoot in the response is significantly reduce. virtual impedance. addition, the peak of overshoot infrequency the frequency response is significantly reduce. Therefore, this avoidsthe the over and minimum frequency deviation and enhanced Therefore, this avoids the over maximum and minimum frequency deviation and enhanced the stability reduce. Therefore, avoids the over maximum and minimum frequency deviation and enhanced the stability of thethis system. of system. thethe stability of the system.
Figure 26. System frequency. Figure 26. System frequency. Figure 26. System frequency.
6. Conclusions 6. Conclusions 6. Conclusions In this study, an improved VSG controller was proposed for improving the transient response In this and study, an improved VSG controller was proposed for improving the transient response of power frequency in theVSG MGcontroller system. Awas comparison on the control performance of the In this study, an improved proposedstudy for improving the transient response ofproposed power and frequency in the MG system. A comparison study on the control performance of the VSG controller, theMG conventional controller, andonthe droop controller of power and frequency in the system. A VSG comparison study theconventional control performance of the proposed VSG controller, the conventional VSG controller, and the conventional droop controller was presented. The sensitive analysis resultVSG showed that the proposed VSG controller could provide proposed VSG controller, the conventional controller, and the conventional droop controller was presented. The and sensitive analysis result showed that the proposed VSG controller could provide higher damping lower overshoot than the conventional VSG controller. The proposed VSG was presented. The sensitive analysis result showed that the proposed VSG controller could provide higher damping and lower overshoot than the conventional VSG controller. The proposed VSG controller couldand improve overshoot of the response the inertia response of the MG higher damping lowerthe overshoot than thetransient conventional VSGand controller. The proposed VSG controller could improve the overshoot oftransient the transient response and the inertia significantly response of the MG system. Although the overshoot of the response could be improved by using controller could improve the overshoot of the transient response and the inertia response of the MG system. Although the overshootthe of the transient response could be improved significantly by using the proposed VSG low frequency oscillation output and system frequency system. Although the controller, overshoot of the transient response could of be power improved significantly by using the the proposed VSG controller, the low frequency oscillation of power output and system frequency was slightly application, the gain of theoutput powerand derivative of the proposed proposed VSG reduced. controller,For thepractical low frequency oscillation of power system frequency was was slightlyshould reduced. For practical application, the gain of the power derivative of the proposed controller chosen carefully tothe ensure stability the power converter. The proposed slightly reduced. Forbe practical application, gain the of the powerof derivative of the proposed controller controller should be chosen carefully to ensure the stability of the power converter. The proposed controller is suitable for to anensure MG system that consists of both distributed and energy should be chosen carefully the stability of the power converter. The generations proposed controller is controller is suitable for anaMG system that consists of both distributed generations and isenergy storage systems. It is also potential solution for a wind farm where the power converter usedItto suitable for an MG system that consists of both distributed generations and energy storage systems. storage systems. It isutility also a potential solution for a wind farm where the power converter is used to with the is integrate also a potential solution grid. for a wind farm where the power converter is used to integrate with the integrate with the utility grid. utility grid.
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Acknowledgments: This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 20168530050030). Author Contributions: Cao-Khang Nguyen conceived and designed the experiments; Thai-Thanh Nguyen and Hyeong-Jun Yoo performed the experiments and analyzed the results; Hak-Man Kim revised and analyzed the results; Cao-Khang Nguyen wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations DGs MGs RESs UPS VSG PSO P-ω P-V k ic k iv Pm md mq k pv k pc Vmax Vmin df dt P∗
V∗
Distributed generations Microgrids Renewable energy sources Uninterruptable power supply Virtual synchronous generator Partial swarm optimization Active power-frequency Active power-voltage Integral gain of current controller Proportional gain of current controller Mechanical power Modulating signal in d-frame Modulating signal in q-frame Proportional gain of voltage controller Integral gain of voltage controller Maximum AC voltage Minimum AC voltage Frequency derivation Active power reference RMS voltage reference
Qmax Qmin J D θ ω ωN kp kq dP dt
P kd v∗o K Zvir Lvir io vre f Q∗ ω∗
Maximum reactive power Minimum reactive power Virtual inertia Virtual damping factor Electrical angle Angular frequency Rated angular frequency Droop coefficient Droop coefficient Active power derivation Measured power of inverter Derivative coefficient Output voltage reference Rating coefficient of proposed VSG control Virtual output impedance Virtual inductive component Output current Output voltage reference using virtual impedance Reactive power reference Angular frequency reference
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