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Hierarchical control for flexible microgrid based on three-phase voltage source inverters operated in parallel
Electrical Power and Energy Systems 95 (2018) 188–201
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Review
Hierarchical control for flexible microgrid based on three-phase voltage source inverters operated in parallel Islam Ziouani a,⇑, Djamel Boukhetala a, Abdel-Moumen Darcherif b, Bilal Amghar b, Ikram El Abbassi c a
Laboratoire de Commande des Processus, Ecole Nationale Polytechnique, El Harrach, Algeria ECAM-EPMI, Quartz-Lab, Cergy-Pontoise, France c ECAM-EPMI, LR2E-Lab, Cergy-Pontoise, France b
a r t i c l e
i n f o
Article history: Received 3 March 2017 Received in revised form 6 June 2017 Accepted 21 August 2017
Keywords: Hierarchical Control Flexible microgrid Universal droop controller Voltage source inverters Grid-connected mode Islanded mode
a b s t r a c t In this paper, a hierarchical control for flexible operation of a microgrid is proposed. The structure of the hierarchical control consists of inner, primary and secondary levels. The inner control is used to regulate the output voltage of the inverter which is commonly referred as zero-level. The primary control based on the universal droop control which we improve it to handle both operation modes. It is used to share the active and reactive power accurately with regardless of the output impedance of the inverters. The secondary control compensates the deviation of the microgrid voltage caused by the primary control as well as synchronizes the microgrid voltage with the grid for a smooth transition. Thus, the microgrid can operate either in grid-connected or in islanded mode by using the same control scheme. The small-signal stability of the ameliorated universal droop control is analyzed for both modes, and other levels of control are modeled. Moreover, a technique based on meta-heuristic optimization to design the hierarchical control parameters optimally is introduced. Finally, the simulation was performed on a microgrid that has three voltage source inverters (VSIs) connected in parallel and a local nonlinear load. The results demonstrate the disturbance rejection performance and the flexibility of the proposed control scheme. Ó 2017 Elsevier Ltd. All rights reserved.
Contents 1. 2. 3.
4. 5.
6.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Microgrid structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hierarchical control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Inner control of VSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Primary control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. Small-signal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Secondary control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1. Voltage restoration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. Frequency restoration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3. Synchronization loop for seamless transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimal controller design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Islanded operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Transition from islanded to grid-connected mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Grid-connected operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
188 189 190 190 192 193 194 195 196 196 196 197 197 200 200 201 201
⇑ Corresponding author. E-mail addresses: [email protected] (I. Ziouani), [email protected] (D. Boukhetala), [email protected] (A.-M. Darcherif), b.amghar@ ecam-epmi.fr (B. Amghar), [email protected] (I. El Abbassi). http://dx.doi.org/10.1016/j.ijepes.2017.08.027 0142-0615/Ó 2017 Elsevier Ltd. All rights reserved.
I. Ziouani et al. / Electrical Power and Energy Systems 95 (2018) 188–201
1. Introduction Motivated by the climate change and the global warming, the most countries have adopted the Paris Agreement in December 2015 [1]. This agreement draws lines to limit the global warming below 2 °C above pre-industrial levels and making efforts to reduce the greenhouse gas emissions. According to the International Energy Agency, the largest source of the greenhouse gas emissions comes from the electricity generation based on fossil fuels (i.e., coal, oil, natural gas, etc.) [2]. Hence, the world starts looking at alternative ways to generate the electricity mainly in using clean and renewable sources such as wind energy, photovoltaic, thermal energy and tidal energy [3–6]. These prime sources are distributed by nature and come with deferent form, some are DC sources, and others are AC sources. Therefore, the distributed generations (DGs) were introduced in the literature, in order to supply the demand locally [7,8]. The DGs are connected to the utility grid through a power electronic interface which is responsible for controlling the injected power. However, the increasing integration of DGs into the utility grid can cause as many problems [9]. Thus, the microgrid is used as a bridge between them and the grid. In other words, a microgrid is a local electrical distribution network which gathering a combination of DG units, distributed energy storage systems, and loads. The microgrid operates in grid-connected mode when is connected to the main grid through the point of common coupling (PCC), where it can export or import energy. And can operates in islanded mode when is disconnected from the grid [10–17]. The DGs are interfaced with the synchronous AC microgrid bus through inverters, as they can generate either DC power or asynchronous frequency AC power which can be transferred into DC power via an uncontrolled rectifier [18,12]. The inverters behave as current source inverter (CSI) when the microgrid is operated in grid-connected mode, and as voltage source inverter (VSI) when it operates in islanded mode. Nowadays, the VSIs are most used as electronics interface where they can be implemented with a current controller (CC-VSI) to transfer the maximum power into the local grid, or they can be implemented with a voltage controller (VC-VSI) to regulate the voltage amplitude and frequency of the microgrid. According to Gao and Iravani [19], VC-VSI can be operated either in islanded mode or in grid-connected mode. The control strategy of the paralleled VSIs is based on the droop method which uses the local measurements to operate independently without external communications between the VSIs. This method was inspired from the conventional droop control of power system, where it is used by the synchronous generators to re-establish the active power balance [20]. Furthermore, the objectives of the droop control in the microgrid are: Accurate active and reactive power sharing among the paralleled VSIs in proportion to their power ratings. Stabilize the microgrid voltage amplitude and frequency at the PCC. Inject the demanded power when the microgrid is operated in grid-connected mode. In order to achieve these objectives, several droop methods were proposed in the literature, and some of them are reviewed by Bidram et al. [14]. Recently, a new method is developed by Zhong et al. [21–23] which called the universal droop control. This method can operate in islanded mode which is robust to disturbances, noise and component mismatches. Moreover, it works regardless of the output impedance of the inverters.
189
However, the universal droop control can’t handle the gridconnected mode, and it would cause a deviation in amplitude and frequency of the islanded microgrid voltage which leads to phase difference with the utility grid. In this sense, we have ameliorated the universal droop control, and we have enhanced it via a hierarchical structure which becomes its primary control. The secondary control of the hierarchical structure is used to compensate the voltage and frequency deviation caused by the primary control and synchronizes the microgrid voltage with the grid voltage in order to ensure a smooth transition. The secondary control can be classified in two structures [24,17,25,26,9]: 1. Centralized structure is implemented in the microgrid central controller (MGCC) which is suitable for islanded operation. 2. Decentralized structure allows DG units to interact with each others which is suitable for grid-connected operation. The centralized structure is used throughout this paper. The paper is organized as follows. In Section 2, the microgrid structure is presented, and the hierarchical control is described. In Section 3, the voltage source inverter is modeled, and an improved universal droop control is described with small-signal analysis, as well as the secondary control for voltage restoration and the synchronization process is presented. In Section 4, an optimal controller design technique is given. Section 5 shows the simulation results. In Section 6, gives the conclusion of the paper. 2. Microgrid structure The microgrid structure adopted in this paper is shown in Fig. 1. It consists of three VSIs operating in parallel and a local nonlinear load which is composed of three-phase uncontrolled rectifier loaded with LC filter and a variable resistor (see Table 1). Each VSI is connected to the common bus through LCL filter and line impedance that represents a physical distance (see Table 2). In another hand, the microgrid is interfaced to the main grid via an intelligent static switch (SS) that allows monitoring the voltages of both sides [10,15]. The SS disconnects automatically the microgrid when detects any disturbance or fault in the main grid [27], and when the grid is restored, SS informs the MGCC to start the synchronization process in order to reconnect. We control the microgrid by using a hierarchical scheme that has multiple control loops which are separated into different time scales and it can be classified in the following control levels: 1. Inner Control (Level 0): This level controls and regulates the output voltage and current of the VSI. 2. Primary Control (Level 1): It is a local controller that provides a proportional power sharing among the DGs and mitigates the circulating current that appears when VSIs operate in parallel. The idea comes from the traditional primary control of the synchronous generator that realized by turbine-governors and voltage regulator. 3. Secondary Control (Level 2): When power sharing is achieved by the primary control, the frequency and the voltage amplitude may deviate from their nominal values. Thus, the secondary control is needed to restore the microgrid voltage; this controller is centralized and located in MGCC where it sends the corrected values by using low bandwidth communications to all paralleled VSIs. MGCC can also contain a synchronization loop to facilitate the transition from islanded to gridconnected mode. 4. Tertiary Control (Level 3): This is the last and the slowest control level that is responsible to schedule the power of each DGs. It depends on global economic and current energy prices. One of
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Fig. 1. Single line diagram of the microgrid system.
Table 1 Electrical system parameters. Parameter
Symbol
Value
Units
Nominal frequency Nominal RMS voltage Load filter inductance Load filter capacitance Load
x
2p 50 220 84 500 300/150/80
rad/s V lH lC
E Ll Cl Rl
X
its objectives is to achieve the optimal operation during islanded mode and optimal power flow during grid-connected mode. This tertiary level is not considered in this paper and will be covered in our next works.
3. Hierarchical control This section deals with the development of a control framework based on hierarchical scheme for flexible microgrid, to be able to
operate either in islanded or in grid-connected mode with a smooth transition between them. In islanded mode, the microgrid is disconnected from the main grid and operates autonomously, while the objectives are to achieve an accurate power sharing among the paralleled VSIs in proportion to their power ratings, regardless of their output impedance, as well as maintaining a close regulation of the voltage amplitude and frequency at the PCC. For a seamless connection to the grid, the voltage at PCC must be synchronized to the voltage of the grid using synchronization loop that reduces the phase angle between them. In gridconnected mode, the VSIs are controlled in order to generate their scheduled power into the system. 3.1. Inner control of VSI The inner control of VSI is based on cascaded control structure which consists of an outer voltage loop and an inner current loop (see Fig. 2). The advantages of this scheme are as follows: Achieves a low total harmonic distortion (THD) for the capacitor voltage v Cabc .
Table 2 Inverters parameters with their output impedances. Parameter
Symbol
VSI1
VSI2
VSI3
Units
Inverter-side filter inductor Parasitic resistor 1 Grid-side filter inductor Parasitic resistor 2 Filter capacitor DC voltage PWM switching frequency Output impedance Apparent power rating
Lf1 r1 Lf2 r2 Cf Vdc fs Zo S
1.8 0.03 1.8 0.03 35 650 10 0:7; 2:6 1
1.8 0.03 1.8 0.03 35 650 10 0:5; 1:9 2
1.8 0.03 1.8 0.03 35 650 10 0:8; 1:6 3
mH
X mH
X
lC V kHz X, mH kVA
I. Ziouani et al. / Electrical Power and Energy Systems 95 (2018) 188–201
191
Fig. 2. Block diagram of the VSI with the inner control loops.
Fig. 3. Block diagram of the inner control loops in ab-coordinates.
Keeps the inductor current ilabc within a safe limits. Maintain the same control scheme for different mode of operations (islanded or grid-connected mode). Improves more the disturbance rejection. The role of outer voltage loop is to regulate the capacitor voltage v Cabc to reference signal that is generated by the primary control, and also is responsible for setting the reference of the inner current loop, which in turn regulates the inductor current ilabc . The dynamics of the outer loop must be slower than those of the inner loop [28]. We transform the abc reference frame into ab stationary reference to get two independent single-phase systems by using Clarke transformation as shown in Fig. 3. The PR controllers are applied to get a better voltage regulation with less harmonics, and they can be expressed as follows [29,30]:
Gv ðsÞ ¼ kpv þ Gi ðsÞ ¼ kpi þ
s2
X krv s khv s þ þ xc s þ x2o h¼3;5;7 s2 þ hxc s þ ðhxo Þ2
X kri s khi s þ 2 2 s þ xc s þ xo h¼3;5;7 s2 þ hxc s þ ðhxo Þ2
ð1Þ ð2Þ
where kpv and kpi are the proportional gains, krv and kri are the resonant gains at the fundamental frequency, khv and khi are the resonant gains at the h-harmonic, xc is the resonant bandwidth used to
avoid the instability problems associated with the infinite gain, xo is the fundamental frequency. From the block diagram of Fig. 3 with using Mason’s theorem [31], the closed loop transfer function (CLTF) of the inner current loop and outer voltage loop of the acoordinate can be expressed by:
Gi ðsÞGPWM ðsÞ i ðsÞ Z l ðsÞ þ Gi ðsÞGPWM ðsÞ la 1 v C a ð sÞ Z l ðsÞ þ Gi ðsÞGPWM ðsÞ Gol ðsÞ v Ca ðsÞ ¼ v ref a ðsÞ Z C ðsÞ þ Z l ðsÞ þ Gin ðsÞ þ Gol ðsÞ Z C ðsÞðZ l ðsÞ þ Gin ðsÞÞ ioa ðsÞ Z C ðsÞ þ Z l ðsÞ þ Gin ðsÞ þ Gol ðsÞ ila ðsÞ ¼
ð3Þ
ð4Þ
where
Gol ðsÞ ¼ Gv ðsÞGi ðsÞGPWM ðsÞZ C ðsÞ Gin ðsÞ ¼ Gi ðsÞGPWM ðsÞ GPWM ðsÞ ¼
V dc =2 1 þ 1:5T s s
Z l ¼ sLf 1 þ r 1 ; Z C ¼ sC1 and GPWM is the transfer function of the PWM delay, T s is the sampling time which equals to f1s . The same model can be developed in b-coordinate. In Section 4 we discus how to tune optimally the parameters of PR controllers.
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Table 3 Optimal parameters of the hierarchical control. Inner Control Controller
Gi Gv
Parameters kp
kr
k3
k5
k7
xc
0.2131 0.2027
211.62 205.66
32.21 25.35
101.1 22.14
61.74 61.08
0.0015 0.0015
Primary Control Inverter
Parameters ke
n
m
nd
md
ng
mg
VSI1
7
0.2178
3:1 104
0.003
2:0 106
0.03
2
VSI2
7
0.1089
1:6 104
0.0015
1:0 106
0.03
2
VSI3
7
0.0726
1:0 104
0.001
6:6 107
0.03
2
Secondary Control PI
Voltage loop
Frequency loop
Synchronization
kp ki
1.8151 4.2968
2.2298 7.6729
4.5 0
3.2. Primary control The primary control adopted in this paper is based on the universal droop control that was developed by Zhong [21], which we have improved it by introducing a derivative term to enhance the transition response and a hybrid term to distinguish between different mode of operation. The primary control can be described as:
dðP P Þ K e E V pcc nðP P Þ nd g c þ g c ng dt dðQ Q Þ x ¼ x þ mðQ Q Þ þ md g c þ g c mg dt
E_ ¼
ð5Þ ð6Þ
where E and x are amplitude (RMS) and frequency of the capacitor voltage of VSI, respectively; E and x are their nominal values. P and Q are the desired active and reactive power to be injected during the grid-connected mode, normally are set to zero in islanded mode. V pcc is the amplitude (RMS) of the voltage at PCC, n and m are the droop coefficients, nd and md are the derivative droop coefficients of the active and reactive power, respectively. K e is an
amplifier used to maintain the PCC voltage within a desired range and is chosen the same for all VSIs operated in parallel (see Table 3). ng and mg are used to improve the response and the stability of the microgrid during grid-connected mode. g c is a hybrid variable which can be written as:
gc ¼
1 if Microgrid operates in grid-connected mode
0 if Microgrid operates in islanded mode gc ¼ 1 gc
ð7Þ ð8Þ
The instantaneous active and reactive power of VSI that is injected into the microgrid common bus is expressed in the abstationary reference frame as follows [32]:
pðtÞ ¼v pcca ioa þ v pccb iob qðtÞ ¼v pccb ioa v pcca iob
ð9Þ ð10Þ
where v pcc and io are voltage at PCC and the output current of the VSI, respectively. The average power of P and Q in Fig. 4 is calculated by integrating (9) and (10) over one fundamental cycle T and is described as:
Fig. 4. Block diagram of the primary control in ab-coordinates.
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Fig. 5. The simulink diagram of power calculator of the Fig. 14.
DPðsÞ ¼ kpe DEðsÞ þ kpd DdðsÞ DQ ðsÞ ¼ kqe DEðsÞ kqd DdðsÞ sDEðsÞ ¼ nDP mes ðsÞa1 nd sDPmes ðsÞa1 DxðsÞ ¼ mDQ mes ðsÞa2 þ md sDQ mes ðsÞa2
ð18Þ ð19Þ ð20Þ ð21Þ
where
a1 ¼g c þ g c ng a2 ¼g c þ g c mg
Fig. 6. Simplified model of the three-phase VSI.
Z 1 t pðtÞdt T tT Z t 1 Q¼ qðtÞdt T tT P¼
ð11Þ ð12Þ
By applying the Laplace transformation to (11) and (12), we obtain the following equations [26]:
PðsÞ ¼FðsÞpðsÞ
ð13Þ
Q ðsÞ ¼FðsÞqðsÞ
ð14Þ
where FðsÞ is the transfer function of the integration filter and is expressed as follows:
FðsÞ ¼
1 1 eTs Ts
ð15Þ
The expressions from (9)–(15) are used to construct the power calculator of the Fig. 4 (see Fig. 5).
2
P¼ Q¼
V pcc EV pcc cos d Zo Zo V 2pcc
EV pcc cos d Zo Zo
! cos h þ
EV pcc sin d sin h Zo
ð16Þ
sin h
EV pcc sin d cos h Zo
ð17Þ
!
The above equations and the ameliorated universal droop controller (5) and (6) can be linearized around the equilibrium as:
ð23Þ
V pcce ðcos de cos h þ sin de sin hÞ Zo Ee V pcce ðcos de sin h sin de cos hÞ kpd ¼ Zo V pcce ðcos de sin h sin de cos hÞ kqe ¼ Zo Ee V pcce ðsin de sin h þ cos de cos hÞ kqd ¼ Zo kpe ¼
ð24Þ ð25Þ ð26Þ ð27Þ
For small-signal analysis, the integration filter (15) used to calculate the real and reactive power is approximated using the well known second order Padé approximation and is expressed as follows [26]:
F ðsÞ
1 T2 2 s 12
ð28Þ
þ T2 s þ 1
The measured active and reactive power becomes:
DPmes ðsÞ ¼ 3.2.1. Small-signal analysis A small-signal analysis can be used to investigate the stability of the primary control, considering small disturbance around the stable equilibrium point defined by de ; V pcce ; Ee , where V pcce is the amplitude (RMS) of the voltage at PCC, Ee is the amplitude (RMS) of the VSI’s capacitor voltage and de is the phase angle difference between them. Fig. 6 shows the three-phase inverter which is modeled as an ideal single-phase voltage source in series with the output impedance Z o \h. The real and reactive power flowing from the source to the terminal v pcc through the impedance Z o \h are as follows [33]:
ð22Þ
DQ mes ðsÞ ¼
1 T2 2 s 12
þ T2 s þ 1 1
T2 2 s 12
þ T2 s þ 1
DPðsÞ
ð29Þ
DQ ð s Þ
ð30Þ
Substituting (18)–(29) into (20) gives:
sDEðsÞ ¼ a1
nd s þ n T2 2 s 12
þ
T s 2
þ1
kpe DEðsÞ þ kpd DdðsÞ
ð31Þ
and (19)–(30) into (21) gives:
DxðsÞ ¼ a2
md s þ m T2 2 s 12
þ T2 s þ 1
kqe DEðsÞ kqd DdðsÞ
ð32Þ
Since:
DxðsÞ ¼ sDdðsÞ
ð33Þ
It implies to the following sixth-order homogeneous equation:
a6 s6 DdðsÞ þ a5 s5 DdðsÞ þ a4 s4 DdðsÞ þ a3 s3 DdðsÞ þ a2 s2 DdðsÞ þ a1 sDdðsÞ þ a0 DdðsÞ ¼ 0
ð34Þ
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with:
a6 a5 a4 a3 a2 a1 a0
¼ ¼ ¼ ¼ ¼ ¼ ¼
a¼ b¼ A¼ C¼ D¼
The eigenvalues of this Eq. (35) have been studied for both operation modes when h of output impedance changes from p2 to p2 with Ro ¼ 0:7X ðZ o ¼ Ro þ jRo tan ðhÞÞ, the terminal load Z l ¼ 17 þ j28 and the primary control parameters are presented in Table 3 (we used the VSI1 values). Ee and de can be calculated according to output impedance, load impedance and V pcce . Fig. 7 shows that all eigenvalues of both modes are in the left half plane which means that regardless to output impedance of VSI the system is always stable during both operation mode, and for this reason we choose the universal droop control.
2
a 2ab 2 aC þ b þ a þ a2 md kqd a aD þ bC þ b þ a2 mkqd a þ a2 md kqd b bD þ C þ a2 mkqd b þ a2 md Ckqd þ kqe a1 nd kpd D þ a2 m Ckqd þ kqe a1 nd kpd þ a2 md A a2 m Dkqd þ kqe a1 nkpd T 2 =12 T=2 Dkqd þ kqe a1 nkpd 1 þ a1 nd kpe a1 nkpe
3.3. Secondary control
Eq. (34) describes the small-signal dynamics of the closed-loop system around the equilibrium point de ; V pcce ; Ee . Thus, the system stability can be analyzed by the following characteristic equation:
a6 s6 þ a5 s5 þ a4 s4 þ a3 s3 þ a2 s2 þ a1 s þ a0 ¼ 0
ð35Þ
The secondary control is used to compensate the deviations in amplitude and frequency of the PCC voltage caused by the primary control and restores them to their nominal values. The restoration controllers can be presented as follows:
Z dx ¼ kpx xref xMG þ kix xref xMG dt Z Eref EMG dt dE ¼ kpE Eref EMG þ kiE
ð36Þ ð37Þ
Fig. 7. Root locus plot of the closed-loop system (34) when the phase angle of output impedance change from p2 to p2 with a resistive inductive load. (a) Islanded mode (g c ¼ 0) and (b) grid-connected mode (g c ¼ 1).
I. Ziouani et al. / Electrical Power and Energy Systems 95 (2018) 188–201
195
Fig. 8. Block diagram of the secondary control in ab-coordination for voltage restoration, frequency restoration and grid synchronization.
Fig. 9. P E and Q x of primary and secondary control principles.
Fig. 10. Block diagram of the voltage restoration control.
where kpx ; kix ; kpE and kiE are the PI controllers parameters. dx and dE are sent to all primary controllers as shown in Fig. 8. The Fig. 9 shows the principle of this technique that lays on uniform shifting of all primary controllers by an amount of dx and dE. As we use the hierarchical control, the dynamics response of the secondary control is slower than the primary control which allow us to design the controllers separately, and in order to don’t exceed the tolerable
frequency and amplitude, the secondary controller must be bounded. 3.3.1. Voltage restoration Fig. 10 shows the model of the voltage restoration control that consists of primary controller, PI controller cascaded with a delay caused by the low bandwidth communication lines Gd . This model
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e ¼ sin ð/G /MG Þ
ð44Þ
Then, for small values of ð/G /MG Þ; e becomes:
e ¼ /G /MG
ð45Þ
Therefore, e can be fed to a simple PI controller. The synchronization control can be expressed as:
xs ¼ v pcca v gb v pccb v ga
is used to analyze the stability of the system and to design the PI controller. Based on the block diagram, the model as follow:
K e GEsec ðsÞGd ðsÞ Eref ðsÞ s þ K e GEsec ðsÞGd ðsÞ þ K e nGLPF ðsÞ P ðsÞ s þ K e GEsec ðsÞGd ðsÞ þ K e
ð38Þ
where the transfer functions are given as:
GEsec ðsÞ ¼ kpE þ Gd ðsÞ ¼
kiE s
1 0:24 s þ 1
xf GLPF ðsÞ ¼ s þ xf
ð39Þ ð40Þ ð41Þ
4. Optimal controller design In this paper, the controller parameters of each control level of the hierarchical structure are designed by solving an optimization problem in order to find their optimal values. The optimization problem is defined as minimization of a fitness function that its optimization vector is the controller parameters. The concept stands on evaluating the fitness function after each adjustment of the optimization vector until we find its smallest possible value, which we assume that corresponds to the optimal controller parameters. Therefore, the key points of this method are the fitness function and the solver that adjust the optimization vector intelligently. For PR controllers of the inner control, the optimization problem is defined as follows:
The details of the PI controller design is given in next section.
minimize 3.3.2. Frequency restoration The frequency restoration control has been modeled and analyzed using the same procedure as the voltage restoration control. In Fig. 11, Gxsec is a PI controller, and GFLL is simplified first-order transfer function of SOGI-FLL [34] that used to estimate the frequency of the microgrid voltage at PCC. 3.3.3. Synchronization loop for seamless transition During the islanded mode, the microgrid may need to connect to the main grid in order to import power in the case where the local demand is not supplied by the paralleled VSIs, or to export the exceed power. We consider that the amplitude and the frequency of the PCC voltage is restored to their nominal values which are assumed to be equal to the nominals of the grid. However, this is not enough to make a smooth transition, because the phase angles are different. Thus, a sudden transition without planning would cause a large circulating current flow from the grid to the VSIs. In order to avoid this issue, the microgrid voltage must be synchronized to the grid voltage before turning ON the SS and starting the grid-connecting mode. The synchronization process mitigates the phase angle between the two voltages by sending an amount of frequency xs to each VSI as shown in Fig. 8 through the secondary control. By using the a b components of the two voltages, we can calculate the grid error as:
e ¼ v pcca v gb v pccb v ga
ð42Þ
This error gives a useful index of the synchronization process, which consists of orthogonal product. For simplicity, we assume that v pcc and v g are purely sinusoidal, then e becomes:
e ¼ E2 sin ð/G /MG Þ
ð46Þ
where wf is a cut-off frequency which is fixed over one decade below the fundamental frequency, kps and kis are the PI coefficients.
Fig. 11. Block diagram of the frequency restoration control.
EMG ðsÞ ¼
xf kps s þ kis s þ xf s
ð43Þ
where E is the voltage amplitude of the grid and the microgrid after restoration, /MG and /G are the phase angles. After normalizing (43), e equals to:
h
1 P t¼0
2
v trefa v tCa ðhÞ
þ
v trefc v tCc ðhÞ
þ
2
v trefb v tCb ðhÞ
2
ð47Þ
subject to 0 < hi 6 himax ; i ¼ 1; . . . ; 11: where we choose the integral of squared-error (ISE) as a fitness function since it give us a good index on the signal quality of the capacitor voltage v Cabc ; h is the optimization vector which is the parameters of PR controllers and equals
T h ¼ kpi kri k3i k5i k7i kpv krv k3v k5v k7v xc and hmax is the upper bound of the parameters which is determined by analyzing the stability of the model (3) and (4). For primary controller and PI controllers of secondary level, we have developed a new fitness function in time domain inspired from the integral of time weight absolute-error (ITAE) [35] in order to increase the robust performance and to cope the oscillation.
minimize h
subject to
1 X
t jet ðhÞj½1 þ k k sign ðet ðhÞ þ OS yd Þ
t¼0
ð48Þ
0 < hi 6 himax ; i ¼ 1; . . . ; N:
where et ðhÞis the error between desired and actual value by using h values for the controller parameters at the sampled time t (et ðhÞ ¼ yd yt ðhÞ), OS is the overshoot and k is a constant value used to penalize the oscillations that are upper then ð1 þ OSÞ yd . The optimization vector of the primary controller is split in two vecT
tors as there are two operation modes, h1 ¼ ½ke nd md for simula
T tion in islanded mode and h2 ¼ ng mg for simulation in gridconnected mode with using the optimal h1 ; the droop coefficients n and m are calculated according to desired voltage droop ratio n S
eP ¼ K ei Ei and frequency boost ratio eQ ¼
mi Si
x
.
T The optimization vector of PI controller is h ¼ kp ki . It’s good to mention that secondary level has many control loops such as voltage restoration, frequency restoration and synchronization loop which each loop is tunned separately.
I. Ziouani et al. / Electrical Power and Energy Systems 95 (2018) 188–201
To solve the optimization problem of (47) and (48), we apply a meta-heuristic algorithm which is based on PSO (Particle Swarm Optimization) and is called SLPSO (Self-Learning Particle Swarm Optimizer) [36]. The optimal parameters of the hierarchical control are presented in the Table 3, where k ¼ 50; OS ¼ 0; eP ¼ 0:1 and eQ ¼ 103 . 5. Simulation results In this section, we evaluate the proposed hierarchical control developed in Section 3 by simulating the system shown in Fig. 1 using MATLAB/Simulink. Three studies with different scenarios are carried out to test the robustness and the performance of the system. 5.1. Islanded operation Initially, a black start was performed to operate the microgrid in islanded mode, where the three inverters start operating in parallel at same time and supplying the nonlinear load. we assume that the load demand still lower than the total power ratings of the inverters during the islanded simulation, which we would like to focus just on the power sharing and the voltage restoration. Fig. 13 show the active and reactive power of the inverters and the nonlinear
197
load while the primary control is running. These figures show clearly that the inverters share both active and reactive power accurately in a ratio of 1 : 2 : 3. To test the robustness of power sharing of the primary control, we suddenly disconnect the third inverter at t ¼ 15, and letting just two inverters supplying the power demand of the nonlinear load. As we see in the Fig. 13, the both inverters are handling well the load with time respond of 0.3 s, but if we give a closer look at the load’s active power (or reactive power) within the time range of 14–16 s, we observe that its power is dropped from 930 W to 880 W after disconnection of the third inverter. This due to the amplitude of PCC voltage which drops from 220 V to 216 V (see Fig. 12(a)) and to its quality where the THD increases from 2:1% to 2:8% as presented in Fig. 14 but this still below 5% as recommended by [37]. At t ¼ 30, the load demand is increased to double, and regardless of that the inverters still sharing the power with the ratio of 1:2. However, this sharing process which is based on the primary control causes a deviation in amplitude and frequency of the PCC voltage when a disturbance occurs as shown in Fig. 12a and b. After each static deviation within 3 s, the secondary control starts to restore the amplitude and the frequency to the nominal values, and after that, it will deactivate and letting just the primary control acting. It appears in Fig. 13a, that the secondary control affects on the active and reactive power of the load which in turn affects the power
Fig. 12. PCC voltage for a black start of the islanded mode. (a) Amplitude (RMS) and (b) frequency.
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Fig. 13. Power sharing during the islanded mode. (a) Active power and (b) Reactive power.
Fig. 14. The THD of the microgrid PCC voltage.
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Fig. 15. Synchronization of the microgrid voltage to the grid voltage. (a) Phase-a voltage waveforms of microgrid and grid before the synchronization process and (b) after 3 s of acting, the microgrid starts the grid-connected mode at t ¼ 48 s.
Fig. 16. The phase difference between the PCC voltage and the grid voltage.
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Fig. 17. Active and reactive power of the microgrid during grid-connected mode.
delivered by the inverters, and this is evident as the secondary control increases the amplitude of PCC voltage from 212 V to 220 V RMS at t ¼ 34 s. 5.2. Transition from islanded to grid-connected mode For a seamless transition to grid-connected mode, the synchronization control is activated at t ¼ 45 s. Fig. 15 shows the phase-a voltage waveform of the microgrid and the grid before and after the synchronization process, it can be observed that within 3s the both voltages are synchronized. The phase error between them is shown in Fig. 16, where it starts from around 53 and is still decreasing until arrives to around 0 at 48 s. However, this process is realized by adjusting the voltage frequency of the microgrid, and this may lead to instability in real world if the frequency exceeds the allowable limit. Thus, there is a trade-off between the time respond of the synchronization process and the maximum deviation of the frequency caused by this process. In Fig. 12b, the maximum deviation is about 0.6 Hz which is tolerable according to Nordel’s (North of Europe) grid exigencies. As seen in Fig. 12a, the synchronization does not affect on the amplitude of PCC voltage, and this is obvious since the synchronizer compromise just the frequency of each inverter with same amount xs . At t ¼ 48 s, the SS is closed and the microgrid starts the grid-connected mode. The synchronization control is then deactivated.
5.3. Grid-connected operation Once the microgrid is operated in grid-connected mode, the inverters change their behavior from stabilizing the PCC voltage to injecting the scheduled active and reactive power by setting the P and Q of the primary control. In order to inject the maximum active power from each inverter, the power factor must be set to zero with P 1 ¼ 1000 W and P2 ¼ 2000 W (the third invert is still disconnected). The reactive demand of the nonlinear load is carried out by the main grid. Hence, the inverters together deliver 3000 W and the load consumes about 1920 W as shown in Fig. 17a. The excess power is exported to the grid as presented in Fig. 17a where the grid’s active power is negative (Pg ¼ 1080 W). At t ¼ 60 s the demand is increased to 3565 W which is greater than the power delivered by the both inverters. Therefore, the microgrid imports the missed power from the grid to satisfy and balance the demand and this demonstrates the bidirectional power flow between the grid and the microgrid. 6. Conclusion This paper proposes an improved control strategy based on the hierarchical approach to operates a three-phase microgrid in islanded mode and in grid-connected mode with a seamless transition between them. The control structure is based on the station-
I. Ziouani et al. / Electrical Power and Energy Systems 95 (2018) 188–201
ary reference frame and is composed of three levels: inner, primary and secondary level. The inner control is used to regulate the capacitor voltage of the VSI, which it consists of cascaded voltage and current loops with proportional resonant controllers. The primary control is based on the universal droop control which we improve it to be able to handle the both modes of operation. When the microgrid operates in islanded mode, the primary control shares the active and reactive power demand among the paralleled VSIs with regardless of their output impedances and when it operates in grid-connected mode, each VSI inject its scheduled power. The secondary control restores the amplitude and the frequency of the PCC voltage caused by the primary control in order to stabilize the microgrid during the islanded mode, and it is responsible for synchronizing the PCC voltage with the grid voltage to make a smooth transition to the grid-connected mode. The model of different control level has been developed to analyze the system stability and to aid to design their controller parameters. Moreover, these parameters have been tuned optimally by solving an optimization problem using a meta-heuristic algorithm called SLPSO. The simulation results demonstrate the robustness and the performance of the proposed hierarchical control for the flexible microgrid.
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Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Review
Hierarchical control for flexible microgrid based on three-phase voltage source inverters operated in parallel Islam Ziouani a,⇑, Djamel Boukhetala a, Abdel-Moumen Darcherif b, Bilal Amghar b, Ikram El Abbassi c a
Laboratoire de Commande des Processus, Ecole Nationale Polytechnique, El Harrach, Algeria ECAM-EPMI, Quartz-Lab, Cergy-Pontoise, France c ECAM-EPMI, LR2E-Lab, Cergy-Pontoise, France b
a r t i c l e
i n f o
Article history: Received 3 March 2017 Received in revised form 6 June 2017 Accepted 21 August 2017
Keywords: Hierarchical Control Flexible microgrid Universal droop controller Voltage source inverters Grid-connected mode Islanded mode
a b s t r a c t In this paper, a hierarchical control for flexible operation of a microgrid is proposed. The structure of the hierarchical control consists of inner, primary and secondary levels. The inner control is used to regulate the output voltage of the inverter which is commonly referred as zero-level. The primary control based on the universal droop control which we improve it to handle both operation modes. It is used to share the active and reactive power accurately with regardless of the output impedance of the inverters. The secondary control compensates the deviation of the microgrid voltage caused by the primary control as well as synchronizes the microgrid voltage with the grid for a smooth transition. Thus, the microgrid can operate either in grid-connected or in islanded mode by using the same control scheme. The small-signal stability of the ameliorated universal droop control is analyzed for both modes, and other levels of control are modeled. Moreover, a technique based on meta-heuristic optimization to design the hierarchical control parameters optimally is introduced. Finally, the simulation was performed on a microgrid that has three voltage source inverters (VSIs) connected in parallel and a local nonlinear load. The results demonstrate the disturbance rejection performance and the flexibility of the proposed control scheme. Ó 2017 Elsevier Ltd. All rights reserved.
Contents 1. 2. 3.
4. 5.
6.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Microgrid structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hierarchical control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Inner control of VSI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Primary control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. Small-signal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Secondary control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1. Voltage restoration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. Frequency restoration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3. Synchronization loop for seamless transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimal controller design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Islanded operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Transition from islanded to grid-connected mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Grid-connected operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
188 189 190 190 192 193 194 195 196 196 196 197 197 200 200 201 201
⇑ Corresponding author. E-mail addresses: [email protected] (I. Ziouani), [email protected] (D. Boukhetala), [email protected] (A.-M. Darcherif), b.amghar@ ecam-epmi.fr (B. Amghar), [email protected] (I. El Abbassi). http://dx.doi.org/10.1016/j.ijepes.2017.08.027 0142-0615/Ó 2017 Elsevier Ltd. All rights reserved.
I. Ziouani et al. / Electrical Power and Energy Systems 95 (2018) 188–201
1. Introduction Motivated by the climate change and the global warming, the most countries have adopted the Paris Agreement in December 2015 [1]. This agreement draws lines to limit the global warming below 2 °C above pre-industrial levels and making efforts to reduce the greenhouse gas emissions. According to the International Energy Agency, the largest source of the greenhouse gas emissions comes from the electricity generation based on fossil fuels (i.e., coal, oil, natural gas, etc.) [2]. Hence, the world starts looking at alternative ways to generate the electricity mainly in using clean and renewable sources such as wind energy, photovoltaic, thermal energy and tidal energy [3–6]. These prime sources are distributed by nature and come with deferent form, some are DC sources, and others are AC sources. Therefore, the distributed generations (DGs) were introduced in the literature, in order to supply the demand locally [7,8]. The DGs are connected to the utility grid through a power electronic interface which is responsible for controlling the injected power. However, the increasing integration of DGs into the utility grid can cause as many problems [9]. Thus, the microgrid is used as a bridge between them and the grid. In other words, a microgrid is a local electrical distribution network which gathering a combination of DG units, distributed energy storage systems, and loads. The microgrid operates in grid-connected mode when is connected to the main grid through the point of common coupling (PCC), where it can export or import energy. And can operates in islanded mode when is disconnected from the grid [10–17]. The DGs are interfaced with the synchronous AC microgrid bus through inverters, as they can generate either DC power or asynchronous frequency AC power which can be transferred into DC power via an uncontrolled rectifier [18,12]. The inverters behave as current source inverter (CSI) when the microgrid is operated in grid-connected mode, and as voltage source inverter (VSI) when it operates in islanded mode. Nowadays, the VSIs are most used as electronics interface where they can be implemented with a current controller (CC-VSI) to transfer the maximum power into the local grid, or they can be implemented with a voltage controller (VC-VSI) to regulate the voltage amplitude and frequency of the microgrid. According to Gao and Iravani [19], VC-VSI can be operated either in islanded mode or in grid-connected mode. The control strategy of the paralleled VSIs is based on the droop method which uses the local measurements to operate independently without external communications between the VSIs. This method was inspired from the conventional droop control of power system, where it is used by the synchronous generators to re-establish the active power balance [20]. Furthermore, the objectives of the droop control in the microgrid are: Accurate active and reactive power sharing among the paralleled VSIs in proportion to their power ratings. Stabilize the microgrid voltage amplitude and frequency at the PCC. Inject the demanded power when the microgrid is operated in grid-connected mode. In order to achieve these objectives, several droop methods were proposed in the literature, and some of them are reviewed by Bidram et al. [14]. Recently, a new method is developed by Zhong et al. [21–23] which called the universal droop control. This method can operate in islanded mode which is robust to disturbances, noise and component mismatches. Moreover, it works regardless of the output impedance of the inverters.
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However, the universal droop control can’t handle the gridconnected mode, and it would cause a deviation in amplitude and frequency of the islanded microgrid voltage which leads to phase difference with the utility grid. In this sense, we have ameliorated the universal droop control, and we have enhanced it via a hierarchical structure which becomes its primary control. The secondary control of the hierarchical structure is used to compensate the voltage and frequency deviation caused by the primary control and synchronizes the microgrid voltage with the grid voltage in order to ensure a smooth transition. The secondary control can be classified in two structures [24,17,25,26,9]: 1. Centralized structure is implemented in the microgrid central controller (MGCC) which is suitable for islanded operation. 2. Decentralized structure allows DG units to interact with each others which is suitable for grid-connected operation. The centralized structure is used throughout this paper. The paper is organized as follows. In Section 2, the microgrid structure is presented, and the hierarchical control is described. In Section 3, the voltage source inverter is modeled, and an improved universal droop control is described with small-signal analysis, as well as the secondary control for voltage restoration and the synchronization process is presented. In Section 4, an optimal controller design technique is given. Section 5 shows the simulation results. In Section 6, gives the conclusion of the paper. 2. Microgrid structure The microgrid structure adopted in this paper is shown in Fig. 1. It consists of three VSIs operating in parallel and a local nonlinear load which is composed of three-phase uncontrolled rectifier loaded with LC filter and a variable resistor (see Table 1). Each VSI is connected to the common bus through LCL filter and line impedance that represents a physical distance (see Table 2). In another hand, the microgrid is interfaced to the main grid via an intelligent static switch (SS) that allows monitoring the voltages of both sides [10,15]. The SS disconnects automatically the microgrid when detects any disturbance or fault in the main grid [27], and when the grid is restored, SS informs the MGCC to start the synchronization process in order to reconnect. We control the microgrid by using a hierarchical scheme that has multiple control loops which are separated into different time scales and it can be classified in the following control levels: 1. Inner Control (Level 0): This level controls and regulates the output voltage and current of the VSI. 2. Primary Control (Level 1): It is a local controller that provides a proportional power sharing among the DGs and mitigates the circulating current that appears when VSIs operate in parallel. The idea comes from the traditional primary control of the synchronous generator that realized by turbine-governors and voltage regulator. 3. Secondary Control (Level 2): When power sharing is achieved by the primary control, the frequency and the voltage amplitude may deviate from their nominal values. Thus, the secondary control is needed to restore the microgrid voltage; this controller is centralized and located in MGCC where it sends the corrected values by using low bandwidth communications to all paralleled VSIs. MGCC can also contain a synchronization loop to facilitate the transition from islanded to gridconnected mode. 4. Tertiary Control (Level 3): This is the last and the slowest control level that is responsible to schedule the power of each DGs. It depends on global economic and current energy prices. One of
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Fig. 1. Single line diagram of the microgrid system.
Table 1 Electrical system parameters. Parameter
Symbol
Value
Units
Nominal frequency Nominal RMS voltage Load filter inductance Load filter capacitance Load
x
2p 50 220 84 500 300/150/80
rad/s V lH lC
E Ll Cl Rl
X
its objectives is to achieve the optimal operation during islanded mode and optimal power flow during grid-connected mode. This tertiary level is not considered in this paper and will be covered in our next works.
3. Hierarchical control This section deals with the development of a control framework based on hierarchical scheme for flexible microgrid, to be able to
operate either in islanded or in grid-connected mode with a smooth transition between them. In islanded mode, the microgrid is disconnected from the main grid and operates autonomously, while the objectives are to achieve an accurate power sharing among the paralleled VSIs in proportion to their power ratings, regardless of their output impedance, as well as maintaining a close regulation of the voltage amplitude and frequency at the PCC. For a seamless connection to the grid, the voltage at PCC must be synchronized to the voltage of the grid using synchronization loop that reduces the phase angle between them. In gridconnected mode, the VSIs are controlled in order to generate their scheduled power into the system. 3.1. Inner control of VSI The inner control of VSI is based on cascaded control structure which consists of an outer voltage loop and an inner current loop (see Fig. 2). The advantages of this scheme are as follows: Achieves a low total harmonic distortion (THD) for the capacitor voltage v Cabc .
Table 2 Inverters parameters with their output impedances. Parameter
Symbol
VSI1
VSI2
VSI3
Units
Inverter-side filter inductor Parasitic resistor 1 Grid-side filter inductor Parasitic resistor 2 Filter capacitor DC voltage PWM switching frequency Output impedance Apparent power rating
Lf1 r1 Lf2 r2 Cf Vdc fs Zo S
1.8 0.03 1.8 0.03 35 650 10 0:7; 2:6 1
1.8 0.03 1.8 0.03 35 650 10 0:5; 1:9 2
1.8 0.03 1.8 0.03 35 650 10 0:8; 1:6 3
mH
X mH
X
lC V kHz X, mH kVA
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Fig. 2. Block diagram of the VSI with the inner control loops.
Fig. 3. Block diagram of the inner control loops in ab-coordinates.
Keeps the inductor current ilabc within a safe limits. Maintain the same control scheme for different mode of operations (islanded or grid-connected mode). Improves more the disturbance rejection. The role of outer voltage loop is to regulate the capacitor voltage v Cabc to reference signal that is generated by the primary control, and also is responsible for setting the reference of the inner current loop, which in turn regulates the inductor current ilabc . The dynamics of the outer loop must be slower than those of the inner loop [28]. We transform the abc reference frame into ab stationary reference to get two independent single-phase systems by using Clarke transformation as shown in Fig. 3. The PR controllers are applied to get a better voltage regulation with less harmonics, and they can be expressed as follows [29,30]:
Gv ðsÞ ¼ kpv þ Gi ðsÞ ¼ kpi þ
s2
X krv s khv s þ þ xc s þ x2o h¼3;5;7 s2 þ hxc s þ ðhxo Þ2
X kri s khi s þ 2 2 s þ xc s þ xo h¼3;5;7 s2 þ hxc s þ ðhxo Þ2
ð1Þ ð2Þ
where kpv and kpi are the proportional gains, krv and kri are the resonant gains at the fundamental frequency, khv and khi are the resonant gains at the h-harmonic, xc is the resonant bandwidth used to
avoid the instability problems associated with the infinite gain, xo is the fundamental frequency. From the block diagram of Fig. 3 with using Mason’s theorem [31], the closed loop transfer function (CLTF) of the inner current loop and outer voltage loop of the acoordinate can be expressed by:
Gi ðsÞGPWM ðsÞ i ðsÞ Z l ðsÞ þ Gi ðsÞGPWM ðsÞ la 1 v C a ð sÞ Z l ðsÞ þ Gi ðsÞGPWM ðsÞ Gol ðsÞ v Ca ðsÞ ¼ v ref a ðsÞ Z C ðsÞ þ Z l ðsÞ þ Gin ðsÞ þ Gol ðsÞ Z C ðsÞðZ l ðsÞ þ Gin ðsÞÞ ioa ðsÞ Z C ðsÞ þ Z l ðsÞ þ Gin ðsÞ þ Gol ðsÞ ila ðsÞ ¼
ð3Þ
ð4Þ
where
Gol ðsÞ ¼ Gv ðsÞGi ðsÞGPWM ðsÞZ C ðsÞ Gin ðsÞ ¼ Gi ðsÞGPWM ðsÞ GPWM ðsÞ ¼
V dc =2 1 þ 1:5T s s
Z l ¼ sLf 1 þ r 1 ; Z C ¼ sC1 and GPWM is the transfer function of the PWM delay, T s is the sampling time which equals to f1s . The same model can be developed in b-coordinate. In Section 4 we discus how to tune optimally the parameters of PR controllers.
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Table 3 Optimal parameters of the hierarchical control. Inner Control Controller
Gi Gv
Parameters kp
kr
k3
k5
k7
xc
0.2131 0.2027
211.62 205.66
32.21 25.35
101.1 22.14
61.74 61.08
0.0015 0.0015
Primary Control Inverter
Parameters ke
n
m
nd
md
ng
mg
VSI1
7
0.2178
3:1 104
0.003
2:0 106
0.03
2
VSI2
7
0.1089
1:6 104
0.0015
1:0 106
0.03
2
VSI3
7
0.0726
1:0 104
0.001
6:6 107
0.03
2
Secondary Control PI
Voltage loop
Frequency loop
Synchronization
kp ki
1.8151 4.2968
2.2298 7.6729
4.5 0
3.2. Primary control The primary control adopted in this paper is based on the universal droop control that was developed by Zhong [21], which we have improved it by introducing a derivative term to enhance the transition response and a hybrid term to distinguish between different mode of operation. The primary control can be described as:
dðP P Þ K e E V pcc nðP P Þ nd g c þ g c ng dt dðQ Q Þ x ¼ x þ mðQ Q Þ þ md g c þ g c mg dt
E_ ¼
ð5Þ ð6Þ
where E and x are amplitude (RMS) and frequency of the capacitor voltage of VSI, respectively; E and x are their nominal values. P and Q are the desired active and reactive power to be injected during the grid-connected mode, normally are set to zero in islanded mode. V pcc is the amplitude (RMS) of the voltage at PCC, n and m are the droop coefficients, nd and md are the derivative droop coefficients of the active and reactive power, respectively. K e is an
amplifier used to maintain the PCC voltage within a desired range and is chosen the same for all VSIs operated in parallel (see Table 3). ng and mg are used to improve the response and the stability of the microgrid during grid-connected mode. g c is a hybrid variable which can be written as:
gc ¼
1 if Microgrid operates in grid-connected mode
0 if Microgrid operates in islanded mode gc ¼ 1 gc
ð7Þ ð8Þ
The instantaneous active and reactive power of VSI that is injected into the microgrid common bus is expressed in the abstationary reference frame as follows [32]:
pðtÞ ¼v pcca ioa þ v pccb iob qðtÞ ¼v pccb ioa v pcca iob
ð9Þ ð10Þ
where v pcc and io are voltage at PCC and the output current of the VSI, respectively. The average power of P and Q in Fig. 4 is calculated by integrating (9) and (10) over one fundamental cycle T and is described as:
Fig. 4. Block diagram of the primary control in ab-coordinates.
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Fig. 5. The simulink diagram of power calculator of the Fig. 14.
DPðsÞ ¼ kpe DEðsÞ þ kpd DdðsÞ DQ ðsÞ ¼ kqe DEðsÞ kqd DdðsÞ sDEðsÞ ¼ nDP mes ðsÞa1 nd sDPmes ðsÞa1 DxðsÞ ¼ mDQ mes ðsÞa2 þ md sDQ mes ðsÞa2
ð18Þ ð19Þ ð20Þ ð21Þ
where
a1 ¼g c þ g c ng a2 ¼g c þ g c mg
Fig. 6. Simplified model of the three-phase VSI.
Z 1 t pðtÞdt T tT Z t 1 Q¼ qðtÞdt T tT P¼
ð11Þ ð12Þ
By applying the Laplace transformation to (11) and (12), we obtain the following equations [26]:
PðsÞ ¼FðsÞpðsÞ
ð13Þ
Q ðsÞ ¼FðsÞqðsÞ
ð14Þ
where FðsÞ is the transfer function of the integration filter and is expressed as follows:
FðsÞ ¼
1 1 eTs Ts
ð15Þ
The expressions from (9)–(15) are used to construct the power calculator of the Fig. 4 (see Fig. 5).
2
P¼ Q¼
V pcc EV pcc cos d Zo Zo V 2pcc
EV pcc cos d Zo Zo
! cos h þ
EV pcc sin d sin h Zo
ð16Þ
sin h
EV pcc sin d cos h Zo
ð17Þ
!
The above equations and the ameliorated universal droop controller (5) and (6) can be linearized around the equilibrium as:
ð23Þ
V pcce ðcos de cos h þ sin de sin hÞ Zo Ee V pcce ðcos de sin h sin de cos hÞ kpd ¼ Zo V pcce ðcos de sin h sin de cos hÞ kqe ¼ Zo Ee V pcce ðsin de sin h þ cos de cos hÞ kqd ¼ Zo kpe ¼
ð24Þ ð25Þ ð26Þ ð27Þ
For small-signal analysis, the integration filter (15) used to calculate the real and reactive power is approximated using the well known second order Padé approximation and is expressed as follows [26]:
F ðsÞ
1 T2 2 s 12
ð28Þ
þ T2 s þ 1
The measured active and reactive power becomes:
DPmes ðsÞ ¼ 3.2.1. Small-signal analysis A small-signal analysis can be used to investigate the stability of the primary control, considering small disturbance around the stable equilibrium point defined by de ; V pcce ; Ee , where V pcce is the amplitude (RMS) of the voltage at PCC, Ee is the amplitude (RMS) of the VSI’s capacitor voltage and de is the phase angle difference between them. Fig. 6 shows the three-phase inverter which is modeled as an ideal single-phase voltage source in series with the output impedance Z o \h. The real and reactive power flowing from the source to the terminal v pcc through the impedance Z o \h are as follows [33]:
ð22Þ
DQ mes ðsÞ ¼
1 T2 2 s 12
þ T2 s þ 1 1
T2 2 s 12
þ T2 s þ 1
DPðsÞ
ð29Þ
DQ ð s Þ
ð30Þ
Substituting (18)–(29) into (20) gives:
sDEðsÞ ¼ a1
nd s þ n T2 2 s 12
þ
T s 2
þ1
kpe DEðsÞ þ kpd DdðsÞ
ð31Þ
and (19)–(30) into (21) gives:
DxðsÞ ¼ a2
md s þ m T2 2 s 12
þ T2 s þ 1
kqe DEðsÞ kqd DdðsÞ
ð32Þ
Since:
DxðsÞ ¼ sDdðsÞ
ð33Þ
It implies to the following sixth-order homogeneous equation:
a6 s6 DdðsÞ þ a5 s5 DdðsÞ þ a4 s4 DdðsÞ þ a3 s3 DdðsÞ þ a2 s2 DdðsÞ þ a1 sDdðsÞ þ a0 DdðsÞ ¼ 0
ð34Þ
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with:
a6 a5 a4 a3 a2 a1 a0
¼ ¼ ¼ ¼ ¼ ¼ ¼
a¼ b¼ A¼ C¼ D¼
The eigenvalues of this Eq. (35) have been studied for both operation modes when h of output impedance changes from p2 to p2 with Ro ¼ 0:7X ðZ o ¼ Ro þ jRo tan ðhÞÞ, the terminal load Z l ¼ 17 þ j28 and the primary control parameters are presented in Table 3 (we used the VSI1 values). Ee and de can be calculated according to output impedance, load impedance and V pcce . Fig. 7 shows that all eigenvalues of both modes are in the left half plane which means that regardless to output impedance of VSI the system is always stable during both operation mode, and for this reason we choose the universal droop control.
2
a 2ab 2 aC þ b þ a þ a2 md kqd a aD þ bC þ b þ a2 mkqd a þ a2 md kqd b bD þ C þ a2 mkqd b þ a2 md Ckqd þ kqe a1 nd kpd D þ a2 m Ckqd þ kqe a1 nd kpd þ a2 md A a2 m Dkqd þ kqe a1 nkpd T 2 =12 T=2 Dkqd þ kqe a1 nkpd 1 þ a1 nd kpe a1 nkpe
3.3. Secondary control
Eq. (34) describes the small-signal dynamics of the closed-loop system around the equilibrium point de ; V pcce ; Ee . Thus, the system stability can be analyzed by the following characteristic equation:
a6 s6 þ a5 s5 þ a4 s4 þ a3 s3 þ a2 s2 þ a1 s þ a0 ¼ 0
ð35Þ
The secondary control is used to compensate the deviations in amplitude and frequency of the PCC voltage caused by the primary control and restores them to their nominal values. The restoration controllers can be presented as follows:
Z dx ¼ kpx xref xMG þ kix xref xMG dt Z Eref EMG dt dE ¼ kpE Eref EMG þ kiE
ð36Þ ð37Þ
Fig. 7. Root locus plot of the closed-loop system (34) when the phase angle of output impedance change from p2 to p2 with a resistive inductive load. (a) Islanded mode (g c ¼ 0) and (b) grid-connected mode (g c ¼ 1).
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Fig. 8. Block diagram of the secondary control in ab-coordination for voltage restoration, frequency restoration and grid synchronization.
Fig. 9. P E and Q x of primary and secondary control principles.
Fig. 10. Block diagram of the voltage restoration control.
where kpx ; kix ; kpE and kiE are the PI controllers parameters. dx and dE are sent to all primary controllers as shown in Fig. 8. The Fig. 9 shows the principle of this technique that lays on uniform shifting of all primary controllers by an amount of dx and dE. As we use the hierarchical control, the dynamics response of the secondary control is slower than the primary control which allow us to design the controllers separately, and in order to don’t exceed the tolerable
frequency and amplitude, the secondary controller must be bounded. 3.3.1. Voltage restoration Fig. 10 shows the model of the voltage restoration control that consists of primary controller, PI controller cascaded with a delay caused by the low bandwidth communication lines Gd . This model
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e ¼ sin ð/G /MG Þ
ð44Þ
Then, for small values of ð/G /MG Þ; e becomes:
e ¼ /G /MG
ð45Þ
Therefore, e can be fed to a simple PI controller. The synchronization control can be expressed as:
xs ¼ v pcca v gb v pccb v ga
is used to analyze the stability of the system and to design the PI controller. Based on the block diagram, the model as follow:
K e GEsec ðsÞGd ðsÞ Eref ðsÞ s þ K e GEsec ðsÞGd ðsÞ þ K e nGLPF ðsÞ P ðsÞ s þ K e GEsec ðsÞGd ðsÞ þ K e
ð38Þ
where the transfer functions are given as:
GEsec ðsÞ ¼ kpE þ Gd ðsÞ ¼
kiE s
1 0:24 s þ 1
xf GLPF ðsÞ ¼ s þ xf
ð39Þ ð40Þ ð41Þ
4. Optimal controller design In this paper, the controller parameters of each control level of the hierarchical structure are designed by solving an optimization problem in order to find their optimal values. The optimization problem is defined as minimization of a fitness function that its optimization vector is the controller parameters. The concept stands on evaluating the fitness function after each adjustment of the optimization vector until we find its smallest possible value, which we assume that corresponds to the optimal controller parameters. Therefore, the key points of this method are the fitness function and the solver that adjust the optimization vector intelligently. For PR controllers of the inner control, the optimization problem is defined as follows:
The details of the PI controller design is given in next section.
minimize 3.3.2. Frequency restoration The frequency restoration control has been modeled and analyzed using the same procedure as the voltage restoration control. In Fig. 11, Gxsec is a PI controller, and GFLL is simplified first-order transfer function of SOGI-FLL [34] that used to estimate the frequency of the microgrid voltage at PCC. 3.3.3. Synchronization loop for seamless transition During the islanded mode, the microgrid may need to connect to the main grid in order to import power in the case where the local demand is not supplied by the paralleled VSIs, or to export the exceed power. We consider that the amplitude and the frequency of the PCC voltage is restored to their nominal values which are assumed to be equal to the nominals of the grid. However, this is not enough to make a smooth transition, because the phase angles are different. Thus, a sudden transition without planning would cause a large circulating current flow from the grid to the VSIs. In order to avoid this issue, the microgrid voltage must be synchronized to the grid voltage before turning ON the SS and starting the grid-connecting mode. The synchronization process mitigates the phase angle between the two voltages by sending an amount of frequency xs to each VSI as shown in Fig. 8 through the secondary control. By using the a b components of the two voltages, we can calculate the grid error as:
e ¼ v pcca v gb v pccb v ga
ð42Þ
This error gives a useful index of the synchronization process, which consists of orthogonal product. For simplicity, we assume that v pcc and v g are purely sinusoidal, then e becomes:
e ¼ E2 sin ð/G /MG Þ
ð46Þ
where wf is a cut-off frequency which is fixed over one decade below the fundamental frequency, kps and kis are the PI coefficients.
Fig. 11. Block diagram of the frequency restoration control.
EMG ðsÞ ¼
xf kps s þ kis s þ xf s
ð43Þ
where E is the voltage amplitude of the grid and the microgrid after restoration, /MG and /G are the phase angles. After normalizing (43), e equals to:
h
1 P t¼0
2
v trefa v tCa ðhÞ
þ
v trefc v tCc ðhÞ
þ
2
v trefb v tCb ðhÞ
2
ð47Þ
subject to 0 < hi 6 himax ; i ¼ 1; . . . ; 11: where we choose the integral of squared-error (ISE) as a fitness function since it give us a good index on the signal quality of the capacitor voltage v Cabc ; h is the optimization vector which is the parameters of PR controllers and equals
T h ¼ kpi kri k3i k5i k7i kpv krv k3v k5v k7v xc and hmax is the upper bound of the parameters which is determined by analyzing the stability of the model (3) and (4). For primary controller and PI controllers of secondary level, we have developed a new fitness function in time domain inspired from the integral of time weight absolute-error (ITAE) [35] in order to increase the robust performance and to cope the oscillation.
minimize h
subject to
1 X
t jet ðhÞj½1 þ k k sign ðet ðhÞ þ OS yd Þ
t¼0
ð48Þ
0 < hi 6 himax ; i ¼ 1; . . . ; N:
where et ðhÞis the error between desired and actual value by using h values for the controller parameters at the sampled time t (et ðhÞ ¼ yd yt ðhÞ), OS is the overshoot and k is a constant value used to penalize the oscillations that are upper then ð1 þ OSÞ yd . The optimization vector of the primary controller is split in two vecT
tors as there are two operation modes, h1 ¼ ½ke nd md for simula
T tion in islanded mode and h2 ¼ ng mg for simulation in gridconnected mode with using the optimal h1 ; the droop coefficients n and m are calculated according to desired voltage droop ratio n S
eP ¼ K ei Ei and frequency boost ratio eQ ¼
mi Si
x
.
T The optimization vector of PI controller is h ¼ kp ki . It’s good to mention that secondary level has many control loops such as voltage restoration, frequency restoration and synchronization loop which each loop is tunned separately.
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To solve the optimization problem of (47) and (48), we apply a meta-heuristic algorithm which is based on PSO (Particle Swarm Optimization) and is called SLPSO (Self-Learning Particle Swarm Optimizer) [36]. The optimal parameters of the hierarchical control are presented in the Table 3, where k ¼ 50; OS ¼ 0; eP ¼ 0:1 and eQ ¼ 103 . 5. Simulation results In this section, we evaluate the proposed hierarchical control developed in Section 3 by simulating the system shown in Fig. 1 using MATLAB/Simulink. Three studies with different scenarios are carried out to test the robustness and the performance of the system. 5.1. Islanded operation Initially, a black start was performed to operate the microgrid in islanded mode, where the three inverters start operating in parallel at same time and supplying the nonlinear load. we assume that the load demand still lower than the total power ratings of the inverters during the islanded simulation, which we would like to focus just on the power sharing and the voltage restoration. Fig. 13 show the active and reactive power of the inverters and the nonlinear
197
load while the primary control is running. These figures show clearly that the inverters share both active and reactive power accurately in a ratio of 1 : 2 : 3. To test the robustness of power sharing of the primary control, we suddenly disconnect the third inverter at t ¼ 15, and letting just two inverters supplying the power demand of the nonlinear load. As we see in the Fig. 13, the both inverters are handling well the load with time respond of 0.3 s, but if we give a closer look at the load’s active power (or reactive power) within the time range of 14–16 s, we observe that its power is dropped from 930 W to 880 W after disconnection of the third inverter. This due to the amplitude of PCC voltage which drops from 220 V to 216 V (see Fig. 12(a)) and to its quality where the THD increases from 2:1% to 2:8% as presented in Fig. 14 but this still below 5% as recommended by [37]. At t ¼ 30, the load demand is increased to double, and regardless of that the inverters still sharing the power with the ratio of 1:2. However, this sharing process which is based on the primary control causes a deviation in amplitude and frequency of the PCC voltage when a disturbance occurs as shown in Fig. 12a and b. After each static deviation within 3 s, the secondary control starts to restore the amplitude and the frequency to the nominal values, and after that, it will deactivate and letting just the primary control acting. It appears in Fig. 13a, that the secondary control affects on the active and reactive power of the load which in turn affects the power
Fig. 12. PCC voltage for a black start of the islanded mode. (a) Amplitude (RMS) and (b) frequency.
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Fig. 13. Power sharing during the islanded mode. (a) Active power and (b) Reactive power.
Fig. 14. The THD of the microgrid PCC voltage.
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Fig. 15. Synchronization of the microgrid voltage to the grid voltage. (a) Phase-a voltage waveforms of microgrid and grid before the synchronization process and (b) after 3 s of acting, the microgrid starts the grid-connected mode at t ¼ 48 s.
Fig. 16. The phase difference between the PCC voltage and the grid voltage.
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Fig. 17. Active and reactive power of the microgrid during grid-connected mode.
delivered by the inverters, and this is evident as the secondary control increases the amplitude of PCC voltage from 212 V to 220 V RMS at t ¼ 34 s. 5.2. Transition from islanded to grid-connected mode For a seamless transition to grid-connected mode, the synchronization control is activated at t ¼ 45 s. Fig. 15 shows the phase-a voltage waveform of the microgrid and the grid before and after the synchronization process, it can be observed that within 3s the both voltages are synchronized. The phase error between them is shown in Fig. 16, where it starts from around 53 and is still decreasing until arrives to around 0 at 48 s. However, this process is realized by adjusting the voltage frequency of the microgrid, and this may lead to instability in real world if the frequency exceeds the allowable limit. Thus, there is a trade-off between the time respond of the synchronization process and the maximum deviation of the frequency caused by this process. In Fig. 12b, the maximum deviation is about 0.6 Hz which is tolerable according to Nordel’s (North of Europe) grid exigencies. As seen in Fig. 12a, the synchronization does not affect on the amplitude of PCC voltage, and this is obvious since the synchronizer compromise just the frequency of each inverter with same amount xs . At t ¼ 48 s, the SS is closed and the microgrid starts the grid-connected mode. The synchronization control is then deactivated.
5.3. Grid-connected operation Once the microgrid is operated in grid-connected mode, the inverters change their behavior from stabilizing the PCC voltage to injecting the scheduled active and reactive power by setting the P and Q of the primary control. In order to inject the maximum active power from each inverter, the power factor must be set to zero with P 1 ¼ 1000 W and P2 ¼ 2000 W (the third invert is still disconnected). The reactive demand of the nonlinear load is carried out by the main grid. Hence, the inverters together deliver 3000 W and the load consumes about 1920 W as shown in Fig. 17a. The excess power is exported to the grid as presented in Fig. 17a where the grid’s active power is negative (Pg ¼ 1080 W). At t ¼ 60 s the demand is increased to 3565 W which is greater than the power delivered by the both inverters. Therefore, the microgrid imports the missed power from the grid to satisfy and balance the demand and this demonstrates the bidirectional power flow between the grid and the microgrid. 6. Conclusion This paper proposes an improved control strategy based on the hierarchical approach to operates a three-phase microgrid in islanded mode and in grid-connected mode with a seamless transition between them. The control structure is based on the station-
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ary reference frame and is composed of three levels: inner, primary and secondary level. The inner control is used to regulate the capacitor voltage of the VSI, which it consists of cascaded voltage and current loops with proportional resonant controllers. The primary control is based on the universal droop control which we improve it to be able to handle the both modes of operation. When the microgrid operates in islanded mode, the primary control shares the active and reactive power demand among the paralleled VSIs with regardless of their output impedances and when it operates in grid-connected mode, each VSI inject its scheduled power. The secondary control restores the amplitude and the frequency of the PCC voltage caused by the primary control in order to stabilize the microgrid during the islanded mode, and it is responsible for synchronizing the PCC voltage with the grid voltage to make a smooth transition to the grid-connected mode. The model of different control level has been developed to analyze the system stability and to aid to design their controller parameters. Moreover, these parameters have been tuned optimally by solving an optimization problem using a meta-heuristic algorithm called SLPSO. The simulation results demonstrate the robustness and the performance of the proposed hierarchical control for the flexible microgrid.
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