Control of Master-Slave Microgrid Based on CAN Bus Asma Alfergani, Ashraf Khalil, Zakariya Rajab, Mohammad Zuheir, Ali Asheibi Electrical and Electronics Engineering Department University of Benghazi Benghazi, Libya
[email protected]
Abstract— In this paper, the control of parallel voltage-source inverters Microgrid based on Controller Area Network (CAN) is introduced. The design is based on the maximum time delay that guarantees the stability where the system is composed of threephase DC/AC inverters with master-slave control strategy in the rotational reference frame (dq frame). The reference current signals are sent from the master to the slave converters through Controller Area Network bus (CAN bus). A model for masterslave communication-based Microgrid is presented and the system is modeled as a general time delay system. The maximum time delay that guarantees the stability of the system is calculated using a Lyapunov-Krasovskii based linear matrix inequalities method. The results are tested through Matlab/Simulink and True-Time 2.0 simulation. Keywords— CAN; LMI; Low-pass filter; master-slave control strategy; Microgrid; Parallel inverters; Phased locked loop; Time delay; True-time simulator
I.
INTRODUCTION
Renewable or sustainable energy technologies such as photovoltaic panels, wind turbines, and fuel cells; have attracted widespread attention during the last decades. This is because their generated power is environmentally friendly, and the sources are not subject to the instability of price and availability that are common to the conventional energy sources. Most of the renewable energy sources are usually equipped with DC/AC inverters, which form a parallel inverters system in order to share the load, that can be connected to the grid. This system is known as Microgrid [1]. The unpredictable and intermittent nature of renewable energy sources has kept them from integrating with the utility grid. However, the concept of Microgrid has opened the scope to incorporate renewable energy sources into the conventional grid, without a direct coupling with the conventional grid components. This is possible due to the unique feature of the Microgrid, which allows both synchronized grid connected operation and islanded operation. Integrating many energy sources makes the control of Microgrids very challenging and an active research area, and one of these challenges is how to apply a reliable control strategy. With the advances in network technology, a communication network can be used for the control signals exchange. The use of the communication network for control purposes reduces the cost and the complexity of the system,
Sheroz Khan, Ezzidin Hassan Elmabrouk Aboadla, Khairil Azhar Bin Azna, Majdee Tohtayong Department of Electrical and Computer Engineering, KOE International Islamic University of Malaysia (IIUM) Kuala Lumpur, Malaysia
[email protected]
however, the induced time delay has a strong impact on the system stability. The role of the controller in the Microgrid is to have good current sharing while maintaining the system stability. Also, the controller must achieve synchronization, and to guarantee that the frequency and the voltage are within the allowable range. The control strategies are divided into communication-based and communication-less. There are many reviews on the control strategies in inverter-based Microgrids. For more detailed surveys on the control strategies in parallel connected inverters the reader can refer to [2-3] and the references therein. The control strategies based on communication include centralized, distributed and masterslave control strategies [2]. The control strategies without communication are generally based on the well-known droop control method. In the centralized control strategy, all the information is collected by the centralized controller and then the commands are issued back to the system. In this control strategy, all the inverters work as current sources and the voltage is controlled in the central controller. The current sharing is forced at all times even during the transient, and different power rating inverters can be connected without changing the control structure [2]. The main disadvantages of this strategy is the single point of failure and the need for sending the reference voltage to all the inverters in the network, which requires high bandwidth communication link and the system is sensitive to nonlinear loads [2]. In the distributed control strategy the rotational reference frame (dq0) is used instead of the stationary reference frame (abc). It can be applied only in balanced systems. The voltage controller controls the output voltage by setting the average current demands [2]. In current/power sharing control method the average unit current can be determined by measuring the total load current and dividing this current by the number of units in the system. There are excellent features of the current/power sharing, the load sharing is forced during transient and the circulating currents are reduced. In addition, a lower-bandwidth communication link is needed. The decentralized controller relies only on local information. This technique is usually used when the distance between the parallel inverters is long, and it can be applied in islanded mode or grid-connected mode. One of the most widely used decentralized control is the Droop control [4]. The main idea is to regulate the voltage and the frequency by regulating the reactive and the active power respectively
which can be sensed locally. The Droop control method has many desirable features such as expandability, modularity, redundancy, and flexibility. There are as well, some drawbacks such as slow transient response and possibility of circulating currents. As the interconnections are neglected the overall system stability is questionable. In the master-slave control strategy, one of the converters is known to be the master while the others are the slaves, the master controller contains the voltage controller while the slaves contain current controllers and have to track the master’s reference current [5]. In this control strategy, there is a transfer of information between the master controller and the slaves controllers. In order to reduce the complexity and the cost while increasing the reliability, the control signals are exchanged through shared networks. In this case, the system becomes what is known as a networked control system (NCS). Because it involves less information transfer the master-slave control strategy is preferable for NCS applications. Many researchers have reported the application of the master-slave control strategy over a communication network, but there are no studies on how the delay could affect the stability of the system when the reference signals of parallel inverters of Microgrid are exchanged over shared communication network. In [6] the Controller Area Network (CAN) is used to exchange the control signals from the master to the slave. The signals which are sent are: the reference currents, id , iq and the synchronization signal, however, the authors do not point out how to guarantee the stability of the system in terms of the maximum time delay. In [7] the communication platform for a Microgrid implementing master-slave control strategy is proposed. The CAN-open protocol is used for the communication between the master and the slave. The automaster-slave control strategy is presented in [8]. The system is implemented practically and the power sharing is precise. The master distributes the real power and the reactive power signals among the slave converters. The CAN is used for both synchronization and current sharing exchange in [9]. The authors pointed out that there is a communication delay, but the controller does not take it into account. The impact of the communication delay and the data drop outs on the stability of parallel inverters is presented in [10]. The master-slave control strategy has been implemented over a communication network, but the real power and the reactive power are used as the reference signals. These signals are then sent through the CAN to the slave converters in the network. The real power and the reactive power are correlated to the frequency and the voltage respectively. A small signal model is then developed and the stability with the time delay is analyzed using a stability criterion method based on Lyapunov-Krasovskii functional. The performance of the system with the masterslave control strategy with a communication network is better than the performance with the droop control strategy as reported in [11]. In this paper, a model for the Microgrid with master-slave control strategy over a CAN bus is presented. When the control loop is closed through a communication network, the time delay and data loss are unavoidable which can lead to system instability. In order to achieve system stability, a stability analysis with the communication delay is carried out.
In the next sections, the master-slave control strategy over the CAN bus is explained. Then mathematical model of parallel inverters based on the switching averaging is briefly described. In section IV, a mathematical model of the inverter based Microgrid with communication delay is described. A stability criterion in the form of Linear Matrix Inequalities (LMIs) is used to identify the maximum allowable delay bound (MADB). A simulation using Matlab/Simulink and True-Time 2.0 simulator is carried out to test the control strategy operation with the presence of the delay in the CAN bus. II.
MASTER-SLAVE CONTROL STRATEGY OF MICROGRID OVER CAN BUS
The typical circuit of two parallel inverters Microgrid with different DC sources is shown in Fig.1. The CAN implements the carrier-sense multiple access protocol with arbitration on message priority (CSMA/AMP) where each node must listen to the network before trying to transmit. When a master controller node tries to transmit, it listens to the network if it is idle, then the node starts to transmit directly. If many nodes are trying to transmit at the same time the arbitration is used to gain access to the network. When two nodes are transmitting at the same time the identifiers are sent if one node receives the same bit it has sent, then that node will win the arbitration. The slave controller node will receive a delayed current reference signal. The CAN has different speeds. The bit rate decreases with increasing the distance [12].
Fig. 1.
III.
The system of two parallel inverters with networked based control
MATHEMATICAL MODEL OF PARALLEL INVERTERS
The average model of the phase leg is derived based on the switching averaging. The two parallel inverters are shown in Fig. 2. After transformation of the variables in the stationary coordinates Xabc into the rotating coordinates Xdqz, the average model can be simplified [13-16] based on iz=iz1=iz2≈ 0:
d vd 1 id 1 id 2 1 / RC − ω vd = + − ⋅ 1 / RC vq dt vq 2C iq1 iq 2 ω d id 1 1 d d 1 1 vd 0 − ω id 1 i = d Vdc1 − v − ⋅ dt q1 L1 q1 L1 q ω 0 iq1 d id 2 1 d d 2 1 vd 0 − ω id 2 ⋅ i = d Vdc 2 − v − dt q 2 L2 q 2 L2 q ω 0 iq 2
(1)
(2)
(3)
Fig. 2.
dφd / dt = ( v d - ref - vd )
(7)
dφq / dt = (v q - ref - v q )
(8)
dγ 1 / dt = ( K vdp ( v d - ref - v d ) + K vdiφd - id 1 )
(9)
dγ 2 / dt = ( K vqp ( v q - ref - v q ) + K vqiφq - iq1 )
(10)
dγ 3 / dt = ( K vdp (v d - ref - v d (t − τ )) + K vdiφd (t − τ ) - id 2 )
(11)
dγ 4 / dt = ( K vqp ( v q - ref - v q (t − τ )) + K vqiφq (t − τ ) - iq 2 )
(12)
The two parallel inverters Microgrid [13]
where C, L1, and L2 are the capacitor and the inductor of the filter respectively, ω is the radian frequency. id1, id2, iq1 and iq2 are the dq currents of the first and the second inverter. vd and vq are the voltages in the dq reference frame. The Vdc1 and Vdc2 represent the renewable energy sources such as the wind turbine or the PV array after they are converted to DC [14] [15]. Writing (1), (2) and (3) in general matrix form: (4) x& = Ax (t ) + Bu (t ) The state vector and the control vector are given as: x = [vd v q id 1 iq1 id 2 iq 2 ]T
u = [d d 1 d q1 d d 2 d q 2 ]T where d is the duty ratio, the matrices A and B can be obtained as: − 1 / RC −ω − 1 / L1 A= 0 − 1 / L2 0
0 0 B= 0 0
1 / 2C 0 1 / 2C 0 − 1 / RC 0 1 / 2C 0 1 / 2C 0 0 0 0 ω − 1 / L1 −ω 0 0 0 0 0 0 0 ω − 1 / L2 0 0 −ω 0
ω
0 Vdc1 / L1
0
0
0
0
Vdc1 / L1
0
0
0
0
Vdc 2 / L2
0
0
0
0
IV.
0 0 Vdc 2 / L2 0
(5)
T
(6)
MASTER-SLAVE CONTROL STRATEGY
The master-slave control strategy is used where the first inverter has two control loops and the second inverter has only current control loop. The inner control loop of the master controller independently regulates the inverter output current in the rotating reference frame, id and iq. The outer loop of the master controller in the voltage control mode are used to produce the dq axis current references id-ref and iq-ref, then these control signals are sent through the CAN to the slave controller as shown in Fig. 3. The slave controller will receive a delayed version of current reference signals and some data may be lost. A proportional-Integral (PI) control scheme is used in both the master and slave controllers. The controller model is then given by:
Fig. 3.
Control loops of two parallel inverters [16]
Equations (7)-(12) can be written in matrix form as: z& = Ex(t ) + Fz (t ) + Ed x (t − τ ) + Fd z (t − τ ) where; −1 0 − K vdp E= 0 0 0
0
0
−1 0
0 −1
− K vqp 0
0 0
0
0
0 0 0 Ed = 0 − K vdp 0
[
z = Φd
Φq
0
0
0
0
0
0
0
0
0
0
− K vqp
0
0 0 0 0 0 0 0 0 0 Fd = −1 0 0 0 0 Kvdi 0 0 −1 0 0 0 − 1 0 Kvqi 0 0 0 0 0 0 0 0 0 0 0 0 0 K vdi 0 F = 0 0 0 0 K vqi 0 0 0 0 0 0 0 0 0 0 0
0
0 0
0 0
0 0 0 0 0
0 0 0 0 0
(13) 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0
γ1 γ 2 γ 3 γ 4]
T
The duty cycle equations are given as: d d 1 = ( K idp1 )( K vdp (vd - ref - vd ) + K vdiφd - id 1 ) + K idi1γ 1
(14)
d q1 = ( K iqp1 )( K vqp (v q - ref - vq ) + K vqiφq - iq1 ) + K iqi1γ 2
(15)
d d 2 = K idp 2 ( K vdp (vd - ref - vd (t − τ )) + K vdiφd (t − τ ) - id 2 ) + K idi 2γ 3 d q 2 = K iqp 2 ( K vqp (vq - ref - vq (t − τ )) + K vqiφq (t − τ ) - iq 2 ) + K iqi 2γ 4
(16) (17)
Equations (14-17) can be written in matrix form as: u = u (t ) + u (t − τ )
u = Cx (t ) + C d x (t − τ ) + Dz (t ) + Dd z (t − τ ) where; 0 − K idp1 0 − K idp1 K vdp 0 − K iqp1 K vqp 0 − K iqp1 C= 0 0 0 0 0 0 0 0
(18) (19)
0 0 − K idp 2 0
0 − K iqp 2 0 0
0 0 0 0 0 0 0 0 0 0 0 0 Cd = - Kidp 2 K vdp 0 0 0 0 0 0 - Kiqp 2 K vqp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Dd = K idp 2 K vdi 0 0 0 0 0 K iqp 2 K vqi 0 0 0 0 0 0 K idi1 0 0 0 K idp1 K vdi 0 K iqp1 K vqi 0 K iqi1 0 0 D= 0 0 0 0 K idi 2 0 0 0 0 0 K iqi 2 0 Substituting (19) into (4) and writing the resulting equation in matrix form along with (13) we get; x& (t ) A + BC BD x(t ) BC d BDd x(t − τ (t )) (20) + z& (t ) = E Fd z (t − τ (t )) F z (t ) E d Equation (20) can be further written as: x&cl (t ) = A0 x(t ) + Ad x(t -τ (t ))
x(t ) = Φ(t ) where;
(21)
t ∈ [ − ρ ,0 ]
(22)
BC BDd A + BC BD x (t ) Ad = d x cl (t ) = A0 = Fd F z (t ) E Ed Φ (t ) is the initial condition of the system for the time interval
t ∈ [− ρ ,0] . The time-varying delay is τ(t) and satisfies the following: 0 ≤ τ (t ) ≤ ρ , τ&(t ) ≤ µ ≤ 1 (23) where ρ is the upper bound of the time delay, µ is the upper bound on the variable rate of the time delay. V.
inverters give the same power to shared the load. Moreover, the gains of the master-slave controller must be tuned for a stable system operation.
RESULTS
In order to validate the networked control Microgrid model a Matlab/Simulink simulation has been carried out as shown in Fig. 4. The parallel inverters parameters are as follows: the capacitance of the filters are 22 µF. The load resistance R equals 4.25 Ω. The frequency reference is set to be 50 Hz. The Phase locked loop (PLL) is used to estimate phase angle and frequency. The reference angle for the abc−dq transformation is provided by the PLL. The dq based PLL was used in this system to synchronize the two parallel inverters since the two
Fig. 4.
The Simulink model of two parallel inverters with Master-Slave controllers system with CAN
The sampling time, Ts of the system must be less than the MADB of the system [17-19]. Choosing the gain without considering the sampling time, may give some oscillation in the reactive power of the load. The controllers parameters of the parallel inverter-based Microgrid are as follows: the gains of the master voltage PI controller are Kvdp=5, Kvqp=5, Kvdi=400, and Kvqi=400, and the master current PI controllers are Kidp1=1, Kidi1=100, Kiqp1=100, and Kiqi1=60. In addition, the gains of PI slave controller are Kidp2=1, Kidi2=100, Kiqp2=100, and Kiqi2=60. Theorem 1 [20]: Given scalars ρ > 0 and µ > 0 , the time-delay system (21) is asymptotically stable if there exist
P = PT > 0 , Q = Q T > 0 and Z = Z T > 0 , asymmetric semi-positive-
symmetric
positive-definite
matrices
X 12 X definite matrix X = 11 ≥ 0 , and any appropriate T X X 22 12 dimensioned matrices Y and T such that the following LMIs are true:
Φ 11 Φ 12 ρAT Z X 11 X 12 T T T Φ = Φ 12 Φ 22 ρAd Z < 0 Ψ = X 12 X 22 T ρZA ρZA Y − ρZ TT d where; Φ 11 = PA + AT P + Y + Y T + Q + ρX 11
Y T ≥ 0 Z
Φ 12 = PAd − Y + T T + Q + ρX 12 Φ 22 = −T − T T − (1 − µ )Q + ρX 22 The MADB is calculated through solving the above LMIs set using the LMI toolbox in Matlab and the binary iteration algorithm [21-22], the MADB is found to be 0.61 ms. To verify the current balancing ability of the control algorithm, the values of the inductance of the two inverters must be selected carefully. The inductance of the filters is set to 13 mH. The communication among the parallel inverters is achieved by the CAN, with less mutual wires. The CAN has been implemented using True-Time 2.0 simulator as shown in
Fig. 7.
The output currents of the first and second inverters
100 80 60 The 3-ϕ load current, A
Fig. 4. The most effective parameter is the sampling time of sending reference current signal, which is must be chosen carefully, to receive the correct reference current signals at the slave controller. The bit rate of the CAN network must be adjusted in proper value, from the simulation it can be concluded that as the bit rate becomes less than 2 Mbit/s the performance of the system becomes unaccepted. The bit rate that used in this paper for CAN FD (flexible data-rate) is 10 Mbit/s. The three-phase output voltages of the parallel inverters are shown in Fig. 5, which shows a stable operation of the system. The output power of the first and the second inverters are shown in Fig. 6. As can be seen, the power of the second inverter accurately tracks the power of the first inverter. The output currents of the first inverter, the second inverter, and the load current are shown in Fig. 7 and Fig. 8 respectively. The balancing current and good current sharing are clear from Fig. 7. Since the two inverters are synchronized using the PLL, there is no phase difference between the phase current of the first and second inverter as shown in Fig. 9.
40 20 0 -20 -40 -60 -80 -100 0
0.02
Fig. 8.
Fig. 5.
0.08
0.1
The three-phase load current
The output three-phase voltages
Fig. 9.
Fig. 6.
0.04 0.06 Time, (seconds)
Syncronised phase currents of first and second inverters
The active and reactive power of first and second inverters
The reference currents are sent from the first inverter to the second inverter through CAN. The id1, iq1, id2 and iq2 are shown in Fig. 10. When the currents and voltage are transformed from the abc to dqz frame there will be oscillations in id and iq because of the harmonics from the 50 Hz, so a low-pass filter is used to remove the harmonics and the cut-off frequency of the low pass filter is 100 Hz. The low-pass filter removes the oscillation, however, it slows the response of the system.
Fig. 10.
The dqz current of first and second inverters
The network schedule is shown in Fig. 11. In some cases the time delay may be random and governed by Markov chains, in this case the system can be modeled as Markovian Jump system and the stability is analyzed using the stochastic stability criterion [23-25].
Fig. 11.
The network schedule in the CAN
VI. CONCLUSION In this paper, the stability of parallel inverters controlled over CAN bus is investigated. The parallel inverters implement master-slave control strategy where the master inverter sends the reference signal to the slave inverter through the CAN bus. The parameters that affect the maximum time delay are investigated; these are the gains of the master and slave controllers, and the time constant of the low-pass filter. Changing the inductance of the filters has no effect on the maximum time delay margin. The stability criterion is formulated as a set of LMIs which is solved using the LMI Matlab toolbox. The controller gains are used as the controller parameters. The controller is tested using the nonlinear models in the Matlab/Simulink. The CAN bus is implemented using True-time 2.0 beta simulator. The master-slave control scheme for the Microgrid system based on the CAN bus has showed a good current balance between the two inverters. REFERENCES [1]
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