2016 Smart Grids Conference (SGC), 20-21 Dec. 2016, Graduate University of Advanced Technology, Kerman, Iran
A Fractional Order Proportional-Integral Controller Design to Improve Load Sharing between DGs in Microgrid Mahdi Zolfaghari, Ali Asghar Khodadoost Arani, G. B. Gharehpetian, Mehrdad Abedi Department of Electrical Engineering Amirkabir University of Technology Tehran, Iran
[email protected]
Abstract— This paper presents a control scheme based on fractional proportional-integral controller for improving the load sharing among parallel-connected inverter based distributed generation in microgrid. The control context is based on the current control in which through the use of the proposed strategy dynamically preserves the proportional power sharing properties of the DG units. The results show that the controller is locally stabilizing, without relying on the communication links between DGs, a proper power sharing among these resources as well as the minimization of circulating current. The results can also be extended for a parallel topology of inverters and hold for generic interconnections of inverters and loads. Keywords— Microgrid, DG, load sharing, fractional order controller
I. INTRODUCTION Increasing high energy demand along with low cost and higher reliability requirements, are driving the modern power systems towards clean and renewable power. In the context of integrating the renewable sources with utility, microgrid has been defined as a small electric power system which is able to physically operate islanded or interconnected with utility girds [1]. It is meant to be mainly supplied by renewable energy sources (RES) whereas specific control devices (e.g. energy storage systems) maintain the required power quality [2-4], improve service reliability [5] and provide better economics and reduced dependence on local utility. Typically, the greatest beneficiaries of microgrids are customers with large mission critical facilities or large power consumers in the areas prone to frequent and/or prolonged outages [5,6]. One of the technical issues related to microgrid is proper control strategy to guarantee load sharing among parallel-connected inverterbased DGs under different loads and system conditions. In the past decades, many control strategies have been introduced to overcome the problems of load sharing in parallel operations, one of which is conventional voltage and frequency droop method [6] that utilizes power flow theory in large power systems and uses Q–V and P–ω characteristic droop to regulate load sharing among parallel-connected inverters. Distinctive feature of this droop method is that no control interconnection of inverters is needed. Therefore, it has advantages in terms of
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high modularity and good reliability. However, there are several drawbacks that limit its operation such as slow transient response [7], frequency and phase deviation, and tradeoff between output regulation and output power sharing accuracy [8]. To improve this control scheme, some researchers have proposed modified droop, adaptive droop, combined droop, network control, and virtual frequency–voltage frame schemes [9-11]. In [12], a network control based on droop control was proposed which made full use of network data to achieve relatively good performance. In order to obtain a faster transient response, a control unit was added to the conventional droop method in [13], in which nominal frequency and voltage of inverters were changed to control the circulating current during transients. In [14], to improve reactive power sharing accuracy, an enhanced control strategy was proposed that estimated reactive power control error through injecting small real power disturbances activated by the low-bandwidth synchronization signals from the central controller. Thus, the aim of this paper is to propose a fractional order PI controller to improve the power sharing strategy for between parallelconnected inverter based DGs. II. INVERTER BASED DGS AND MICROGRID MODEL This section deals with the modeling of the microgrid and inverter based DGs. A. Inverter based DG model The DG units considered here are the inverter based DGs. Fig. 1 illustrates a schematic diagram of a single inverter module. Each inverter module employs four controllable switches (such as IGBT‚…)‚ four free-wheeling diodes and a low pass filter (L-C filter) trapping the switching harmonics embedded in the inverter output voltage. The inverter converts the dc input to an ac output based on the modulation signal from the sinusoidal pulse width modulation (SPWM) modulator. Actually, a voltage source inverter (VSI) can be represented as a controlled voltage source that is controllable through the SPWM unit. The switching signals for the controllable switches are produced the SPWM unit. The current error signal is calculated by comparing the output current I with the reference current
I * and the PI controller
2016 Smart Grids Conference (SGC), 20-21 Dec. 2016, Graduate University of Advanced Technology, Kerman, Iran tries to minimize the error and based on the output signal of this controller, the SPWM unit produces the switching signals. Lf ‚Rf and Cf represent the inductance‚ resistance and capacitance of the output filter‚ respectively. The output terminals of the inverter passing through the L–C filter and line impedance are connected to the load. The line impedance between the inverter and the load network is the equivalent impedance due to the connecting lines or cables. The load can be resistive‚ inductive‚ capacitive‚ or linear or nonlinear. Fig. 2 shows the signal flow of an inverter model with current control mode. The feedback gain K c is unity and the compensator K I is the current controller which can be considered a PI controller.
th nominal power of i inverter. The injected power to the microgrid, n Pi , is [13]; (1) Pi ViV j Yij sin(i j )
j 1
That is based on ac power flow.
B. Modeling of microgrid based on graph theory Modeling of a microgrid using graph theory may facilitate the process of control design. An interconnected graph of a microgrid that has been disconnected from the upstream distribution network, or in the other words, the islanded mode of operation, is shown in Fig. 3. As shown, the microgrid contains only the inverter based DGs and related loads. This model can be represented as a graph with N s source nodes to which the DGs are connected and Nl nodes to which the loads are connected with total numbers of nodes n. Using the algebraic graph theory [14], this model can be denoted as a weighted graph G( N , , A) with N is a set of nodes NN (here N n ), N N is the set of edges and A is the adjacency matrix. If a number ℓ ∈ {1, . . . , } and an arbitrary direction is assigned to each edge i, j then the N node-edge incident matrix B is defined componentwise as Bkℓ= -1 if node k is the source node of edge ℓ with all N other elements being zero. For , B T is the vector with components i j with i, j . If diag ( aij i , j ) is the diagonal matrix of edge weights, then the Laplacian Matrix L is given by L Bdiag (aij i, j ) BT . If the weighted graph is connected, then ker( BT ) ker( L) span(1 N ) and ker( B) . Here, for every 1N there exists a unique satisfying Kirchoff's Current Law (KCL) B . For more details see [13]. In some applications the inverter output impedance can be controlled to be highly inductive and dominate over any resistive effects in the network [14]. Thus, if the lines considered inductive, the bus admittance matrix of this graph with N n nodes is represented as Y j nn . The vector set of nodes can be indicated as N N s , N l corresponding to the inverter and load nodes. The admittance between branch i,j ,for i, j , is Yij . Because the output impedance of the inverter is highly inductive, the output admittance is susceptive and is merged with the line susceptances Im(Yij ) 0, i, j . The voltage at each node i 1....n is defined as Vi (t ) Vi cos( nomt i ) where Vi 0 is the amplitude, nom is the nominal angular frequency and i is the voltage phase angle. The average active power injected to the microgrid nom by each inverter based 0, Pi P nom DG is confined to the interval where i is the
Fig. 1. Model of an inverter based DG with current control mode supplying a load. R
I
*
-
KI -
-
Inverter
f
1 Lf s
io
vo
1 Cf s
I Kc
Fig. 2. Inverter model with current-sharing scheme
Inv. No.1
Inv. No.n
Inv. No.2 Inv. No.3
Fig. 3. A typical graph structure of an islanded microgrid
III. PROPOSED CONTROL SCHEME FOR LOAD SHARING IMPROVEMENT
A. Overall diagram Fig. 4 shows a microgrid containing n parallel-connected inverter based DGs commonly supplying a load. Each inverter is connected to the point of common coupling (PCC) bus through a line with impedance of . The impedance of lines can be different due to the different length of lines. As shown, all inverters use the same reference current and the feedback current loop is used for the output current of each inverter. The current error is given to the fractional order PI controller (FOPI) which tries to minimize this error. The output signal of
2016 Smart Grids Conference (SGC), 20-21 Dec. 2016, Graduate University of Advanced Technology, Kerman, Iran this controller is given to the SPWM unit to generate the switching signals for the controllable switches. B. FOPID controller A typical structure of a FOPID is illustrated in Fig. 5. The fractional-order PI D controller was proposed as a generalization of the PID controller with integrator of real order and differentiator of real order . The transfer function of such type the controller in Laplace domain has form [15]:
s
KD
Y (s)
R (s)
KP
s
+
KI
Fig. 5. Block diagram of a FOPI controller Inverter
Y ( s) C ( s) K P K I s K D s R( s )
(2)
I
*
FOPID -
where KP is the proportional constant, KI is the integration constant and KD is the differentiation constant. Transfer function (2) corresponds in discrete domain with the discrete transfer function in the following expression:
C ( z 1 )
Y ( z 1 ) R( z 1 )
K P K I ( ( z 1 )) K D ( ( z 1 )) (3)
where , are arbitrary real numbers. A classical PI controller is achieved by assuming 1, 0 . Thus, the modification in PI controller provides flexibility and accuracy in the FOPI controller. The increase in robustness makes the system more stable. The optimal values of FOPID controller parameters are tuned with Ziegler Nicholas method to control the overall system performance. Fig. 6 indicates the implementation of the proposed FOPID controller in control of the voltage source inverter. For this model, to have a desired phase margin 45 using the available software package MATLAB [16], we obtain K P 0.67, K D 0.625 , K I 12.5 and 0.5 and the FOPID is;
FOPID 0.67 0.625 s
12.5
(4)
s PCC Inverter No.1
Gate Driver & SPWM
Z line2
Inverter No.2
I2
Load
-
Inverter No.n
Gate Driver & SPWM
FOPI Controller
Output filter
-
Gate Driver & SPWM
FOPI Controller
Z line1
I1
FOPI Controller
I*
Output filter
Output filter
I
Zlinen
n
-
Fig. 4. Proposed control strategy for n parallel-connected inverter based DGs.
G
io
1 Cf s
vo
I Kc
Fig. 6. Block diagram of the proposed FOPID implementation in the control inverter model.
IV. SIMULATION RESULTS In this section, various system conditions are examined to show the effectiveness of the proposed controller. These examinations were extensively evaluated by simulation using MATLAB software [16]. For purpose of comparison, the performance of conventional PID controller (CPID) is also analyzed. The microgrid model is based on the structure proposed in Fig. 4 in which only two parallel-connected inverters are considered to show the performance of the proposed control strategy. Here, two case studies are considered: In the first case, the resistance of the one of transmission line 1, which connects inverter 1 to the load, is changed during simulation and the performance of the FOPID and CPID controllers evaluated. In the same way, in the second case, the inductance of the transmission line 2 was changed and behavior of the two controllers analyzed. The microgrid data are given in Table I. For the two cases, the load is considered with lagging power factor as 1000 W, 400 VAr and the voltage at load bus is 230 V, 50 Hz and the DC side voltage of inverter is 400 V. Case I. In this case, the resistance of transmission line 1, R1 , is reduced from 0.8Ω to 0Ω in 0.1Ω steps and the performance of the two controllers in reducing the circulating current and difference of power of the inverters analyzed. Figs. 7-9 show the results when the CPID and the proposed FOPID controllers are implemented. Fig. 7 shows that the circulating current by using the CPID controller is 0.15A whereas it is reduced to 0.1 A by using the FOPID. Figs. 8-9 show that the active and reactive power differences between the two inverters is more reduced by applying the FOPID controller. Fig. 8 shows the active power difference is 14.4, 11 VAr for the CPID and FOPID controllers respectively. As illustrated in Fig. 9, the reactive power difference by implementing the CPID is 180 VAr whereas it is reduced to 64 VAr by using the FOPID.
2016 Smart Grids Conference (SGC), 20-21 Dec. 2016, Graduate University of Advanced Technology, Kerman, Iran Case II. The inductance of transmission line 2, L2 is increased from 0mH to 0.5mH in 0.1mH steps. Figs. 10-12 show the results for this condition. Fig. 10 shows that the CPID controller reduces the circulating current to 0.55 A while the FOPID is able to reduce it to 0.10 A. The active power difference is also more reduced by using the FOPID, as shown in Fig. 11. The reduction of reactive power difference is also notable as it is illustrated by Fig. 12. Applying the FOPID controller resulted in 1.8 VAr reactive power difference between the two inverters while the CPID controller reduced it to 8 VAr. TABLE I.
Fig. 10. Simulation result, Case II: Circulating current between two inverters during line inductance change.
Parameters of microgrid considered in simulation Description
Value
Resistance of line 1 ( R1 )
0.8 Ω
Resistance of line 2 (
R2 )
0.8 Ω
Inductance of line 1 (
L1 )
0.5 mH
Inductance of line 2 ( L2 )
0.5 mH Fig. 11. Simulation result, Case II: Active power difference between two inverters during line inductance change.
Fig. 7. Simulation result, Case I: Circulating current between two inverters during line resistance change.
Fig. 12. Simulation result, Case II: Reactive power difference between two inverters during line inductance change.
V. CONCLUSION
Fig. 8. Simulation result, Case I: Active power difference between two inverters during line resistance change.
Microgrid is an electrical network comprising loads, microsources and communication & automation systems. One of the technical issues related to microgrid is proper control strategy to guarantee load sharing among parallel-connected inverterbased DGs under different loads and system conditions. In this study, based on fractional proportional-integral controller, a control scheme was proposed to improve the load sharing among parallel-connected inverter based distributed generation in microgrid. The current control considered in which through the use of the proposed strategy dynamically preserved the proportional power sharing properties of the DG units. The simulation results validated the effectiveness of the proposed control strategy.
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