Journal of Electrical Engineering: Theory and Application (Vol.1-2010/Iss.2) Berbaoui et al. / Design of DC Link Voltage Controller Using Ant Colony … / pp. 92-99
Design of DC Link Voltage Controller Using Ant Colony Optimization for Shunt Active Power Filter Brahim Berbaoui, Chellali Benachaiba, Rachid Dehini, Otmane Harici Departement of Electrical Engineering, Bechar University, B.P 417 BECHAR (08000) Algeria e-mail:
[email protected],
[email protected] Submitted: 23/01/2010 Accepted: 18/04/2010 Appeared: 30/04/2010 HyperSciences.Publisher
Abstract—All over the word, harmonics current has been increased and injected by nonlinear loads, such as rectifier equipment used in telecommunication system, power suppliers, domestic appliances, ect. To make the transient behaviours of SAPF system better, researchers improved the system construction, detection method, control strategy and so on. In this work the ant colony optimization has been used to illustrate performance of optimized PI controller parameters of DC link voltage of (SAPF). It is expected to improve the system performances. Computer simulations demonstrate that compared with conventional PI controller, this optimized PI controller has best performances for DC link voltage control and very effective in reducing harmonic.
Keywords: Shunt active power filter, Harmonic compensation, PI controller, Ant colony optimization.
NOMENCLATURE
ACO Pij
Ant Colony Optimization Probability Transition rule
τ ij
Pheromone on edge (i , j )
η ij α β ρ
Visibility on edge (i , j )
kp
1. INTRODUCTION The recent progress of the power electronic devices and its use technology in the industry has caused an unfortunate result. Theses electronic equipments Such as converters, home applications as TVs, electromagnetic cookers and fluorescent lights is considered as a non-linear load which inject harmonic in line distribution (Peng, 1998). The troubles associated to the harmonic components in the power electric system forced the researches to study and propose new technique to eliminate theses harmonics. One of the theories is the instantaneous power theory (p-q theory). This theory was introduced by Akagi, Kanazawa and Nabae in 1983 (Akagi et al., 1983) in Japanese.
Coefficient important of pheromone Coefficient important of visibility. Evaporation coefficient Proportional gain
ki
Integral gain
f os
Overshoot function
f rt
rise time function
f ias F v a ,b , c
integral absolute control error function
i L − a ,b , c p Q
Three phases load current
i * a ,b , c THDi
Harmonic reference current
By tradition, passives filters have been used to eliminate the current harmonic distortion and compensate the reactive power, but can resonate with supply impedance. The proposed optimized shunt active power filter system is a great tool for the compensation not only of current harmonics produced by distorting loads, but also of reactive power of non-linear loads (Mattayelli, 2001).
Fitness function Three phases Source voltage
As the important link influence steady and dynamic index, the optimization of PI regulator’s parameters is crucial (Gu and Xu, 2003).
Active power Reactive power
In this paper, we formulate the problem of design DC link voltage PI controller as an optimization problem. The problem formulation adopts three performances indexes, the maximum overshoot, the rise time and the integral absolute
Current Total harmonic distortion
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Journal of Electrical Engineering: Theory and Application (Vol.1-2010/Iss.2) Berbaoui et al. / Design of DC Link Voltage Controller Using Ant Colony … / pp. 92-99
error of step response as the objective function to determine the PI control parameters for getting a well performance under a given system, the primary design goal is to obtain good load disturbance response by minimizing the integral absolute control error. At the same time, the transient response is assured by minimizing the others three performance indexes. Furthermore, we provide work for solution algorithm based on ant colony optimization (ACO) technique that has developed as effective for combinatorial optimization problems (Dorigo and caro, 1999) such as the traveling salesman problem, quadratic assignment problem, graph coloring problems with successful result. This paper improved the trail update mechanism of ACO applied to PI parameter optimization, reduced dependence of transition probability on relative important parameter of trail intensity, accelerated convergence, an applied the improved ACO to PI parameters of shunt active power filter.
τ ij → (1 − ρ )τ ij m
τ ij → τ ij + ∑ ∆τ ijk 1
∆τ ij =
∑
h∈s
[τ ij ]α [η ih ]β
∀(i, j ) ∈ L
c
k
(3)
arc( i , j )beong toT k
if 0
(4)
othrwise
Where m is the number of ants, L represents the edges of the solution graph, and Ck is the cost function of tour Tk, built by the kth ant. 3. ORGANIZATION OF OBJECTIVE FUNCTION In this work, the optimized parameters objects are proportional gain and integral gain , the transfer function of PI controller is defined by:
The main idea of ACO is to model the problem as the search for a minimum cost path in a graph that base the evolutionary meta-heuristic algorithm. The behavior of artificial ants is inspired from real ants. They lay pheromone trails and choose their path using transition probability. Ants prefer to move to nodes which are connected by short edges with a high among of pheromone. The algorithm has solved traveling salesman problem (TSP), quadratic assignment problem (QAP) and job-shop scheduling problem (JSSP) and so on (Dorigo et al., 2008)-(Wada et al., 2001). The problem must be mapped into a weighted graph, so the ants can cover the problem to find a solution. The ants are driven by a probability rule to choose their solution to the problem (called a tour). The probability rule (called Pseudo-Random-Proportional Action Choice Rule) between two nodes i and j.
[τ ij ]α [η ij ]β
(2)
k =1
2. ANT COLONY OPTIMIZATION
Pij =
∀(i, j ) ∈ L
Gc ( s ) = K p +
Ki s
(5)
The gains and of PI controller are generated by the ACO algorithm for a given plant. As shown in fig.1. the output u(t) of PI controller is (equation 6): ACO
r (t )
e (t )
G s (s)
u (t )
G p (s )
y (t )
Fig. 1. PI control system
(1)
t
u (t ) = K p e(t ) + K i ∫ e(t )dt
(6)
0
The heuristic factor or visibility is related to the specific problem as the inverse of the cost function. This factor does not change during algorithm execution; instead the metaheuristic factor (related to pheromone which has an initial value ) is updated after each iteration. The parameters α and β enable the user to direct the algorithm search in favor of the heuristic or the pheromone factor. These two factors are dedicated to every edge between two nodes and weight the solution graph.
For a given plant, the problem of designing a PI controller is and for getting a desired to adjust the parameters performance of the considered system. Both the amplitude and time duration of the transient response must be kept within tolerable or prescribed limits, for this condition, three key indexes performance of the transient response are utilized to characterize the performance of PI control system. These key indexes maximum overshoot, rise time and integral absolute control error are adopted to create objective function which is defined as:
The pheromones are updated after a tour is built, in two ways: firstly, the pheromones are subject to an evaporation factor , which allows the ants to forget their past and avoid being trapped in a local minimum (equation 2). Secondly, they are updated in relation to the quality of their tour (equations 3 and 4), where the quality is linked to the cost function.
F = f os + f rt + f ias
(7)
The maximum overshoot is defined as:
f os = y max − y ss
93
(8)
Journal of Electrical Engineering: Theory and Application (Vol.1-2010/Iss.2) Berbaoui et al. / Design of DC Link Voltage Controller Using Ant Colony … / pp. 92-99
transitory operations, as well as for generic voltage and current waveforms.
characterize the maximum value of y and denote the steady-state value of . For represent the function of the rise time is defined as the time required for the step response. In the other hand, the integral of the absolute magnitude of control error is written as:
Inputs: Vector of tension: va (t), vb (t) and vc (t) Vector of current: ia (t), ib (t) and ic(t)
∞
f ias = ∫ e(t ) dt
(9)
0
The PQ theory consists of an algebraic transformation (Clarke transformation) of the three phase voltages and current in the abc coordinates to the αβ coordinates (Akagi et al., 1983).
4. CONFIGURATION OF SHUNT ACTIVE POWER FILTER The most important objective of the SAPF is to compensate the harmonic currents due to the non linear load. Exactly to sense the load currents and extracts the harmonic component of the load current to produce a reference current Ir as shown in fig.2, The reference current consists of the harmonic components of the load current which the active filter must supply (Akagi et al., 1983).This reference current is fed through a controller and then the switching signal is generated to switch the power switching devices of the active filter such that the active filter will indeed produce the harmonics required by the load. Finally, the AC supply will only need to provide the fundamental component for the load, resulting in a low harmonic sinusoidal supply.
vα v = β
2 1 3 0
v a −1 2 −1 2 vb 3 2 − 3 2 vc
(10)
i Lα i = Lβ
2 1 3 0
i La − 1 2 − 1 2 i Lb 3 2 − 3 2 i Lc
(11)
The instantaneous power is calculated as:
3 phase AC iia , iib , iic Vc Supply i , i , i sa sb scv sa , v sb , v sc isa isb i sc
iia iib iic
ira Courrent irb Control Detetction irc Circuit S a Sb Sc Lf Lf Lf
p vα q = − v β
(12)
The harmonic component of the total power can be extracted as:
pL = pL + ~ pL Vc
(13)
Where,
iLa i Lb i Lc Ls Ls
v β iα vα i β
p L : The DC component ~ p L : Harmonic component
Ls
Similarly,
RL LL
q L = q L + q~L
(14)
Finally, we can calculate reference current as: Fig.2. Equivalent schematic of shunt SAPF 5. INSTANTANEOUS ACTIVE AND REACTIVE P-Q POWER THEORY
i *fa * i fb = i *fc
The identification theory that we have used on shunt APF is known as instantaneous power theory, or PQ theory. It is based on instantaneous values in three-phase power systems with or without neutral wire, and is valid for steady-state or
here,
94
0 1 2 iα − 1 2 3 2 i 3 β − 1 2 − 3 2
(15)
Journal of Electrical Engineering: Theory and Application (Vol.1-2010/Iss.2) Berbaoui et al. / Design of DC Link Voltage Controller Using Ant Colony … / pp. 92-99
p 1 vα q = 2 2 vα + v β v β
− vβ ~ p ~ vα q
The DC link voltage discretely at the positive zero-crossing point of respective phase source voltage, computes the variation of power according to difference of DC link voltage between two sampling points. The regulation of the error between the capacitor voltage and its reference is assured by The PI controller which its output is multiplied by the mains voltage waveform Vs1, Vs2, Vs3 in order to obtain the supply reference currents. The equivalent schematic diagram of system which is used to maintain the DC link voltage constantly is shown in Fig.4.In this work, the objective of an optimal design of PI controller DC-Link for given plant is to find a best parameters Kp and Ki of PI control system such that the performance indexes on the transient response is minimum.
(16)
6. ACO APPLIED TO OPTIMIZE PI PARAMETERS OF DC-LINK CAPACITOR
In this paper, we present the SAPF as controlled plant, the SAPF diagram is shown in Fig.3. us
is
Load
Each parameter of Kp and Ki is hinted by 100 nodes respectively and there is resolution 0.0001 among each node, one node represents a solution value of parameters Kp and Ki. Thus, the more accuracy trails are updated after having constructed a complete path and the solution found.
L U dc ih*
v
* U dc
In this study, there are 202 nodes including the start node and the end node to form a graph representation Fig.5. Each path defines the performance indexes on the load disturbance response and transient response for a set of Kp and Ki..The following solution algorithm for designing PI controller is presented as:
*
C
Convrter
PI
ih
ref courrent PI _ ACO
genertor
Kp
Ki
Fig.3. Control diagram of SAPF system
ACO
S
D
PI _ cntroller
Kp
U dc
* U dc
G (s )
Fig. 5. ACO graph representation for parameters
Ki s
PI controller
• Initialization. Fig.4. Equivalent schematic diagram system
An initial of ant colony individuals Xi, i=1, 2….m, which is selected randomly. The m ants are placed on the n node. Format the pheromone trail intensity matrix, an initial value for every edge between nodes i and j as well as , generation counter ng
The estimation of the reference currents from the measured DC bus voltage is the basic idea behind the PI controller based operation of the SAPF. The capacitor voltage is compared with its reference value in order to maintain the energy stored in the capacitor constant.
We set the time counter
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Journal of Electrical Engineering: Theory and Application (Vol.1-2010/Iss.2) Berbaoui et al. / Design of DC Link Voltage Controller Using Ant Colony … / pp. 92-99
• Starting tour. Let node counter For ant to m do We place the starting node of the kth ant in t_list (k,s) that is initial tour list. • Searching neighborhood. We repeat until the data t_list is full
A number of simulation results were developed with different cases. The SAPF is connected in parallel with nonlinear load, the first case is the PI-classical using on the system to allow us to see the regulation of DC link voltage and its effect for damping harmonics current and reducing total harmonic distortion (THD). For the second case the proposed optimized PI-controller has been introduced in order to improve a SAPF performance and meet the requirements of harmonic elimination and reactive compensation.
For to m do Ant choose the node j to move to with probability given in (1) Move the kth ant to the node j Insert node j into t_list (k,s) • Calculate the fitness function Fk (cost) for each ant For to m do Compute the function Fk of the tour visited by kth ant Update the shortest path found For every edge For ant to m The pheromone trail is calculated according to the equation (4) • Update the global pheromone For every edge (i,j) update the pheromone value according to the rule (2) and (3) • Check the stop criterion If (ng
