The most effective solution to improve the power quality is the use of filters to reduce harmonics. The basic idea of using a filter is explained in Figure 1, where the filter injects a compensating current that compensates the harmonics in load current. There are different filter topologies in the literature such as- active, passive,

hybrid, TCLC-HAPF. The passive power filters are used to filter out a particular order harmonics and has the problem of parallel resonance. The other solution is the use of Active Power Filter (APF). There are different types of APF like series APF, shunt APF. The shunt APF is costly and is not used for large systems. The series APF works as a harmonic isolator and used to reduce the negative sequence voltage [2]. The combination of passive filter and APF known as Hybrid Filter has also been study but has a narrow compensation range. There is another filter topology which is the TCLC-HAPF which is study in this project.

The main objective of this project is to control the thyristor controlled LC coupling hybrid active power filter (TCLC-HAPF) such that the harmonics in the current waveform are reduced. The control algorithm has the following objectives:

➢ To control the voltage injected by TCLC-HAPF such that it compensates the reactive power and load current harmonics

➢ To improve the passive filter performance

➢ To make the whole compensating equipment to act as linear, balanced, resistive load on the system

The different filters present in the literature are classified into three basic types. They are Active Filters and Passive Filters and Hybrid filter. Each type has its own sub classification. Figure 2 shows the detailed classification of the filters.

Installation of the current quality compensators is one of the solutions for different power quality problems such as the low power factor, harmonic current pollution and unbalanced problem. The historical review of different power

quality compensators are summarized in Table 1 and compared in the following. To compensate the reactive power, current harmonics, the passive power filters (PPFs) were proposed in 1940s. Unfortunately, the PPFs have many disadvantages like poor dynamic performance, resonance problem, and fixed reactive power compensation [1] [2]. The static var compensators (SVCs) were firstly proposed in 1960s. And, the SVCs are popularly used for dynamic reactive power compensation [3]. However, the SVCs still suffer drawbacks such as resonance problem, harmonic.

Current injection and poor harmonic compensation ability. To overcome those drawbacks of SVCs and provide better performances simultaneously, the active power filters (APFs) were proposed in the year of 1976 [4] [5] [6]. Unfortunately, APFs still cannot large scale development in the power quality markets due to the high initial and operational costs. Afterwards, the LC-coupling hybrid active filters (HAPFs) were proposed in the year of 2003 with low active inverter part rating [7] [8] [9]. Since the rating of the active inverter part is proportional to the cost of compensators, the HAPFs are more cost effective than the APFs. However, the HAPFs have a quite narrow compensation range, which limits its compensation ability. When the load reactive power is outside its designed range, it loses its low-inverter rating advantages. From 2014 onwards, the thyristor controlled LC coupling hybrid active power filters (TCLC-HAPFs) have been widely studied in [10] - [16], which have the desirable characteristics of a wider compensation range than HAPFs and lower dc-link voltage than APFs for power quality compensation. Based on above discussions and Table 1, the traditional power quality compensators, PPFs and SVCs have inherent problems like resonance problem, slow response, poor harmonic compensation ability, etc. The above mentioned inherent problems can be solved if the active inverter part has been added to the topologies such as APFs, HAPFs and TCLC-HAPFs. However, the cost of PPF and SVC are lower than that of the active inverter part, thus the reduction of the active inverter part rating can lead to a decrease in the total cost of APFs, HAPFs and TCLC-HAPFs. After serious compariation the conclution was drawn, the comparisons among the APF, HAPF and TCLC-HAPF have been provided in terms of V-I characteristic (compensation range and

require DC-link voltage) cost, reliability, power loss and tracking performance. Compared TCLC-HAPF with APF and HAPF, it has higher reliability and lower power loss than both APF and HAPF. Besides, the TCLC-HAPF can be more cost effective than the APF for medium/high voltage level applications (≥10 kV). In addition, the TCLC-HAPF has wider reactive current compensation range than the HAPF and lower DC-link voltage than the HAPF. Therefore, the TCLC-HAPF has a large potential to be further developed for medium/high voltage level applications.

In this section, a parameter design method is discussed and explained into three parts. In Part A, the relationship between the required TCLC-HAPF fundamental impedances (X_af + X_ACTxf) and the load powers is deduced based on power flow analysis. The parameter design of the required fundamental dc-link voltage V_DCf, C_PF and L_PF is proposed under the fundamental frequency consideration. In Part B, the parameter design of the required harmonic dc-link voltage V_DCh is proposed under harmonic frequency consideration. In Part C, the design of L_c is given.

Referring to Figure 4, the required TCLC-HAPF impedance (X_xf + X_ACTxf) can be calculated by applying the Ohm’s Law as:

j X x f + j X A C T x f = ( V → x f − V → n f ) / I → c x f (1)

where V_xf and I_cxf are the fundamental load voltage and compensating current phasors respectively, where x stands for phase a, b and c. V_n is the fundamental common point voltage. By using the Kirchhoff’s circuit laws (KCL), the compensating current relationship can be expressed as:

I → c a f + I → c b f + I → c c f = V → a − V → n f j X a f + j X A C T a f + V → b − V → n f j X b f + j X A C T b f + V → c − V → n f j X c f + j X A C T c f = 0 (2)

Simplifying (2.2), the expression of V_nf can be obtained as:

V → n f = ( X b f + X A C T b f ) ( X c f + X A C T c f ) X E Q f ⋅ V → a f + ( X c f + X A C T c f ) ( X a f + X A C T a f ) X E Q f ⋅ V → b f     + ( X a f + X A C T a f ) ( X b f + X A C T b f ) X E Q f ⋅ V → c f (3)

where

X E Q f = ( X a f + X A C T a f ) ( X b f + X A C T b f ) + ( X b f + X A C T b f ) ( X c f + X A C T c f )     + ( X c f + X A C T c f ) ( X a f + X A C T a f ) (4)

The I_cxf can be expressed in terms of V_fx (V_x = V_fx for V_x is assumed to be pure sinusoidal without harmonic components [11] - [18] and the compensating active and reactive power P_cx and Q_cx as:

j X x f + j X A C T x f = ( V → x f − V → n f ) / I → c x f (5)

I → c x f = [ ( P c x + j Q c x ) / V → x ] * (6)

where the note “*” denotes the conjugate. For unbalanced compensation, the TCLC-HAPF can provide the same amount of Q_cx as the loading required but with opposite directions and balance the three-phase source active power to their average values ( P L a + P L b + P L c ) / 3 simultaneously. Thus, the compensating P_cx and Q_cx can be expressed as:

Q c x = − Q L x     a n d     P c x = − ( P L x − P L a + P L b + P L c 3 ) (7)

Referring to Figure 2(a), the fundamental inverter voltage V_invxf can be obtained as:

V i n v x f = X A C T x f ⋅ I c x f (8)

where X_ACTxf and I_cxf are the fundamental active impedance and compensating current, and I_cxf is design to compensate load fundamental reactive current I L x f q ( I c x f = − I L x f q ) . The relationship between the V_invxf and V_DCxf can be expressed as:

V D C x f = 6 ⋅ V i n v x f (9)

In (9), the scale of 6 ( = 2 ⋅ 3 ) can be explained by the following two reasons:

1) To transfer the phase voltage V_invxf to line-to-line voltage, the scale of 3is required,

2) To guarantee the sufficient V_DCxf, the peak value of fundamental inverter voltage needs to be considered

V i n v x f ( p ) = 2 ⋅ V i n v x f (10)

Moreover, the final required V_DCf is designed to be the maximum value among each phase. Therefore, the final required V_DCf can be expressed as:

V D C f = max ( 6 V i n v a f , 6 V i n v b f , 6 V i n v c f ) (11)

The X_ACTxf is directly proportional to the required V_DCf. The low dc-link voltage is one of the major advantages of TCLC-HAPF. This can be achieved when the value of X_ACTxf is designed to be zero (X_ACTxf ≈ 0). In other words, the value of V_DCf is minimized (V_DCf ≈0). With such minimum V_DCf design, the TCLC part is mainly used to compensate reactive power and balance the active power, while the active inverter part is mainly used to improve the harmonic compensation ability of TCLC part. The TCLC part is an L_c (X_Lc) in series with a paralleled combination of a L_PF (X_LPF) and a C_PF (X_CPF), in which the X_xf can be deduced as:

[ X a f ( α a ) X b f ( α b ) X c f ( α c ) ] = [ π X L P F X C P F X C P F ( 2 π − 2 α a + sin 2 α a ) − π X L P F + X L c π X L P F X C P F X C P F ( 2 π − 2 α b + sin 2 α b ) − π X L P F + X L c π X L P F X C P F X C P F ( 2 π − 2 α c + sin 2 α c ) − π X L P F + X L c ] (12)

In (12), X_Lc, X_CPF, X_LPF are the fundamental impedances of L_c, C_PF and L_PF. α_x is the firing angle of the thyristor. The TCLC part has two back-to-back connected thyristors T1x, T2x, and they are triggered alternately in every half cycle. When α_x = 180˚ (thyristors are opened for the whole cycle), the TCLC part has the maximum capacitive impedance XCap(Max) (<0). On the other hand, when the firing angle α_x = 90˚ (one of thyristors is closed for whole cycle), the TCLC part has the minimum inductive impedance XInd(Min) (>0). Therefore, XCap(Max) and XInd(Min) can be expressed as:

X c a p ( M a x ) = X L C − X C P F = w L c − 1 w C p F (13)

X i n d ( M i n ) = X L P F X C P F X C P F − X L P F + X L c = w L P F 1 − C P F W 2 L P F + W L c (14)

where ω (=2πf) is the angular frequency. To guarantee the TCLC part has inductive compensation range and capacitive compensation range, the basic conditions of XCap(Max) < 0 and XInd(Min) > 0 need to be satisfied. Thus, from (13) and (14), the following relationships can be obtained:

C P F < 1 L c W 2 and L P F < 1 C P F W 2 (15)

To control the series connected APF the reference vector should be generated and compared with the actual voltage vector [1]. The reference voltage vector given by Equation (21) is generated by the following control block. The fundamental component calculation needs the grid voltage angle to calculate the value. The grid voltage angle necessary for this calculation is extracted by using a Phased Lock Loop (PLL) (Figure 6).

A Low pass filter (LPF) is used in the fundamental calculation block to filter out the harmonics and extract the fundamental component. A comparison is made between the actual and reference values of the output voltage of TCLC-HAPF. The error is passed through a PID controller. The gain values of the controller are tuned in such a way that the error is zero and the actual value matches almost with the reference value. If this condition is achieved perfectly then the TCLC-HAPF improves the quality of power generated to the load by filtering out the harmonics and thus improving the performance of the system.

The H-∞ command (still called advanced frequent control or multivariable robust command) is a new approach to the Frequency Automatic; it was initiated by Zames in the early 1980s and developed, in particular by Doyle, Glover, Khargonekar and Francis; it has in recent years become one of the flagship methods of “robust control” [23]; it is used for the rapid development of robust

control laws of stationary and multivariable linear systems [1] [24] the principle of the H-∞ Command provides a solution (if it exists) to the control problem with a number of constraints [15]. It takes into account the specifications which can be classified into four classes of specifications: [15] [25]

- Reference trajectory tracking (guidelines): this is to study the influence of the reference signal r(t) on the error signal E(t)

- Rejection/mitigation of disturbance signals: this is the to study the influence of the b(t) disturbance signal on the Error Signal E(t)

- Measurement Noise Mitigation: it was intended to study the influence of noise signals w(t) on the signal U(t) and on the output signal y(t)

- Moderate control: it is a question of studying the influence of the reference signals r(t) and the disturbance signal b(t) on the command signal u(t)

The H-∞ synthesis uses the concept of standard problem, which is shown in Figure 7: the P(s) transfer matrix models the dynamic interactions between 2 sets of inputs and 2 sets of outputs: vector IV represents external inputs, such as reference signals, disturbances, noises; The vector II represents the commands; the e signals are chosen to characterize the right functioning of “system”; Finally, y represents the measures available to develop the order.

Riccati Equation Solution

From the following model below;

{ x ( t ) = A x ( t ) + B w w ( t ) + B u u ( t ) Z ( t ) = C z x ( t ) + D z w w ( t ) + D z u u ( t ) y ( t ) = C y x ( t ) + D y w w ( t ) + D y u u ( t ) (18)

with x(t): is the state vector

u(t): is the vector input or command

y(t): is the observation vector or exit.

A = evolution or state matrix

B_u = control or input matrix

C_y = observation matrix

D_zu = coupling inputs outputs matrix (direct transmition)

For the problem H-∞ standard certain assumption must be respected:

➢ H1) -the even (A B_U) is stabilized or commendable

-The pair (C_Y, A) is detectable or observable

These two conditions guarantee the existence of the corrector that stabilizes the closed loop system.

➢ H2) rank(D_ZU) = M_U and rank(D_YW) = P_Y these are the conditions to ensure that the K_(P) corrector is clean. That is there are many Z controlled outputs as U(P_Z ≥ M_U) and that there are at least many W-screen entries as there are Y(M_W > P_Y).

Ø H3) rank [ A − j w I n B u C z D z u ] = n + m u guarantees that the transfer P_ZU has no zero on the imaginary axis. (19)

➢ H4) rank [ A − j w I n B w C y D y w ] = n + P y guarantee that the transfer P_YW has no zero on the imaginary axis.

These four hypotheses must be verified. Using Matlab

To obtain the simplest expressions, the following additional conditions are introduced.

D z w = 0 ; D z u T [ C z D z u ] = [ 0 I m u ] ; D y u = 0 ; [ B w D y w ] D y w T = [ 0 I p y ] (20)

So there is a K(p) corrector solution to the problem Hꚙ standard

1) The Hamiltonian Matrix

[ A γ − 2 B w B w T − B u B u T − C z T C z − A T ] has no values of its own on the imaginary axis and there is a sysmmetrical matrix X ∞ ≥ 0 such as:

X ∞ A + A T X ∞ + X ∞ ( γ − 2 B w B w T − B u B u T ) X ∞ + C z T C z = 0 (21)

2) The Hamiltonian Matrix

[ A T γ − 2 C z T C z − C y T C y − B w B w T A ] has no values of its own on the axis imaginary and there is a symmetrical matrix Y ∞ ≥ 0 such as

Y ∞ A + A T Y ∞ + Y ∞ ( γ − 2 C z T C z − C y T C y ) Y ∞ + B w B w T = 0 (22)

3) − ρ ( X ∞ Y ∞ ) < γ 2 or ρ corresponds to the module of the highest value (spectral radius). In addition, all K(P) correctors responding to the problem are given by K ( P ) = F l [ K a ( P ) , ∅ ( P ) ] or ∅ ( P ) is a stable function, standard H ∞ is below the Y and K a ( P )

K a ( P ) = [ A ∞ ^ − Z ∞ L ∞ Z ∞ B u F ∞ 0 I m u − C y I p y 0 ] (23)

with

A ∞ ^ = A + γ − 2 B w B w T X ∞ + B u F ∞ + Z ∞ L ∞ C y (24)

F ∞ = − B u T X ∞

L ∞ = − Y ∞ C y T

Z ∞ = ( I n − Y − 2 X ∞ Y ∞ ) − 1

A particular corrector can be obtained as the central corrector, obtained by taking 0, which gives:

K 0 ( P ) = [ A ∞ ^ − Z ∞ L ∞ F ∞ 0 ] (25)

4) Equivalent model of the HAPF (applying H-∞ to filter) (Figure 8)

The equivalent reactance gives us:

X T c L c x f = π X l   P F f X c P F f X c P F f ( 2 π − 2 α x + sin 2 α x ) − π X l   P F f + X l   P F f (26)

Avec X l   c f = w l c ; X l   P F f = w l P F ; X c f P F = 1 / w C P F ; w = 2 π f

From the equivalent model we have the mesh equation;

V x + X T c L c x f I c x n − V a f = 0 (27)

suppose β = π X l   P F f X c P F f X c P F f ( 2 π − 2 α x + sin 2 α x ) − π X l   P F f

where V x + β I c x n + X l c f I c x n − V a f = 0 by posing U l c f = X l c f I c x n this implies U l c f = − β I c x n + V a f − V x and L c d I c n x d t = − β I c x n + V a f − V x which ultimately gives

d I c n x d t = − β L c I c x n + V a f L c − V x L c (28)

However, the current at the entrance to the active Filter gives:

I a f = I F a − I F b which is equivalent to d Q a f d t = I F a − I F b

C d c d V a f d t = I F a − I F b which is still equivalent to:

d V a f d t = 1 C d c ( I F a − I F b ) (29)

So we obtain these two equations

d I c n x d t = − β L c I c x n + V a f L c − V x L c (30)

d V a f d t = 1 C d c ( I F a − I F b )

Lets translate these two equations into Parks landmark

d I d d t = − β L c I d + w I q − V x d L c

d I q d t = − β L c I q − w I d − V x q L c

d V a f d d t = 1 C d c ( I d − I l d ) + w V a f q (31)

d V a f d d t = 1 C d c ( I q − I l q ) − w V a f d

with

− I d et I q : represents variations in park components associated with line currents at the entrance to the LCL filter

V a f d et V a f q : presents variations in Park components associated with voltage in the LCL filter capacitive bus.

− I l d et I l q : presents variations in Park components associated with currents at the right straightener entrance.

The appearing command vector U, which includes the non-linearities of the system, is written as follows:

U = ( I l d , I l q ) t

The state vector X

X = ( I d , I q , V a f d , V a f q ) t (32)

Finally we deduct our state matrix, entry and exit

- Matrice d’état A

A = ( − β L c w − 1 L c 0 − w − β L c 0 − 1 L c − 1 C d c 0 0 w 0 1 L c − w 0 ) (33)

- Matrice d’entrée B

B = ( 0 0 0 0 − 1 L c 0 0 − 1 L c ) (34)

- Matrice de sortie C

C = ( 0 0 1 0 0 0 0 1 ) (35)

with the matrice obtain above will permit us to have a good functioning of the H∞ corrector.

A comparative study is made to analyze the performance of the system at various operating conditions when operating with balanced load, unbalanced load and balanced voltage. The comparison is given in Table 4. From the results it is clear that the system behavior can be improved after the filter is connected and the source current THD will be very less and is within the IEEE permissible standards.

The power system may experience unbalanced load and voltage source conditions at many times. Thus, the behavior of the proposed control strategy is analyzed

by simulating it under non-linear load, unbalanced non-linear load and voltage condition. Here the non-linear load is created by connecting three single-phase uncontrolled rectifiers and resistor. The load voltage values are given in Table 5.

A passive filter is connected at PCC to eliminate fifth order harmonics. Also an active filter is also connected at the output of the VSI. The values of these filters along with load values are given in Table 5. The filter impedance should be less

than the system impedance for effective filtering. The simulation is carried out under the following conditions; -balanced non-linear load-unbalanced non-linear load (phase 1, 2 and 3).

From observation and assumption the phase 3 of the unbalanced non-linear load will produced a level of THD with after filtering will respect the norms of THD. With the system parameters in Table 5, the proposed control strategy is simulated and the circuit diagram is shown in Figure 14. The MATLAB SIMULINK results are presented in Figures 15-17 respectively. Figure 18 shows the source current after compensation. The THD of this current is shown in Figure 16 which is (3.16%) Now the THD of the current is less and the harmonic analysis is shown in Figure 17. The use of adaptive hybrid active power filter increases the performance of the system and the overall power factor is also improved. In addition, 5th order harmonics are greatly reduced.

Thus, from the above results it is clear that the harmonic filtering is effected when the source impedance is less than the filter impedance. Hence, to have better performance characteristics the source impedance should be always greater than the filter impedance.

The robust adaptive h-infinity control offers us a THD of 3.16% after filtering a result admissible by the IEEE 519-1996 standard this result is consolidated by the work of [4]. The harmonic currents reach 8 A. for the case of a balanced network.

In the case of an unbalanced non-linear load the simulation is done and observation is taken per phase since an additional non-linear load is added to each phase with different values causing each phase to obtain different THD. The table of values for the additional load is given in Table 6 below.

The h-infinity command here at this level allows the filter to produce harmonic currents adapted to the disturbance of the network depending on the nature of the disturbance of each phase with THD concerned of 1.8%, 3.29%, 2.78%.

A comparative study of the three phase source current THD during unbalanced and balanced load at various operating conditions is presented in Table 7. From these results it is clear that the proposed control strategy works better at almost all operating conditions and thus helps in improving the quality of electric power delivered to the end user.