Dynamic Modeling and Control of Shunt Active Power Filter

Transcription

1 Dynamic Modeling and Control o Shunt Active Power Filter Utkal Ranjan Muduli Electrical Engineering Indian Institute o Technology Gandhinagar Gujarat, India utkalranjan muduli@iitgn.ac.in Ragavan K Electrical Engineering Indian Institute o Technology Gandhinagar Gujarat, India ragavan@iitgn.ac.in Abstract Overall perormance o the shunt active power ilter depends on the method o reerence current extraction. The conventional extraction methods or harmonic and reactive currents is having inaccuracy, in case o distorted and unbalanced supply; non-linear and unbalanced load. Based on adaptive intererence cancelling theory, a method is presented to estimate the harmonic, undamental requency unbalanced and reactive current components. A simulation is perormed in MATLAB/SIMULINK environment which to veriy the easibility o the proposed method. This method can be useul or the dynamic compensation equipment such as static Var compensator, uniied power quality conditioner and so on. Keywords: Adaptive cancellation theory, Adaptive detection algorithm, Instantaneous power theory, Instantaneous symmetrical components, Shunt active power ilter, Voltage source inverter. I. INTRODUCTION Recently, there has been a rapid development o nonlinear loads due to the intensive use o power electronic control in industry as well as by the general consumers. This results many undesirable phenomena in the operation o power system. The most important among these are harmonic contamination, increased reactive power demand and power system voltage luctuations. Harmonic current components increase power system losses, cause excessive heating and vibration in rotating machinery. Also, some precision instruments and communication equipment will be interered by the EMI. Thereore, utility power quality has become an important issue in the recent past. Oten, end user must maintain nearly sinusoidal line currents at a high power actor to comply with the speciied in the IEEE- 519 and limits proposed by the IEC-555 [1]. However, the most signiicant limit on the total harmonic distortion (THD) is speciied by the IEEE-519 standard and is 5% or a load connected to a utility system. Conventionally, a passive LC ilter is used to compensate the harmonics; capacitors being used to compensate the lagging power actor. However, they have many disadvantages such as, large size, resonance and ixed compensation characteristics. These diiculties bring the alternative solution as shunt active power ilter (SAPF) which use voltage source inverter to /14/$1.00 c 2014 IEEE nulliy the harmonic. In addition, shunt active power ilter can be optimized or power actor correction, power low control, load balancing, voltage regulation. In this paper, a simpliied dynamic model o the shunt active power ilter is proposed with an PI controller or dc-link voltage regulation. Using the derived dynamic model, analysis o DC-link voltage response and current tracking capability or the active power ilter will be easier. Applying the proposed control strategy, the current harmonics o a nonlinear and unbalanced load can be compensated quickly. Also, luctuations o DC-link voltage during transient and steady states are eectively suppressed. A detailed simulation program o the scheme is developed to predict its perormance or dierent operating conditions. The salient eatures o this paper are summarized as ollows: 1) The current injected by the SAPF, passes through a ilter inductor. The behavior o ilter inductors is requency dependent [2]. The inluence o these parameter uncertainties on stability and perormance o the current controller can be avoided by using the dynamic model o SAPF. 2) The delay times o both current response o SAPF and DC-link voltage eedback are considered. This results in decreasing the settling time o the DC-link voltage and reducing the high requency current components o the power system. ) The control scheme is suitable or both distorted and unbalanced supply; non-linear and unbalanced loads. II. SAPF DYNAMIC MODELLING A. System Coniguration The coniguration model o shunt active power ilter using a voltage source converter (VSC) is shown in Fig. 1 [4]. In this model, the resistance R in series with the voltage source inverter represents the sum o the coupling inductor resistance losses and the inverter conduction losses. The inductance represents the leakage inductance o the coupling inductor. The sum o the switching losses o the inverter and the power

2 losses in the capacitor is represented by R dc which is in shunt with the DC-link capacitor C dc. In Fig. 1, v a, v b, and v c are the three-phase SAPF output voltages; v la, v lb, and v lc are the three phase bus voltages at load-side; i a, i b, and i c are the three-phase SAPF output currents. With dq-transormation rom equation (1), d T 1 i d i q i o = R T 1 T 1 i d i q i o + T 1 v d v q v o The above equation can be simpliied as: T d ( T 1 ). i d i q + T 1. d i d i q Fig. 1. Equivalent circuit o SAPF i o = R i d i q i o v d + v q (4) i o v o B. Modeling In order to analyze the balanced three-phase system more conveniently, the three-phase voltages and currents are converted to synchronous rotating rame by abc/dq0 transormation. The dq-rame rotate with an angle θ = ωt rom the reerence axis o the abc-rame. By this transormation, the control problem is greatly simpliied since the system variables become DC values under the balanced condition. The transormation rom phase variables to d and q coordinates is given as ollows: where v d v q v 0 = T v a v b v c (1) cos θ cos(θ 2π ) cos(θ + 2π ) 2 T = sin θ sin(θ 2π ) sin(θ + 2π ) A linear mathematical model or each phase o the SAPF shown in Fig. 1 can be written as: di a di b di c = R i a + v a v La = R i b + v b v Lb (2) = R i c + v c v Lc Equations (2) can be written in ollowing orm: d i a i b i c = R i a i b i c + v a v b v c v la v lb v lc () where d ( T 1 ) sin θ cos θ 0 2 = ω sin(θ 2π ) cos(θ 2π ) 0 sin(θ + 2π ) cos(θ + 2π ) 0 T. d ( T 1 ) = ω dθ = ω Applying all the above relations in equation (4) R i d L d ω 0 i d i q = R ω 0 i q + 1 L R i o 0 0 i o 1 v d v q v o (5) Suppose, the output voltage o the SAPF can be expressed as: v d = Kv dc cos α (6) v q = Kv dc sin α (7) where K is a actor that relates the DC voltage to the peak phase-to-neutral voltage on the AC side; v dc is the DC-link voltage; α is the phase angle which the SAPF output voltage leads the bus voltage. Using the relation (6) and (7), the equation (5) can be modiied as [ ] [ R ][ K cos α id ] [ vld ] d id ω L = i q 1 (8) i q ω R K sin α v dc

3 From the SAPF input-output power balance equation, it can be written as: or, or, or, p dc = p v dc i C + v dc i R = v a i a + v b i b + v c i c dv dc v dc C dc dv dc + v2 dc R dc = v d i d + v q i q = K cos α i d + K sin α i q v dc (9) C dc C dc R dc C dc From the equations (8) and (9), the relation or the dynamic model o the SAPF can be derived and is given below: R i K d L d ω cos α i d R i q = ω K sin αi q v K K 1 dc C dc cos α C dc sin α v R dc C dc dc 1 (10) III. PROPOSED REFERENCE CURRENT EXTRACTOR The source could be balanced or unbalanced, spectrally pure or distorted. At the same instant, the load could be balanced or unbalanced, linear or nonlinear. Irrespective o the nature o the load, the proposed algorithm is reliable to estimate the reerence current which is shown in Fig. 2. The role o SAPF is to supply the desirable current components such that the utility source supply only the active current component required by the load. The total compensation current or the SAPF is given by i c,abc = i h,abc + i 1u,abc + i + 1q,abc (11) The voltage across DC-link capacitor decays due to switching losses in the voltage source inverter. In order to maintain this voltage constant, SAPF will draw the necessary amount o current rom the utility source. So, the reerence current should be the combination o the compensation current i c,abc and the switching loss component i loss,abc and is given by A. Deriving i h,abc i,abc = i c,abc + i loss,abc (12) Based on the principle o adaptive noise cancelling theory [5], adaptive detecting algorithm (ADA) extracts harmonic current rom the load current which is shown in Fig.. The system is composed o an adaptive ilter, a band pass ilter (BPF) with 50Hz cut-o requency and 90 0 phase-shiter. The primary input is the load current: i L,abc = i 1,abc +i h,abc, where i 1,abc is the undamental load current, i h,abc is the sum o all harmonic components.in the Fig. v L,abc and v 1,abc are the load voltage and its undamental component, respectively. Fig.. Adaptive detection algorithm B. Deriving i 1u,abc Fig. 2. Proposed reerence current extractor The current drawn by the load is measured through the current sensor at the point o common coupling. The measured current is then decomposed into ollowing components: Harmonic component: i h,abc Unbalanced component o undamental requency: i 1u,abc Active component o the undamental requency: i + 1p,abc Reactive component o the undamental requency:i + 1q,abc Instantaneous symmetrical component (ISC) method is a timedomain approach which is mainly deployed in power system protection applications []. ISC can only be applicable to the system with single requency component. With ADA, the signals (load current and voltage) and its shited orms are readily available. The load current at undamental requency is given by i 1,abc = i L,abc i h,abc (1) By using this method, load current i La, i Lb, i Lc could be mapped onto positive sequence components as, i + 1a (t) = 1 [i La(t) 1 2 (i Lb(t) + i Lc (t)) 2 (Γi Lb(t) Γi Lc (t))] i + 1b (t) = 1 [i Lb(t) 1 2 (i Lc(t) + i La (t)) 2 (Γi Lc(t) Γi La (t))] i + 1c (t) = 1 [i Lc(t) 1 2 (i La(t) + i Lb (t)) 2 (Γi La(t) Γi Lb (t))]

4 where Γi La (t), Γi Lb (t), Γi Lc (t) are 90 0 shited orm o i La, i Lb, i Lc respectively. Similarly, load voltage v La, v Lb, v Lc could be mapped onto positive sequence components (v 1a +, v+ 1b, v 1c + ) using ISC method. The unbalance component corresponding to the undamental requency can be derived by subtracting the positive sequence current rom the load current due to the undamental requency. multiplied to three phase unit vector gives three-phase loss current. C. Deriving i + 1q,abc The instantaneous power (pq) theory can be deined or three phase systems, with or without neutral conductor. Zerosequence components are absent in three phase three-wire systems, i.e. i 0 = 0. The instantaneous power only exists on the dq-axes, as the product v 0 i 0 is zero. Hence,the instantaneous power p represents total energy low per unit time, in terms o dq-components. The instantaneous imaginary power q represents the quantity o the o energy that is being exchanged between the phases o the system [6]. [ ] [ ][ ] p vd v q id = (14) q v q v d The above powers can also be expressed in terms o the real and reactive powers corresponding to undamental ( p and q) and harmonic requencies ( p and q). That is, i q p = p + p (15) q = q + q (16) As the active and reactive current component due to harmonics is eliminated, they are excluded rom the calculation o the reerence dq-rame current. Hence, the pq-theory is supposed to supply the reactive power component corresponding to undamental requency ( q). So, the reerence current in dqrame is given by: [ ] [ ] 1 [ ] i d vd v q 0 i = q v q v d q [ ][ ] 1 vd v q 0 = vd 2 + (17) v2 q v q v d q The pq-theory ollowed by inverse Clarke transormation (dq to abc) gives the reactive current component (i + 1q,abc ) corresponding to undamental requency. D. Deriving i loss,abc Ater a ew moment o SAPF operation, DC-link voltage will decay and become zero because o switching losses in VSI. In order to maintain DC-link voltage constant, the compensating current should low along with the loss current drawn rom the utility source. Initially, the DC-link voltage is sensed through a voltage sensor and then is compared with constant reerence voltage. To nulliy the comparator error, a PI regulator is used to get the corresponding loss current. Further, this current Fig. 4. Voltage controller using PI regulator IV. RESULTS AND DISCUSSION Distortion and unbalanceness o both load and source is considered or simulation study. Initially, a balanced load o R = 100 Ω and L = 75 mh and balanced supply with phase-a voltage, V sa = 12 sin (100πt) is taken or all the cases. The reerence current would be equal to the undamental reactive component. The waveorms corresponding to all the cases are shown in Fig. 5 between 0 and 0.4 s. The eectiveness o the proposed algorithm can be explicitly studied by considering the ollowing cases. A. Non-linear Load The nonlinear load is ormed by using three-phase uncontrolled rectiier module with load o R = 100 Ω and L = 250 mh. The output current o this load has % o harmonic content. The waveorms corresponding to above case are shown in Fig. 5 between 0 and 0.1 s. This harmonic current is generated by the SAPF and is injected in anti-phase with the load current at the point o common coupling. Ater compensating the current harmonic, it is observed that the total harmonic distortion is 1.96% within IEEE-519 limits. B. Non-linear and Unbalanced Load Functioning o the SAPF during a non-linear and unbalanced load condition is shown in Figure 5. A three-phase unbalance load (R a = 100 Ω, L a = 75 mh, R b = 50 Ω, L b = 90 mh, R c = 150 Ω, L c = 65 mh) and a non-linear load o previous case is taken into consideration. As load current contains an unbalance current along with the harmonic one, the compensating current must contain these components. The waveorms corresponding to above case are shown in Fig. 5 between 0.1 and 0.2 s. Ater supplying the compensating ilter current, the source current becomes balanced, sinusoidal and in phase with the source voltage.

5 C. Linear Load and Distorted Supply A sample case o distorted supply with 20% ith and 1% seventh harmonic is considered or the simulation study. The waveorms corresponding to above case are shown in Fig. 5 between 0.2 and 0. s. These harmonic content (i h,abc ) would obviously be relected on the load current which is being extracted by ADA. The undamental component can be derived by subtracting the harmonic one rom the original load current (Fig. 5(e)). I the load is having some lagging power actor, it will deinitely require reactive power. Due to balanced load and supply, the harmonic current component will be zero. As a result, The compensating current is the algebraic sum o harmonic and undamental reactive current components (Fig. 5(d)). [4] Bhim Singh, Kamal Al-Haddad, A review o active ilters or power quality improvement, IEEE Transactions on Industrial Electronics, vol. 46, NO. 5, Oct [5] B. Widrow, J.R.Glover, Jr., J.M. McCool, Adaptive noise cancelling: Principles and applications, Proceedings o the IEEE, vol.6, no.12, pp.1692,1716, Dec [6] H. Akagi, Y. Kanazawa and A. Nabae, Instantaneous reactive power compensators comprising switching devices without energy storage components, IEEE Trans. on Industry Applications, vol. 20, no., May/June [7] G. C. Paap, Symmetrical components in the time domain and their application to power network calculations, IEEE Trans. on Power System, vol. 15, pages , [8] M. K. Ghartemini, M. R. Iravani and F. Katirei, Extraction o signals or harmonics, reactive current and network-unbalance compensation, lee Proc. on Generation, Transmision and Distribution, vol. 152, pages 17-14,2005. D. Linear Load, Distorted and Unbalanced Supply The perormance o the proposed technique can be evaluated precisely by considering the case o both distorted and unbalanced supply (20% o ith and 1% harmonics, 20% o undamental negative sequence voltage). The waveorms corresponding to above case are shown in Fig. 5 between 0. and 0.4 s. The results represent the robustness o the proposed algorithm or estimating compensating current even when the supply is distorted and unbalanced. It is observed rom [8] that three cycles is the minimum time required to estimate the reerence current. But the proposed algorithm is ast enough to give the response in less than one cycle which is shown in ig. 5. V. CONCLUSION In this paper, a novel reerence current extraction method using adaptive detection algorithm is proposed which is able to extract the harmonic content rom the load current. Along with instantaneous symmetrical component method and pq theory, this algorithm is able to estimate the reerence current even with distorted and unbalanced supply, as well as the non-linear and unbalanced load. This closed loop system is independent o parameter variation and behave as a notch ilter. The proposed method is studied analytically and veriied by MATLAB/Simulink simulation environment. Finally, simulation result is given to conorm the easibility o the hardware realization. REFERENCES [1] C.K. Duey, R.P. Stratord, Update o harmonic standard IEEE-519- IEEE recommended practices and requirements or harmonic control in electric power systems, Industry Applications Society Annual Meeting,vol.2, pp , Oct [2] W. L. A. Neves, H. W. Dommel, and W. Xu, Practical distribution transormer models or harmonic studies, IEEE Trans. on Power Delivery, vol. 10, pp , Apr [] W. V. Lyon, Transient analysis o alternating-current machinery, New York, John Wiley, 1954.

6 Fig. 5. Simulation results o SAPF by proposed method