The paper deals with AC substation inverter control for power quality improvement in high speed railways. The advanced substation configuration, alrea... Inverters - Voltage control - Substations - Control systems - Rail transportation - Power harmonic filters - Power quality - invertors - nonlinear control systems - power factor - power supply quality - power system control - railways - substations - traction power supplies - variable structure systems - AC electrified transportation systems - AC substation inverter control - power quality improvement - high speed railways - parameter identification - two-phase inverter - nonlinear control system - variable-structure control system - single-phase AC-supply railways - constant load voltage - power factor - numerical simulations - Power Quality - Railway Systems - Kalman Filter

0 downloads 181 Views 467KB Size

No documents

Substation Inverter Control for AC Electrified Transportation Systems L. Battistelli, D. Proto Department of Electrical Engineering, Università degli Studi di Napoli Federico II, Naples (Italy)

voltage and current unbalances have been solved either by duly distributing on the three primary phases the total power of single-phase transformation groups of the traction substations, or else by using substations with phase-transformation methods. Both the solutions are aimed at obtaining an uniform distribution of the traction power on the three phases of the network. However, the main drawback of the above techniques is that the perfect compensation is gained only for specified load conditions. Other significant PQ problems in the AC single-phase traction systems are caused by current and voltage harmonics and interharmonics due to the onboard locomotive converters. In this case passive filters are commonly used for the reduction of the harmonic contents to acceptable levels. However, the filtering action becomes very difficult when there is a rapid change of loads as usually happens in case of traction loads. In order to overcome the Power Quality problems described above a two-phase compensator has been proposed by the authors in [1], able to counteract both the unbalances and harmonics. The basic configuration is shown in Fig. 1.

Abstract-- The paper deals with AC substation inverter control for Power Quality improvement in high speed railways. The advanced substation configuration, already proposed by the authors in previous publications, has been further improved with reference to compensator configuration, inverter control and parameter identification. The configuration is based upon a two-phase inverter, employing modular topology, with nonlinear and variable-structure control system. This solution shows a great ability in single-phase AC-supply railways for obtaining full compensation of load unbalances, constant load voltage, satisfactory power factor and reduction of both disturbances and nonlinear-load effects. The performances highly depend on both the inverter control and selection of the parameters. In this paper, useful considerations are performed, allowing to fully accomplish the Power Quality requirements. Numerical simulations have been performed for demonstrating the feasibility and the efficiency of the compensator action. Index Terms-- Power Quality, Railway Systems, Kalman Filter.

I. INTRODUCTION Single-phase AC Traction Systems can cause Power Quality disturbances in the three-phase supply network. The effects of those disturbances could compromise the operation of both the railway system and the feeding electrical network. With reference to the railway operation, harmonic distortions can cause interference with signalling systems so rendering the effects more dangerous especially when dealing with high speed railways due to the high levels of the traction power. With reference to the three phase power system operation, two main problems arise due to the connection of traction systems: 1. voltage unbalances at fundamental frequency, as a consequence of different active and reactive phase-powers absorbed at substation terminals; 2. voltage and current distortions, due to the AC traction locomotives which use controlled-converters. In particular in AC traction systems the overhead line is fed by electrical substations directly connected to the three-phase power supply. These substations are equipped with single-phase transformers with the primary windings connected to two generic phases of the system. This connection determines current unbalances and, hence, voltage unbalances in the three phase supply network voltages with well known harmful consequences on the other loads connected to that network. Usually, the problems related to the compensation of

978-1-4244-1664-6/08/$25.00 ©2008 IEEE

Main threephase power transformer Intermediate voltage level

60 kV

Two-phase inverter

Traction transformer 25 kV

Traction load

Traction load

Fig. 1 Substation system scheme

The solution proposed in [1], however, has to face with the complex problem of high frequency switching of high current levels. In this paper the solution proposed in [2], which is essentially based upon a number of parallel connected converters, is applied to for railway applications. These converters are controlled adequately for ensuring a balanced current sharing among them. Another difficulty to overcome is the need to realize the dc capacitor voltage equalization, since dc voltages unbalance could occur during transient

1038

LfA,1 ifA,1 Lt

ifA,n Inverter 1

Inverter n

Rt

LfA,n ic,A

uA,1 C1

Lch

Cf

uA,n

Vdc,1

Rch C1

eA

iA’

Vdc,2

IB’

Cf

uB,n

eB ic,B

uB,1 LfB,n

ifB,1 ifB,n

Lt

Rt

LfC,1

Fig. 2. Equivalent circuit diagram of substation

conditions or as a consequence of asymmetrical circuit configuration. The equalization is ensured by a dc-dc converter circuit [3]. Furthermore, a simpler dc section control is proposed aimed at avoiding the crucial identification of the traction load current. The new inverter control leads to a full compensation of the PQ problems, being wholly independent from the loads. Moreover, since the compensator performances highly depend on the selected parameters, an accurate choice of these last has been performed based on a trial and error approach. Computer simulations have been performed in order to evidence the effectiveness of the compensation action. The results of the numerical applications demonstrate the feasibility of the proposed solution. II. COMPENSATOR CONFIGURATION The proposed electronic compensation device is a twophase inverter, based on a convenient number of parallel connected converters with a non-linear and variable structure control system. The two-phase topology allows to reduce the number of power semiconductors with respect to the solution employing six-switch bridge voltage-source inverters so implying both a cost reduction and a reliability increase. The modular configuration is intrinsically a way for solving the difficulties related to the high frequency switching of high current levels. Once this configuration has been assigned, the various modulus have to be controlled adequately for guaranteeing a balanced current sharing among them. The rationale behind this configuration is the inverter ability in distributing the electrical powers among the various circuits according with balance and power factor correction requirements. The proposed control system is developed on two different time scales, corresponding to two different dynamic modes [1-4]. The former “fast” regulation refers to the problem of stabilizing load voltages, by generating sinusoidal waveforms with opportune amplitude and constant frequency equal to the network frequency. The latter “slow” regulation refers to the active power

control. More specifically, with reference to steady state conditions, the inverter must not exchange active power with the traction loads, so that only the AC supply network furnishes the active power required by the traction loads and the active power needed to compensate inverter losses. In other words, the control system slowly “adapts” the phase angles α between the inverter output voltages and the network side line-to-line voltages. Having this in mind, two capacitors at the d.c. side of the inverter are foreseen, whose voltage mean value has to be controlled. The equalization of the two dc voltages Vdc,1 and Vdc,2 are ensured by a dc-dc converter circuit [3]. The controlled system is regarded as a two-phase system whose first subsystem (A) is supplied by the lineto-line voltage eab and the second one (B) by ebc. The twophase inverter generates the two voltages uA and uB, whereas a Lf-Cf filter is arranged at the inverter output for each phase. It is easy to show that, for a given phase angle α between the voltage of each inverter phase and the network one, assuming inverter losses as negligible, the network will supply the whole power absorbed by loads PA e PB; the compensator delivers no active power, when the following condition is satisfied:

α A = αB = α* = = β − ar cos( PA + PB +

2 U Cref Rt

Z t2

)

Zt EU Cref

(1)

where Zt is the transformer equivalent impedance, β = arctan( X t / Rt ) is the internal angle of the transformer impedance. UCref is the reference voltage rms value, evaluated in order to vanish the reactive power supplied by network. More specifically, the reactive power supplied by network vanishes when the following condition is satisfied: U = U c,ref =

EX t Rt senα + X t cosα

(2)

If the power factor correction has to be guaranteed only at the intermediate voltage level, the following condition maintains:

1039

U = U c ,ref = E cos α −

ERt senα Xt

(3)

Naturally, in order to guarantee that voltage is within an admissible range, the following constraints are required: (4) U c, min ≤ U c, ref ≤ U c, max As previously outlined, a further regulation has to be designed for guaranteeing the constancy of the mean value of the capacitor voltage on the D.C. section. The variation law of the dc capacitor voltages C1 mean value, can be easily expressed as functions of the conduction state of the semiconductor devices, depending on the sliding control technique. A further simple PI control is foreseen for ensuring the constancy of the dc voltage, avoiding the estimation of load power:

α = k p (vcrif − vc ) +

kI (vcrif − vc ) . s

(5)

The system of Fig.2 can be described by the following equations, where for notation clarity, the voltages eab and ecb will be respectively written by eA and eB:

d d e j = 2 Lt i j + 2 Rt i j + ucj + Lt ik + Rt ik dt dt

icj = C f

d i fj ,h + ucj dt

d ucj dt

h = 1,......., n j , k ∈ { A, B}

(6)

k≠ j

n

i j + ∑ i fj ,h = i 'j + icj h =1

For sake of clarity, the mathematical description is carried out with respect to a single module, being immediate the extension to n modules. By defining the state vector x j = (u& cj , u cj )T the mathematical model of the system can be expressed as follows: (7) x& j = A j x j + B j u j + B dj d j where: ⎡1 ⎤ ⎡0 c 2 j ⎤ ⎡c 3 j ⎤ Aj = ⎢ ⎥ B j = ⎢ 0 ⎥ B dj = ⎢0⎥, j ∈ {A, B} 1 0 ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ and: ⎛ 1 1 ⎞⎟ 1 c 2 j = −⎜ + c = , j ∈ {A, B} ⎜ L f C f 2 Lt C f ⎟ 3 j L f C f ⎝ ⎠ dj =

ej 2 Lt C f

−

Rt 1 d ' 1 d Rt ij − ij − ik − ik j Lt C f C f dt 2C f dt 2 Lt C f

∆=

S1 (v'c2 −ueq2 ) 4 f c L f C f v 'c

(8)

where fc is the commutation frequency and v’c= vc/2. Naturally, the maximum value of switching frequency is obtained for ueq = 0:

III. MATHEMATICAL DESCRIPTION OF THE SYSTEM

u fj = L f ,h

The quantities dj could be considered as disturbances. The following description is very interesting because it suggests to control the two legs independently each other, whereas the interacting terms are included in dj. Moreover, since the system satisfies the matching conditions, i.e. dj is in the subspace spanned by Bj, the sliding mode is invariant with respect to dj. The controlled system performances are heavily affected by the parameter selection. The choice of them is quite difficult, this requiring to satisfy the inequalities related to the equivalent control existence and the maximum value of the switching frequency. Besides, the equivalent control and the switching frequency are related by the hysteresis band by the expression:

f c max =

S1v'c 4∆L f C f

(9)

The hysteresis band ∆ can be easily deduced, once the other parameters are known. A dynamic optimization should be performed, since the controller exhibits an intrinsic discontinuous dynamics. Hence, a trial and error procedure is implemented in order to evaluate the trajectory sensitivity of the interest variables, obtaining suboptimal values of the design parameters. In the case of n modules, the further control objective of balanced current sharing among parallel connected inverters has to be taken into account. This can be efficiently made by properly defining the sliding surface in the state space. More specifically once this sliding surface is reached, the balanced current sharing is automatically guaranteed [2]. IV. CONTROL ARCHITECTURE The control depends on the equivalent quantity E which is a power signal usually corrupted with noise and disturbances, whose evaluation requires an estimation algorithm to be performed. Furthermore, Fourier fundamental angular frequency ω has to be estimated for generating the reference voltages. Under the simplifying assumption that the frequency components other than the fundamental are regarded as noise, the estimation is performed with respect to the phasor E , where the estimation algorithm provides also the estimated Fourier fundamental angular frequency ω . With no loss of generality, we consider that a single sinusoid has to be estimated e = 2 E sin( kωTs + ϕ ) , where Ts is the sampling time. The signal can be represented in the following autoregressive complex form [5]:

u j = uIj = ± vc

1040

⎡ ⎤ ⎡ δ ⎤ ⎢1 0 0 ⎥ ⎡ δ ⎤ ⎢ ξ ⎥ = ⎢0 δ 0 ⎥ ⋅ ⎢ξ ⎥ + w k k ⎢ k +1 ⎥ ⎢ 1 ⎥ ⎢ *⎥ ⎢ ⎥ ⎢⎣ξ * k +1 ⎥⎦ ⎢0 0 ⎣ξ k ⎦ δ ⎥⎦ ⎣

(10)

⎡δ ⎤ 1⎤ ⎢ ⎥ ⎡ 1 z k = ⎢0 − ⎥ ⋅ ⎢ξ k ⎥ + vk 2⎦ * ⎣ 2 ⎢⎣ξ k ⎥⎦

(11)

where:

A critical case is investigated referring to a fast traction loads change, where the compensator is requested to balance the power. Initially, the single traction load PA=3 MW is supplied; hence at t = 0.7 s the load PB=9 MW is inserted. For both the loads an harmonic content is added, in order to verify also the filtering action of the compensator. As it can be easily observed by examining the Fig.4, the equivalent control, expressed in normalized form

δ = e j ωT ξ k = 2 E e j ( kωT +ϕ ) ; s

s

ξ k* = 2 E e − j ( kωT +ϕ ) ; w k = combination of white noise and harmonics; z k = measurement data; vk = measurement noise. s

wK and vK are uncorrelated Gaussian white noise sequences with zero means [6]:

[

]

[

]

⎧R E v k viT = ⎨ k ⎩0

i=k i≠k

u eq , A / vc' , is constrained in the range [-1,1]. The delay angle, allowing to stabilize efficiently dc voltage, is reported in Fig.5. Fig.6 shows the full balanced network currents. 0.8

i=k

0.6

i≠k

0.4

The state variable vector is estimated by the Kalman filter equations. The control scheme is shown in Fig. 3. α

PI control

1

(12)

Voltage references

ucref,A ucref,B

Sliding mode control

ueq,A [p.u.]

⎧Q E w k wTi = ⎨ k ⎩0

TABLE I SIMULATION PARAMETERS I5,A [A] 7.5 I7,A [A] 5.3 I5,B [A] 22.5 I7,B [A] 15.8 100 C1 [µF] Lf [H] 0.3 3.7 Cf [µF] fcmax [kHz] 1.5 S1 [s] 0.001

0.2 0 -0.2 -0.4

ucA

-0.6

ucB

-0.8

vc

Vcref

-1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.2

1.4

t [s]

Ê

Inverter, filter, chopper.

ƒ

Fig. 4: Equivalent control. 0.14

Estimation

Supply system

0.12

0.1

V. NUMERICAL APPLICATIONS

0.08

The performed numerical application aims at highlighting the effectiveness of the whole system control technique. The selection of the various parameters have been made in order to satisfy the various constraints and in particular with respect to the equivalent control. The rated power of the main three-phase transformer is An=15 MVA, whereas the secondary rated voltage (intermediate voltage level) is equal to 60 kV. The parameters relative to the simulations are reported in Table 1 and they are referred to the base voltage equal to 60 kV.

1041

α [rad]

Fig. 3. Control scheme.

0.06

0.04

0.02

0

0

0.2

0.4

0.6

0.8 t [s]

Fig. 5: Delay angle.

1

1 0.8 0.6

ia, ib, ic [p.u.]

0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 1.38

1.382 1.384 1.386 1.388

1.39 t [s]

1.392 1.394 1.396 1.398

1.4

Fig. 6: Network currents.

VI. CONCLUSIONS A novel configuration of AC railway substation is analyzed. The proposed solution is based upon a twophase inverter, employing modular topology, with nonlinear and variable-structure control system. This solution shows a great ability in obtaining full compensation of various Power Quality disturbances. The numerical application performed has confirmed the validity of the proposed control architecture. REFERENCES [1] L.Battistelli, D.Lauria, D.Proto: Two-phase controlled compensator for alternating current quality improvement of electrified railway systems, IEE Proc.-Electr. Power Appl., Vol. 153, No. 2, March 2006 pp.177-183. [2] A.Griffo, D.Lauria: Two-Leg Three-Phase Inverter Control for STATCOM and SSSC Applications, IEEE Transactions on Power Delivery, Volume 23, Issue 1, Jan. 2008 Page(s):361 - 370 [3] M.K.Mishra, A.Joshi, A. Ghosh: Control schemes for equalization of capacitor voltages in neutral clamped shunt compensator, IEEE Transactions on Power Delivery, Vol. 18, N.2, 2 April 2003. [4] L.Battistelli, D. Lauria, P. Vernillo: Control strategy of advanced 25 kV- 50 Hz electrified railway systems, IEE Proc. –Electr. Power Appl., Vol. 148, No.1, January 2001, pp. 97-104. [5] P.K.Dash, R.K.Jena, G.Panda, and A.Routray: An extended complex Kalman filter for frequency measurement of distorted signals, IEEE Trans. Instrum. Meas., 2000, 49, (4), pp. 746–753 [6] A. Papoulis: Probability, random variables, stochastic processes, (McGraw–Hill, New York, 1991, 3rd edn.).

1042