A new control system methodology for high voltage links · A new control system methodology for...

A new control system methodology for high voltage links

V. Vita, P. Kyrtsopoulos, A. Goutis, D.I. Karvouniari, L. Ekonomou

A.S.PE.T.E. - School of Pedagogical and Technological Education, Department of Electrical Educators,

Ν. Ηeraklion, 141 21 Athens, Greece

e-mail: [email protected]

Abstract: Constant current (CC) control at the inverter and minimum ignition angle (MIA) at the rectifier is

proposed for HVDC links supplying weak AC systems. This type of control enhances the voltage stability at

AC/DC interconnections, a factor crucial for the operation of the HVDC links. In order to compare the

proposed method with the conventional control system, where the CC is on the rectifier and the constant

extinction angle (CEA) is on the inverter, the “Voltage Sensitivity Factor” (VSF) is calculated in both cases

for a characteristic integrated AC/DC test system. The advantage of the proposed control scheme is proved

by the graphical representation of the VSF in all the steady state operational points and the detailed

simulation of the test system response.

Key-Words: HVDC links; Voltage Sensitivity Factor, Minimum Ignition Angle; Constant Current Control.

1. Introduction

High voltage direct current (HVDC) links use

modifiers where the fundamental alternating

current component (AC) always delays in relation

to the modifier’s connector voltage component

(AC). That leads to the absorption of reactive

power by the modifier, proportional to the real

power and reaches up to 60 % of the real power at

steady state operation. In most cases, the AC

system does not obtain the ability to supply that

amount of reactive power, without its voltage to

sink to impermissible low levels.

For the evasion of such cases, modern

compensators or compensation capacitors are used,

that are also utilized as harmonic filters. However

in these cases, a sudden imbalance of the reactive

power at the converter, involves big voltage

fluctuations. Overvoltage is usually important

factor for the design of converter appliances and

can lead to impermissible expensive converter

manufactures, in case no measures for their

restriction are taken [1].

Problems such as: transient overvoltage, low

frequency resonance, dangers of instability of

voltage/power, extended time of re-operation and

high probability of transfer failure, are especially

intense in direct current links, which supply weak

AC systems. Because of the importance of these

problems, international organisms such as CIGRE

and IEEE have created special teams of work that

deal with them. The most important, is the problem

of AC voltage stability at the modifier that

influences considerably, not only the total link

cost, but the response as well [2].

Connection of modern compensators in order to

increase the resistance of the bus bar in case of

short-circuits is a solution to the mentioned

problems. However this solution is uneconomic,

has big losses and has slow response compared to

other static methods. Alternative solution is the

reactive compensation adjustment with static

voltage compensators (SVC), such as inductions

regulated by thyristors, capacitors connected with

thyristors or combination of the two methods. In

this case, as long as the SVC are of suitable size,

the problems of voltage stability can be eliminated

in steady state as well as in transient state.

The most economic and reliable solution is the

modifier’s absorbed reactive power regulation in

relation to voltage (AC) variations. This process is

achieved through supervisory control systems that

act on the link’s basic control systems.

In this paper, the link’s basic control system

exploits this attribute at the modifier. The modifier

supplies the weak AC system where the most

significant voltage problems appear. Specifically,

an AC voltage dump leads to rapid increase of the

constant current (CC) and the inverter operating

with CC control increases rapidly the ignition

angle delay. This leads to inverter’s direct voltage

increase and direct current restriction, as well as to

Proceedings of the 9th WSEAS/IASME International Conference on ELECTRIC POWER SYSTEMS, HIGH VOLTAGES, ELECTRIC MACHINES

ISSN: 1790-5117 196 ISBN: 978-960-474-130-4

the modifier’s absorbed reactive power reduction

and increment of the AC voltage at the bus bar.

The rectifier, operating with Minimum Ignition

Angle (MIA), determines the final direct voltage at

the link [3].

In order to evaluate the effectiveness of the

proposed control method in resolving the AC

voltage control problem, the Voltage Sensitivity

Factor (VSF) is calculated, at all parts of operation

for a characteristic integrated AC/DC test system.

VSF is used because it is evaluated as a very

reliable voltage stability indicator, as it takes the

control system, the reactive power/ voltage of the

AC system, the output and the system’s load into

consideration.

In order to obtain a more explicit behavior analysis

of the controlled system, the system’s response is

recorded with the help of a digital simulation

program. Then the system’s response is compared

with the conventional control response.

2. Proposed control system and

electrical test system

For HVDC links, constant current (CC) control at

the inverter and minimum Ignition Angle (MIA) at

the rectifier is proposed. This control method is

compared with the conventional control system,

where the rectifier is under constant current control

and the inverter operates under constant extinction

angle (CEA). In Figs 1 and 2, the combined

operating characteristics of both methods are

shown.

Figure 3: The integrated AC/DC test system

Figure 1: Combined HVDC links operating

characteristics: Conventional control method.

Vd

cc cc

Id

RectifierInverter

MIA CEA

Figure 2: Combined HVDC links operating

characteristics: Proposed control method.

Both, the proposed as well as the conventional

control method are applied to an integrated AC/DC

electrical test system.

Filters

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ISSN: 1790-5117 197 ISBN: 978-960-474-130-4

In order to evaluate the prospects as well as the

advantages and disadvantages, the test system does

not have any local production at the inverter’s side

and moreover a modern compensator, in order to

stabilize frequency, is used [4].

The system is classified as a “weak” system, due to

its 1.65 “short circuit rms ratio”. In Fig. 3, the

integrated AC/DC test system, a strong system at

the rectifier’s side, is shown.

3. Voltage Sensitivity Factor (VSF)

One of the most significant problems of HVDC

links, that supply “relatively weak” AC systems, is

the voltage fluctuations. In order to evaluate the

severity of those voltage fluctuations, the short

circuit ratio is used (short circuit ratio equals the

system’s resistance to short-circuit, at the

modifier’s side over the nominal power of HVDC

links). This simplified method does not take the

voltage/reactive power characteristics, the link’s

control system and the reactive power

compensation method into consideration [5].

The Voltage Sensitivity Factor (VSF) at the

terminal stations of HVDC links can be defined in

the same way as the “voltage stability” of AC links

for different charge levels and power factor. Due to

complexity of such links, it is more convenient to

define voltage stability for small fluctuations

around the operating point. Hence, the VSF could

be defined as the per unit AC voltage difference

for each per unit reactive power difference

supplied to the HVDC link modifier, i.e.:

Q∆

∆=

VVSF (1)

VSF is positive for stable systems and negative for

unstable systems in terms of voltage. Voltage

fluctuations are proportional to VSF, meaning that

a high positive VSF denotes large transient.

4. Computation of the Voltage

Sensitivity Factor (VSF)

All the equations of the modifier and the AC

systems become linear, around a nominal operating

point, in order to compute VSF. VSF emerges from

the elimination of all independent variables. In Fig.

4, a general inverter’s busbar type supplying weak

AC current is shown.

d refers to inverter’s variables, a refers to weak AC system’s

variables, in which the compensation systems (e.g. modern

compensators, capacitors) and the inverter’s filters are

included.

Figure 4: Busbar of AC inverter.

The total reactive power fluctuation at the busbar

is:

(2)

By substitution of (2) in (1):

(3)

5. Computation of reactive power/

voltage characteristic curves

The ratio, for an AC system with n bus bars,

is computed with the help of the static load flow

equations. The AC system’s load flow at the

busbars is expressed in terms of voltage amplitude

and angle. (Vi<δi and i=1,2,……..,n)

(4)

where:

∆P, ∆Q, ∆δ, ∆V are vectors of nx1 dimension.

J is the Jacobian matrix of 2nx2n dimension.

The Jacobian matrix is irreversible as one of its

columns is linearly dependent from the others. By

eliminating both row and column that corresponds

to real power and busbar’s voltage angle, the


ISSN: 1790-5117 198 ISBN: 978-960-474-130-4

Jacobian matrix becomes Jt of (2n-1)x(2n-1)

dimension and reversible.

(5)

A small reactive power shift ∆Qa at the inverter’s

busbar j (Fig. 3) will lead to a voltage amplitude

shift ∆V. ∆V can be computed with the help of (5),

where the power Pa of busbar j is regarded as

stable and all ∆Pi and ∆Qi of the rest busbars are

regarded as zero. Hence:

where:

refers to the (j, j) element of

matrix.

For every HVDC link modifier, the steady state

linear basic equations are:

(7)

where:

∆y=[∆Vd ∆Ιd ∆φ ∆V ∆α]Τ,

φ is the power angle,

α is the ignition angle,

∆u=[∆Pd ∆Qd],

A is a 4x5 dimension matrix and

B is a 4x2 dimension matrix.

In order to calculate one more equation is

required so as the A matrix becomes rectangular

and invertible. This equation emerges from the

HVDC link’s control method. For the proposed

control method, where the inverter is under

constant current control CC, the linear control

equation is as follows:

(8)

where:

N is the turns ratio of the inverter’s transformer,

K is the CC graph slope and

Y0 is the minimum extinction angle.

For the conventional control method, where the

inverter operates with minimum extinction angle,

the equivalent equation is as follows:

(9)

where:

xt is the leakage inductive reactance of the

inverter’s transformer and

M is the number of 6-pulse bridge in series, that

form the inverter.

The incorporation of (8), or alternative (9) and (7),

transformation of matrix A to Matrix At of 5x5

dimension and Matrix B to Matrix Bt of 5x2

dimension and setting ∆Pd=0, lead to the following

equation:

(10)

6. Voltage sensitivity curves -

Steady state evaluation of the

proposed control method

By applying (3), (6) and (10) in the (Fig. 2)

electrical system, the VSF can be computed, for

both the proposed and conventional control

system, at different charge levels Pd. The outcomes

are presented in Fig. 5.

After examination of Fig. 5, it is concluded that the

proposed control method constrains the AC voltage

sensitivity. This is due to its ability to constrain the

modifier’s reactive power necessitation (Fig. 6,

curves b, c, d) in comparison with conventional

control (curve a) and moreover compensation of

the system becomes more straightforward

compared to the AC system (curve e). When

compensation becomes impossible for certain Pd

value, the VSF becomes discontinuous, alters its

sign and the AC voltage becomes unstable

(asymptotic curves a and b for cases a and b). The

Pd value, at which VSF changes its sign, refers to

the maximum power transmission with stability in

steady state through the HVDC link. The proposed

method increases this static stability limit, as well

(Fig. 5). Voltage sensitivity can be constrained by

reducing the characteristic curves CC slope K (Fig.

5, curves b, c, d), but such an action reduces the

control system response speed. Therefore, K value

is chosen in such a way as to reconcile both

counter requirements.

(6)


ISSN: 1790-5117 199 ISBN: 978-960-474-130-4

a) EA inverter control and CC rectifier control

b) CC inverter control and MIA rectifier control (K=1.00)

c) CC inverter control and MIA rectifier control (K=0.70)

d) CC inverter control and MIA rectifier control (K=0.36)

Figure 5: The Voltage Sensitivity Factor (VSF).

Figure 6: Reactive power/voltage characteristic

curves.

7. Evaluation of the proposed control

method in transient state

An explicit digital simulation program records in

Figs 7 and 8 the electrical system’s (Fig. 3)

response, for a 31 % of the total system’s load

increase. Conventional control produces the

response recorded in Fig. 7, while the proposed

control method produces the response in Fig. 8.

Due to the local production lack in the AC system,

where the modifier is connected, frequency

regulation is accomplished with a supervisory

integral frequency control system for both basic

control systems

Figure 7: System response under conventional

control.

After comparison of both Figs 7 and 8, is made

obvious the contribution of the proposed control

method, in terms of voltage maintenance and


ISSN: 1790-5117 200 ISBN: 978-960-474-130-4

effective HVDC link operation, mainly in cases

where the implementation of the conventional

control method leads to system failure.

Figure 8: System response under proposed control.

8. Conclusions

Constant current (CC) control at the inverter and

minimum ignition angle (MIA) at the rectifier is

proposed for HVDC links supplying weak AC

systems. In order to prove the advantages of the

proposed control method compared to

conventional control, the Voltage Sensitivity

Factor is calculated in both cases for a

characteristic integrated AC/DC test system at all

steady state situations. Through voltage sensitivity

curves comparison, it is concluded that the

proposed control method constrains the AC voltage

sensitivity significantly, which is one of the most

significant problems of HVDC links supplying

weak AC systems. Moreover, it increases the upper

limit of power transmission with stability through

the HVDC link at steady state. Finally, the system

response for severe power fluctuations is compared

for both methods with the help of a digital

simulation program. This comparison leads to the

assumption that the proposed control method

improves the transient system response.

References:

[1] L. Wang, D.J. Lee, W.J. Lee, Z. Chen, Analysis

of a novel autonomous marine hybrid power

generation/energy storage system with a high-

voltage direct current link, Journal of Power

Sources, Vol. 185, No. 2, 2008, pp. 1284-1292.

[2] P.K. Dash, A.C. Liew, A. Routray, Design of

robust controllers for HVDC links in AC-DC

power systems, Electric Power Systems

Research, Vol. 33, No. 3, 1995, pp. 201-209.

[3] A.R. Messina, M.A. Pérez, E. Hernández,

Coordinated application of FACTS devices to

enhance steady-state voltage stability, Electrical

Power & Energy Systems, Vol. 25, No. 4, 2003,

pp. 259-267.

[4] M.N. Kumar, K. Vasudevan, Bi-directional real

and reactive power control using constant

frequency hysteresis control with reduced losses,

Electric Power Systems Research, Vol. 76, No.

1-3, 2005, pp. 127-135.

[5] W.T. Chung, A.K. David, Arresters-Buyer’s

Guide, Development of a laboratory AC-DC

simulator for on-line control study, Electric

Power Systems Research, Vol. 46, No. 1, 1998,

pp. 27-33.

Emails list:

V. Vita: [email protected]

P. Kyrtsopoulos: [email protected]

A. Goutis: [email protected]

L. Ekonomou: [email protected]

D.I. Karvouniari: [email protected]


ISSN: 1790-5117 201 ISBN: 978-960-474-130-4

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