Artificial Intelligence in Power System Optimization

CHAPTER

6

OPTIMAL REACTIVE POWER

DISPATCH

*

6.1 INTRODUCTION

Reactive power (or reactive volt-amperes) is a specifi c phenomenon occurring in

an alternative current (AC) system. This kind of power does no real work for the

electricity consumers but plays a very important role in power system engineering.

Since the impedances of the network components are predominantly reactive, the

transmission of real power requires a difference in voltage phase angle between

the sending and receiving points, whereas the transmission of reactive power

requires a difference in voltage magnitudes of these two adjacent buses, which

are usually restricted to a 5-percent margin. Hence, to stay within the voltage

limits, transmission of reactive power doesn’t reach very far and is regarded as

local [1].

Reactive power is consumed not only by most of the network elements which

are passive but also by most of the consumer loads, predominantly caused by

induction motors [2, 3]. So, reactive power must be supplied somehow, either by

passive or active elements at power systems.

Overhead lines, depending on the load current, either absorb or supply reactive

power. At loads transmitted along the line below the natural (surge impedance)

load, lines produce net reactive power; at loads above the natural load, lines absorb

reactive power (see 6.2.1.A). Underground cables, owing to their high capacitance,

have high natural loads; they are always loaded below their natural loads, and

hence generate reactive power under all operating conditions [2]. Transformers

always absorb reactive power regardless of their loading; at zero load, the shunt

magnetizing reactance effects predominate while at full load, the series leakage

inductance effects predominate [2].

*This chapter has been written with assistance from Chira Achayuthakan

318 Artifi cial Intelligence in Power System Optimization

Compensating devices, which are active elements, are usually added to supply

or absorb reactive power and thereby control the system voltage in the desired

manner balancing reactive power. This chapter begins with the discussing the

essence of reactive power in power systems and continues with optimal reactive

power dispatch methodologies: in both conventional and deregulated electricity

markets.

6.2 REACTIVE POWER IN POWER SYSTEMS

In the context of power systems, transferring power from sources to loads makes

the passive elements of the network either consume reactive power from or inject

it into the system which is also the case with parts of the load themselves. With the

restriction of reactive power to travel from afar sources, compensation of reactive

power to such passive elements or reactive loads highly depends on local reactive

sources. As the reactive compensation requirements change over time, the reactive

devices should be controllable—so called active elements.

6.2.1 Reactive Power with Passive Elements

For power system analysis, most of the passive elements in a network are modeled

by admittance matrix. The simple network model of a two bus system may help

understand the phenomena of reactive power fl ow in a passive network system.

This section explains some key terms of surge impedance load (SIL) and steady

state voltage stability.

A. Surge Impedance Load (SIL)

The fundamental concept of SIL or natural load can be found in many textbooks

[2, 4, 5, 6]. SIL is a conventional analytical model explaining the reactive power-

related system characteristics. The term SIL is usually reserved for the special case

of lossless line [6]. SIL can be formulated as V

2

/Z

0

, where V is the rated voltage, Z

0

=

BX /

(pure resistive), X is the line reactance and B is the line susceptance, see

Fig. 6.1. Most approaches deriving SIL involve an ordinary differential equation.

Put in simple terms, it means that SIL is critical dependent on the load side when

production of reactive power equals consumption, V

2

B = I

2

X, and that Z

0

= V/I

=

BX /

[4]. In this case, the load level constituting a balance of inductive and

capacitive effects (netted out) is called SIL [7]. Firstly, SIL cancels out reactive

power required by the network, secondly, voltage and current profi les become

uniform (fl at) along the line [4]. A uniform voltage profi le is especially desirable

as it allows the voltage to be held near the maximum value.