Burton T. (et. al.) Wind energy Handbook

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I ¼ S



¼ (P þ jQ)=V



(10:5)

The voltage rise in the circuit is given by IZ and so:

¼ V

þ IZ ¼ V

þ (R þ jX)(P þ jQ)=V



(10:6)

It is common for the network voltage V

to be deﬁned and the generator busbar

voltage V

to be required. V

can be obtained using the simple iterative expression:

(nþ1)

¼ V

þ (R þ jX)(P þ jQ)=V



(n)

(10:7)

where n is the iteration number.

This is a very simple form of the conventional Gauss–Seidel load ﬂow algorithm

(Weedy and Cory, 1998). Once the calculation converges an accurate solution is

obtained. More complex load ﬂow calculations may be carried out using commer-

cially available programs. These include models of transformers, with their tap

changers, and can solve large interconnected circuits in only a few iterations using

more advanced algorithms.

Example 10.1 Calculation of Voltage Rise in a Radial

Circuit (Figure 10.10)

Consider a 5 MW wind farm operating at a leading power factor of 0.98. The

network voltage (V

)is(1þ j0) per unit and the circuit impedance (Z)is

(0:05 þ j0:1) per unit on a 10 MVA base.

A power factor of 0.98 leading implies a reactive power draw of 1.01 MVAr.

Thus, following Equation (10.7), the calculation becomes

(nþ1)

¼ 1 þ (0:05 þ j0:1)(0:5 þ j0:101)=V



(n)

Source

⫽ 1 ⫹ j0 V

R ⫽ 0.05 X ⫽ j 0.1

acos 0.98 P ⫽ 0.5

Q ⫽ 0.101

P ⫽ 0.5

Figure 10.10 Example of Calculation of Voltage Rise on a Radial Circuit (All Values in Per-

unit)

CALCULATION OF VOLTAGE RISE IN A RADIAL CIRCUIT (FIGURE 10.10) 575

For the 1st iteration (n ¼ 0) assume V



(0)

¼ 1 þ j0; then V

(1)

may be calculated to be

(1)

¼ 1:0149 þ j 0 :0551

For the 2nd iter ation (n ¼ 1)



(1)

¼ 1:0149  j 0 :0551

then

(2)

¼ 1:0117 þ j 0 :0549

For the 3rd iteration (n ¼ 2)



(2)

¼ 1:0117  j0:0:0549

then

(3)

¼ 1:0117 þ j 0 :0551

and the procedure has converged.

Therefore V

¼ 1:013 per unit at an angle of 3

, i.e., the voltage at the generator

terminals is 1.3 percent above that at the source. The angle between the two voltage

vectors is small (3

The approximate calculation (V

¼ V

þ PR  XQ) indic ates a voltage V

of 1.015

per unit (i.e., a rise of 1.5 percent).

The current (I) in the circuit may be calculated from:

I ¼ S



¼ (0:5 þ j0:101)=(1:0117  j0:0551)

¼ 0:4873 þ j0:1264 per unit

jIj¼0:503 per unit

With a connecti on voltage of 33 kV the base current is given by

base

¼ VA

base

ﬃﬃﬃ

3 V

base

¼ 5 3 10

=1:732 3 33 3 10

¼ 87:5A

and so the magn itude of the current ﬂowing in the 33 kV circuit is 44 A.

The real power loss in the circuit (W)isW ¼ I

R ¼ 0:0127 per unit, or 127 kW.

The symmetrical short-circuit level at the generator, before connection of the

generators is simply:

S0 ¼ 1=jZj¼1=(0:05

þ 0:1

)

1=2

S0 ¼ 8:94 per unit or 89.4 MVA.

Once the induction generators of a wind farm are connected then they will make

576 ELECTRICAL SYSTEMS

a contribution to the short-circuit current seen by a circuit breaker as it closes on to

a fault. This is typically some ﬁve times the rating of the generator, e.g., some

25 MVA in this case. However, for a three-phase symmetrical fault the fault current

contribution from an induction machine decays rapidly and will make only a small

contribution to the fault current which must be interrupted by an opening circuit

breaker. Detailed guidance on the calculation of fault currents, including the

contribution from induction generators is given in IEC (1998).

10.4.6 Connection of embedded wind generation

Distribution utilities have an obligation to operate the electrical distribution net-

works in such a way as to provide power to their custo mers at an agreed quality. At

present, power quality require ments are based on national standards although a

common European position is emerging described in British Standard (1995b).

However, it should be noted that this document describes minimum standards of

supply which a customer may expect and is not directly applicable to the connec-

tion of embedded generation.

The main parameters relevant to the connection of wind turbines are:

slow (or steady-state) voltage variations,

rapid voltage changes (leading to ﬂicker),

waveform distortion (i.e., harmonics),

voltage unbalanc e (i.e., negative phase sequence voltage), and

transient volta ge variations (i.e., dips and sags).

Therefore consideration of whether a wind generation scheme may be connected

to a distribution circuit is based on its impact on other users of the network. Similar

considerations apply to the connection of any load. The steady-state voltage

variations are generally considered assuming conditions of minimum network load

with maximum generation and maximum network load with minimum generation.

These are rather onerous and conservative assumptions to ensure that steady-state

voltage limits will never be violated. In some cases, local agreements have been

reached between the network and generator operators so that some wind turbines

are constrained off at times of low network load or abnormal network conditions.

This then allows a larger wind farm to be connected than would otherwise be the

case. Considerations of power quality (i.e., maximum instantaneous real and

apparent power, reactive power, voltage ﬂicker and harmonics) were considered

recently by an IEC Working Party and a draft standard has now been issued (IEC,

2000b).

For wind farms of relatively large capacity connected to weak distribution

networks the calculations required can be involved. Hence some countries have

adopted an assessment approach to allowing connection based on the ratio of wind

farm capacity (in MW) to symmetrical short-circuit level, without the wind farm

connected (in MVA). This is sometimes known as the short-circuit ratio. Typical

CALCULATION OF VOLTAGE RISE IN A RADIAL CIRCUIT (FIGURE 10.10) 577

values chosen range from 2 percent–5 percent based on studies and on experience

(Gardner, 1996). However, such simple rules can be too restrictive and lead to

refusal of permission to conn ect or to excessive reinforcement of the distribution

system. Table 10.5 gives data on two large wind farms in successful commercial

operation in the UK with much higher ratios of wind farm capacity to short-circuit

level. Both wind farms have operated successfully for some years but it should be

noted that the number of turbines on each site is large and so the impact of any

individual machine is small. Also, both sites are connected to 33 kV circui ts from

which no other customers are supplied directly.

Figure 10.11 shows the calculated variation of voltage with wind farm output at

one site. The generator voltage of the turbines was 690 V and each turbine had a

local 690=33 kV transformer. The 33 kV curve refers to the voltage at the point of

connection of the wind farm to the public distribution network. With zero wind-

farm output the system voltag e is close to nominal as the distribution network is

lightly loaded. As the wind farm output increases the voltage rises but, once rated

power is reached, then the reactive power drawn by the generators increases

rapidly and so the voltage drops. At 140 percent output power the load ﬂow

calculation fails to converge indicating that the ne twork voltage is likely to collapse.

1.03

1.02

1.01

0.99

0.98

0.97

0.96

0 20 40 60 80 100 120 140 160

Wind-farm output %

Voltage per unit

33 kV

690V

Figure 10.11 Variation of Wind-farm Voltage with Output Power (Generator Voltage 690 V,

Connection Voltage, 33 kV)

Table 10.5 Ratio of Site Capacity to Connection Short-circuit Level for Two Large Wind

Farms

Site

capacity

(MW)

Number of

turbines

Voltage of

connection (kV)

Short circuit level

of connection

(MVA)

Ratio of site capacity

to short-circuit

level (%)

21.6 36 33 121 18

30.9 103 33 145 21

578

ELECTRICAL SYSTEMS

Although such overloads are unlikely on wind farms with many turbines, indivi-

dual machines can produce up to 200 percent of their rated output and so this

phenomenon of voltage instability can be signiﬁcant when considering the connec-

tion of large wind turbines to weak networks.

10.4.7 Power system studies

Power system studies are often required in order to assess the impact of embedded

wind generators on the network and to ensure that the network conditions are such

as to allow the wind gene rators to operate effectively. In the past simple manual

calculations were used but sophisticated computer programs are now available at

relatively low cost. However, considerable care is necessary when using these

programs as a number of them were designed primarily to investigate systems with

conventional generation using synchronous machines.

Load ﬂow (or power ﬂow) programs take as input the network topology and

parameters of the lines, cables and transformers. The customers’ load and gene rator

outputs are then used to calculate the steady-state performance of the network in

terms of voltages, real and reactive power ﬂows and losses. Generally a balanced

three-phase system is assumed. For wind-energy applications it is important that

the load ﬂow package includes a good model of the tap changers on the network

transformers and an effective representation of induction generators. A simple

load-ﬂow gives a ‘snap-shot’ analysis of the network but some commercially avail-

able programs allow the use of daily load and generator proﬁles to repeat the

calculations many times and so show the network performance over a period of

time.

Fault calculators use the method of symmetrical components (Wagner and Evans,

1933) to calculate the effect of short-circuits on the power system. Both balanced

and unbalanced faults may be investigated. Simple faul t calculators tend to be of

limited use when considering embedded wind generation as they often do not have

good models of the induction generators or power electronic converters. Fault

calculators give as outpu t the fault ﬂows and network voltages at particular times

after the fault is applied. Some of the more sophisticated programs use analytical

methods to estimate the decay of fault currents with time.

Transient stability programs allow investigation of how embedded wind genera-

tors will respond to disturbances on the network. A balanced network is assumed

as the calculation is bas ed on fundamental frequency phasors with an integration

algorithm to calculate how the network conditions change over time. Traditionally,

transient stability programs were used to investigate the angle stability of synchro-

nous generators and so a good model of the wind turbines is required for useful

results. In particular, the representation of induction machines in transient stability

programs is often simpliﬁed and so this class of tools is not good for investigating

voltage stability.

Electromagnetic programs are among the more sophisticated tools and unlike the

previous programs do not assume perfect, fundamental frequency waveforms.

Detailed representation of both the induction generators and power electronic

converters is possible. These programs use detailed time-domain simulations which

CALCULATION OF VOLTAGE RISE IN A RADIAL CIRCUIT (FIGURE 10.10) 579

allow reconstruction of the distorted wave forms generated by power electronic

converters as well as investigation of high-frequency transients such as those due to

lightning. They may be used to investigate almost any condition on the power

system but at the cost of considerable complexity. Electromagnetic simulations are

not routinely used for wind farm design but only to investigate particular

problems.

There are of course many more specialized calculation techniques and associated

tools including probabilistic power ﬂow, optimal power ﬂow, har monic load ﬂow

and various earthing/grounding codes. However, their use requires specialist

knowledge and so they are not in common use for small wind-farm projects.

10.5 Power Quality

Power quality is the term used to describe how closely the electrical power

delivered to customers corresponds to the appropriate standards and so operates

their end-use equipment correc tly (Dugan, McGranaghan and Beaty, 1996). Thus, it

is essentially a customer-focused measure although greatly effected by the opera-

tion of the distrib ution and transmission network. There are a large number of ways

in which the electrical supply (i.e., current, voltage or frequency) can deviate from

the speciﬁed values. These range from transients and short-duration variations

(e.g., voltage sags or swells) to long-term waveform distor tions (e.g., harmonics or

unbalance). Sustained complete interruptions of supply are generally considered an

issue of netw ork reliability rather than power quality. In the UK, complete interrup-

tions lasting more than 1 min are recorded and used as one indicator of the quality

of supply, as distinct from power quality, provided by the distribution utility. The

growing importance of power quality is due to the increasing use of sensitive

customers’ load equipment including co mputer-based controllers and power elec-

tronic converters as well as the awareness of customers of the commer cial con-

sequences of equipment mal-operating due to disturbances originating on the

power system.

The issues of power quality are of particular importance to wind turbines as

individual units can be large, up to 2 MW, feeding into distribution circuits with a

high source impedance and with customers connected in close proximity. For

variable-speed designs, which use power electronic conve rters the issues of harmo-

nic distortion of the network voltage must be carefully considered while the

connection of ﬁxed-speed turbines to the network needs to be man aged if excessive

voltage transients are to be avoided. During normal operation wind turbines

produce a continuously variable output power. The power variations are mainly

caused by the effects of turbulence, the wind shear, tower shadow, and the

operation of the control systems. These effects lead to periodic power pulsatio ns at

the frequency with which the blades pass the tower (typically around 1 Hz for a

large turbine) which are superimposed on the slower variations caused by changes

in wind speed. There may also be higher-frequency power variations (at a few Hz)

caused by dynamics of the turbine. Variable-speed operation of the rotor has the

advantage that many of the faster power variations are not transmitted to the

580 ELECTRICAL SYSTEMS

network but are smoothed by the ﬂywheel action of the rotor. However, ﬁxed-speed

operation, using a low-slip induction generator, will lead to cyclic variations in

output power and hence network voltage.

It is essential that wind turbines do not degrade the power quality of the

distribution network as otherwise permission for their connection or continued

operation will be refused by the distribution utility. The particular importance of

the inﬂuence of wind turbines on power quality has been recognized in the creation

of an international standard (IEC, 2000b). This standard (which is presently only in

draft form) lists the following data as being relevant for characterizing the power

quality of a wind turbine:

• maximum output power (10 min average, 60 s average and 200 ms average

values),

• reactive power (10 min average) as a function of active power,

• ﬂicker coefﬁcient for continuous operation as a function of network source

impedance phase angle and annual average wind speed,

• maximum number of wind turbine starts within 10 min and 120 min periods,

• ﬂicker step factor and voltage step factor at start-up as a function of network

source impedance phase angle,

• harmonic currents duri ng continuous operation as 10 min averages for each

harmonic up to the ﬁftieth.

It is general experience that the main power quality issue when conn ecting wind

farms with a large number of generators (.10) is steady-state voltage rise while for

individual large turbines on weak networks the limiting factor is often transient

voltage changes. Power quality is an important consideration in the design and

development of new large wind turbines and is one factor in the increasing

popularity of variable-speed operation and ‘active stall’ control as both of these

features reduce the transient variations in output power.

Figure 10.12 shows a representation of how power quality issues may be viewed

with respect to wind generation. Figure 10.12(a) shows the various effects which

may be considered to originate in the transmission and distribution networks and

which can effect the voltage to which the wind turbines are connected. Voltage sags

(i.e., a decrease to between 0.1 and 0.9 per unit voltage for a period of up to 1 min

which is usually caused by faults on the trans mission/distribution network) are of

particular concern as they will cause ﬁxed wind turbines to overspeed as the load

on the generator is removed. This in turn can lead to a high demand for reactive

power which further depresses the network voltage. The depressed voltage may

also cause contactors to open and voltage-sensitive control circuits to operate.

Voltage swells (an increase in voltage over 1.1 per unit) are less common and tend

not to be a major problem for wind turbines. Ambient harmonic voltage distortion

is increasing in many power systems, due to the power supplies of TVs and PCs,

POWER QUALITY 581

and in the UK it is not uncommon to ﬁnd levels at some times of the day in excess

of that which is considered desirable by network planners (Electricity Association,

1976). Harmonic voltage distortions will lead to increased losses in the generators

of wind turbines and may also disturb the control systems and harmonic current

performance of power electronic converters. It is common practice to use power

factor correction capacitors with induction generator (ﬁxed-speed) wind turbines

and these will, of course, have a low impedance to harmonic currents and the

potential for harmonic resonances with the inductive reactance of other items of

plant on the network. Transient interruptions (caused by the use of auto-reclosure

on distribution networks) can potentially be very damaging due to the possibility of

out-of-phase reclosure on to induction generators which are still ﬂuxed, and hence

developing a voltage. It is usual to apply fast acting loss-of-mains protection against

this condition so that the turbine is isolated once the supply is interrupted.

Network voltage unbalance will also effect rotating induction generators by

increasing losses and introducing torque ripple. Voltage unbalance can also cause

power converters to inject unexpected harmonic currents back into the network

unless their design has included consideratio n of an unbalanced supply. Figure

10.13 shows the negative phase sequence equivalent circuit of an induction machine

(Wagner and Evans, 1933). It may be seen that during normal operation (i.e., when

the slip (s ) is close to zero) the effective rotor resistance to negative sequence

(unbalanced) voltages is only R

=2. Thus any small unbalance in the applied

voltage will lead to high unbalanced currents. This has been found to be a particular

problem for wind turbines connected to 11 kV distribution networks in the UK. It is

common on rural 11 kV public supply networks to connect transformer s and small

spur lines between two phases only to supply farms and other small loads. These

single-phase connections tend to unbalance the voltages (up to 2 percent voltage

Network

Wind

turbine

Wind

turbine

Voltage sags/swells

Harmonic voltage

distortions

Voltage unbalance

Transient interruption

Harmonic currents

Unbalanced currents

Reactive power (⫹/⫺)

Flicker

Fault-level contribution

Active power

(a)

(b)

Figure 10.12 Origin of Power Quality Issues

582

ELECTRICAL SYSTEMS

unbalance is not uncommon) and so generate high unbalanced currents (up to

15–20 percent) in wind turbines connected to the main 11 kV three-phase circuit.

The wind-turbine control systems will detect excessive unbalanced current and

cause a shut-down. Nuisance tripping often occurs in the night when heating loads

in the farms are switched in automatically to take advantage of reduced price

electrical energy tariffs.

Figure 10.12(b) indicates how an embedded wind generator might introduce

disturbances into the distribution network and so cause a reduction in power

quality. Thus, a variable-sp eed turbine using a power electronic converter may

inject harmonic currents into the network. Similarly, unbalanced operation will lead

to negative phase sequence currents being injected into the network which, in turn,

will cause network voltage unbalance. As has been discussed earlier, variable-speed

wind-turbine generators can either produce or absorb reactive power while export-

ing active power and, depending on the details of the network, load and generation,

this may lead to undesirable steady-state voltage variations. Voltage ﬂicker refers to

the effect of dynamic changes in voltage caused by blade passing or other transient

effects. Fixed-speed wind generators will increase the network fault level and so

will effect power quality, often to im prove it. There is considerable similarity

between the power quality issues of wind turbines and large industrial loads and,

in general, the same standards are applied to both.

There is extensive literature on power quality of wind turbines (Heier, 1998). Fiss,

Weck and Weinel (1993) wrote an important early paper setting out the policy of

the North German utility Schleswag at that time. Rather than carry out individual

studies on each proposed installation Schleswag applied the following rules for

connection based on short-circuit level.

For voltage change:

WKA



KSS



For voltage ﬂuctuation

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

WKA



⫺R

(1⫺s)/(2⫺s)

Figure 10.13 Negative Phase Sequence Equivalent Circuit of an Induction Machine (s ¼ slip

(negative for generator); R

¼ stator resistance; jX

¼ stator reactance; jX

¼ magnetizing

reactance; jX

¼ rotor reactance (referred to the stator); R

¼ rotor resistance (referred to the

stator))

POWER QUALITY 583

For light ﬂicker

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

WKA



where S

WKA

is wind generator apparent power, P

WKA

is wind generator real power,

is short-term ﬂicker severity, S

is short-circuit level at connection point, and

KSS

is short-circuit level at MV transformer station busbar.

The limit on the voltage change was based on the impedance of the circuit

between the point of connection and the MV transformer busbar together with the

apparent power of the wind-turbine generators. The voltage ﬂuctuation limit was

simply based on the root of the sum of the squares of the short-circuit ratio of the

wind turbines while light ﬂicker limit was the same calculation but with the value

of P

measured for that type of wind turbine included. Simple rules such as these

are now of historical interest only but they do serve to illustrate the dominan t

inﬂuences on aspects of power qua lity.

Davidson (1995, 1996) carried out a comprehensive, two-year, measurement

campaign to investigate the effect of a wind farm in Wales on the power quality

of the 33 kV network to which it was connected. The 7.2 MW wind farm of

24 3 300 kW ﬁxed-speed induction generator turbines was connected to a weak

33 kV overhead network with a short-circuit level of 78 MVA. Each wind turbine

was a WEG MS3-300 which are two-bladed, pitch-regulated machines with a

teetering hub. A pole amplitude modulated (PAM) induction machine was used to

give a rotor speed of 32 r.p.m. in low winds and 48 r.p.m. in high winds. An anti-

parallel thyristor soft-start unit was used to connect each generator to the network

and power factor correction capacitors were connected to each unit once the turbine

started generating. Each wind turbine fed the wind-farm electrical system via a local

0:66=11 kV transformer. Power was collected by two undergrou nd cable feeders

and passed to the 33 kV network via a conventional 11=33 kV distribution transfor-

mer with an on-load tap changer. The wind turbines were located along a ridge at

an elevation of 400 m in complex upland te rrain and so subject to turbulent winds.

Measurements to assess power quality were taken at the connection to the distribu-

tion network and at two wind turbines. The results are interesting as they indicate a

complex relationship of a general improvement in power quality due to the

connection of the generators, and hence the increase in short-circuit level, and a

slight increase in harmonic voltages caused by resonances of the generator wind-

ings with the power factor correction capacitors.

The operation of the wind farm raised the mean of the 33 kV voltage slightly but

reduced its standard deviation. This was expected as, in this case, the product of

injected active power and network resistance was approximately equal to the

product of the reactive power absorbe d and the inductive reactance of the 33 kV

connection. The effect of the generators was to increase the short-circuit level and so

reduce the variations in network voltage but with little effect on the steady-state

value. The connection of increasing numbers of induction generators caused a

dramatic reduction in negative phase sequence voltage from 1.5 percent with no

generators conn ected to less than 0.4 percent with all generators operating. This

584 ELECTRICAL SYSTEMS