Principles and functions of UPFC

CHAPTER

Principles and functions of UPFC

2

2.1 TECHNICAL PRINCIPLE OF THE UPFC The unified power flow controller (UPFC) realizes real-time control over power flow in transmission lines by adjusting the line parameters, including node voltages, phase angle, and line impedance, which cover all adjustable parameters of other FACTS [1]. As shown in Fig. 2.1, static synchronous compensator (STATCOM), static var compensator (SVC), phase shifters, thyristor controlled series compensation (TCSC), the short-circuit current limiter, and the UPFC adjust line parameters to control the power flow. Functions of the STATCOM, SVC, phase shifter, TCSC, short circuit current limiter (SCCL), and UPFC are listed in Table 2.1. In this chapter, the functions and principle of the UPFC will be introduced.

2.1.1 SYSTEM ARCHITECTURE OF THE UPFC Fig. 2.2 is a system configuration diagram of the UPFC, consisting of the main circuit (series unit and shunt unit) and a control unit. The main UPFC circuit consists of two VSCs (voltage-sourced converters) with a common dc-side capacitor, and these two VSCs connect to the systems via two transformers respectively: VSC 1 connects to the transmission line parallelly via transformer T1; VSC 2 connects to the transmission line serially via transformer T2. VSC 1 and transformer T1 are defined as shunt-side. VSC 2 and transformer T2 are defined as serial-side. The output voltage of the two sides can be controlled separately and independently, supplying or absorbing reactive power [2]. Active power is absorbed or emitted by the UPFC shunt VSC via shunt transformers from the connection point, and is transmitted via the DC (Direct Current) side of the UPFC and serial VSC, ultimately delivered to transmission lines via the serial transformers. Therefore, the UPFC provides an active power transmission channel for the line, enabling the total active power line transmission capacity to be increased or decreased. Reactive power exchange occurs on the UPFC shunt side and serial side, between VSC and transformer. Owing to the existence of a DC side capacitor, there is no reactive power exchange between shunt side and serial side, as shown in Fig. 2.3 UPFC power flow schematic diagram. According to this analysis, a UPFC can be regarded as parallelly composed of the DC side of a STATCOM and an SSSC (static synchronous series compensator) device, as shown in Fig. 2.4. Therefore, the UPFC device has not only the Unified Power Flow Controller Technology and Application. DOI: http://dx.doi.org/10.1016/B978-0-12-813485-6.00002-9 Copyright © 2017 China Electric Power Press Ltd. Published by Elsevier Inc. All rights reserved.

19

20

CHAPTER 2 Principles and functions of UPFC

U1∠δ1

U2∠δ2

X

System1

System 2

Static var compensator

P TCSC

X α

P=

U1U2 sin(δ1 – δ2) X

STATCOM

SCCL

Increasing impendance Normal

Fault time

. Us

UPFC

. . Uc Ur

. Ur

Phase . shifter . Uc Ur

. Us

. . Uc Us

. Ur

. Uc . Us

FIGURE 2.1 Circuit parameters control schematic diagram of various FACTS devices.

Table 2.1 Comparison of Different FACTS Devices Control Parameters and Effects Static synchoronous compensator Static var compensator Phase shifter Thyristor controlled series compensation SCCL Unified power flow controller

Control Parameter

Regulation Goal

U1 , U2 U1 , U2 δ1 , δ2 X X U1 , U2 , δ1 , δ2 , X

Node voltage Node voltage Phase angle Line impedance Line impedance All

advantages of STATCOM and SSSC, providing both strong transmission line voltage compensation ability and reactive power compensation capabilities, but also four-quadrant operating ability: absorbing or emitting not only reactive power but also active power. Additionally, the shunt portion can provide access for active power to the serial portion, which means UPFC has a throughput active power capability, hence it has a very strong ability to control the power flow [3
5].

2.1.2 THE PRINCIPLE OF THE UPFC Fig. 2.5 briefly illustrates various control functions of the UPFC. UPFC voltage regulation function is shown in Fig. 2.5(A), where UPFC series compensation

2.1 Technical Principle of the UPFC

. U2

. U1

T2 T1 Converter 1

Voltage Power

Converter 2 DC side

Phase

Control system

Impendance

FIGURE 2.2 UPFC structure diagram. . U2

. U1 T1

Q1

Q2

T2

UPFC P12

FIGURE 2.3 UPFC power flow schematic diagram.

voltages ΔU_ 0 have the same phase as U_ 0 or its opposite, only regulating the amplitude of the voltage, not changing the phase of the voltage. Owing to the flexible control of series output voltages, the UPFC can easily achieve voltage regulation. Series compensation in UPFCs is the same as general series compensation. As shown in Fig. 2.5(B), the series part has no active power exchange with transmission lines, so offset voltage U_ c should be perpendicular to the line current I._ Fig. 2.5(C) is a schematic diagram of the phase angle compensation, which changes the voltage phase angle, but does not change its magnitude. UPFC compensation voltage is on the arc shown in Fig. 2.5(C), hence, a UPFC is equivalent to a phase shifter. Fig. 2.5(D) is a schematic diagram of UPFC comprehensive functionality, integrating former three functions, which changes the amplitude and phase of the voltage according to system operation.

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CHAPTER 2 Principles and functions of UPFC

⋅ U1

⋅ U2

T2

T1 Converter 1

Converter 2 DC2

DC1

Capacitor 1 Capacitor 2 Control system 2

Control system 1 STATCOM

SSSC

FIGURE 2.4 Equivalent of STATCOM and SSSC. .

.

U&0 + ΔU&0

.

.

Uc

Uc

.

Uα

.

ΔU0

.

Uα

.

U0

.

.

U0

.

.

.

U0+Uc

U0 α

.

.

U0 + Uα

.

U0

.

.

.

.

U0 + ΔU + U0 + Uα

I (A)

(B)

(C)

(D)

FIGURE 2.5 UPFC control functions (A) Voltage regulation; (B) Series compensation; (C) Phase angle compensation; (D) Comprehensive functionality.

The UPFC parellel VSC is equivalent to a controllable current source; the series VSC is equivalent to a controllable voltage source. Ignoring the original line impedance and admittance, a UPFC equivalent circuit, as shown in Fig. 2.6, is obtained. As shown in Fig. 2.6, the node voltage of U1 is assumed as reference point of the phase, the injection current of the shunt-side VSC is Ish +αsh , and the corresponding output voltage is Ush +δsh . The output voltage of the series-side VSC is Use +δse , and current flowing through the series side is Ise +αse . Xsh and Xse are the leakage reactance formulae of shunt transformer T1 and series transformer T2 respectively. Rsh is the equivalent resistance, including the loss of VSC1 loss and

2.1 Technical Principle of the UPFC

U1∠0

Use∠δse Rse + jXse + –

U2∠δ2 Ise ∠ αse

Rsh + jXsh Ush ∠ δsh

+ Ish ∠ αsh –

FIGURE 2.6 UPFC equivalent circuit model. ⋅ U2

I&se(Rse + jXse) ⋅ Use ⋅ Ush

δ2 δsh αsh ⋅ Ish

U1

XshIsh RshIsh

FIGURE 2.7 UPFC equivalent circuit vector diagram.

transformer T1, and Rse is the equivalent resistance including the loss of VSC 2 loss and transformer T2. The voltage phasor and current phasor diagram of a UPFC equivalent circuit are shown in Fig. 2.7. UPFC power flow actual control characteristics are illustrated with the phasor diagram in Fig. 2.7. As previously described, the phasor of the compensation voltage generated by a UPFC varies in the circle whose center lies on the endpoint of U_ 1 , as shown in Fig. 2.7. To simplify the analysis, it is assumed that UPFCs change the voltage series in the grid to achieve the regulation of power flow when U_ 1 is a constant. And the shunt-side VSC is assumed to only maintain the shared DC bus voltage constant. If all the resistance loss cases are not counted, the power of the receiving end, power of the sending end, and injection power in the series side are obtained, P2 2 jQ2 5 U_ 2



 U_ 1 2 U_ se 2 U_ 2 U_ 1 2 U_ 2 U_ 1 U_ se 5 U_ 2 2 jXse jXse 2 jXse

(2.1)

23

24

CHAPTER 2 Principles and functions of UPFC



 U_ 1 2 U_ se 2 U_ 2 U_ 1 2 U_ 2 U_ 1 U_ se _ _ P1 2 jQ1 5 U 1 5 U1 2 jXse jXse 2 jXse

 2 Use U_ 1 2 U_ se 2 U_ 2 U_ 1 2 U_ 2 5 U_ se 2 Pse 2 jQse 5 U_ se jXse jXse 2 jXse

(2.2)

(2.3)

Before a UPFC is installed, the power of the receiving end is as follows. P02 2 jQ02 5 U_ 2 P01 2 jQ01 5 U_ 1





U_ 1 2 U_ 2 jXse U_ 1 2 U_ 2 jXse

 (2.4)  (2.5)

Assuming the UPFC transmission system sending-end voltage, receiving-end voltage, and compensation voltage are U_ 1 5 U1 +0

(2.6)

U_ 2 5 U2 +δ2 5 U2 ðcosδ2 1 jsinδ2 Þ

(2.7)

U_ se 5 Use +δse 5 Use ðcosδse 1 jsinδse Þ

(2.8)

and the formulae (2.6), (2.7), and (2.8) substituted for the formulae (2.1) and (2.5), the power of the receiving end of a transmission line is obtained after the installation of a UPFC: U1 U2 U2 Use sinδ2 2 sinðδ2 2 δse Þ 5 P2 ðδ2 ; δse Þ Xse Xse

(2.9)

U22 U1 U2 U2 Use 2 cosδ2 1 cosðδ2 2 δse Þ 5 Q2 ðδ2 ; δse Þ Xse Xse Xse

(2.10)

P2 5 Q2 5

The output power of the sending end is P1 5 2 Q1 5

U1 Use U1 U2 sinδse 2 sinδ2 5 P1 ðδ2 ; δse Þ Xse Xse

U1 U2 U1 Use U2 cosδ2 1 cosδse 2 1 5 Q1 ðδ2 ; δse Þ Xse Xse Xse

(2.11) (2.12)

The power of the receiving end before the intallation of UPFC is U1 U2 sinδ2 5 P02 ðδ2 Þ Xse

(2.13)

U22 U1 U2 2 cosδ2 5 Q02 ðδ2 Þ Xse Xse

(2.14)

P02 5 Q02 5

The power of the sending end is P01 5 2

U1 U2 sinδ2 5 P01 ðδ2 Þ Xse

(2.15)

2.1 Technical Principle of the UPFC

Q01 5

U1 U2 U2 cosδr 2 1 5 Q01 ðδ2 Þ Xse Xse

(2.16)

Thus, the receiving-end power of a transmission system with the UPFC compensating device is expressed as P2 ðδ2 ; δse Þ 5 P02 ðδ2 Þ 1 Pse ðδse Þ

(2.17)

Q2 ðδ2 ; δse Þ 5 Q02 ðδ2 Þ 1 Qse ðδse Þ

(2.18)

where the power change of the receiving end when the UPFC compensating device is employed is Pse ðδse Þ 5

U2 Use sinðδse 2 δ2 Þ Xse

Qse ðδse Þ 5 2

U2 Use cosðδ2 2 δse Þ Xse

(2.19) (2.20)

Supposing the maximum compensation voltage the UPFC series side can generate is Use;max , the increment of receiving-end power fulfilling the following formula:   Pse ðδse Þ # U2 Use;max Xse

(2.21)

  Qse ðδse Þ # U2 Use;max Xse

(2.22)

Thus, the receiving-end power fulfills the constraint condition below: P02 ðδ2 Þ 2

U2 Use;max U2 Use;max # P2 ðδ2 ; δse Þ # P02 ðδ2 Þ 1 Xse Xse

(2.23)

Q02 ðδ2 Þ 2

U2 Use;max U2 Use;max # Q2 ðδ2 ; δse Þ # Q02 ðδ2 Þ 1 Xse Xse

(2.24)

To further illustrate the flow control of various parts of the UPFC, the power characteristics of a UPFC with certain network parameters are drafted. Power grid parameters are assumed as follows: U1 5 U2 5 1, δ2 5 2 π=6, Xse 5 0:5 p:u:, Use;max 5 0:25 p:u:, and thus the varying range of active and reactive power could be acquired when the angle of U_ se varies in the range of 0B2π. As shown in Fig. 2.8(A) and (B), a UPFC effectively controls the transmission capacity of the line in which it is installed through the series-side voltage. If the amplitude and phase angle of the series-side voltage were adjusted, the sendingend power and receiving-end power could change within a certain range, which covers a circular area in the phasor diagram. If the amplitude of the compensation voltage is fixed, the phasor ends of sending-end inspecting power and receivingend inspecting power vary on a circumference, when δse changes in the range of 0B2π. Since the voltage a UPFC injects into the power line is mainly determined by the DC bus voltage, so for a fixed DC bus, the capacity of the UPFC to

25

CHAPTER 2 Principles and functions of UPFC

Receiving-end power

Sending-end power

0.6

0.1

0.5

0

0.4

–0.1

0.3

–0.2 Ps

Qs 0.2

–0.3

0.1

–0.4

0

–0.5

–0.1 –1.25

–1.1

–1.05

–1

–0.95

–0.9

–0.95

–0.8

–0.6 0.7

0.8

0.9

1

Pr

1.1

1.2

1.3

1.4

Ps

Series output characteristic 0.3 0.2 0.1 0 Y2

26

–0.1 –0.2 –0.3 –0.4 –0.4

–0.3

–0.2

–0.1

0

0.1

0.2

0.3

P2

FIGURE 2.8 The active and reactive power change range of the UPFC. (A) Power change range of receiving end (B) Power change range of sending end (C)Power change range of serial converter.

regulate power flow is limited. Taking into account the capacity of the UPFC inverter, the transformer, and its own ability to withstand current, the power flow regulation capacity of the entire UPFC system is less than that shown in Fig. 2.8. Fig. 2.8(C) reveals that during power flow regulation, the UPFC injects some active and reactive power into the grid. Thus the system will absorb some of the active power from the grid through the shunt VSC in order to balance the active power inside the UPFC. As shown in Fig. 2.8, when δse varies from 0 to 2π, the vectors’ phasor of receiving-end inspecting power and sending-end inspecting power rotates counterclockwise, and the vectors’ phasor of injecting inspecting power of the UPFC via the series side is in a clockwise direction.

2.2 UPFC Control Function Analysis

2.2 UPFC CONTROL FUNCTION ANALYSIS 2.2.1 CONTROL FUNCTION OF THE SHUNT SIDE The shunt-side VSC exchanges power with the transmission line via a paralled transform, thus realizing the active power transmission and reactive power compensation. The purposes of regulation include: (1) active power regulation, namely absorbing active power from the grid to compensate the active power consumed in the series side and active power loss of the whole UPFC system; (2) reactive power regulation, namely stabilizing the terminal voltage of the connection point by absorbing or emitting reactive power. In order to maintain a constant capacitor voltage in the DC side, the inflow and outflow active power of the UPFC should be equal, excluding internal losses throughout the UPFC device, otherwise the DC capacitor will continuously be charged (or discharged), which makes capacitor voltage increase (decrease). Shuntside VSC current is able to be decomposed into two parts, an active component and a reactive component. The active component supplies active power of the UPFC’s series side. In different situations the reactive component functions differently.

2.2.1.1 Reactive power control mode In the reactive power control mode, an inductive or capacitive reactive power control object in the shunt side is converted to the reference value of the reactive current, which is compared with the actual reactive current. The difference between input value and reference value of the reactive current is converted into voltage which is utilized as the input signal of the shunt VSC controller. The shunt part can emit or absorb active power in order to maintain the stability of the DC capacitor voltage and compensate active power loss inside the system.

2.2.1.2 Node voltage control mode In the voltage control mode, the shunt portion may control and maintain the voltage at the point of connection. Additionally, the shunt side functions as a STATCOM, the schematic shown in Fig. 2.9. In Fig. 2.9, the voltage at the connection point of the UPFC system is U_ 1 . U_ 1 goes through a section of the transmission line (whose impedance is R 1 jX, taking into account the ground capacitance of the transmission line) and then connects to an infinite bus system. Namely the voltage at the end of the line U_ 2 is assumed to be constant (selected as a reference phasor), and the power flow of the transmission line is P2 1 jQ2 . When the UPFC shunt side does not connect to the system and the transmission power is fixed, the voltage drop on the line will be 0 1  P 1 jQ 2 2 A 5 RP2 1 XQ2 1 j XP2 2 RQ2 ΔU 5 ðR 1 jXÞ@ U2 U2 U2

(2.25)

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28

CHAPTER 2 Principles and functions of UPFC

. U1

. U2

. I12

R + jX P2 + jQ2

R sh + jX sh

Qsh

FIGURE 2.9 Equivalent mathematical model of a UPFC in a node voltage control model. .

U1

.

jXI12 δ .

ϕ

U2

. I12

.

RI12

FIGURE 2.10 Reactive power compensation voltage and current phasor diagram.

where RP2 U12XQ2 is the real part of the voltage drop, and XP2 U22RQ2 is the imaginary part of the voltage drop. The phasor diagram of voltage and current is shown in Fig. 2.10. For a high-voltage transmission line, the imaginary part of the voltage drop XP2 2 RQ2 is negligible, as the resistance R is small enough in comparison with U2

2 inductance X. The real part of the voltage drop RP2 U12XQ2 is approximated as XQ U2 . So the voltage drop phasor can be simplified to a voltage loss scalar as follows:

ΔU 5

XQ2 U2

(2.26)

Eq. (2.26) reveals that voltage loss on the transmission line depends mainly on reactive power transmitted. When the shunt side of a UPFC (STATCOM) whose reactive power compensation is Qsh is connected to the system, the reactive power transmitted on the line is Q1 5 Q2 2 Qsh . According to Eq. (2.26), the voltage loss on the line is approximated as ΔU 5

XðQ2 2 Qsh Þ U2

(2.27)

2.2 UPFC Control Function Analysis

Adjusting the reactive power compensation Qsh can reduce the reactive power transmitted on the line Q1 5 Q2 2 Qsh , thus the voltage loss on the line will be reduced. If the compensation capacity of the UPFC shunt side is large enough to compensate the reactive power on the line, it can make the voltage loss zero.

2.2.2 CONTROL FUNCTION OF SERIES SIDE The main purpose of a UPFC is to adjust and control the power flow of the grid. The principle of the series-side converter is adding a series voltage phasor with adjustable amplitude and phase angle into the transmission line; and the voltage phasor generates a commutation or forced circulation power, which adds to and naturally distributes the power flow and achieves the desired power flow distribution. As the added series voltage can change the amplitude and phase angle of the line voltage, equivalently to adding capacitance or inductance in a series, the UPFC can control the power by changing the parameters of the transmission line. As shown in the equivalent circuit in Fig. 2.6, U_ 1 and U_ 2 are voltages at the points where the UPFC connects to the transmission line, U_ 1 at the send end and U_ 2 at the receive end; U_ sh and U_ se are the voltages of the UPFC shunt-side VSC and series-side VSC; I_sh and I_se are currents flowing through the UPFC shunt side and series side; Rsh 1 jXsh and Rse 1 jXse are equivalent impedances of the UPFC shunt VSC and series VSC. In the following discussion the loss of the device itself will be neglected, and only equivalent reactances jXsh and jXse will be considered.

2.2.2.1 Series compensation Series compensation occurs when the UPFC connects to the transmission line through the series transformer, injecting voltage U_ se perpendicular to current I_se into the system by the serial VSC. Under this circumstance, the series VSC is equivalent to an inductor or capacitor, functioning as a TCSC. Given compensation coefficient k, U_ se is U_ se 5 2 jkXse I_se

(2.28)

I_se 5 Ise +αse ; U_ se 5 Use +δse

(2.29)

U_ se 5 kXse Ise +αse 6 π=2

(2.30)

if

then when k . 0 (inductive reactance), Use 5 kXse Ise , δse 5 αse 2 π=2; when k , 0 (capacitive reactance), Use 5 2 kXse Ise , δse 5 αse 1 π=2. As shown, with a given compensation coefficient, the amplitude and phase angle of the series VSC output are determined taking account of transmission line current amplitude and phase angle. In this condition, the UPFC and the system have only reactive power exchange (no active power exchange). The corresponding phasor diagram is shown in Fig. 2.11.

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CHAPTER 2 Principles and functions of UPFC

. Use

. . U1 + Use

. . U1 + Use

. U1

. Use . U1

. Ise

. Ise

(A) K>0

(B) K>0

FIGURE 2.11 Voltage vector diagram showing series compensation under way. .

(A)

.

(B)

Use

Use

.

U1 .

.

.

U1 + Use

U1

.

.

U1 + Use

FIGURE 2.12 Voltage vector diagram with phase shift in process. (A) Advance phase shift. (B) Lag phase shift.

2.2.2.2 Phase shifting effect The UPFC phase shift effect is realized by the series-side VSC’s injecting a voltage U_ se through transformer T2. U_ 1 and U_ se superimposed generate a voltage with the same amplitude as U_ 1 and a given phase angle. The phase shift angle is δ, whose unit is rad. If

then

U_ 1 5 U1 +δ1 ; U_ se 5 Use +δse

(2.31)

  Use 5 U_ 2 2 U_ 1 ; δse 5 δ1 6 ðπ=2 1 δ=2Þ

(2.32)

when δ . 0, δse 5 δ1 1 π=2 1 δ=2, is advance phase shift; and when δ , 0, δse 5 δ1 2 π=2 2 δ=2, is lag phase shift. As shown, if phase shift angle δ is given, the amplitude and phase angle of series-side VSC output voltage U_ se can be determined according to the amplitude and phase angle of line voltage U_ 1 . At this time, since U_ se is not perpendicular to I_se , between the series-side VSC and the system there is an active power exchange, which is balanced by the UPFC shunt-side VSC. The phasor diagram is shown in Fig. 2.12.

2.3 UPFC Optimization Function in Power Network

. Use . Use . U1

. U1

(A)

(B)

FIGURE 2.13 Voltage phasor diagram under terminal voltage regulation.

2.2.2.3 Terminal voltage regulation Terminal voltage regulation is realized when the series-side VSC injects voltage U_ se parallel to U_ 1 , via series transformer T2. If U_ 1 5 U1 +δ1 ; U_ se 5 Use +δse

(2.33)

Use 5 λU1 ; δse 5 δ1 6 Nπ

(2.34)

then where λ is the voltage accommodation coefficient. When λ . 0, then Use 5 λU1 , δse 5 δ1 ; when λ , 0, U2 5 2 λUs , then δse 5 δ1 1 π. As shown, if the voltage accommodation coefficient is given, the amplitude and phase angle of series-side VSC output voltage U_ se can be determined according to the amplitude and phase angle of the transmission line voltage U_ 1 . In this case, between the series-side VSC and the system there is active power exchange, which is balanced by the UPFC shunt-side VSC. The corresponding phasor diagram is shown in Fig. 2.13.

2.2.2.4 Comprehensive functionality The UPFC can also achieve a combination of the above three functions. The output UPFC can be composed of the three basic methods above, as shown in Fig. 2.14.

2.3 UPFC OPTIMIZATION FUNCTION IN POWER NETWORK UPFCs are mixed FACTS devices with strong ability to regulate power flow. With changes to the control rules they can simultaneously or separately achieve

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CHAPTER 2 Principles and functions of UPFC

. λU1 . . U1 + Use . U1

δ

. Ise

FIGURE 2.14 Comprehensive regulation schematic.

parallel compensation, series compensation, phase shifting, and terminal voltage regulation, and realize the adjustment of active and reactive power flow and node voltages of a single line or the entire power grid. In addition, UPFCs play an important role in improving power transmission capacity, optimizing power flow control methods, and enhancing the damping and stability of the system. But for the actual power grid, with a largescale, complex structure, and changing operating modes, the effect of UPFCs differ when they are installed on different lines. Additionally, the capacity of the UPFC is related to manufacturing and installation costs and economic problems. For example, an inappropriate installation location will undoubtedly lead to wasted investment, limited regulation ability, and other issues. Therefore, optimization techniques of UPFCs in a power network are introduced in this section, including the selection of installation location and optimization of UPFC capacity [6
10].

2.3.1 SELECTION OF UPFC INSTALLATION LOCATION Optimization of the UPFC installation location is usually conducted in the early stages of a practical project. Usually the mathematical model of the power grid including the UPFC is established, and the optimized UPFC installation location is calculated with algorithms to maximize the economy and stability of the power grid operation after the installation of the UPFC. The present optimization algorithms of the UPFC installation location optimization algorithm can be divided into the following three categories.

2.3.1.1 Using the experience of experts This method is applied in a small-scale grid with simple structure and a repetitive operating mode. Usually the optimum location for a UPFC is selected based on

2.3 UPFC Optimization Function in Power Network

A

B

C

G

D

FIGURE 2.15 Network structure diagram.

the working experience of dispatchers or experts. In Fig. 2.15, e.g., the load center is located at the bus C, and the power grid supplies power to load center C through the lines A
B
C, A
D
C. Owing to the heavy load of C, the power flow in line BC often reaches the limit, while the A
D
C channel has a comparatively light load. Construction of a UPFC is planned to solve this problem. The substation B is located in the city center and line B
C goes through a residential area, where neither new lines nor a UPFC project can be constructed. But substation A is located in the suburbs, where there is enough space for UPFC construction. Therefore, a UPFC may be installed at the line A
B to control active power flow through the line B
C. Although this expert experience method is simple but effective, its application is limited. For a large-scale power grid with a complex operational mode and multiple overloaded lines, in a condition of limited investment costs, it is difficult to obtain a satisfactory optimization result using the experience of experts.

2.3.1.2 Heuristic method The heuristic method is used to calculate power flow in maximum load conditions before the installation of a UPFC and to select the line to be optimized based on the overload extent. The installation of UPFCs on alternative sites are simulated in turns, and the power flow of the grid considering UPFC regulation is calculated for each. With statistical analysis for the operation of the overload line and control situation, a UPFC installation location preference table is established as a basis for selecting the optimal UPFC installation site. The object of the heuristic algorithm is to optimize the power flow throughout the grid with an overload line. Based on enumeration, the heuristic algorithm successively calculates the power flow distribution of each potential installation site and establishes a site preference table. Although the method is simple and feasible, the workload becomes enormous when the scale of the grid expands and the number of alternative UPFC installation sites increases. Additionally, this method takes into consideration only the power flow control ability of the UPFC, and voltage control and stability adjustment of the UPFC are ignored. This method is not the best, but it is widely used because of its simple theory.

33

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CHAPTER 2 Principles and functions of UPFC

2.3.1.3 Mathematical analysis The mathematical analysis method uses analysis of the grid mathematical model to select optimized UPFC installation sites. At present sensitivity analysis is commonly used. For example, sensitivity analysis is established by a UPFC optimal load reduction model with UPFC inequality constraints and the control parameters of Lagrange multipliers. Other researchers also introduce topological energy function theory to analyze the system transient potential energy distribution and characteristics of change, select the best location for the UPFC by the evaluation of the cut set using steady quantitative indicators. In addition, there is definite Jacobian matrix analysis, a variety of mathematical class line power flow performance index, voltage phase boundary analysis, cost analysis, and several other methods. Take the following active power performance index as an example and introduce the application of sensitivity analysis in UPFC installation site optimization [10
12]. First, build a UPFC equivalent power injection model as shown in Fig. 2.16. Equivalent power injection can be calculated from Fig. 2.16, as follows: Pis 5 2 Vs2 gij 2 2Vi Vs gij cosðφs 2 δi Þ 1 Vj Vs ½gij cosðφs 2 δj Þ 1 bij sinðφs 2 δj Þ

(2.35)

Qis 5 2 Vi Iq 1 Vi Vs ½gij cosðφs 2 δi Þ 1 ðbij 1 B=2Þcosðφs 2 δi Þ

(2.36)

Pjs 5 Vj Vs ½gij cosðφs 2 δj Þ 1 bij sinðφs 2 δj Þ

(2.37)

Qjs 5 2 Vj Vs ½gij sinðφs 2 δj Þ 1 bij cosðφs 2 δj Þ

(2.38)

With the power system in a normal or emergency situation, the severity of the load line can be expressed by an active power flow performance index, which is defined as follows: PL 5


 N X ωm Plm 2n m51

(2.39)

2n Pmax lm

In the formula, N is numbers of the system general branch, Plm is the active power of the branch, Pmax lm is the rated active power of branch, ωm is a weighting coefficient that reflects the importance of the branch, n is the index coefficient. PL defined in this way is based not only on a visual comparison of the actual

i

j

rij + jxij

ΔSi

FIGURE 2.16 UPFC power injection model.

ΔSj

2.3 UPFC Optimization Function in Power Network

current and the rated current, but also includes transmission line load severity information as part of the system. As per the analyses in previous sections, the UPFC series side achieves a change in power distribution by injecting a phase angle and amplitude variable voltage to the grid. Then, take partial derivatives of voltage amplitude Vs and phase angle φs by PL . Two sensitivity parameters, would be obtained to determine the installation location of the UPFC. When the branch k is equipped with a UPFC, and partially derive the line power flow performance to the control parameters xk ðVs ; φs Þ, and then sensitivity parameters are obtained as follows: @PL jVs 5 0 @Vs

(2.40)

@PL jφ 5 0 Vs @φs s

(2.41)

ck1 5 ck2 5

In the above formula, the sizes of ck1 , ck2 represent the regulation performance of the two UPFC controllable parameters Vs , φs of line power flow. The larger the absolute value, the better the indication of performance by adjusting the active power flow for the line. According to the definition PL , there is
 N X @PL 1 2n @Plm 2n21 5 ωm Plm Pmax @Xk @Xk lm m51

(2.42)

@Plm @Plm @Pi @Plm @Pi 5 1 @Xk @Pi @Xk @Pj @Xk

(2.43)

In the formula, i, j are start and end nodes of branch k. The influence coefficient matrix of active power injected by a branch and calculated by DC load flow on the active power flow of the branch is θ 5 XP. There, owing to their linear characteristic: Δθ 5 XP

(2.44)

θi 2 θj Pij 5 xij

(2.45)

The system matrix of active power flow injected by node n affecting line m (node i flow to node j ) is: Smn 5


 dPij 1 dθi dθj xin 2 yjn 5 5 2 dPn dPn xij xij dPn

(2.46)

In the formula, xij is the reactance of branch m;Pn is the node injection power; xin , xjn is the corresponding element in the matrix X. When a UPFC installed in branch m, m 5 k; Plm 5

NB X n51; n6¼s

Sij Pn 1 Pjs

(2.47)

35

36

CHAPTER 2 Principles and functions of UPFC

Node S is a balancing bus, NB is the number of nodes. When branch m is not the branch installing the UPFC, m 6¼ k; Plm 5

NB X

Sij Pn

(2.48)

n51; n6¼s

So, when m 5 k, @Plm @Pis @Pjs @Pjs 5 Smi 1 Smj 1 Smi @Xk @Xk @Xk @Xk

(2.49)

@Plm @Pis @Pjs 5 Smi 1 Smj 50 @Xk @Xk @Xk

(2.50)

When m 6¼ k,

The following formula is obtained:   @Pis j 5 2 2Vi gij cosðφs 2 δi Þ 1 Vj gij cosðφs 2 δj Þ 1 bij sinðφs 2 δj Þ @Vs Vs 50

(2.51)

  @Pis j 5 2 2Vi gij sinδi 1 Vj gij sinδj 1 bij cosδj Vs @φs φs 50

(2.52)

  @Pjs j 5 Vj gij cosðφs 2 δj Þ 2 bij sinðφs 2 δj Þ @Vs Vs 50

(2.53)

  @Pis j 5 Vj gij sinδi 1 bij cosδj Vs @φs φs 50

(2.54)

Solving the formula to get ck1 , ck2 , which is the power flow control sensitivity when the UPFC is installed in branch k.

2.3.2 UPFC CAPACITY DETERMINATION UPFC constant capacity is found by the optimized calculation of the maximum condition ability of the UPFC series and parallel lateral side, to ensure that UPFC control function and the safe and stable operation of the power grid are attained at the same time, with the best economy. Next, UPFC capacity optimization modeling and optimization methods are introduced.

2.3.2.1 Modeling method Take the UPFC equivalent power injection model shown in Fig. 2.16 as an example. It is worth mentioning that, in order to reduce the complexity of the optimization calculation, parallel side voltage is usually expressed as the following form: V_ c 5 Vc +φc 5 kVi +φc

(2.55)

Vi is the voltage amplitude of the access point of the parallel side, k is the amplitude control parameter, φc is the phase angle of the series voltage side; for the parallel side, without considering the UPFC power loss situation, the active

2.3 UPFC Optimization Function in Power Network

power absorbed from the parallel side is equal to the active power injected from the series side, and so only the reactive power exchanged between the parallel side and the power grid can be considered, and therefore, in the establishment of the UPFC capacity optimization model, just consider three arguments, k, φc , Qsh . First, the UPFC optimal configuration with mathematical model is as shown below: obj: s:t:

min:f ðxÞ hðxÞ 5 0 g # gðxÞ # g

(2.56)

In the formula x 5 ½Pg ; QR ; θ; V; kc ; ϕc ; Qsh , Pg , QR are respectively the active and the reactive power generated by the generator, θ, V are the node voltage phase angle and amplitude, kc , ϕc are the amplitude control parameters and phase angle control parameters of the UPFC controllable voltage source, and Qsh is the control parameters of the UPFC reactive control . f ðxÞ is the objective function, generators’ costs generally: f ðxÞ 5

X ða2i P2gi 1 a1i Pgi 1 a0i Þ 1 1000ða0 S3 1 a1 S2 1 a2 SÞτ=8760; i

Pgi is the active power from generators i, a2i , a1i , a0i are constant coefficients of UPFC investment costs, S is the UPFC capacity, τ is the coefficient of present value transfer to annual value, τ 5 rð11rÞny =rð11rÞny 2 1, r are the power investment recovery, ny is the UPFC’s economic life; hðxÞ is the equality constraints for the AC (Alternating Current) system power balance equation, assuming the number of equality constraints to be m; gðxÞ is the inequality constraints, including the AC system voltage amplitude, phase angle, power line transmission constraints, amplitude parameters of the UPFC controllable voltage source, and phase angle control parameters, assuming the number of inequality constraints to be r. ΔPij ; jΔQij are the active power and reactive power equivalents injected to the node i, ΔPji ; jΔQji are the active power and reactive power equivalents injected to the node j, U_ i , U_ j are the voltage phasors of node i, j, U_ c is the voltage phasor of the UPFC controllable voltage source, I_sh is the current phasor of the UPFC controllable current source, gij , bij are the conductance and susceptance nodes of the line between i, j, and B is admittance to the ground line. The UPFC basic equation under the system is as follows: ΔPij 5 ð2 2kc Ui2 cosϕc 2 kc2 Ui Þgij 1 kc Ui Uj ðgij cosðθij 1 ϕc Þ 1 bij sinðθij 1 ϕc ÞÞ

(2.57)

ΔQij 5 kc Ui2 ðbij cosϕc 1 gij sinϕc Þ 1 0:5kc BUi2 cosϕc 1 Qsh

(2.58)

ΔPji 5 kc Ui Uj ðgij cosðθij 1 ϕc Þ 2 bij sinðθij 1 ϕc ÞÞ

(2.59)

ΔQji 5 2 kc Ui Uj ðbij cosðθij 1 ϕc Þ 1 gij sinðθij 1 ϕc ÞÞ

(2.60)

Depending whether the node of the AC system connects to the UPFC or not, the node is divided into ordinary nodes and UPFC node. kc is the UPFC controllable voltage source amplitude parameters, ϕc is the UPFC controllable voltage

37

38

CHAPTER 2 Principles and functions of UPFC

phase angle source parameters, Qsh is the UPFC reactive power control parameters. Formula (2.56) and formula (2.60) compose a UPFC power system capacity configuration optimization model, which is essentially a UPFC model with the optimal power flow calculation, and when determining the installation location of the UPFC, a conventional optimal power flow calculation method can be used, such as the interior point method, mixed integer programming, or the nonlinear programming algorithm.

2.3.2.2 Optimization method Normally, UPFC optimal capacity and installation location are calculated simultaneously, and then the problem becomes a typical nonlinear, high latitude, mixed integer optimization problem, difficult to calculate using a traditional mathematical optimization algorithm, and artificial intelligence algorithms, which use biologically evolved algorithms as prototypes, have a good convergence, and therefore the calculation, takes less computing time, and is more robust. Common AI systems include: simulated annealing, genetic algorithms, particle swarm optimization, artificial neural network algorithms, and differential evolution algorithms. All can be used to achieve UPFC capacity optimization [9,13]. Since the differential evolution algorithm (Differential Evolution, DE) is simple, with strong search capabilities, few adjustable parameters, is applicable to hybrid optimization, and has good interior point method convergence and strong robustness, therefore the following calculations take the differential evolution algorithm as an example, to calculate the established UPFC optimal configuration mathematical model. The main steps are as follows: Step 1: Obtain the network parameters of the power system; Step 2: Set the DE algorithm population size Np , maximum number of iterations Kmax , scale factor F, and crossover probability CR , with discrete variables to be optimized being the UPFC installation location n0p , UPFC capacity Q0sh ; initialih i h i zation DE population, X 0 5 x01 ; . . .; x0Np , x0i 5 n0p ; Q0sh , to set up the evolutionary algebra kiter 5 0; Step 3: Use the interior point method to optimize ½Pg ; QR ; θ; V; kc ; ϕc , and then get the objective function value as the fitness of DE individuals and optimal objective function value; Step 4: The variation of DE populations: vt11 5 xtr1 1 Fðxtr2 2 xtr3 Þ i

In the formula: vit11 is the population after variability; F is the scaling factor, take ½0; 2; xtr1 , xtr2 , xtr3 are three different individuals randomly selected from the population.

2.3 UPFC Optimization Function in Power Network

Interlace operation of DE populations: ( 11 ci;kiter j

5

11 vi;kiter j

xki;iter j

randðjÞ # CR randðjÞ . CR

or

j 5 randnðiÞ

and j 6¼ randnðiÞ

t11 In the formula: ci;j is obtained after crossing populations; randðjÞ is a random number between ½0; 1; j is the component of the individual; CR is the crossover probability; randnðiÞ is a random amount between ½1; . . .; N;

Beginning

Parameters of power system

Setting NP,Kmax,F,CR of DE algorithm

Initialization

Variation of DE

Cross of DE

Interior point method is used to establish fitness

t=t+1

Select DE

Over Kmax?

N

Y The optimal parameter of UPFC

End

FIGURE 2.17 UPFC optimal installation location and flow capacity calculation with the DE algorithm

39

40

CHAPTER 2 Principles and functions of UPFC

To obtain a test population UPFC installation location nt11 and UPFC p capacity Qt11 ; sh Step 5: Adaptations of the original value of stocks and test populations are selected to give a new generation of select populations:  xt11 5 i

ct11 i xti

t f ðct11 i Þ , f ðxi Þ t f ðct11 Þ $ f ðx i iÞ

In the formula, f ðcit11 Þ, f ðxti Þ are the fitness of cit11 and xti t11 Update the optimal value of the objective function fbest ; Step 6: Determine if the number of iterations is greater than Kmax , and if it is, quit the program and output the calculated message “non-convergence,” if not, the value of iteration numbers plus 1, and return to step 3. The whole algorithm process is shown in Fig. 2.17. The above is the calculation process of the DE algorithm for the UPFC optimal installation location and capacity established in this section.

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