Load Frequency Control of Interconnected Restructured Power System along with DFIG and Coordinated Operation of TCPS-SMES Praghnesh Bhatt, S.P. Ghoshal, Member, IEEE, Ranjit Roy and Sankarsan Ghosal Abstract—The increased penetration of wind power by doubly fed induction generator (DFIG) in power system results in higher frequency excursion and increased rate of change of frequency in the event of generation loss or increased load demand. This paper presents the added feature of frequency regulation capability of the DFIG by incorporating an extra frequency control support function, tested on an interconnected two-area restructured power system. Frequency control support function responding proportionally to the frequency deviation is proposed to take out the kinetic energy of the wind turbine for improving the frequency response of the system. The presence of Thyristor controlled phase shifter (TCPS) in series with the tie-line near one area and Superconducting Magnetic Energy Storage (SMES) at the terminal of the other area in conjunction with dynamic active power support from the DFIG results in optimal transient performance for PoolCo transactions. Integral gains of AGC loop and parameters of TCPS and SMES are optimized through craziness based particle swarm optimization (CRPSO) in order to have optimal transient responses of area frequencies and tieline power deviation. Keywords-Doubly Fed Regulation, SMES, TCPS
D
Induction
Generator,
Frequency
I. INTRODUCTION
ISPATCHING electricity in a way that ensures the security of the system has always been a priority of system operators. This priority has not changed during the transition from vertically integrated utilities to competitive market based operation [1]. Electricity systems are evolving rapidly and the inertial and dynamic characteristics of many new sources of generation differ from that of conventional plants in the past. The increasing penetration of wind generation in systems has caused concern about the availability of the turbines’ stored kinetic energy to the system [2]. In isolated systems which
Praghnesh Bhatt is with Department of Electrical Engineering, CIT – Changa, Gujarat (
[email protected]) S.P. Ghoshal is in Department of Electrical Engineering, National Institute of Technology, Durgapur, WB (
[email protected]) Ranjit Roy is with Department of Electrical Engineering, National Institute of Technology, Surat, Gujarat (
[email protected]) Sankarsan Ghosal is in Department of Electrical Engineering, National Institute of Technology, Durgapur, West Bengal
978-1-4244-7781-4/10/$26.00 ©2010 IEEE
already have a relatively small inertial base, the penetration of wind generation causes further reduction in system inertia. This imposes significant problems to operators trying to ensure the system security. The increasing integration of DFIG controlled by static converters for wind generation into power grids is currently a generalized tendency in various countries. However, in case of the DFIG, the inertia of the turbine is effectively decoupled from the system. The static converter at the heart of the DFIG controls the performance and acts as an interface between the machine and the grid [3]. Hence, with the increased penetration of the DFIG based wind farms, the effective inertia of the system "seen" by the grid will be reduced which results in increased rates of change of frequency (ROCOF) due to disturbances. In order to allow operation with large shares of wind power penetration, several utilities have put frequency control requirement on wind farms. [4]. With the emergence of the distinct identities of GENCOs, TRANSCOs, DISCOs and the ISO, many of the ancillary services of the vertically integrated utilities have to be modeled differently. One of the ancillary services is the ‘‘frequency control’’ based on the concept of the load frequency control [5]-[6]. Moreover, in competitive electricity market, Independent Power Producers (IPPs) with various kinds of larger capacity and fast power consumption apparatus do not possess sufficient frequency control capabilities and may cause a serious problem of frequency oscillations. Under this situation, the conventional frequency control, i.e. a governor, may no longer be able to absorb large frequency oscillations due to its slower response. Therefore, a new service of stabilization of frequency oscillations becomes challenging and is highly expected in the future competitive environment. Hence, the impact of coordinated control of superconducting magnetic energy storage (SMES) [7] and thyristor controlled phase shifter (TCPS) [8] is analyzed for load frequency control. The SMES unit is located at the terminal of area 2 and TCPS is considered in series with the tie-line. The objectives of the paper are to analyze the load frequency control (LFC) problem of an interconnected twoarea restructured power system with the integration of wind power generation by the DFIG and to show the effectiveness of coordinated control of TCPS-SMES for LFC. In Section II, the modeling of PoolCo transactions in restructured power system has been discussed. Linearized model of an interconnected two-area restructured power system along with the integration of the DFIG’s generation and TCPS-SMES is presented in Section III. The modeling of the DFIG is given in
f ref
I cmd 1 Pcmd 1 VWT 1 + sTcon
VWT
ΔPe
Pcmd 0
27 0
β ≈0
Pe
00
C p (λ, β )
Pmt
1 Pef 1 + sT f Pa
÷
Ta
ω wt 0 P
×
Lp
Tcmd 0
ω ω re f
1 ω wt 0 2 HWT s
ω er r
K pt +
Kf
Δf
f grid
ΔPHH / ΔPTT ΔPDFIG
1 2H eq2s+D 2
Kit s
1 R TH
1 R TH Fig.2. Block diagram of the DFIG model with frequency support function ΔPTT1
sFHP TRH +1
1 1+s TG ,T H
-K i1 s
( sTCH +1) ( sTRH +1)
1 2 H1 s+D1
sFHP TRH +1 ( sTCH +1)( sTRH +1) ΔPTT2
1 1+s TG ,T H
T 12
ΔPTCPS
α 12 1 1+s TG,HY
-K i2 s 1 R HY
1 1+s TG,HY
1-s TW 1+s 0.5TW
1+s TR 1+s (R T /R P ) TR 1+s TR 1+s (R T /R P ) TR
ΔPHH1
1-sTW 1+s0.5TW
Δω1
s
α12
ΔPHH2
1 2 H 2 s+D 2
Δω2
ΔPDFIG ΔPSMES
1 R HY
Fig.1. Schematic of two-area system in restructured environment
Section IV. Objective function to have the optimal transient response and craziness-based particle swarm optimization technique (CRPSO) [9] to optimize the gains of integral controller and parameters of TCPS and SMES are outlined in Section V. Simulation results are discussed in Section VI followed by conclusion. II. RESTRUCTURED POWER SYSTEM The traditional electric industry is vertically integrated with all generation, transmission and distribution. In the restructured environment, vertically integrated utilities no longer exist; instead, there are three different entities, viz., GENCOs (generation companies), TRANSCOs (transmission companies) and DISCOs (distribution companies). As there are several GENCOs and DISCOs in the restructured power system, a DISCO has the freedom to have a contract with any GENCO for the transaction of power. A DISCO of one control area may have a contract with a GENCO in another control area. A. DISCO Participation Matrix The concept of a ‘‘DISCO participation matrix’’ (DPM) is used to make the easier visualization of the contracts between the GENCOs and DISCOs [5]-[6]. Each area is having two GENCOs and two DISCOs as shown in Fig. 1. Let GENCO1, GENCO2, DISCO1 and DISCO2 be in area1 and GENCO3, GENCO4, DISCO3 and DISCO4 be in area2. Unlike the
traditional AGC system, a DISCO asks/demands a particular GENCO(s) for load power. Thus, as a particular set of GENCOs is supposed to follow the total load demanded by a DISCO, information signals must flow from the DISCO to particular GENCO(s) specifying corresponding demands. There are also uncontracted loads like delPuncot1 and delPuncot2 in area 1 and 2 respectively as shown in Fig. 1. The individual total demands on GENCO(s) are specified by cpf s (elements of DPM) and the pu MW load of a DISCO. These signals which were absent in the traditional AGC will carry information as to which GENCO has to follow a load demanded by which DISCO. apfi ( i = 1, 2,3, 4 ) are the area control error (ACE) participation factors of different GENCOS, which were also absent in the traditional AGC. ⎡ cpf11 ⎢cpf DPM = ⎢ 21 ⎢cpf31 ⎢ ⎣⎢cpf 41
cpf12 cpf 22 cpf32 cpf 42
cpf13 cpf14 ⎤ cpf 23 cpf 24 ⎥⎥ cpf33 cpf34 ⎥ ⎥ cpf 43 cpf 44 ⎦⎥
(1)
III. LINEARIZED MODEL OF INTERCONNECTED TWO-AREA MULTI UNITS RESTRUCTURED POWER SYSTEM ALONG WITH TCPS AND SMES Fig. 1 shows the linearized model of an interconnected twoarea restructured power system along with the integration of
Δ ω i (s)
T 12
1+s T1 1+s T2
1+s T3 1+s T4
KSMES
7.5 m/s
Beta = 3
Pmech
Δ PSMES 1 1+s TSMES
C p ( λ, β ) =
i, j β
i j
λ
(2)
i =0 j =0
The values of the coefficient α i , j are given in [12]-[13]. ωω t (3) ωs where ωωt is the rotor speed in pu, ωs is the wind speed in m/s, ω0 is the rotor base speed in rad/s and R is the rotor radius in meter. The mechanical power captured by the turbine is given by (4). λ = ω 0R
6 8 Lam bda
10
0 0.5
12
0.6
0.7 0.8 0.9 1 Rotor Speed (pu)
1.1
⎛1 ⎜ ρ Ar =⎜2 C p , opt Sn ⎜⎜ ⎝
⎞ ⎟ 3 ⎟ ws ⎟⎟ ⎠
where ρ is the air density in kg/m3 , C p,opt
(4)
Ar
is the rotor swept area
is the maximum value of the
C p ( λ ) curve
at
0
(C p ) value of the turbine is given by (2).
∑∑α
4
11.2 m/s
0.4
(b)
in m ,
DFIG, being in the category of variable-speed wind turbine generators, can offer increased efficiency in capturing the energy from wind over a wider range of wind speeds, along with better power quality and the ability to regulate the power factor. The power electronic converter in the DFIG is attached to the rotor. The rotor is connected to the power system through the back-to-back ac/dc/ac converter, while the stator is connected directly to the power system. Normally, the control scheme of the DFIG decouples the rotational speed of the rotor from the grid frequency, thus preventing the generator from responding to the system frequency changes. However, modern DFIG is designed to be able to vary its rotational speed in a wider range during normal operations which gives the possibility to utilize the rotational energy in the turbine-generator to provide short term active power support in the event of network frequency excursion [11]. A model of a multi-megawatt commercial DFIG (GE 3.6 MW) is used in this work, adopted from [12]-[13]. The block diagram of the DFIG is shown in Fig. 2. The DFIG is integrated with GENCO(s) in area 2. The generated mechanical power ( Pmt ) is a complex functions of wind speed (ωs ) , rotor speed (ωωt ) and pitch angle ( β ) . The 4
2
10.5 m/s
0.2
Beta = 9
0
9.5 m/s
0.6
wind turbine rotor speed for different wind speeds
Fig. 4 Structure of SMES as a frequency stabilizer
4
Beta = 1
0.2
2
power coefficient
Pm ec h (pu)
Beta = 0
8.5 m/s
Fig.5. (a) C p → λ (b) Wind turbine mechanical power as a function of the
Δ PTCPS
Fig. 3 Structure of TCPS as a frequency stabilizer
Δ ωi (s)
6.5 m/s
0.8
0.4
(a)
IV. MODELING OF DFIG Kϕ 1+s TPS
1
Cp
the DFIG’s generation for the load frequency control. The control areas are having thermal/hydro GENCO(s). DFIG is placed along with the hydro GENCOs in area 2. The generating units of GENCOs are represented by traditional units’ blocks as given in [10]. The parameters are given in the Appendix. The presence of TCPS in series with tie-line near area 1 and SMES at the terminal of area 2 is also represented in Fig. 1. The linearized model of TCPS and SMES are shown in Fig. 3 and Fig. 4, respectively.
β ≈ 0 , λopt is the optimal value of λ for which the value of
the DFIG rating in MW, ω0 is the rotor base speed in rad/s and R is the rotor radius in meter. The values of these parameters for the GE 3.6 MW DFIG are given in the Appendix. The C p curves of the turbine based on (2)-(3) are plotted C p,opt
is maximum,
Sn is
for different pitch angles ( β ) and shown in Fig. 5(a). Fig. 5(b) presents the static dependency of the captured mechanical power by the turbine as function of rotor speed for different wind speeds. As may be seen from Fig. 5(b), there exists an optimal rotor speed, for a given wind speed, when the captured mechanical power is the maximum. This represents the normal operation of the DFIG where it operates at the maximum point of the C p ( λ ) curve. Other than these optimal rotor speeds, the captured mechanical power reduces significantly.
A. Frequency Control Support Function added to the DFIG Under normal operation, the convertor controllers of the DFIG keep the turbine at its optimal speed in order to extract maximum power. The controller gives a torque set point that is based on measured speed and power. The power set point is an input for the converter control that realizes the torque by controlling the generator currents. To emulate the inertia and to facilitate the excess active power injection from the DFIG for the frequency support, an additional auxiliary signal is considered and shown shaded in Fig. 2. Upon the detection of a network frequency disturbance, an active power increment as a function of the grid frequency deviation in addition to the pre-disturbance value of nominal active power is fed to the DFIG converter controller. Hence, the electrical torque of the DFIG is now greater than the mechanical torque generated for a given wind speed and the DFIG rotor will experience the deceleration torque. As a result, the rotational speed of the DFIG deviates from its optimal operating point and extra rotational energy is emulated from the rotor blades. This extractable kinetic energy from the DFIG is used to supply more power to the
grid in order to reduce the initial fall of frequency of the system after the load disturbance. The deceleration of the rotor and consequently extractable kinetic energy that is utilized to generate dynamic active power support depends upon the grid frequency deviation. It should be noted that the DFIG’s extra active power supports the grid frequency in transient period only. The integral controller in the AGC loop of the generating units restores the frequency to the nominal value. As a result, under stady state, additional power demand on the convertor controller which is a function of the grid frequency deviation shown in Fig. 2 is eliminated and normal operation of the DFIG at the optimal rotor speed will be restored again. V. MATHEMATICAL PROBLEM FORMULATION AND CRAZINESS-BASED PARTICLE SWARM OPTIMIZATION
A. Figure of Demerit The objective of the AGC is to reestablish primary frequency regulation, restore the frequency to its nominal value as quickly as possible and minimize the tie-line power flow oscillations between neighboring control areas. In order to satisfy the above requirements, gains ( K I1 , K I2 ) of integral controllers in the AGC loops and parameters of TCPS and SMES are required to be optimized. In the present work, an Integral Square Error (ISE) criterion is used to minimize the objective function defined as "Figure of Demerit (FDM)": FDM=
∑ ⎡⎣Δf
2 2 2 ⎤ 1 +Δf 2 +ΔPtie ⎦ ΔT
(5)
where ΔT = a given time interval for taking 200 samples, Δfi = sample value of the incremental change in frequency of
ith area and ΔPtie = sample value of the incremental change in the tie-line power. The samples are obtained from their respective plots derived through transfer function analysis. The objective function is minimized with the help of CRPSO based optimization technique [9]. B. Craziness-based Particle Swarm Optimization The PSO was first introduced by Kennedy and Eberhart [14]. It is an evolutionary computational model, a stochastic search technique based on swarm intelligence. Velocity updating equation:
(
)
(
vik +1 = vik + c1× r1× p Best i − xik + c 2 × r 2 × gBest − xik
)
(6)
Position updating equation: xik +1 = xik + vik +1 (7) The following modifications in velocity help to enhance the global search ability of PSO algorithm as observed in CRPSO [9]. (i) Velocity updating as proposed in [9] may be stated as in the following equation: vik +1 = r 2 × vik + (1 − r 2 ) × c1× r1× ( p Best i − xik ) (8) + (1 − r 2 ) × c 2 × (1 − r1) × ( gBest − xik ) Local and global searches are balanced by random number r2 as stated in (9). Change in the direction in velocity may be modeled as given in the following equation:
vik +1 = r 2 × sign(r3) × vik + (1 − r 2 ) × c1× r1
(
)
(
× p Best i − xik + (1 − r 2 ) × c 2 × (1 − r1) × gBest − xik
)
(9)
In (9), sign (r3) may be defined as ⎪⎧ −1 ( r 3 ≤ 0.05 ) sign(r 3) = ⎨ ⎪⎩ 1 ( r 3 > 0.05 ) (ii) Inclusion of craziness: Diversity in the direction of birds flocking or fish schooling may be handled in the traditional PSO with a predefined craziness probability. The particles may be crazed in accordance with the following equation before updating its position. vik +1 = vik +1 + Pr (r 4) × sign(r 4) × vicraziness (10) where Pr(r4) and sign(r4) are defined respectively as:
( r 4 ≤ Pcraz ) ( r 4>Pcraz ) ⎪⎧ 1 ( r 4 ≥ 0.5 ) sign(r 4) = ⎨ ⎪⎩ -1 ( r 4
