Optimal wide-area monitoring and nonlinear adaptive ...rtpis.org/documents/mypaper/RTPIS_publication_1281818821.pdf · Optimal wide-area monitoring and nonlinear adaptive coordinating

Neural Networks 21 (2008) 466–475www.elsevier.com/locate/neunet

2008 Special Issue

Optimal wide-area monitoring and nonlinear adaptive coordinatingneurocontrol of a power system with wind power integration and multiple

FACTS devicesI

Wei Qiaoa,∗, Ganesh K. Venayagamoorthyb, Ronald G. Harleya

a Intelligent Power Infrastructure Consortium, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250, USAb Real-Time Power and Intelligent Systems Laboratory, Department of Electrical and Computer Engineering, University of Missouri-Rolla, Rolla,

MO 65409-0249, USA

Received 8 August 2007; received in revised form 30 October 2007; accepted 3 December 2007

Abstract

Wide-area coordinating control is becoming an important issue and a challenging problem in the power industry. This paper proposes a noveloptimal wide-area coordinating neurocontrol (WACNC), based on wide-area measurements, for a power system with power system stabilizers, alarge wind farm and multiple flexible ac transmission system (FACTS) devices. An optimal wide-area monitor (OWAM), which is a radial basisfunction neural network (RBFNN), is designed to identify the input-output dynamics of the nonlinear power system. Its parameters are optimizedthrough particle swarm optimization (PSO). Based on the OWAM, the WACNC is then designed by using the dual heuristic programming (DHP)method and RBFNNs, while considering the effect of signal transmission delays. The WACNC operates at a global level to coordinate the actionsof local power system controllers. Each local controller communicates with the WACNC, receives remote control signals from the WACNC toenhance its dynamic performance and therefore helps improve system-wide dynamic and transient performance. The proposed control is verifiedby simulation studies on a multimachine power system.c© 2007 Elsevier Ltd. All rights reserved.

Keywords: Adaptive critic designs; FACTS devices; Particle swarm optimization; Radial basis function network; Wide-area control; Wind power

1. Introduction

Power systems are large-scale, nonlinear, nonstationary,multivariable, complex systems distributed over large geo-graphical areas. System-wide disturbances in power systemsare a challenging problem for the utility industry. Further,because of new constraints placed by economical and envi-ronmental factors, the trend in power system planning andoperation is toward maximum utilization of existing electric-ity infrastructure, with tight operating margins, and increasedpenetration of renewable energy sources such as wind power.

I An abbreviated version of some portions of this article appeared in Qiao,Venayagamoorthy, and Harley (2007) as part of the IJCNN 2007 ConferenceProceedings, published under IEE copyright.

∗ Corresponding address: 329156 Georgia Tech Station, Atlanta, GA 30332-1255, USA. Tel.: +1 404 894 5563; fax: +1 404 894 4641.

E-mail addresses: [email protected] (W. Qiao), [email protected](G.K. Venayagamoorthy), [email protected] (R.G. Harley).

0893-6080/$ - see front matter c© 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.neunet.2007.12.008

Under these conditions, power systems become more complexto operate and to control, and, thus, more vulnerable to a distur-bance (Begovic, Novosel, Karlsson, Henville, & Michel, 2005).When a major disturbance occurs, protection and control ac-tions are required to stop the power system degradation, restorethe system to a normal state, and minimize the impact of thedisturbance.

The standard power system controllers, such as thegenerator exciter and automatic voltage regulator (AVR)(Kundur, 1994), speed governor (Kundur, 1994), power systemstabilizer (PSS) (Kundur, 1994) and power electronics-basedflexible ac transmission system (FACTS) devices (Hingorani& Gyugyi, 2000), are local noncoordinated linear controllers.Each of them controls some local quantity to achieve alocal optimal performance, but has no information on theentire system performance. Further, the possible interactionsbetween these local controllers might lead to adverse effectscausing inappropriate control effort by different controllers.

W. Qiao et al. / Neural Networks 21 (2008) 466–475 467

When severe disturbances or contingencies occur, these localcontrollers are not always able to guarantee stability (Okou,Dessaint, & Akhrif, 2005).

To improve the system-wide dynamic performance andstability, wide-area coordinating control (WACC) is becomingan important issue in the power industry. A WACC operatesat a global level, e.g. the control center of a power systemto coordinate the actions of local controllers. It receivesremote signals from different devices over wide areas (calledwide-area measurements) in the power system, and generatesthe global coordination/control signals. Each local controllercommunicates with the WACC, reports to and receivescoordination/control signals from the WACC, to help attain thesystem-wide performance goals.

With the increased availability of advanced computer, com-munication and measurement technologies (e.g. synchronizedphasor measurement units (PMUs) based on a global position-ing satellite (GPS) system) (Begovic et al., 2005), the develop-ment of WACC is becoming feasible. By employing the GPSsynchronized PMUs, it is possible to deliver remote synchro-nized real-time signals to the control centre at a speed of as highas 60 Hz sampling rate (Begovic et al., 2005). This samplingrate is high enough for damping control of the typical powersystem oscillating modes. However, an unavoidable problem isthe delay involved between the instant of measurement and thatof the signal being available to the controller. This delay cantypically be in the range of 0.01–1.0 s (Begovic et al., 2005;Chaudhuri, Majumder, & Pal, 2004) depending on the signaltransmission hardware, distance, protocol of transmission, etc.As the delay might be comparable to the time periods of somecritical oscillating modes, it should be considered in the designof the WACC to ensure satisfactory control performance.

Moreover, designing the WACC needs knowledge of theentire power system dynamics to be available to the designers.Due to the large-scale, nonlinear, stochastic and complex natureof power systems, the traditional mathematical tools and controltechniques are not sufficient to design such a WACC. Thisproblem can be overcome by using neural networks (NNs) andadaptive-critic-design (ACD)- (Prokhorov & Wunsch, 1997;Werbos, 1992) based intelligent nonlinear optimal controltechniques.

During the past years, many works have been proposedon ACD-based optimal neurocontrol to improve power sys-tem dynamic and transient performance (Park, Harley, & Ve-nayagamoorthy, 2004; Qiao & Harley, 2006b; Venayagamoor-thy, Harley, & Wunsch, 2003). However, these previous worksall focused on the local control of individual power system de-vices. Our previous work (Qiao et al., 2007) proposed an ACD-based wide-area coordinating neurocontrol (WACNC), whichis the first neural-network-based WACC for different types ofdevices in a power system with renewable energy generation.This WACNC improved the system-wide dynamic and transientperformance of the power system, but without considering thedelay involved in transmitting the remote signals.

This paper extends the work in Qiao et al. (2007) byproposing an optimal WACNC while considering signaltransmission delays for a power system with PSSs, a large wind

farm, and multiple FACTS devices. First, an optimal wide-areamonitor (OWAM) is designed by using a radial basis functionneural network (RBFNN) (Qiao & Harley, 2007) and particleswarm optimization (PSO) (Kennedy & Eberhart, 1995), toidentify the input-output dynamics of the nonlinear powersystem. Based on this OWAM, the dual heuristic programming(DHP) method (Prokhorov & Wunsch, 1997; Werbos, 1992)and RBFNNs are then used to design the WACNC. It uses wide-area measurements and operates at a global level to coordinatethe actions of the local synchronous generator (equipped withPSS), wind farm, and FACTS controllers. Each local controllercommunicates with the WACNC, and receives remote controlsignals from the WACNC as external input(s), to help improvesystem-wide dynamic and transient performance.

2. Power system model

The 4-machine 12-bus power system in Jiang, Annakkage,and Gole (2006) was proposed as a platform for studyingFACTS device applications and integration of wind generation,and was extended in Qiao, Harley, and Venayagamoorthy(2006) to include a large wind farm, a static synchronouscompensator (STATCOM) (Hingorani & Gyugyi, 2000) and astatic synchronous series compensator (SSSC) (Hingorani &Gyugyi, 2000), as shown in Fig. 1. The system covers threegeographical areas. Area 1 is predominantly a generation areawith most of its generation coming from hydro power (G1and G2). Area 2, located between the main generation area(Area 1) and the main load centre (Area 3), has a large windfarm (G4), but it is insufficient to meet local demand. Area 3,situated about 500 km from Area 1, is a load centre with somethermal generation (G3). Further, since the generation units inAreas 2 and 3 have limited energy available, the system demandmust often be satisfied through transmission. The transmissionsystem consists of 230 kV transmission lines except for one 345kV link (line 7–8) between Areas 1 and 3.

The STATCOM is a shunt connected FACTS device. Itis placed at bus 4 in the load area (Area 3), for steadystate and transient voltage support. This relieves the under-voltage problems in Area 3 (Jiang et al., 2006). The SSSCis a series FACTS device. It is placed at the bus 7 end ofline 7–8 to regulate its power flow. This arrangement canrelieve the possible transmission congestion on line 1–6 causedby some contingencies in Area 3 (Jiang et al., 2006; Qiaoet al., 2006). Both synchronous generators G2 and G3 areequipped with PSSs to improve damping of the local generatorrotor oscillation modes. The synchronous generator (equippedwith PSS), wind farm, SSSC, and STATCOM controllersare each designed at the local level using standard linearcontrol techniques and local signals, but are coordinated by theWACNC at a global level to achieve the desired system-wideperformance goals.

The system is simulated in the PSCAD/EMTDC (ManitobaHVDC Research Centre, 2005) environment. G1 is modelled asa three-phase infinite source, while the other two synchronousgenerators (G2 and G3) are modeled in detail, with the turbinegovernor and AVR/exciter (equipped with PSS) dynamics

468 W. Qiao et al. / Neural Networks 21 (2008) 466–475

Fig. 1. Single-line diagram of the 4-machine 12-bus power system with a large wind farm, a STATCOM and an SSSC coordinated by an WACNC.

Fig. 2. Block diagram of the PSS.

taken into account. The function of each PSS is to improvethe damping of its generator rotor oscillations by controllingits generator’s excitation using auxiliary stabilizing signal(s),e.g. the deviation of generator rotor speed (Kundur, 1994). Theblock diagram of the PSS is shown in Fig. 2.

The wind farm consists of over one hundred individual windturbines. Each wind turbine is equipped with a doubly fedinduction generator (DFIG) (Qiao et al., 2006). In this paper,the wind farm is represented by an aggregated model, namely,one equivalent DFIG driven by a single equivalent wind turbine(Qiao et al., 2006), as shown in Fig. 3. Here the block “Grid”denotes the power network in Fig. 1 to which the wind farmis connected. The wound-rotor induction machine is fed fromboth stator and rotor sides. The stator is directly connectedto the grid, while the rotor is connected to the grid through avariable frequency converter (VFC). The VFC consists of twoIGBT PWM converters (the rotor-side converter RSC and thegrid-side converter GSC) connected back-to-back by a dc-link

capacitor. The crow-bar is used to protect the RSC from over-current in the rotor circuit during grid faults. Control of theDFIG is achieved by control of the RSC and GSC. The detailedcontrol schemes of the RSC and the GSC are provided in Qiaoet al. (2006).

The STATCOM and the SSSC are each modelled as a gateturn-off thyristor (GTO)-based PWM converter with a dc-linkcapacitor. The schematic diagram of the STATCOM and itscontrol scheme are shown in Fig. 4 (Qiao et al., 2006). Theobjective of the STATCOM is to regulate the voltage at theconnection bus (bus 4 in Fig. 1) rapidly over the desired rangeand keep the dc-link voltage constant. The voltage commandV ∗

4 is the summation of two terms, the fixed setpoint valueV40 and the remote control signal ∆V4 from the WACNC.The objective of using the supplementary control signal, ∆V4,is to enhance the dynamic performance, such as the dampingperformance, of the local STATCOM controller.

The schematic diagram of the SSSC and its control schemeare shown in Fig. 5 (Qiao et al., 2006). The main objectiveof the SSSC control is to inject a controllable capacitive orinductive reactance to line 7–8 that is independent of the linecurrent, as well as keeping the dc-link voltage of the inverterconstant at steady state. The total commanded value of the

Fig. 3. Aggregated wind farm model: one equivalent DFIG driven by a single equivalent wind turbine.

W. Qiao et al. / Neural Networks 21 (2008) 466–475 469

Fig. 4. Schematic diagram of the STATCOM and its control scheme.

Fig. 5. Schematic diagram of the SSSC and its control scheme.

compensating reactance X∗

C at the input of the SSSC localcontroller consists of two terms, a fixed setpoint value XC0and a supplementary control signal ∆XC from the WACNC.This external control signal provides a supplementary dampingduring transient power swings.

3. Design of the WACNC

Fig. 6 shows the schematic diagram of the proposedWACNC which coordinates different local controllers of thesynchronous generators, wind farm, STATCOM and SSSC. TheWACNC operates at the control centre of the power system.It receives the remote signals from different devices over wideareas in the power system, including the signals from G2 (speeddeviation ∆ω2), G3 (speed deviation ∆ω3), wind farm G4(output active power deviation ∆Pg4 and voltage deviation ∆V6at bus 6), SSSC (active power deviation ∆P78 of line 7–8),and STATCOM (active power deviation ∆P54 of line 5–4 thatis connected to the STATCOM bus 4). These remote signalscontain the important dynamic/transient information of thelocal devices and the power network. The use of ∆V6 is becauseof its direct coupling with the wind farm reactive power. In thispaper, it is simply assumed that the remote signals, ∆ω2, ∆ω3,∆V6, ∆Pg4, ∆P78, ∆P54, are transmitted to the control centrefrom each local device with the same time delay of τ1. These

delayed remote signals are fed into the WACNC to generatea set of global optimal control signals, ∆VT 2, ∆VT 3, ∆Qs ,∆Qg , ∆V4, ∆XC . They are then used as the auxiliary inputsignals to coordinate the actions of local controllers. Again, it isassumed that these remote control signals are transmitted fromthe control centre to each local controller with the time delay ofτ2. Therefore, the total time delay of the global control signalsfrom the WACNC being available to each local controller isτ = τ1 + τ2 (assuming τ1 = τ2 in this paper). When adisturbance occurs, the coordination by the WACNC ensuresthat the power system returns back to the desired operatingpoint as fast as possible after the disturbance with a minimumcontrol effort.

At the local level, each local device is controlled by its localcontrollers. These local controllers use both local signals andauxiliary remote control signals from the WACNC to achievelocal as well as global dynamic and transient performanceimprovement of the power system. For instance, for the reactivepower control of the wind farm RSC, the command Q∗

s is thesummation of two terms, Qs0 and ∆Qs . The fixed setpointvalue Qs0 is determined by the local reactive power demandwhile taking into account the limit of the RSC rating. Thesupplementary command ∆Qs is a remote signal generated bythe WACNC, which enhances the dynamic performance of thelocal controller.

470 W. Qiao et al. / Neural Networks 21 (2008) 466–475

Fig. 6. Schematic diagram of the synchronous generator, wind farm, STATCOM, and SSSC local controllers coordinated by the WACNC considering signaltransmission delays.

The transfer functions between (∆VT 2, ∆VT 3, ∆Qs , ∆Qg ,∆V4, ∆XC ) and (∆ω2, ∆ω3, ∆V6, ∆Pg4, ∆P78, ∆P54) arecomplicated, nonlinear and depend on the network topology.To avoid having to derive such analytical functions, an ACDapproach — DHP, and RBFNNs are used to design theWACNC. In this paper, the sampling rate for the WACNCimplementation is chosen as 50 Hz in order to meet the PMUrequirements for delivering the synchronized signals. Designof the WACNC should take into account the dynamics of localcontrollers. Therefore, the plant to be controlled includes thepower network, the local devices and their controllers, as shownin the dash–dot-line block in Fig. 6.

3.1. Radial basis function neural network

The neural networks used in this paper are three-layerRBFNNs with a Gaussian density function as the activationfunction in the hidden layer. The overall input-output mappingof the RBFNN, f : X ∈ Rn

→ Y ∈ Rm is

yi = bi +

h∑j=1

v j i exp(−‖x − C j‖2/β2

j ) (1)

where x is the input vector; C j ∈ Rn and β j ∈ R are the centreand width of the j th RBF units in the hidden layer, respectively;h is the number of RBF units; bi and v j i are the bias term andthe weight between hidden and output layers, respectively; andyi is the i th output.

3.2. Adaptive critic designs and DHP

Adaptive critic designs, proposed by Werbos (1992), is aneural network based optimization and control technique whichsolves the classical nonlinear optimal control problems bycombining concepts of reinforcement learning and approximatedynamic programming.

The DHP, belonging to the family of ACDs, requires fiveNNs for its implementation: two for the model (called wide-area monitor in this paper), two for the critic, and one for theaction network (Park et al., 2004; Prokhorov & Wunsch, 1997;Venayagamoorthy et al., 2003; Werbos, 1992). The wide-areamonitor is used to identify the input-output dynamics of theplant. The critic network estimates the derivatives of the cost-to-go function J with respect to the states of the plant Y , and Jis given by

J (k) =

∞∑q=0

γ qU (k + q) (2)

where U (·) is the utility function or one stage cost (user-definedfunction), and γ is a discount factor for finite horizon problems(0 < γ < 1). The ACD method determines optimal controllaws for a system by successively adapting the critic and actionnetworks. The adaptation process starts with a nonoptimalcontrol by the action network; the critic network then guides theaction network towards the optimal solution at each successiveadaptation. During the adaptations, neither of the networksneeds any information of the desired control trajectory, only thedesired cost needs to be known.

3.3. Design of the optimal wide-area monitor (OWAM)

The wide-area monitor is a three-layer RBFNN. Theplant inputs A = [∆VT 2,∆VT 3,∆Qs,∆Qg,∆V4,∆XC ]

and outputs Y = [∆ω2,∆ω3,∆V6,∆Pg4,∆P78,∆P54]

at time instants k, k − 1 and k − 2 are fed into thewide-area monitor to estimate the plant outputs Y =

[∆ω2, ∆ω3, ∆V6, ∆Pg4, ∆P78, ∆P54] at time k + 1, asshown in Fig. 7. The wide-area monitor is an essential partfor designing the WACNC because it provides a dynamic plantmodel for training the critic and action networks.

W. Qiao et al. / Neural Networks 21 (2008) 466–475 471

Fig. 7. Structure of the wide-area monitor: TDL denotes time delay lock.

The wide-area monitor is firstly pretrained offline using asuitably selected training data set (Qiao & Harley, 2006b) fromtwo sets of training: forced training and natural training (Parket al., 2004; Qiao & Harley, 2007; Venayagamoorthy et al.,2003). The forced training and natural training are carried out atseveral different operating points to form the training data set,given by:

Z = {A, Y} =

{m⋃

i=1

ZFi ,

m⋃i=1

n⋃j=1

ZNi j

}(3)

where Z is the entire training data set selected from moperating points; A and Y are the input and output data setsof the plant, respectively; Z Fi is the subset collected from theforced training at the operating point i ; Z Ni j is the subsetcollected from the natural training caused by the j th naturaldisturbance event at the operating point i . The selected trainingdataset ensures that the wide-area monitor can track the systemdynamics over a wide operating range.

The performance of RBFNNs relies on a set of parameters,including the number of RBF units, the RBF centres, widths,and the output weights. Given the number of RBF units,the locations of RBF centers are determined by a k-meansclustering algorithm (Alsabti, Ranka, & Singh, 1998) using thedata from the training dataset. After locating the RBF centres,a good method to determine the RBF widths is the p-nearestneighbours heuristic (Moody & Darken, 1989), in which thewidth βi of the i th RBF unit is given by:

βi =

(1p

p∑j=1

∥∥Ci − C j∥∥2

)1/2

(4)

where C j are the p-nearest neighbours to the centre Ci . In thispaper, p is chosen the same as the number of RBF units h in thehidden layer. After determining the RBF centres and widths, theoutput weights of the RBFNN are then calculated by singularvalue decomposition (SVD) method (Haykin, 1998).

However, the widths given by (4) are still nonoptimal. InQiao and Harley (2006a), the authors have shown that the RBFwidths can be optimized to achieve an optimal RBFNN withfewer RBF units and better performance. This section presentsa method to design an OWAM by using PSO.

Suppose an initial width βi = βi,ini of the i th RBF unit hasbeen calculated using (4), then the optimal width βi,opt can bedefined by a set of equations, given by

βi,opt = si,opt · βi,ini i = 1, 2, . . . , h (5)

where si,opt ∈ R is the optimal scaling factor for βi .Now the problem becomes using PSO to find out the setof optimal scaling factors sopt = {si,opt} in the problem

Fig. 8. Performance of the wide-area monitor with the optimized widths.

space. In PSO implementation, the range of the scaling factors(i.e. the searching space of the PSO) should be appropriatelydetermined in order to quickly locate the optimal solution. Inthis paper, the scaling factors are within a small range of [0, 10]since (4) has already provided a set of good initial widths in (5).

Locating the set of optimal scaling factors sopt is achieved byoptimizing the following mean-square error (MSE) in dB overthe training data set:

MSE = 10 log

(NT∑

k=1

‖Y (k) − Y (k)‖2/NT

)(6)

where NT and Y (k) are the number of data samples and the kthoutput data sample of the plant in the training set Z describedby (3), respectively; Y (k) is the kth output sample from thewide-area monitor. In this paper, the training data set Z isselected from five different operating points (i.e. m = 5 in (3)).At each operating point, the forced training and two differentnatural training events (i.e. n = 2 in (3)) are applied with 1000data samples selected from each forced training and 300 datasamples selected from each natural training event. Therefore,the total number of data samples in the training set is NT =

8000. The MSE in (6) is employed as the performance measurefunction for PSO implementation.

The MSEs over the selected training data set are plotted inFig. 8 to show the performance of the wide-area monitor withthe optimized widths but different numbers of RBF units. Theminimum MSE is around −64 dB that can be achieved by using35 or more RBF units, and any further increase over 35 does notimprove the MSE significantly. Therefore, the optimal numberof RBF units is chosen as 35 for the wide-area monitor.

Fig. 9 shows the MSE as a function of the number ofiterations in PSO during the RBF width optimization procedurefor the wide-area monitor with 35 RBF units. The MSE atiteration no. 0, which denotes the RBFNN with initial widthsfrom (4), is 280 dB. After 10 iterations, the MSE decreasesto about −63 dB. These results indicate that the performanceof the wide-area monitor is significantly improved by theproposed method. Further optimization using PSO with morethan 10 iterations only slightly improves the MSE. Therefore,the optimal RBF widths can be found by PSO within only 10iterations.

The final OWAM therefore has 35 RBF units, the RBFcentres determined by the k-means clustering algorithm, the

472 W. Qiao et al. / Neural Networks 21 (2008) 466–475

Fig. 9. Performance of the wide-area monitor with 35 RBF units during RBFwidth optimization procedure.

optimized RBF widths found by PSO, and the output weightscalculated by SVD method. It is now used for furtherimplementation of the DHP.

3.4. Design of the critic network

The critic network is a three-layer RBFNN. The inputs tothe critic network are the estimated plant outputs, Y (from theOWAM) and their two time-delayed values. The outputs of thecritic network are the derivative, λ = ∂ J/∂Y , of the function Jin (2) with respect to the estimated plant outputs Y , as shownin Fig. 10. The critic network learns to minimize the followingerror measure over time (Prokhorov & Wunsch, 1997):

‖EC‖ =

∑k

ETC (k)EC (k) (7)

where

EC (k) =∂ J [Y (k)]

∂Y (k)− γ

∂ J [Y (k + 1)]

∂Y (k)−

∂U (k)

∂Y (k). (8)

The utility function is defined as

U (k) =12

6∑i=1

wi [Y2i (k) + 0.5Y 2

i (k − 1) + 0.1Y 2i (k − 2)] (9)

where Y is the vector of the plant outputs, and wi is a weightingfactor for Yi . Generally, two critic networks are required inDHP to estimate ∂ J/∂Y arising from the present state Y (k)

and the future state Y (k + 1). The adaptation of the criticnetwork in DHP takes into account all relevant pathways ofbackpropagation as shown in Fig. 10. The output weights ofthe critic network are then updated by

∆WC (k) = −ηC ETC (k)

∂2 J [Y (k)]

∂Y (k)∂WC (k)(10)

where ηC is a positive learning gain.

3.5. Design of the action network

As shown in Fig. 11, the inputs to the action network are theplant outputs, Y , at time k − 1, k − 2 and k − 3. The outputsof the action network are the plant inputs, A, at time k. Theadaptation of the action network, is achieved by propagatingλ(k + 1) back through the OWAM to the action network

Fig. 10. Adaptation of the critic network in DHP.

Fig. 11. Adaptation of the action network in DHP.

(Prokhorov & Wunsch, 1997). The objective of such adaptationis to find out the optimal control trajectory A∗ in order tominimize the cost-to-go function J over time, given by

A∗(k) = arg minu

[J (k)] = arg minu

[U (k) + γ J (k + 1)]. (11)

The output weights of the action network are then updated by

∆WA(k) = −ηA

[∂U (k)

∂ A(k)+ γ

∂ J (k + 1)

∂ A(k)

]T∂ A(k)

∂WA(k). (12)

The detailed training procedure of the critic and actionnetworks can be found in Prokhorov and Wunsch (1997),Venayagamoorthy et al. (2003), and Park et al. (2004).

4. Simulation results

In this section, simulation studies are carried out to showthe dynamic performance enhancement of the power system inFig. 1 with the WACNC, while considering the effect of signaltransmission delays.

4.1. Case I: a three-phase short circuit without line tripping

The power system in Fig. 1 is operated at a normal operatingcondition (OP-I) as specified in Qiao et al. (2006), where theactive power generated by the wind farm is Pg4 = 300 MW.

W. Qiao et al. / Neural Networks 21 (2008) 466–475 473

Fig. 12. Comparison of power system dynamic performance with and withoutthe WACNC for Case I.

Thereafter at t = 51 s, a three-phase short circuit is applied tothe bus 7 end of line 7–8, which is a critical transmission lineconnecting Areas 1 and 3. The fault is cleared after 150 ms.

The dynamic performance of the power system, reinforcedwith the WACNC, is compared with the case without theWACNC. Fig. 12 shows the responses of ∆ω2, ∆ω3, and ∆Pg4with and without the WACNC. The curves τ = 0, τ = 100 ms,and τ = 160 ms indicate the results by using the WACNCwithout any signal transmission delay, with 100 ms delay, andwith 160 ms delay, respectively. This grid fault is not a severedisturbance. Therefore the local controllers are able to restorethe system to the prefault normal operating condition withoutthe coordination from the WACNC.

On the other hand, the WACNC improves the rotoroscillation damping of synchronous generators (G1 and G2)and power oscillation damping of the wind farm (G4). However,the performance of the WACNC depends on the period of thedelay involved in the signal transmission. A larger delay willresult in a further degradation of the WACNC performance.

In this design, the WACNC improves the damping of ω2, ω3,and Pg4 with the delay up to 160 ms, but cannot provide thesatisfactory coordinating control action for the system witha delay over 160 ms. These results show that the WACNChas the capability to improve the transient performance ofall generation units in a power system with small signaltransmission delays.

4.2. Case II: a three-phase short circuit with line tripping

At the same operating condition OP-I, a three-phase shortcircuit is now applied to the bus 3 end of one of the paralleltransmission lines 3–4 at t = 51 s. The fault is cleared after150 ms by tripping the faulted line and the system changes to adifferent operating condition.

The dynamic responses of ∆ω2, ∆ω3, and ∆Pg4 with andwithout the WACNC are compared in Fig. 13. Compared toCase I, Case II is a more severe fault. The power oscillationsof G2, G3, and G4 cannot be effectively damped by only usingthe local controllers. These results indicate that without theWACNC, the local controllers cannot restore the system to anormal operating condition after this severe disturbance. As aresult, the power system will lose stability.

On the other hand, the WACNC significantly improves thedamping of ω2, ω3, and Pg4 with the signal transmission delayup to 160 ms. However, further increase of the delay over 160ms will result in unsatisfactory coordinating control action fromthe WACNC, and the system may become unstable. It is wellknown that synchronous generators are the key componentsfor power system stability. In addition, with the increasedpenetration of wind generation, the transient behaviour of windfarms during grid disturbances begins to influence the stabilityof the associated power system. Fig. 13 shows important resultsthat the WACNC has the capability to improve the transientperformance of all generation units in the power system,and therefore the overall power system stability, without anycompensation for the small delays involved in the signaltransmission. These results are expected because the WACNCis designed at a global level to optimize the entire powersystem performance. This system-wide damping performanceimprovement and stability, however, could not be achieved byany single local controller.

4.3. Tests at a different operating condition

The same 150 ms three-phase short circuit tests as forOP-I are now applied at another operating condition (OP-II),where the active power generated by the wind farm becomesPg4 = 350 MW. Applying Prony analysis on the simulationwaveforms, the eigenvalues, frequencies, and damping ratios ofthe dominant oscillation modes in ω2 and ω3 can be obtained,as shown in Table 1. In this investigation, a 100 ms signaltransmission delay is considered in the WCANC design. Atboth operating conditions in Case I, the WACNC improvesthe rotor oscillation damping of both synchronous generators.While at both operating conditions in Case II, the real partsof the eigenvalues are nearly zero and the resulting damping

474 W. Qiao et al. / Neural Networks 21 (2008) 466–475

Table 1Dominant oscillation modes in ω2 and ω3: a 100 ms signal transmission delay is considered in the WACNC design

Fault Operating condition Signal Eigenvalues λ = σ ± jω Frequency (Hz) Damping ratio (%)

Case I OP-I Without WACNC ω2 −0.539 ± j5.174 0.83 10.36ω3 −0.874 ± j7.320 1.17 11.85

With WACNC ω2 −0.660 ± j5.252 0.84 12.46ω3 −1.025 ± j8.085 1.29 12.58

OP-II Without WACNC ω2 −0.732 ± j5.232 0.84 13.86ω3 −0.683 ± j5.890 0.94 11.52

With WACNC ω2 −0.854 ± j5.443 0.88 15.50ω3 −0.786 ± j6.235 1.00 12.51

Case II OP-I Without WACNC ω2 −0.014 ± j5.267 0.84 0.27ω3 −0.089 ± j5.702 0.90 1.57

With WACNC ω2 −0.310 ± j4.910 0.78 6.30ω3 −1.312 ± j8.698 0.92 14.91

OP-II Without WACNC ω2 −0.288 ± j5.227 0.83 5.51ω3 −0.545 ± j6.107 0.98 8.89

With WACNC ω2 −0.446 ± j5.647 0.90 7.87ω3 −0.846 ± j5.933 0.95 14.12

Fig. 13. Comparison of power system dynamic performance with and withoutthe WACNC for Case II.

ratios are nearly zero without the WACNC. Therefore, thepower system may lose stability after this severe disturbance.On the other hand, the WACNC is able to stabilize the systemby coordinating the actions of the local controllers at a globallevel through its optimal control law. There results indicate thatthe WACNC increases the stability margin of the entire powersystem, and therefore more active power can be transmitted tothe loads while maintaining the system stable during transientdisturbances.

5. Conclusion

Wide-area coordinating control is becoming an importantissue in power industry. This paper has proposed a novel wide-area measurements based optimal wide-area monitor and wide-area coordinating neurocontrol, for a power system with PSSs,a large wind farm, and multiple FACTS devices. The OWAM,which identifies the input-output dynamics of the nonlinearpower system, is a PSO-optimized radial basis functionneural network. Based on the OWAM, the dual heuristicprogramming method and RBFNNs have been employed todesign the WACNC, while considering the delays involvedin the wide-area signal transmission. The proposed WACNCoperates at a global level to coordinate the actions of localpower system controllers. Each local controller receives remotecontrol signals from the WACNC to help improve system-widedynamic and transient performance and stability.

Simulation studies have been carried out on a multimachinepower system to evaluate the dynamic performance of theWACNC during transient events. The effect of different signaltransmission delays has been investigated on the performanceof the WACNC. Results have shown that the WACNC improveddamping of all the generating units in the power system andtherefore the entire power system transient performance andstability, without the need to compensate for the small signaltransmission delays.

W. Qiao et al. / Neural Networks 21 (2008) 466–475 475

Acknowledgement

This work was supported in part by the National ScienceFoundation, USA, under grant ECS # 0524183.

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