Modeling Of Custom Hydro Turbine And Governor Models For .
1Modeling of Custom Hydro Turbine and Governor Models forReal-Time SimulationWei Li, Student Member, IEEE, Luigi Vanfretti, Member, IEEE, Mostafa Farrokhabadi, Student Member, IEEEAbstract—This article develops three different hydro turbineand governor (HTG) models to fulfill adequate modeling requirements for the representation of hydro power generation inthe Nordic grid. To validate the performance of the developedmodels, both off-line and real-time simulation studies on a singlemachine infinite-bus (SMIB) system are carried out. Apart fromSMIB system, real-time simulations are also executed for alarger scale power system—the IEEE Reliability Test System1996 (IEEE RTS 96) in this article to determine the models’dynamic performance in larger and more complex networks. Inaddition, how to properly transfer an off-line models developedin SimPowerSystems (SPS) for real-time simulation in RT-LABis addressed; including valuable experiences obtained from thesesimulation exercises.Index Terms—Hydro Turbine and Governor, Real-Time SimulationI. I NTRODUCTIONOday, hydro-power accounts for one half of Sweden’selectricity net production of electrical power generationand 56% of Nordic system [1], respectively. As one of the mostimportant energy sources, the exploitation of hydro-power hasnaturally attracted more and more attention particularly in theNordic region [2]. In hydro power production systems, it is notpossible to neglect turbine and governor’s functions, whichparticipate in the primary frequency control of synchronousmachines. With the continuous development of power systemsimulation software, engineers have more choices for includingvarious components in simulation, however, there are stillmany cases that custom HTG models need to be designedand implemented to meet particular modeling and simulationrequirements.The purpose of this article is to develop three differentHTG models to fulfill adequate modeling requirements for therepresentation of hydro power generation in the Nordic grid.Different scales of test systems, the SMIB system and IEEERTS 96 system, are used to validate the models’ performance.In addition, real-time simulations for both test systems are carried out, which allows for future hardware-in-the-loop (HIL)testing of prototype turbine controls [3]. As supplementary,valuable experiences obtained from these simulation exercisesare shared at last.TII. M ODELING OF HYDRO TURBINES AND GOVERNORSThe hydro turbine and its governor are normally combinedtogether for representation. When the output of turbine governor is the gate position, it can connect with the hydroInvited Paper for the Panel Session: “RT and HIL Simulation Applications for Approaching Complexity in Future Power & Energy Systems,2012 IEEE Workshop on Complexity in Engineering, June 11-13, 2012.Aachen, Germany.The authors are with the Electric Power Systems Division, School ofElectrical Engineering, KTH Royal Institute of Technology, Teknikringen33, SE-100 44, Stockholm, Sweden.E-mail: ne directly. However, for some cases, the output is thederivative of the gate position, which does not match the inputof the turbine, therefore, a desired gate position referenceis applied to add to the gate position derivative. In thissection, three custom HTGs are introduced with the structuraldiagrams and initialization. In addition, for reference, the HTGmodel provided in SPS is also presented following other threemodels.A. Model 1The structural diagram of Model 1 is shown in Fig. 1. Itconsists of a typical hydro turbine governor model [4] [5] anda linearized hydro turbine model [4] [5]. The output of turbinegovernor is the gate position derivative ( G), while the inputof the turbine is the gate position (G). Consequently, a positionreference Gref , which is regarded as equal to Pref , is requiredbetween them.ref v1Tg (1 Tp s )-PILOT VALVE G1sa 23 (a13a 21 a11a 23 ) sTw1 a11sTw DISTRIBUTORPOSITIONVALVE AND GATELIMITSERVOMOTORRATE LIMITG PrefPmGref PERMANENT DROOPCOMPENSATIONTr s1 Tr sTRANSIENT DROOPCOMPENSATIONLinearized TurbineTypical Tubine GovernorFig. 1.Diagram showing the general structure of Model 1To implement models in computer software and determineits future behaviors under different scenarios, normally, a setof state variables that consist of coupled first-order differentialequations are necessary. However, it is hard to determine thestate variables in the structural diagram. The solution is toutilize a canonical realization by redrawing the models usingsingle integrators and gain blocks. In this way, along the signalflow each state variable is located behind each integrator, whilethe derivative of state variable in the front (see in Fig. 2).xg 1ref1Tg Tp --ca -d1sxg1xg 2bvxg 21s1Tpxg 4GG Prefxg 4 1s-1a11Twa11a 23 a13a 21a11 xg 3Tr1sxg 3 -1TrFig. 2.a13a 21a112 TwBlock Diagram Realization of Model 1 Pm
2refKpKi1s 1Tg (1 Tp s )-PILOT VALVE 1sRATE LIMITGa 23 (a13a 21 a11a 23 ) sTw1 a11sTwDISTRIBUTORPOSITIONVALVE AND GATELIMITSERVOMOTOR ref11 Tp s-PmKpKi 1s-1TgPI CONTROLLERG1s2QG 1Tw-HRATE LIMIT DISTRIBUTOR POSITIONVALVE AND GATE LIMITSERVOMOTOR Hs1sPmQ1- PrefPERMANENT DROOPCOMPENSATIONTurbine GovernorNonlinear TurbineTr s1 Tr sFig. 4.TRANSIENT DROOPCOMPENSATIONPI ControllerTypical Turbine GovernorDiagram Showing the General Structure of Model 3Linearized TubinedKpFig. 3.Diagram Showing the General Structure of Model 2PrefFrom the block diagram realization in Fig. 2, the differentialalgebraic equation (DAE) set can be derived and utilized forcalculating the integrators’ initial values. The derived DAEsare!"1δ1ẋg1 (ωref ω) (σ δ) G xg3 xg1Tg TpTrTp xg1if vmax xg1 vminvmaxif vmax xg1ẋg2 v vif vmin xg1min1ẋg3 G xg3Tra13 a211ẋg4 ( G Pref ) xg4a11 2 Twa11 Tw xg2if Gmax Pref xg2 Gmin PrefGmax Prefif Gmax Pref xg2 G Gif Gmin Pref xg2min Prefa11 a23 a13 a21Pm xg4 ( G Pref ).a11When the system is in steady state, ω ωref , the rate ofthe gate movement v 0, and the gate is fixed as G 0.The initial values for Model 1 can be obtained by setting thederivatives to zero:a13 a21xg1 xg2 xg3 0, xg4 Pref , Pm a23 Pref .a11This initial values can also be determined by analyzing Fig. 2.When the system is in steady state, ω ωref , all thederivatives of all state variables are zero. Consequently, aswe can see, point a and b are zero. Because c b a, c isaccordingly equal to zero. Similarly, point d is also zero as(ωref ω) and c are zero. With this recurrence method, it ispossible to obtain all the state variables’ initial values that areas those obtained with the DAEs, and hence, this method canbe used to check if the DAE initialization is correct.B. Model 2As shown in Fig. 3, the difference between Model 2 toModel 1 is a simple PI controller added in the front of theturbine governor [6] [7]. The integrator in the PI controllercomputes the integral of the error between ωref and ω, whichaffects the input of turbine governor model. In this case theoutput of turbine governor becomes the gate position itself,which is also the input of the turbine model. The integratorsinitial values in Model 2 can be obtained from its DAEs:G Pref , xg1 σPref , xg2 0, xg3 Pref ,a13 a21xg4 Tr Pref , xg5 Pref , Pm Pref .a11 refPeRp1sKi -Ka sTa s 11sgG1g maxg minQG2 Turbine Governor-HKd sTd s 1PID CONTROLLERFig. 5. Hs 1Tw1sQPm1SERVOMOTORNonlinear TurbineBlock Diagram Showing the General Structure of Model 4C. Model 3Model 3 is taken from [8], in which the main differenceto the previous models is that a nonlinear turbine model isused. For nonlinear turbine models, when calculating Jacobianmatrices, the partial derivatives of the differential function fwith respect to state variables x still contain state variables,which means that the partial derivatives change with time. Thistranslates to different performances when compared with linearturbine models. When the system is in steady state, ω ωref ,all differential variables are equal to zero, thus M and G areequal to Pref . The calculation results for integrators’ initialvalues areG Pref , xg1 0, xg2 Pref ,xg3 Pref , xg4 Pref , Pm Pref .D. Model 4The HTG model in SPS is encapsulated into one blocknamed HTG, which contains a nonlinear hydro turbine model,a PID governor system, and a servomotor. An additionaldistinction is that this model makes use of ω̇ as another inputto the turbine, which can accelerate the system reaction whenit is subjected to a large transient perturbation. The turbineand governor model can be transfered into the diagram shownin Fig.5. The integrators’ initial values are calculated fromG Pref , xg1 g (gmax gmin ) Pref , xg2 xg3 0,xg4 g (gmax gmin ) Pref , xg5 Pref , Pm Pref .III. S IMULATION OF CUSTOM HYDRO TURBINE ANDGOVERNOR MODELS IN A SMIB SYSTEMNext, the off-line and real-time performances of the developed HTG models in a SMIB system are examined. Theevaluation of a power system’s performance is concernedwith the stability of that system: i.e. if it remains in anequilibrium after being subjected to a disturbance [9]. Offline simulation makes use of variable step solvers to computethe next simulation time as the sum of the current simulationtime and a variable step size. Variable step size solvers cantake flexible steps along with the variables varying rapidly or
3A. Introduction for the SMIB systemBus 2 (infinite bus)Bus 3L1: j0.1Machine:991MVA 20kVFig. 6.Transformer:20kV/230kVL2: j0.1The SMIB systemB. Off-line simulation for each SMIB systemA three-phase fault is applied at Bus 3 at t 5 s andremoved at t 5.02 s. After computing the power flow, timedomain simulations show the model responses in SPS. Figure 7depicts the generator rotor speed of off-line simulation resultsfor SMIB systems with each HTG model in SPS.Rotor Speed (p.u.)Rotor Speed of the SMIB system1.0021Fig. 7.Hydro TG1Hydro TG2Hydro TG3Hydro TG40.9980.9960510Simulation Time (s)Rotor Speed of the SMIB system with Hydro TG 21.0021.0011.001110.9990.999Step Size 20usStep Size 50us0.9980510150.9982005101520Rotor Speed of the SMIB system with Hydro TG 31.002Rotor Speed of the SMIB system with Hydro TG 41.0021.0011.001110.9990.9990.9980.9980Fig. 8.510152005101520Rotor speed of the SMIB system for different HTG modelsRotor Speed of the SMIB system with Hydro TG 11.110.90.8Step Size 20us0.7Step Size 50usStep Size 100us0510Simulation Time (s)1520Fig. 9. Rotor speed of the SMIB system with HTG1 for different step sizesFigure 6 shows a SMIB system consisting of one 991 MVA,20 kV, 50 Hz generator, one transformer operating 20 kV onthe primary and 230 kV on the secondary, two lines withreactance of 0.1 p.u. and an infinite bus.Bus 1Rotor Speed of the SMIB system with Hydro TG 11.002Rotor Speed (p.u.)slowly. This ability to change step sizes to meet the errortolerances can increase computational efficiency. However,variable step size solvers are not appropriate for deterministicreal-time applications because the variable step size can notbe mapped to a real-time clock, which is important in HILtests.Compared to conventional hardware prototype testing, HILreal-time simulation takes advantage of decreasing damage onequipment, reducing expense as well as extending simulationtime during the development process of a product [10]. Forreal-time simulation, the amount of time spent calculating thesolution for a given time step must be fixed, and moreover, itshould be less than the length of that time step. In this case,a fixed-step solver must be used instead of a variable stepsize solver for real-time simulation. To ensure that the resultsobtained with the fixed-step solver are accurate and the fixedstep size is suitable, the off-line simulation with a variablestep solver will be set as the reference.The real-time simulations shown in this article are performed in the SmarTS Lab at KTH, which includes two realtime targets of Opal-RT’s eMegaSim real-time simulator [11].1520Off-line simulation results for SMIB systems with HTG modelsC. Real-time simulation for each SMIB systemFigure 8, 9, 10, 11, 12 show the real-time simulation resultsfor the SMIB system with each HTG model. All the realtime simulation data can be written to a MATLAB file bythe “OpWriteFile” block. As depicted in Fig. 8, all the SMIBsystems with different HTG models show the nearly sameperformances with the off-line simulation above. At the sametime, these results indicate that the applied step sizes (50 µs,20 µs) are capable for running this real-time simulations.By contrast, 100 µs is too large to capture the true realtime dynamic performance and finally results in the numericalinstability shown in Fig. 9. This is an intuitive instance to showhow the fixed step size significantly influences the simulationperformance. But it does not mean that the shorter step size,the better solution, particularly when the given step size isshorter than the time for computing the solution (referred asoverruns). Generally speaking, decreasing step size increasesthe accuracy of the results while increasing the computationalresources required to simulate the system up to the limitsimposed by Amdahl’s law.In order to obtain the accurate timing information of realtime simulation, the RT-LAB library is equipped with a set ofsystem monitoring blocks. For instance, the OpMonitor blockprovides timing information including “Computation time”,“Real step size”, “Idle time” and “Number of overruns” [12],which could be used to analyze if the current step size isappropriate for real-time simulation and if there is still spaceto reduce the step size for better performance. According toFigs. 10 and 11, the computation time is far smaller than thestep size only except when a fault occurs, which guaranteesvery small amount of overruns during real-time simulation asshown in Fig. 12.IV. R EAL - TIME SIMULATION OF CUSTOM HYDRO TURBINEAND GOVERNOR MODELS IN IEEE RTS 96 S YSTEMA. Introduction for the IEEE Reliability Test System 1996The IEEE RTS 96 system was developed and publishedwith the objective of assessing deterrent reliability modeling
4Computation Time of the SMIB system with Hydro TG 1 Computation Time of the SMIB system with Hydro TG 22.52.54237Area 4393 UnitsSC402515921.5051032Step15Size 100us201.5570510151.50510152005101520Fig. 10. Computation time for the SMIB system with different HTG models(enlargement)90753331 3214101311122316 9Area 6754783Bus168076818425102 1783518485569853828888Bus188754551001066Area 1Computation Time of the SMIB system with Hydro TG 66203364582819855 Bus1863 UnitsArea 94 Units6 UnitsArea 81000Fig. 11.Fig. 13. One area of the modified IEEE Reliability Test System 1996 (takenfrom [14])Step Size 20usStep Size 50us500Step Size 100usVoltage Magnitude of Bus1 in the IEEE RTS 96 system00510Simulation Time (s)15Voltage Magnitude (p.u.)Computation Time (us)172115609390377468 6963615741Bus571187015 16Bus1018 38 39237222Bus681418765307634Bus4146911 Bus340253595Area 5661163 Units28120Computation time overview of the SMIB system with HTG1and evaluation methodologies as well as meeting the newchanges in the electric utility industry [13]. The single linediagram of IEEE RTS 96 system which has been carried outin SPS for a new implementation is shown in Fig. 13. Thissystem comprises of 10 synchronous generators, 66 lines and34 buses; it consists of 24 substations, with configurations suchas Single Bus Single Breaker, Double Bus Double Breaker,Breaker and a Half, and Ring [14].B. Real-time simulation for the IEEE Reliability Test System1996The (modified) IEEE RTS 96 system is divided into 9subsystems as shown in the Fig. 13, called Area 1 to 9.Adding the console subsystem, which contains all the scopesand controllers and plays the role of interfacing between therunning model and the host monitoring console, there are 10subsystems for the whole model in RT-LAB. Each subsystemwill take account for one core in the real-time simulator, wherethere are 12 in total.Number of Overruns for the SMIB system with Hydro TG 1 Number of Overruns for the SMIB system with Hydro TG 2332Hydro TG1Hydro TG2Hydro TG3Hydro TG41.011.00510.9957580859095100105Simulation Time (s)110115120Fig. 14. Voltage Magnitude of Bus 1 in the modified IEEE RTS 96 systemwith HTG modelsIn this article the IEEE RTS 96 system implements HTGsfor all the 10 generators and carries out the real-time simulation with fixed step size 50 µs. The designed test scenariois to open the breaker 18 at 85 s. Since bus 1 and bus 5are two directly connected buses with breaker 18, the voltagemagnitude of bus 1 and bus 5 are depicted in Fig. 14 andFig. 16, respectively, to analyze the IEEE RTS 96 systemstability particularly with the HTGs. While Fig. 15 focuseson the instant when the fault occurs.Implemented in a large scale power system, the HTGmodels perform differently. Instead of directly inputting apower reference or gate reference signal, HTG of Model 2(Fig. 3) utilizes a PI controller to integrate the error untilthe reference value is reached. Depending on the controllerparameters, there is a risk in that the response will largelydeviate from the reference, and therefore, the HTG of Model22Step Size 20usStep Size 50usStep Size 100us051015Voltage Magnitude of Bus1 in the IEEE RTS 96 system (enlargement)120005101520Number of Overruns for the SMIB system with Hydro TG 3 Number of Overruns for the SMIB system with Hydro TG 433221105101520005101520Fig. 12. Number of overruns for the Master Subsystem in the SMIB systemwith HTG modelsVoltage Magnitude (p.u.)10Bus20424326Bus91184 Units09694291213334Bus12 49507848474427 36Bus24Area 225277Bus1111731454620Computation Time of the SMIB system with Hydro TG 3 Computation Time of the SMIB system with Hydro TG 42.521.5Area 356Area 76061114 112 110107 62111113Bus231099710811553798038Step Size 50usBus13356 Units553658Bus14Step Size 20us541.01Hydro TG1Hydro TG2Hydro TG3Hydro TG41.00510.99584.9958585.00585.0185.015Simulation Time (s)85.0285.025Fig. 15. Voltage Magnitude of Bus 1 in the modified IEEE RTS 96 systemwith HTG models (enlargement)
5Voltage Magnitude (p.u.)Voltage Magnitude of Bus5 in the IEEE RTS 96 systemComputation time of the SMIB system with Hydro TG 1 in non XHP mode2010.95Hydro TG1Hydro TG2Hydro TG3Hydro TG40.90.857580859095100105Simulation Time (s)11011510005101520Simulation Time (s)Number of Overruns for the SMIB system with Hydro TG 1 in non XHP mode100001205000Fig. 16. Voltage Magnitude of Bus 5 in the modified IEEE RTS 96 systemwith HTG modelsComputation Time (us)Computation Time for Master Subsystem in the IEEE RTS 96 system3836Hydro TG134Hydro TG2Hydro TG332Hydro TG430287580859095100105Simulation Time (s)110115120Fig. 17. Computation time for the modified IEEE RTS 96 system with HTGmodelsis more sensitive to the perturbation. Containing a nonlinearturbine component, the HTG of Model 3 (Fig. 4) results in aslower response. The obvious phenomenon is sustaining smalloscillations around steady state. An improvement in HTG ofModel 4 (Fig. 5) is to introduce the derivative of rotor speed,which increases the reaction speed.As seen from Fig. 17, the computation time is below 50µs for all the cases, which guarantees that the overruns arekept low and take place only when the system initializes orthe breaker opens.V. I SSUES RELATED TO REAL - TIME PERFORMANCETo transfer an off-line model developed in SPS to real-timesimulation in RT-LAB (the software used by the Opal-RT realtime simulator), some changes have to be considered. The firsttask is to regroup the SPS model into subsystems accordingto RT-LAB rules. As mentioned before, each subsystem willtake account for one core in the simulator and only onemaster subsystem is allowed in one single model. Master
In hydro power production systems, it is not possible to neglect turbine and governor’s functions, which participate in the primary frequency control of synchronous machines. With the continuous development of power system simulation software, engineers have more choices for including various components in simulation, however, there are still
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Since we have a custom component in the model we can open the Custom component editor. Edit custom 1. Select the User_end_plate component symbol. component 2. Right-click and select Edit custom component. The Custom component editor opens along with the Custom component editor toolbar, the Custom component browser and four views of the custom .
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