Accurate and Estimation Methods for Frequency Response Calculations of Hydroelectric Power Plant

Transcription

1 Accurate and Estimation Methods for Frequency Response Calculations of Hydroelectric Poer Plant SHAHRAM JAI, ABOLFAZL SALAMI epartment of Electrical Engineering Iran University of Science and Technology IRAN Abstract: - Along ith the deregulation, reduction of poer system stability has to be expected. In this context, dynamic studies of poer plants are necessary and availability of simulation models of poer plants become more and more important. These models are necessary for the estimation of stability limits in different situations. In this paper, evaluation of different methods for frequency response calculations of hydro poer plant ill be presented. ifferent turbine models and various approximations used in calculations are shon in this paper. Estimation methods used for fast and approximate assessment of dynamic changes of poer system frequency generally have serious problems such as lack of real system data. In real applications hen sufficient poer plant data is available, it is better to use accurate models. A nonlinear model developed for dynamic studies of hydro poer plants is presented. In this paper simulation results are highlighted based on different models and situations. Key-Words: - Frequency Response, Hydro Poer Plant, Turbine Model, ynamic Modelling, Estimation Methods, Accurate Model Introduction Computer simulation dealing ith different scenarios for electrical netorks need much more detailed model of poer plants and poer systems components than those for stability scenarios. Poer and frequency oscillations normally occur in generator units due to different actions. Operators often rely on their intuition and experience acquired during normal system operation or on crude rules to predict the system frequency behaviour hen loads are changed. There are different methods for prediction of frequency behaviour of prime movers for stability studies [-3]. It is obvious that the poer plant models are the most complicated elements of a poer system model. The increasing use of hydro poer plant as part of poer systems generation brings a need for modelling and simulation of this type of poer plants in assessment of poer system dynamic performance. In stability scenarios, often very simple and restricted models of poer plants and equipment for control and security purposes are used. The estimation methods are considered adequate for typical first sing stability simulation. Especially in vie of the fact that for accurate analysis more complex approaches or model development are necessary and unavoidable, but approaches based on methods ith assumption and significant simplifications are not sufficient. The dynamic of hydraulic turbines have a considerable influence on the dynamic stability of the poer system [,4].There are some analysis like restoration after blackout, islanding and isolated system operation, turbine control system and load rejection hich requires dynamic analysis of hydro poer plants. These analysis require ne models to include the ide spread use of poer plant models. It is better to use models describing the actual situation rather than approximate models. Lo order models for hydraulic turbine are used in some orks for stability studies [, 5, 6]. It as found that the idely used first order model, as ell as a second order model based on a Taylor series approximation of the hyperbolic tangent function, are not very accurate in some stability studies, and suitable models are needed for more accurate applications. The dynamic behaviour of hydraulic poer plants has been analysed ith linearized model [7]. This paper proposes a ne evaluation using different models to calculate frequency response of hydro poer plant. This evaluation includes simple and complex models that are effective in different situations. ifferent methods are used for evaluating frequency response rates of hydro poer plants to sudden change in loads. These methods include

2 conventional and developed models of hydro poer plants. The methods are based on conventional models named estimation methods and the other accurate model. Estimation methods are described in section 2 consists of simple method and transfer function methods, hich are fast and sufficient for approximate assessment of poer system frequency. This ork proposes transfer function method, hich is simple, fast, flexible and successful for frequency response calculations. Simulation studies sho accuracy of the proposed method is near complete transfer function model for frequency response calculations. The accurate model is described in section 3, hich uses mathematical models of particular parts of a turbine system for hydro poer plants. The main characteristic of the accurate model is to consider different parts of hydro poer plant. The accurate model shos a more detailed and precise calculation of the frequency response in the poer system. The presented method needs more data from poer plants for simulation as compare to previous methods. In order to test and verify the results of dynamic studies, Simulations have been carried out on dynamic model of hydro units. 2 Frequency Response Estimation Methods In this section, some of frequency response estimation methods ill be explained. These methods are based on conventional model of hydro poer plant. The basic objective of this section is to present the development of simple methods for the rapid and sufficiently accurate assessment of dynamic poer system frequency changes resulting from significant poer imbalances. The main characteristic of these methods are analytical expressions for calculation of frequency response. H: inertia constant, : damping constant, ω : deviation from the nominal frequency, P e : change of electrical poer, P m : change of mechanical poer. According to equation (), folloing a load change of - Pe, a linear function that defines the initial rate of frequency decay, can be ritten as: Pe f ( t) = ( t) f n (2) f n : nominal frequency of system Other frequency behaviour can be developed hen equation () is transformed into the laplace domain and back into the time domain giving the exponential function [8]: Pe t f ( t) = exp( ) TPe f n (3) T Pe = (4) 2.2 Transfer Function Method A simple guideline for the estimation of the frequency response of prime movers is shon in [3]. This method is based on laplace domain calculations and average frequency models. Fig. shos a simple block diagram for the prime mover under consideration. Based on this diagram, the function ω(s) can be determined and then transformed back into the time domain. This function can be used for dynamic studies of hydro poer plant. G (s), G 2 (s), G 3 (s), and G 4 (s) represent the transfer functions of speed-governor systems, the prime movers, the poer system and speed regulation respectively. System frequency, nominal frequency and changes of load are shon by f, f ref, and P L respectively. 2. Simple irect Method The frequency behaviour of islanded system is controlled by the governors. In case of a load change they detect the deviation of frequency and as a consequence, change the gate or valve position, until a ne equilibrium ith an acceptable system frequency is reached. Shortly after a load change, the frequency behaviour is determined by the change in load, the turbines characteristics, inertia constant and damping constant. For changes in poer, it can be ritten in per unit as [8]: d ω = Pm Pe ( ω) () dt f ref - - -P L Governor Turbine Generator G (s) G 2 (s) G 3 (s) G 4 (s) Fig. Simple block diagram of prime mover f

3 The transfer functions and data for typical hydro poer plants are as follos: G ( s) = (5) s st G st G2 ( s) = At (6) 0.5sT G s = 3 ( ) (7) 2 Hs st G4 ( s) = RP Rt (8) st : T G : Gate servomotor time constant T : Water starting time penstock T : ashpot time constant R P : Permanent droop R t : Transient droop A t : Proportionality factor for converting actual gate position to the effective gate position Hoever, the attempts to develop a function taking into account the full block diagram of Fig. leads to an unnecessarily complicated equation. 2.3 Simplified Governor Method The simplification can be accomplished by comparing the time constants. The time constant T G is considerably smaller than the constants T andt, so it can therefore be set to zero. In the next step, e define time constant T Pt as: RP Rt T Pt = T T (9) RP These simplifications results in simple block diagram as shon in Fig.2. f ref - Governor Turbine -P L Generator G (s) G 2 (s) G 3 (s) Fig.2 Simplified control block diagram of hydro unit The transfer function G (s) is as follos: s T G( s) = (0) s s RP Rt T The transfer functions G 2 (s) and G 3 (s) are same as before. f 2.4 Proposed Transfer Function Method The proposed method based on simplified governor model is presented. This method gives an analytical expression for calculation of frequency response using parameters of hydro poer plant, hich is suitable for frequency response calculation. Transfer function of the model, hich is shon in Fig.2, can be formulated as: ( s) () N ω () s = k s () Pe k = (2) 2 () N s = s s T TN (3) At () s = HT T HTT N ( T T ) At HT T s At 2 2 s T HT H T T N N s s TN T (4) TN = (5) R p Rt T Once the roots are available, (s) can be formulated in a factored form as: 4 s = Π s z (6) () ( ) j= j z j : the roots of (s). Equation () can then be expanded in partial fractions to obtain: 4 R j ω () s = k j= s z j (7) R = ω s s z (8) j ( )( ) j s= z j Frequency in time domain is shon as (9): f () t 4 = ( R j exp( z jt ) f n (9) j= This expression can be used to calculate the system frequency fast and accurately.

4 3 Accurate Hydro Unit Models The aim of this section is to present the developed model of hydro poer plants for dynamic studies that are needed in more accurate applications. The plant models, hich are investigated here, consists of penstock, hydro turbine and electro hydraulic actuator system models. The accurate model considers different parts of hydro poer plant, therefore this model consists a more detailed for calculation of the frequency response in the poer system. 3. Penstock Model The dynamic of hydraulic turbines have a considerable influence on the dynamic stability of the poer systems. First order hydraulic turbine model in a realistic, multi machine model of the interconnected system is investigated. It is shon that turbine model of at least the second order is more appropriate for dynamic studies [6]. The penstock dynamic is described in detail in [9, 0]. ynamic of penstock is described ith a set of partial differential equations considering one dimensional average ater flo through certain plane area of the penstock taking into account the speed of the ater flo hich is much sloer than the speed of the ater hammer[4]. These equations are shon as: 2 h a q = 0 (20) t A g x TC q h f ATCg q q ATC t x 2ATCTC h: dynamic pressure at the penstock, q : ater flo at the penstock, a: ater pressure ave velocity, g: gravitational constant, A TC: area of the penstock cross section, f : friction constant, TC : inner diameter of the penstock, α TC : inclination angle g sinα = 0 (2) 3.2 Electro Hydraulic Actuator The ater flo into the turbine is controlled by the guide vane hose position depends upon the control signal from the governor. The guide vane dynamics can be represented as multi stage actuator. Electro hydraulic actuator system model can be represented in a simplified form in hich first order element is considered: TC F = (22) Ta s T a : time constant of the hydraulic piston positioning control system 3.3 Hydro Turbine Model The conventional representation of the penstockturbine is shon as G 2 (s) in previous section, hich relates the incremental change in torque to the guide vane deviation, assuming linearization about the operating point ith the ater starting time T varying ith flo and hence ith load. uring some situations like restoration the load changes anticipated cover the full range, therefore transfer function G 2 (s) is less appropriate for this study. It seems more accurate models of turbine are needed. The hydro turbine is described by ater flo function f Q (h, N,y) and poer function f P (h, N,y) [9]. These functions are represented by: q T = y h TC (23) P = At ( qt q NL ) htc a ( N ) y (24) q NL : ater flo at zero electrical poer in [p.u.] a : ater turbine damping [p.u. /p.u.] A t : transformation coefficient beteen turbine and generator base poer y: gate opening Nonlinear turbine model, hich is linearized in the vicinity of the operating point, is useful. The dynamics of the analyzed system ith respect to the operating point can be observed by changing operating point. The linearized model can be applied as ell as a hydro turbine model for simulations. 4 Simulation Results In order to test the dynamic studies of the hydro poer plant, simulations ere carried out on dynamic model of hydro unit based on hat described in previous sections. In the simulations load rejection or load pick up are used to sho changes of load and based on these modes frequency response of the poer system have been calculated. 4. Simulation of Estimation Methods Simulation of frequency response can be done by change of load. In the simulation, a step load is used hich represents changes of load in the system.

5 Response of islanded configuration to change of load ill be shon in different figures. Result of simulation based on simple method in various modes of linear, exponential and transfer function methods is shon in Fig.3. It shos that some of methods as simple direct method cannot be used for long periods and the results only in primary fe seconds are acceptable and it is necessary that accurate model are used for long periods. Frequency (Hz) Transfer function method Exponential method Linear method simplified governor method are same and near complete model of transfer function. Proposed transfer function method is simple, fast, flexible and successful for frequency response calculations. 4.2 Simulation of Accurate Models In this section, simulation of hydro poer plant is done ith respect to more detailed model of hydro poer unit that named accurate hydro poer plant model. eveloped model needs more data compared to conventional model for simulation. A load rejection or load pick-up simulation can be done based on described model of hydro unit. The results of the load pick-up simulation are shon in figures (5) to (8). A step load is used, as this represents changes of load in the system. Electrical load and mechanical poer are shon in Fig.5. The results are obtained hile load pick-up as 0. p.u Fig.3 Frequency response of simple direct and transfer function method The dynamic response of hydro poer plant using transfer function models is simulated and the results are shon in Fig Proposed and Simplified governor methods Load and mechanical poer (p.u.) Fig.5 Electrical load and mechanical poer Frequency (Hz) Transfer function method ynamic changes of penstock model and gate position are shon in Fig.6 and Fig.7. These parameters ere described in previous section Fig.4 Frequency response of transfer function, simplified governor and proposed methods Comparing these methods shos for more accurate applications, simplified methods are not appropriate and more realistic dynamic model of the poer plants are necessary. Simulation studies sho the frequency responses of the proposed method and ynamic pressure (p.u.) Fig.6 ynamic pressure of penstock

6 Gate openning (p.u.) these methods demonstrate that the accurate model requires more real data of hydro poer plant and in case of lack of data, user is forced to use conventional models. Correctly developed dynamic model of the poer plants are necessary in accurate applications like load rejection or restoration after blackout, and simplified models can be used in some application like typical first sing stability simulation Fig.7 Gate opening Fig.8 shos frequency response simulation of the poer system. Frequency (Hz) Fig.8 Frequency response of system It is obvious that hen the dynamic behaviour of the poer plants is necessary, these models can be used. The advantage of this simulation is that it has considered better model for hydro poer unit than conventional models. 5 Conclusion This paper presented the evaluation of the poer system frequency for hydro poer plants based on different conditions. The proposed methods considered conventional and developed accurate models for hydro poer plant. This paper evaluated proposed transfer function method, hich is simple, fast, flexible and successful for frequency response calculations. Simulation studies of proposed transfer function method shoed accuracy of the proposed method is same as simplified governor model and near complete transfer function model for frequency response calculations. The other method that named accurate method considered different parts of hydro poer plant model. Therefore, this model gives more accurate frequency response than estimation methods. The selection of these methods is based on applications and the study scenarios. Comparison of References: [] P.M. Anderson and M. Mirheydar A Lo- Order System Frequency Model, IEEE Trans. on Poer Systems, Vol. 5 no.3, August 990, pp [2] M.B. jukanovic,.p. Popovic,.J. Sobajic and Y.H. Pao, Prediction of Poer System Frequency Response after Generator Outage using Neural Nets, IEE Proceeding-C, Vol. 40,no.5, September 993, pp [3] M.M. Adibi, J.N. Borkoski, R.J. Kafka and T.L. Volkmann, Frequency Response of Prime Movers during Restoration, IEEE Trans. on Poer Systems, Vol. 4 Issue: 2, May 999, pp [4] O. H. Jr Souza, N. Barbieri and A. H. M. Santos, Study of hydraulic transient in hydro poer plants through simulation of nonlinear model of penstock and hydraulic turbine model, IEEE Trans. on Poer Systems, Vol.4, no.4, Nov. 999, pp [5]. G. Ramey, and J. W. Skooglund, etailed Hydro Governor Representation for System Stability Studies, IEEE Trans. PAS-89, January. 970, pp [6] C.. Vournas, Second Order Hydraulic Turbine Models for Multimachine Stability Studies, IEEE Trans. on Energy Conversion, Vol.5, no.2, June. 990, pp [7] J. M. Undrill, and W. Strauss, Influence of Hydro Plant esign on Regulating and Reserve Response Capacity, IEEE Trans. PAS-93, July. 974, pp [8] P. Kundur, Poer System Stability and Control, McGra-Hill, 994. [9] IEEE Working Group Report, Hydraulic turbine and turbine control models for system dynamic studies, IEEE Trans. on Poer Systems, Vol. 7, no., Feb. 992, pp [0] E. e Jaeger, N. Janssens, B. Malfliet and F. Van e Meulebroeke, Hydro turbine model for system dynamic studies, IEEE Trans. on Poer Systems, Vol.9, no.4, Nov. 994, pp