Dynamic response of hydro power plants to load variations for providing secondary regulation reserves considering elastic water column effects

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1 Juan Ignacio PÉREZ-DIAZ 1, José Román WILHELMI AYZA 1, Ignacio GALASO BAJO 1, Jesús FRAILE-ARDANUY, José Angel SÁNCHEZ FERNANDEZ 1, Olga CASTANEDA CABRERO 1, Jose Ignacio SARASÚA MORENO 1 Deartment of Hydraulic and Energy Engineering. Technical University of Madrid (1) Deartment of Secial Technologies Alied to Telecommunications. Technical University of Madrid () Dynamic resonse of hydro ower lants to load variations for roviding secondary regulation reserves considering elastic water column effects Abstract. In this aer, the dynamic resonse of a hydro ower lant for roviding secondary regulation reserve is studied in detail. Secial emhasis is given to the elastic water column effects both in the enstock and the tailrace tunnel. For this urose, a nonlinear model based on the analogy between mass and momentum conservation equations of a water conduit and those of wave roagation in transmission lines is used. The influence of the lant configuration and design arameters on the fulfilment of the Sanish Electrical System Oerator requirements is analysed. Streszczenie. W artykule analizowano odowiedź dynamiczną elektrowni wodnej użytej jako wtórna rezerwa. Uwzględniono efekt elastycznej kolumny wodnej zarówno w rurociągu jak i w odływie. W tym celu zaroonowano nieliniowy model bazujący na analogii równaniami zachowania masy i momentu a falową roagacją linii transmisyjnej. (Odowiedź dynamiczna elektrowni wodnej na zmiany obciążenia z uwzględnieniem elastycznych efektów kolumny wodnej) Keywords: Dynamic Resonse of Hydro Plants, Water Hammer Effects, Secondary Regulation Reserve. Słowa kluczowe: elektrownia wodna, odowiedź dynamiczna. Introduction The integration of non-disatchable energies in the electric grid may affect the reliability of the electric ower suly, mainly due to their unredictability and to the existing limitations for efficiently storing energy. An increase in the enetration of non-disatchable energies may give rise to an increase in the needs for load-frequency regulation services [1], such increase being esecially critical in isolated systems, where both regulating ower and short-circuit ower are in general smaller. As it can be seen in Fig. 1, in the Sanish electric ower system, there has been an increase both in renewable energy enetration and in the amount of energy required for certain load-frequency regulation services during last years. In addition, wind installed caacity is exected to increase in the next years. Said increase could have significant imacts on the electricity system oeration if it is not accomanied with flexible generation and storage units []. Energy (GWh) Fig. 1: Monthly energy. U secondary regulation reserve Down secondary regulation reserve Renewable energy (without hydro and thermal) Month (Jan. 003-Dec. 009) In order to rovide the above-mentioned services, ower lants must adat their oerating oint and vary the ower outut within very short time frames, in accordance with the requirements of the electric ower system oerator. In Sain, the resonse times required for load-frequency regulation range from a few seconds (rimary reserve) to 15 minutes (tertiary reserve). 6,00 5,00 4,00 3,00,00 1,00 0,00 Energy (10 3 GWh) Hydro ower lants can rovide load-frequency regulation services in an efficient manner [3]. Nevertheless, the ower lant dynamic resonse to load variations of different magnitudes should be studied in detail in order to guarantee the caability of the ower lant for roviding said reserves within the required resonse times, avoiding harmful ressure fluctuations and instabilities. For that urose, several models have been roosed in the technical literature. In outline, the hydro lant models can be classified as elastic or rigid water column models [4], according to whether or not the water comressibility and conduit elasticity are considered. The use of linear or nonlinear models is usually deendent on the magnitude of the disturbances alied to the hydroower lant under study. Linear models are used for small disturbances [5], whereas non-linear models are used for large disturbances such as load rejection or start-us. In [6] a non-linear rigid water column model is roosed for dynamic studies of a enstock sulying water to one or several hydro units. As it is well known, mass and momentum conservation equations can roerly describe the dynamic behaviour of a water conduit; in said equations, the convective terms can be neglected with resect to the roagative terms, due to the higher relative wave seed [7]. Several methods have been roosed to solve the resulting system of artial differential equations. In [8] the well-known characteristics method [9] is alied to calculate the hydraulic transients in a diversion hydroower lant consisting of reservoir, headrace tunnel, surge tank, enstock and tailrace tunnel; the water inertia of the tailrace tunnel was considered in the enstock. In [10], the roblem is formulated and solved in the frequency domain. Finally, the aroaches roosed in [11] and [1] are based on the analogy between the abovementioned equations and those of electromagnetic wave roagation in transmission lines; - and T-equivalent circuits were used, resectively. In this aer, the dynamic resonse of a hydro ower lant for roviding secondary regulation reserve is studied in detail. For this urose, a nonlinear model based on the above-mentioned electrical analogy is used. The hydroower lant is suosed to be connected to an isolated ower system reresented by an equivalent inertial PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 88 NR 1a/01 159

2 model. The dynamic resonse of the lant to load variations and changes in the oerating oint settings is studied. Secial emhasis is given to the elastic water column effects both in the enstock and the tailrace tunnel. The influence of the lant configuration and design arameters on the fulfilment of the Sanish Electrical System Oerator requirements is analysed. Modelling hydraulic transients Mass and momentum conservation equations roerly describe transient-state flows in closed conduits [9]. By assuming uniform ressure and velocity distributions in the cross section and neglecting both the convective and the sloe terms the above-mentioned equations can be exressed as follows: H a Q (1) 0 t ga x Q H fq Q () ga 0 t x DA There exist several aroaches to solve these equations [8-1]. In this aer, a lumed arameters aroach (i.e. a finite difference method) has been used. This aroach leads to a system of ordinary differential equations that can be reresented as a series of -shaed consecutive elements of length L e. As described below, the orientation of the -shaed elements may vary according to the ustream and downstream boundary conditions of the ie. Ancillary services Ancillary services (AS) may be defined as the set of activities aart from the energy roduction, which are related to safety and reliability of a ower system [13]. Five different AS are rovided within the Sanish Electric Power System: Primary, secondary control and tertiary control (reserve) ancillary services Balancing ancillary service Voltage control ancillary service Primary, secondary, tertiary and balancing AS rovide the necessary equilibrium between generation and demand. Voltage control AS is designed to maintain an adequate voltage rofile within the transmission grid. Reserve services differ from each other mainly in two different asects: The resonse time required to rovide the service The market mechanisms around which the service is organized or negotiated The aim of the rimary control ancillary service (PCAS) is reventing large variations of frequency. In order for a unit to rovide the PCAS it must be caable of modifying 1.5% of its rated outut before 15 s for frequency deviations lower than 100 mhz, and linearly u to 30 s for frequency deviations u to 00 mhz. PCAS is a mandatory non remunerable AS. In turn, the main objective of the secondary control ancillary service (SCAS) is to bring the system frequency back to its scheduled value. In order for a unit to rovide the SCAS, its outut ower must vary according to an established resonse criteria, begin before 30 s and be maintained for 15 minutes. The aim of the tertiary control ancillary service (TCAS) is to relace the secondary reserve in use. In order for a unit to rovide the TCAS its outut ower variation must be set in 15 min and sustained for at least hours. This aer is focused on issues related to the rovision of the PCAS and SCAS Model descrition The model used in this aer is comosed of the following comonents: i) Ustream reservoir: the head in the ustream reservoir is considered constant and equal to h ur. ii) Head-race tunnel: a rigid water column model (3) is used to reresent the head-race tunnel behaviour. dq (3) hr 1 r ( h hr ur hs q hr ) dt Thr iii) Surge tank: a surge tank is located between the headrace tunnel and the enstock. The surge tank dynamics is modelled as follows: dhs (4) Fs qhr q 1 dt iv) Penstock: a lumed arameters model has been used to reresent the enstock behaviour. A scheme of the model can be seen in Fig.. The set of equations of the enstock dynamics are as follows: dq, i ne r (5) ( h, i 1 h, i q, i ) ; i 1,,ne dt T ne dh, i Tne (6) ( q,, 1) i q i ; i 1,,ne dt ( L / a ) v) Turbine: the turbine has been modelled according to (7)- (8), following the recommendations of [5]: (7) qt z ( ht htr ) (8) t At ht ( qt qv ) Bz( n0 n) vi) Tail-race tunnel: a lumed arameters model has been used to reresent the tail-race tunnel behaviour. The model scheme is analogous to that of the enstock model, but the configuration of the circuit terminals are interchanged because of the different end conditions; i.e., in the left end the flow must fit the turbine flow, q t, and in the right end the head is given by the tail-race level. Fig.. Scheme of the enstock model. 160 PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 88 NR 1a/01

3 vii) Turbine governor - PI controller: The roosed governor model is shown in Fig. 3 and it is based on [14], [15]. The main function of this regulator is to control the seed and load through the feedback signals of the seed error and the ower variation, modifying the wicket gate osition and regulating the water flow through the enstock. The action of this governor allows eliminating the ower-frequency error under electrical load variations. The error signal is rocessed by a conventional roortional-integral (PI) controller and then the outut of this block is alied to a hydraulic servomotor (with T s time constant) to roduce a change in the wicket gate osition. The limits in the gate osition and its rate of change are considered in the model. viii) Power system: The modelled hydroelectric station is suosed to belong to an isolated network reresenting a secondary regulation area [10,13], where it is the only lant roviding secondary regulation. The unit seed resonse n (.u.) is obtained from the unbalance between the shaft ower and the generated ower according to the equation [10,14]: (9) P P M s D n m g h The generated ower P g is the ower transmitted through the interconnection line, which deends on the hase difference between the internal voltages of the generators connected at the line terminals [10]. Therefore an inertial model similar to the one reresented by the revious equation should be added; the inertia constant should include the equivalent inertial effects of all connected machines and the daming constant reresents the sensitivity of the frequency to load changes. The rimary regulation in the external system is also considered by the corresonding seed-droo R s (.u.); thus the ower-balance equation in the external subsystem results: P 1 n Rs P (10) g s L s s s h M s D n Finally, the angle difference is obtained from the time integral of the relative frequency deviations: (11) 0 s ( n n s ) s where 0 is the base system frequency and is introduced to obtain the angles in radians. The action of secondary regulation can be introduced by the corresonding change in the set-oint of the turbine governor. Case study The model described in the revious section has been used to analyze the dynamic resonse of a hydro ower lant that is currently in the re-lanning stage. Some already decided design arameters of the hydroower lant are included in Table 1. It should be noted that the hydroower lant is lanned to be located between two existing reservoirs; thus, some design arameters, such as the head or the total length of the conduits, are forced. In turn, main arameters of the ower system to which the ower lant is connected are included in Table. These arameters could corresond to a single regulation zone within the Sanish control area. Table 1. Main lant design arameters. Q b m 3 /s r u. H b m a 1000 m/s L hr m L tr m F hr m A t r hr u. B.0.u. F s m q v 0.05.u. L 13.3 m P b 5 MW F 3.76 m Table. Main ower system arameters. M s 6.67 s R s u. D s 8.89.u. P s 1000 MW Several simulations have been done in order to analyze the influence of some arameters on the lant and ower system dynamic resonses. The number of -shaed elements used to model the enstock behaviour, ne, has been set equal to in all simulations. In all cases analyzed, a demand ste of 5% of P s has been simulated at time t=10 s; then, at time t = 160 s, a change in the set-oint of the turbine governor is introduced in order to bring the system back to its nominal frequency, 50 Hz. It is imortant to note that the hydroower lant is assumed to be the only ower lant of the system roviding the SCAS. The first arameter analyzed has been the number of - shaed elements, ne tr used to model the behaviour of the tail-race tunnel, which is considerably longer than the enstock. In Fig. 4, it is shown the frequency and lant ower outut for different ne tr, under the above-mentioned conditions. On the one hand, from this Fig. it can be stated that the influence of ne tr on the lant and ower system resonses is negligible in the case analyzed. On the other hand, it can be seen how the ower lant contributes to roviding both the PCAS and SCAS. According to the Sanish TSO requirements reviously mentioned, the lant should be caable of modifying 1.5% of its rated outut before 15 s for frequency deviations lower than 100 mhz. As it can be seen in the figure, the ower lant modifies its ower outut from 0.68 to 0.7.u. within the first 15 seconds after the load variation; in turn the frequency deviation is lower than 100 mhz and the ower lant achieves to bring the system frequency back to its nominal value as a result of the change introduced in the governor set-oint (SCAS). Fig. 3: Governor model. PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 88 NR 1a/01 161

4 smaller cross-section (higher fluid inertia), the adjustment of the controller gains results in a weak control action which is unable to counteract the changes in the surge tank level. It could be exected that an increase in the controller gains was adequate in these cases, rovided that accetable limits in the ressure at the tail-race inlet as well as in the settling time can be ensured. Nevertheless, further research is therefore needed in order to find a comromise solution between a small and therefore cheaer tail-race cross section and one that allows roviding the above-mentioned ancillary services and that do not jeoardize the lant time life. Fig. 4. System frequency and lant ower outut for different ne tr. Regarding the SCAS, according to the TSO requirements, the lant ower outut should resemble to the ossible extent an exonential of time constant equal to 100 s. This imlies that it should reach the 63 % of the load variation ( P s /P b = 0.14.u.) at time t = 60 s (100 seconds after the change in the governor set-oint) and the final value at time t = 560 s. As it can be seen in Fig. 4, both conditions would be fulfilled in this case. The second arameter analyzed has been the tail-race tunnel cross section, F tr. A first estimation of this design arameter is based on a conservative value of the flow velocity, V tr = 1 m/s for Q = Q b. Fig. 4 was obtained with this value of F tr. The PI controller gains are adjusted using the exressions given in [10], taking as water starting time (T w ) the total value obtained by adding the contributions of the two inertial elements: enstock and tail-race tunnel (T + T tr ). In Fig. 5, the head at the tail-race tunnel inlet (or turbine outlet), h tr1, (uer art) and the lant ower outut (lower art) have been deicted for different cross sections, corresonding to the flow velocities 1, 3 and 5 m/s; the controller gains have been maintained in their original values adjusted for V tr = 1 m/s. As it can be seen in this figure, harmful low ressures aear at the turbine outlet, excet in the case corresonding to the smaller velocity (i.e. the greater cross section). It is imortant to note that the effects of the observed low ressures could be significantly more evident for higher load variations. Also, it is worth mentioning that both ressure fluctuations and low ressures can have harmful effects both in the tail-race tunnel and the turbine, where cavitation could even aear. In addition, the ower resonse is oorly damed in the case with the smaller cross-section. In order to avoid these undesirable resonses, the controller gains should be changed as the cross-section and so the water starting time change. Fig. 6 shows the results of the simulations conducted in that way. No dangerous low ressures aear as the cross-section diminishes (i.e. as the flow velocity increases), but the sloe of the ower resonse after the ste inuts becomes lower. This slower ower resonse could limit the caability of the lant to rovide SCAS. Moreover, after the transient caused by the ste in the governor set oint has ractically extinguished, a ersistent oscillation in the resonses is observed in the cases with higher design velocity. Although, with resect to the revious case, the daming of the ower resonse imroves significantly, this oscillation may revent the lant from roviding the SCAS, since the resulting settling times are considerable higher than those required by the Sanish TSO. Said oscillation is a consequence of the surge tank dynamics; usually it is not observed, because the load-frequency regulator filters it out by modifying the wicket gates osition in oosition to the surge tank level deviation. However in the cases with the Fig. 5: Head at the tail-race tunnel inlet and lant ower outut for different F tr. Constant controller gains. Fig. 6: Head at the tail-race tunnel inlet and lant ower outut for different F tr. Readjusted controller gains. Conclusions A detailed dynamic model of a hydroelectric ower lant has been used to assess its contribution to load-frequency regulation. The asects related to the lant dynamic resonse have been studied in relation with the requirements of the Sanish Electrical System Oerator. The develoed model may be alied for many ossible lant configurations, including head-race tunnel, surge tank and tail-race tunnel. The elasticity of water and ie has been considered by dividing the conduit in several elements. The results indicate that a short number of elements may be sufficient to adequately consider the ressure waves effects. The influence of some critical lant design arameters in the quality of dynamic resonse has been studied. The results obtained in the ractical case highlight the strong imortance that should be given to the consideration of the dynamic resonse asects in early design hases. The section of the tail-race tunnel lays an imortant role in the stabilization of the resonse following a sudden change in the lant set-oint. Thus, during the design hase, the need to satisfy determined requirements 16 PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 88 NR 1a/01

5 concerning the lant dynamic resonse, may lead to a substantial increase in the lant budget. Acknowledgements This work was suorted in art by the Sanish Ministry of Education. The authors also wish to thank the comany SOCOIN for roviding us the technical data of the hydroower lant analyzed in the aer. Aendix - Notation a Wave seed (m/s) a Wave seed in the enstock (m/s) A Pie cross section (m ) A t Turbine arameter B Turbine arameter D Pie diameter (m) D h Hydro lant daming constant (.u.) D s Power system daming constant (.u.) f Darcy-Weisbach coefficient F hr Head-race cross section (m ) F Penstock cross section (m ) F s Surge tank cross section (m ) g Gravity acceleration (m/s ) H Head (m) h dr Head at the downstream reservoir (u) h,i Head at the end of the i-th element of the enstock (.u.) h s Head in the surge tank (.u.) h t Head at the turbine inlet (.u.) h tr Head at the turbine outlet (.u.) h ur Head in the ustream reservoir (.u.) L hr Head-race tunnel length (m) L Penstock length (m) L tr Tail-race tunnel length (m) M h Hydro lant inertia constant (s) M s External ower system inertia constant (s) ne Number of elements used to model the enstock ne tr Number of elements used to model the tail-race tunnel n Turbine seed n 0 Turbine seed set oint (.u.) n s External system frequency (.u.) t Plant outut ower (.u.) P b Base lant ower outut P m Turbine mechanical ower (.u.) P g Generated ower (.u.) (the generator losses being neglected) P L Demand ower (.u.) Q Flow (m 3 /s) q hr Flow in the head-race tunnel (.u.) q,i Flow in the i-th element of the enstock (.u.) q t Flow through the turbine (.u.) q v No-load flow (.u.) r hr Losses coefficient of the head-race tunnel (.u.) r Losses coefficient of the enstock (.u.) R s External ower system equivalent seed-droo (.u.) T hr Water starting time in the head-race tunnel (s) T Water starting time in the enstock (s) z Wicket gates oening (.u.) 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Fraile- Ardanuy (associate rofessor) is with Deartment of Secial Technologies Alied to Telecommunications, Technical University of Madrid, Avda. Comlutense 30, 8040 Madrid (Sain), jfraile@etsit.um.es PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 88 NR 1a/01 163