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Modeling a pumped storage power integration to a hybrid power system with solar-wind power and its stability analysis
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Energy Procedia 158 Energy Procedia 00(2019) (2017)6225–6230 000–000 www.elsevier.com/locate/procedia
th 10 10th International International Conference Conference on on Applied Applied Energy Energy (ICAE2018), (ICAE2018), 22-25 22-25 August August 2018, 2018, Hong Hong Kong, Kong, China China
Modeling aa pumped storage power to aa hybrid ModelingThe pumped storage poweronintegration integration toand hybrid power 15th International Symposium District Heating Cooling power system with solar-wind power and its stability analysis system with solar-wind power and its stability analysis Assessing the feasibility of using thed heat demand-outdoor a,b a,b,c a,b a,b Beibei Xu a,b, Diyi Chena,b,c*, M. Venkateshkumard, Yu Xiaoa,b, Yanqiu Xinga,b Beibei Xu , function Diyi Chen for *, M. Venkateshkumar , Yu Xiao , Yanqiu Xing temperature a long-term district heat demand forecast
a aKey
Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A & F University, Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A & F University, Shaanxi Yangling 712100, P. R. China a,b,c a a b c c Shaanxi Yangling 712100, P. R. China b bInstitute of Water Resources and Hydropower Research, Northwest A&F University, Shaanxi Yangling 712100, P. R. China Institute of Water Resources and Hydropower Research, Northwest A&F University, Shaanxi Yangling 712100, P. R. China c a cCurtin Univ, Sch Built Environm, Australasian Joint Res Ctr Bldg Informat Modellin, Bentley, WA 6102, Australia Curtin Univ, Sch Built Environm, Joint- Instituto Res Ctr Bldg Informat Modellin, Bentley, WA1,6102, Australia IN+ Center for Innovation, Technology Policy Research Superior Técnico, Av. Rovisco Pais 1049-001 Lisbon, Portugal dandAustralasian b dSathyabama University, Chennai, Tamil Nadu, India Sathyabama University, Chennai, Tamil Daniel, Nadu, India Veolia Recherche & Innovation, 291 Avenue Dreyfous 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
I. Andrić
*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre
Abstract Abstract Abstract Global primary energy consumption will continue to increase with a high rate to 2050, which will be a big challenge for countries Global primary energy consumption will continue to increase with a high rate to 2050, which will be a big challenge for countries toDistrict meet both global and regional energy demand. Pumped storage stations (PSS) a hybridsolutions power system (HPS) with heating networks are commonly addressed in the literature as one ofintegrated the most to effective for decreasing the to meet both global and regional energy demand. Pumped storage stations (PSS) integrated to a hybrid power system (HPS) with solar and wind power for China are under construction to tussle with this challenge. Historically, modeling of a PSS integrated greenhouse gaspower emissions from are the under building sector. These systems high investments whichmodeling are returned the heat solar and wind for China construction to tussle withrequire this challenge. Historically, of a through PSS integrated HPS hasDue been ignored the interaction effect between the shaft renovation vibration and the governing strategies, increase the sales. the changed climate conditions and building policies, heat demand in thewhich futurewill could decrease, HPS has beento ignored the interaction effect between the shaft vibration and the governing strategies, which will increase the dynamic risk of PSS disconnected immediately to HPS. Here we unify the models of the hydro-turbine governing system and prolonging return period. dynamic riskthe of investment PSS disconnected immediately to HPS. Here we unify the models of the hydro-turbine governing system and hydro-turbine generator units iswith a novel expression of hydraulic forces. We quantize all the function parameter’s interaction The main scope of this paper to assess the feasibility of using the heat demand – outdoor temperature for heat demand hydro-turbine generator units with a novel expression of hydraulic forces. We quantize all the parameter’s interaction contributions of PSS integration to HPS and validate this model with the existing models. Finally, we show the feasibility of forecast. Theofdistrict of Alvalade, located Lisbonthis (Portugal), wasthe used as a case study. The we district consisted of 665 contributions PSS integration to HPS and in validate model with existing models. Finally, showis the feasibility of PSS’s model in integrating of a HPS under steady and fault scenarios. buildings that vary in both typology. Three weather scenarios (low, medium, high) and three district PSS’s model in integrating of construction a HPS under period steady and fault scenarios. renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Copyright ©with 2018 Elsevier AllElsevier rights reserved. ©compared 2019 The Published by Ltd. results fromLtd. a dynamic heat demand model, previously developed and validated by the authors. Copyright ©Authors. 2018 Elsevier Ltd. All rights reserved. th This is an and openpeer-review access articleunder underresponsibility the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Selection of the scientific committee the 10could International Conference Applied The results that when only weather change is considered, the marginof error be acceptable for someon applications Selection andshowed peer-review under responsibility of the scientific committee ofof the 10th International Conference on Applied Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. Energy (ICAE2018). (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation Energy (ICAE2018). scenarios,Wind/solar/pumped the error value increased up touncertainty 59.5% (depending on thecharacteristics; weather and steady renovation scenarios Keywords: storage system; analysis; dynamic and fault scenarioscombination considered). Keywords: Wind/solar/pumped storage system; uncertainty analysis; dynamic characteristics; steady and fault scenarios The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and 1. Introduction 1.renovation Introduction scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the A hybrid power (HPS) grid, integrated with and power, which are coupled scenarios). The values couldinstances, be used toare modify the function parameters for the scenarios considered, and A hybrid power system system (HPS)suggested grid, in in most most instances, are integrated with wind wind and solar solar power, which are mutual mutual beneficial toaccuracy each other regarding conditions. There are a great many literatures about the combined use of improve the of heat demandweather estimations.
beneficial to each other regarding weather conditions. There are a great many literatures about the combined use of © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Diyi Chen Tel.: 086-181-6198-0277. * Corresponding author. Diyi Chen Tel.: 086-181-6198-0277. E-mail address: [email protected] Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected]
1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 10thth International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10 International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.475
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WPG and PVPG addressing targets of dynamic modeling of a HPS, optimal configuration of WPG or PVPG [1], conversion efficiency improvement of WPG or PVPG, reliable operation by designing suitable controller, pollutant emission evaluation et al [2, 3]. However, there are very few studies with respect to the HPS integrated solar, wind, and PSS, and most of them focus on its optimal system configuration and reliable control of HPS. Hence, it is also important to analyze the operation characteristics and potential risk of the HPS. More importantly, mathematical modeling of PSSs with respect to electric power system performed litter improvements in recent years. Specifically, studies of hydropower models have been divided into two research directions: hydro-turbine governing systems (HTGS) of aspect – oriented electric power systems [4]; and, shaft system of hydro-turbine generator (SSHTG) units regarding aspect – oriented mechanical oscillation analysis [5]. Two main issues are included with these approaches: HTGS models are designed to provide reliable services to the grid by controlling the turbine speed, but ignore shaft axis vibration; conversely, SSHTG modeling attempts to control vibrations rather than speed. Clearly these two models interact with each other, hence a general model coupling both viewpoints is increasingly urgent. Therefore, a detailed model of PPS for HPS considering the two aspects at the same time is also a challenge for engineers and modelers. We present four main contributions in this study. First, by using a novel expression of the hydraulic forces to integrate HTGS with SSHTG we provide a general, unified model of a PSS working in the hydro-turbine condition. Second, using Extended Fourier Amplitude Sensitivity Text method we quantize all the parameter contribution on the contribution of HPS’s output. Third, based on this we validate this model against the existing models. Finally, we verified the feasibility of PSS’s model in integrating of a HPS. 1.1. Modeling of HPS integrated solar-wind and PSS HTGS changes the velocity and direction of water flow through the flow passage under the condition of the hydraulic turbine, and then transfers the energy of flow to the runner in the form of hydraulic forces, so that the rotating runner (an important component of HTGS) is rotated continuously (See Fig.1). It is reasonable that we use the hydraulic forces acting on the runner blades to link the HTGS and SSHTG. Bus_9
Controlled Components Pressure Penstock
Q H
Power Grid
f
y
Guide vane
Turbine scroll
Q
Bearing
PG
O1
Hydro-turbine generating set
H
_
PWM Generator g
Rotor Runner
Controller
Bus_7
Bus_5
VSC1 Control Universal Bridge
+
g
Vdc_mes
Bus_4
+
Three-phases breaker
r0=0.1124, r1=0.045 100km
r0=0.1124, r1=0.045 100km
Hydro Turbine 3 phases 13.8kV 50Hz
r0=0.1124, r1=0.045 100km
f3
Load 2 50Hz P=100MW Q=35Mvar
Uref Iabc_prim
Pulses
PWM Generator 2 kHz2
Universal Bridge1
Feedback module
Load 1 50Hz P=100MW Q=35Mvar r0=0.1124, r1=0.045 100km
+
Setting module
f4
10kV power grid
O
+
Amplification module
230 KV/380V 50Hz Uk=5.86 %
f1
Pulses
O1
_ Main servomotor
Bus_3
r0=0.1124, r1=0.045 100km
m
Stator
Coupling
Bus_8
18KV/230KV 50Hz uk=6.25 %
Qref_pu
y
Rotor
Measuring module
r0=0.1124, r1=0.045 100km
Bus_2
Bus_6
Load 3 50Hz P=100MW Q=35Mvar
380V/230 KV 50Hz uk=5.76 %
D1
Bus_1
O2
D2 D3
Hydro-turbine generating set
Three-phases breaker
Wind Turbine 50Hz 3phases Photovoltaics 50Hz 1phase
f2
(a) A hydro-turbine governing system (b) A hydro-turbine generator set (c) Solar-wind power system (b) Hybrid power system Fig. 1 The two important research directions of the pumped storage station operating in turbine conditions and configuration of solar-wind power system [6] and hybrid power system, e.g. (a) the hydro-turbine governing system (HTGS) [4]; and (b) the hydro-turbine generator set (SSHTG) [5]. The two structure indicate show that HTGS models are designed to provide reliable services to the grid by controlling the turbine speed, but ignore shaft axis vibration; conversely, SSHTG modeling attempts to control vibrations rather than speed. Block of means that the two direction models can be unified by some common factors in the SSHTG. Variables Q, H, y, f, and PG refer to the turbine flow, the head water, the guide vane opening, the rotational frequency, and the generator magnetic power, respectively.
First, we establish a global coordinate system, taking the bottom O of the runner shaft as origin point (O: xyz). The x-axis and z-axis are in line with the direction of water flow and the runner axis. Furthermore, select a horizontal section at height h, and establish a plane coordinate system at the center of the section circle (o: x1y1, see Fig. 2) (b)
(c)
p
y1
z U∞ y1
r
x1
o
H
U
y
h
o
n
p
Blade element
fn
U(
r
U
O
o
V
n
x
Py
m
W
y
x1
(e)
Blade element o
o
(d)
Py ft
x
u ) cos
△h
(a)
n
Fy
p Px
t x
(a) Global coordinate system (b) Plane coordinate system (c) Forces of the blade (d) Body-fixed coordinate system (e) Lift and resistance forces Fig. 2 The coordinate systems of the hydro-turbine runner. Symbols U∞, H, ω, θ, and r refer to the velocity of hydro-turbine flow, turbine height, angular velocity of blade, position angle, radius of locus circle at height h, respectively. The blue line refers to the axis of the blade element in this coordinate system. The two red lines are the axis of the body-fixed coordinate system (Details see Fig. 2d). Symbols U∞, r, ω, θ, t, fn, ft, Ux,
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u, W, V, α, φ, and δ refer to the velocity of hydro-turbine flow, the radius of locus circle at height h, angular velocity of blade, position angle, time, the hydraulic force (Fy, see Fig. 2e) along the radial direction, the hydraulic force along the tangential direction, the velocity of hydroturbine flow in x-direction, induced velocity in x-direction, resultant velocity of hydro-turbine flow and runner, velocity of runner, angle between velocity W and the axis of the blade element (Blue line), angle between velocity V and p-axis of the blade element, and the load angle of blade element (see Fig. 2d), respectively. Variables △h and δ refer to the micro-unit of blade element in p-axis and the load angle of blade element. Symbols m, p, and n are the axis of the body-fixed coordinate system, respectively. Symbols Px, Py, and Fy are the resistance force, the lift force, and the hydraulic force (the resultant force of Px and Py), respectively.
From Fig. 2, the hydraulic force along the radial direction is f n Py cos( ) Px sin( )=
The hydraulic force Fy along the tangential direction is
W 2Ch CL cos( ) CD sin( ) . 2cos
f t Py sin( ) Px cos( )=
The torque caused by force Fy at height h is mt ft r
W 2Ch CL sin( ) CD cos( ) . 2cos
W 2Ch CL sin( ) CD cos( ) r . 2cos
(1) (2) (3)
Assuming that the length of the blade is L, the torque of the hydro-turbine runner caused by flow is L
L
0
0
M t n mt dl n {
0.5W 2Ch CL sin( ) CD cos( )} rdl . cos
(4)
The wind-solar power system and configuration of HPS is presented in Figs. 2b, c. 1.2. Parametric uncertainty on the grid connected PSU
Table 1 describes the definition and parametric uncertainty of the pumped storage model (see Appendix A). Mean values of parameters in SSHTG and HTGS defined in Table 1 is subject to design values of Nazixia hydropower station in China. The model outputs here focus the generator speed (i.e. ω) and the concentric deviation of generator rotor in x-axis (i.e. x11), and the torsional angle of the generator rotor. The random sampling method selects the Monte Carlo method. The EFAST method requires that the sampling times is greater than the number of uncertain parameters multiplied by 65 simulation times. Hence, the number of sampling times is defined as ten thousand times. The main and total sensitivity analysis of the model outputs based on EFAST method is shown in Fig. 3.
(a) Parametric contribution on the generator speed
(b) Parametric contribution on the generator speed
(c) Parametric contribution on x11 (d) Parametric contribution on y11 Fig. 3 Main and total sensitivity results of the pumped storage model integrated into the electric power system. Symbols Si and STi refer to the single parameter’s contribution to the system output uncertainty and the interaction effect of multi-uncertain parameters on the system output uncertainty. Numbers 1 to 67 refer to symbols Us, Xd, Xd1, Xq, Xq1, XL, Td0, θ0, Xad, Xf, ωrated, D, Dt, Tj, Eq1, Ef, r, kp, ki, kd, Wave2, Wave3, bp, KZ, y0, qr, qnl, L0t, L01, L02, D0t, D01, D02, Qr, Hr, Wave1, Ty, ω0, Pm0, ht0, Tj2, e0, m, c1, c3, k1, k3, Ip, R, g0, kr, f0, c0, a0, pp, hg, s1, d1, e00, p, A0, Fjm, Fsm, L, δ1, δ2, and Mrated, respectively. Details see Appendix A. `
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As the generator speed is selected as the model output, the main effect of the initial generator speed (Number 37) is pronouncedly larger than that of other model parameters (see Fig. 3a). Its uncertainty contribution to the generator speed accounts for 76.6% of the contribution of all parameters in model Eq. (4), which means that the initial generator speed directly determines the modeling accuracy of the generator speed. The main effect indexes of parameters except for the initial generator speed changes from 0.47% to 2.19%, meaning that the sensitivity of these parameter interactions are relatively strong. The total effect of uncertainty parameters in the top three are the initial generator speed (2.15%), the bus voltage(1.34%), and the bending stiffness of the shaft in x-axis (0.96%), respectively (see Fig. 3b). The total effect of other parameters is less than 0.3%. This result means that the top ten parameters can indirectly affect the simulation results of generator speed by interacting with other parameters. As the concentric deviation of generator rotor in x-axis (x11 in Eq. (4)) is selected as the model output, the main effect of parameters in the top three is the mass eccentricity of the generator rotor and the excretion coefficient Section headings. Sensitive parameters come from the models HTGS and SSHTG, which indicates that it is correct to propose a unified model both considering the control strategies of HTGS and the shaft vibration of SSHTG. 1.3. Interaction contributions of PSS integration to HPS Parametric interaction contribution analysis of PSS to HPS aims to further quantize the interaction effect of parametric uncertainty to the generator speed.
(a) (b) (c) Fig. 4 Interaction contributions of pumped storage station (PSS) integration to the hybrid power system (HPS). The main sensitive and total sensitive indexes are summarized in the top sixteen. The effect of the leftover fifty-seven parameters to the PSS output is less than 1%. The numbers 5, 22, 24, 33, 36, 38, 40, 42, 46, 50, 52, 55, 56, 57, 58 and 67 refer to Xq1, T, KZ, D02, Wave, ω0, ht0, e, k1, g0, f0, pp, hg, s1, d1, and Mrated.
By comparing the signal and interactions of the sixteen parameters (see Fig. 4a), the deciding factors of the generator speed are more than that of interactions. While the interactions of these parameters are much weaker, which indicates that the coupling effect of parameters for the unified model is relatively weak. This model characterized by this advantage would be helpful to both satisfy the modeling accuracy of vibration responses and generator speed. From Fig. 4c, parameters e, k1, g0, f0, pp, hg, s1, d1 come from the model of SSHTG, indicating that the interaction of SSHTG also has a certain influence on the generator speed. In other words, although coupling effect of parameters for the unified model is relatively weak, the interactions of SSHTG on the generator speed are not to be neglected. Model validation of the unified model about the shaft vibration and the generator speed are verified in Appendix B. 1.4. Dynamic characteristics of HPS in steady and fault states Simulation has been carried out to verify the dynamic characteristics of the HPS integrated PSS, both in steady state and fault A and C of three-phases short-circuit. The terminal voltages and currents of the hybrid power system with the three-phase short-circuit fault of points A and C are shown in Fig. 5.
(a)
(b)
(c)
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(d) (e) Fig. 5 Terminal voltages and currents of the hybrid power system with the three-phase short-circuit fault of point A occurred at 3 seconds, cleared at 3.2 seconds, and the total simulation time is 5 seconds.
From Fig. 5, the HPS works in the steady state from initial to 2 seconds. And at the meanwhile, the SSHTG connects to the HPS, which has little effect on voltage of HPS. The terminal currents of points A and S increase largely and dramatically to be200 times of its rated value when the short-circuit fault occurs at 3 seconds. Note that the terminal voltage (points A, B, and S) reduces substantially. In the fault condition, the three-phase currents of point A spread in a stable periodic motion, but one of the three-phase currents is separated from the others for a moment. Differently, the three-phase current of point B transforms from the stable periodic motion to the stable equilibrium point, and one of the three-phase currents is gradually separated from the others. After the fault is cleared at 3 seconds, the current of point A returns to the stable motion immediately, while it takes some time for point B to restore to stable motion. By comparing the simulation results of points A, B, and S, the nearer the fault location is, the more serious the voltage plunges, especially for the wind power which drops nearly 10% of its rated value. It is thus evident that the current and voltage of PSU can quickly to its normal operation after the three-phase short-circuit fault cleared, while its effect for the current HPS requires certain time to restore. 2. Conclusions In this study, we combined nonlinear mathematical models of the hydro-turbine governing system with the shaft system of a hydro-turbine generator unit. Based on this we proposed and validated the unify model of the PSS integrated to HPS. We perform uncertainty analysis to investigate the interaction effect between the models of SSHTG and HTGS, and investigate the stability of the HPS integrated with solar, wind, and hydro power. Finally, feasibility of the proposed model of PSS integrated to HPS has been verified. Acknowledgements This work was supported by the scientific research foundation of National Natural Science Foundation of China-Outstanding Youth Foundation (No. 51622906), National Natural Science Foundation of China (No. 51479173), Fundamental Research Funds for the Central Universities (No. 201304030577), Scientific research funds of Northwest A&F University (No. 2013BSJJ095), Science Fund for Excellent Young Scholars from Northwest A&F University and Shaanxi Nova program (No. 2016KJXX-55). Appendix A. Specification of parametric uncertainties. Table 1 Specifications of parametric uncertainties in the pumped storage station. Details of physical meanings are obtained from ref. [4, 8]. Nu.
Pa.
Un.
Me.
Va.
Nu.
Pa.
Un.
Me.
Va.
Nu.
Pa.
Un.
Me.
Va.
1 2 3 4 5 6 7 8 9 10 11 12 13
Us Xd Xd1 Xq Xq1 XL Td0 θ0 Xad Xf ωrated D Dt
V Ω Ω Ω Ω Ω
1 1.07 0.34 0.66 0.78 0.3375 5.4 0 0.97 1.29 314 5 0.2
10-3 10-3 10-4 10-4 10-4 10-4 10-4 10-4 10-3 10-3 1 10-1 10-4
24 25 26 27 28 29 30 31 32 33 34 35 36
KZ y0 qr qnl L0t L01 L02 D0t D01 D02 Qr Hr Wave1
-p.u. m3/s m3/s m m m m m m m3/s m m3/s
1 0.95 1 0.15 517 50 30 4.6 2.2 2.2 53.5 312 900
10-3 10-3 10-3 10-4 5 1 10 10 10-2 10-2 1 10 102
47 48 49 50 51 52 53 54 55 56 57 58 59
k3 Ip R g0 kr f0 c0 a0 pp hg s1 d1 k2
N/m kg•m2 m m N/m N•s/m N•s/m rad -p.u. -m N/m
5.76×1010 7.9×107 3.8 10-3 2×108 0.3 6.5×105 0.6 0.5 0.26 1 3.2 5.62×108
1018 1012 10-2 10-8 1014 10-4 109 10-4 10-4 10-4 10-3 0.1 1018
`
N m rad Ω Ω rad/s m --
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14 15 16 17 18 19 20 21 22 23
Tj Eq1 Eft r kp ki kd Wave3 Wave2 bp
s V V -s s s m/s m/s --
0.5 1.4823 2.1847 0.1 0.05 2 0.2 1100 1100 0.04
10-4 10-2 10-2 10-4 10-5 10-2 10-4 102 102 10-5
37 38 39 40 41 42 43 44 45 46
Ty ω0 Pm0 ht0 Tj2 e m c1 c3 k1
s rad/s p.u. p.u. s m kg N•s/m N•s/m N/m
0.5 1 0.5 1.02 0.8 0.8×10-3 3.8×105 7.64×108 2.4×105 7.08×108
10-3 10-3 10-4 10-3 10-3 10-8 108 1014 108 1018
60 61 62 63 64 65 66 67
p A0 Fjm Fsm L δ1 δ2 Pm-rated
-m A A m rad rad kW
3 4π×10-10 2×104 2×104 2.1 π/6 π/7 2.9×104
0.1 10-20 106 106 10-2 10-3 10-4 1016
Appendix B. Model validation
The ability of the PSS containing uncertain random parameters to simulate the HTGS’s responses and SSHTG’s vibration is obtained for some different workiong conditions performed by a hydropower station in China. The key specifications of the hydropower station are given in Tab. 1. Simulations are presented using two conversational models: the HTGS’ model published in ref. 4, and the SSHTG’s model presented in ref. 7. The main difference caused by the interaction effect of SSHTG and HTGS
(a) Dynamic responses of HTGS (b) Structural model of SSHTG (c) Campbell diagram Fig. 6 Model validation of the proposed model. The three dynamic parameters (q, ω, and y) without words “from HTGS” come from simulation results of Eq. (4). The three dynamic parameters (q, ω, and y) with words “from HTGS” come from simulation results of ref. 4. Symbol “ ” refers to the modeling difference from HPS and ref. 6, which indicates that the interaction effect of HTGS and SSHTG changes the responses of q, ω, and y in this part. Model b comes from ref. 7. The software of Pro/E is used to establish the 3D shafting model, and the element solid95 is adopted for its mesh generation. The grid includes 185699 units and 1023789 nodes. Table 2 The comparison of the natural frequencies from Eq. (4) and the model of ref. 38. Source First-order mode (HZ) Eq. (4) 16.85 Ref. (36) 16.62
Second order mode (HZ) 20.45 20.72
From Fig. 6, the main difference in the transient part is caused by the interaction of HTGS and SSHTG. The modeling results of the two models are equal to each other, except for this transient part. Hence, the proposed model in modeling HTGS’s responses is verified. From Fig. 6 and Tab. 2, the natural frequencies calculated from the proposed model correspond closely to the frequencies of the FEW model, which verifies the correctness of the model proposed in modeling the SSHTG’s responses. Therefore, the model proposed in this study is verified.
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Energy Procedia 158 Energy Procedia 00(2019) (2017)6225–6230 000–000 www.elsevier.com/locate/procedia
th 10 10th International International Conference Conference on on Applied Applied Energy Energy (ICAE2018), (ICAE2018), 22-25 22-25 August August 2018, 2018, Hong Hong Kong, Kong, China China
Modeling aa pumped storage power to aa hybrid ModelingThe pumped storage poweronintegration integration toand hybrid power 15th International Symposium District Heating Cooling power system with solar-wind power and its stability analysis system with solar-wind power and its stability analysis Assessing the feasibility of using thed heat demand-outdoor a,b a,b,c a,b a,b Beibei Xu a,b, Diyi Chena,b,c*, M. Venkateshkumard, Yu Xiaoa,b, Yanqiu Xinga,b Beibei Xu , function Diyi Chen for *, M. Venkateshkumar , Yu Xiao , Yanqiu Xing temperature a long-term district heat demand forecast
a aKey
Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A & F University, Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A & F University, Shaanxi Yangling 712100, P. R. China a,b,c a a b c c Shaanxi Yangling 712100, P. R. China b bInstitute of Water Resources and Hydropower Research, Northwest A&F University, Shaanxi Yangling 712100, P. R. China Institute of Water Resources and Hydropower Research, Northwest A&F University, Shaanxi Yangling 712100, P. R. China c a cCurtin Univ, Sch Built Environm, Australasian Joint Res Ctr Bldg Informat Modellin, Bentley, WA 6102, Australia Curtin Univ, Sch Built Environm, Joint- Instituto Res Ctr Bldg Informat Modellin, Bentley, WA1,6102, Australia IN+ Center for Innovation, Technology Policy Research Superior Técnico, Av. Rovisco Pais 1049-001 Lisbon, Portugal dandAustralasian b dSathyabama University, Chennai, Tamil Nadu, India Sathyabama University, Chennai, Tamil Daniel, Nadu, India Veolia Recherche & Innovation, 291 Avenue Dreyfous 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
I. Andrić
*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre
Abstract Abstract Abstract Global primary energy consumption will continue to increase with a high rate to 2050, which will be a big challenge for countries Global primary energy consumption will continue to increase with a high rate to 2050, which will be a big challenge for countries toDistrict meet both global and regional energy demand. Pumped storage stations (PSS) a hybridsolutions power system (HPS) with heating networks are commonly addressed in the literature as one ofintegrated the most to effective for decreasing the to meet both global and regional energy demand. Pumped storage stations (PSS) integrated to a hybrid power system (HPS) with solar and wind power for China are under construction to tussle with this challenge. Historically, modeling of a PSS integrated greenhouse gaspower emissions from are the under building sector. These systems high investments whichmodeling are returned the heat solar and wind for China construction to tussle withrequire this challenge. Historically, of a through PSS integrated HPS hasDue been ignored the interaction effect between the shaft renovation vibration and the governing strategies, increase the sales. the changed climate conditions and building policies, heat demand in thewhich futurewill could decrease, HPS has beento ignored the interaction effect between the shaft vibration and the governing strategies, which will increase the dynamic risk of PSS disconnected immediately to HPS. Here we unify the models of the hydro-turbine governing system and prolonging return period. dynamic riskthe of investment PSS disconnected immediately to HPS. Here we unify the models of the hydro-turbine governing system and hydro-turbine generator units iswith a novel expression of hydraulic forces. We quantize all the function parameter’s interaction The main scope of this paper to assess the feasibility of using the heat demand – outdoor temperature for heat demand hydro-turbine generator units with a novel expression of hydraulic forces. We quantize all the parameter’s interaction contributions of PSS integration to HPS and validate this model with the existing models. Finally, we show the feasibility of forecast. Theofdistrict of Alvalade, located Lisbonthis (Portugal), wasthe used as a case study. The we district consisted of 665 contributions PSS integration to HPS and in validate model with existing models. Finally, showis the feasibility of PSS’s model in integrating of a HPS under steady and fault scenarios. buildings that vary in both typology. Three weather scenarios (low, medium, high) and three district PSS’s model in integrating of construction a HPS under period steady and fault scenarios. renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Copyright ©with 2018 Elsevier AllElsevier rights reserved. ©compared 2019 The Published by Ltd. results fromLtd. a dynamic heat demand model, previously developed and validated by the authors. Copyright ©Authors. 2018 Elsevier Ltd. All rights reserved. th This is an and openpeer-review access articleunder underresponsibility the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Selection of the scientific committee the 10could International Conference Applied The results that when only weather change is considered, the marginof error be acceptable for someon applications Selection andshowed peer-review under responsibility of the scientific committee ofof the 10th International Conference on Applied Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. Energy (ICAE2018). (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation Energy (ICAE2018). scenarios,Wind/solar/pumped the error value increased up touncertainty 59.5% (depending on thecharacteristics; weather and steady renovation scenarios Keywords: storage system; analysis; dynamic and fault scenarioscombination considered). Keywords: Wind/solar/pumped storage system; uncertainty analysis; dynamic characteristics; steady and fault scenarios The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and 1. Introduction 1.renovation Introduction scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the A hybrid power (HPS) grid, integrated with and power, which are coupled scenarios). The values couldinstances, be used toare modify the function parameters for the scenarios considered, and A hybrid power system system (HPS)suggested grid, in in most most instances, are integrated with wind wind and solar solar power, which are mutual mutual beneficial toaccuracy each other regarding conditions. There are a great many literatures about the combined use of improve the of heat demandweather estimations.
beneficial to each other regarding weather conditions. There are a great many literatures about the combined use of © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Diyi Chen Tel.: 086-181-6198-0277. * Corresponding author. Diyi Chen Tel.: 086-181-6198-0277. E-mail address: [email protected] Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected]
1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 10thth International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10 International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.475
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WPG and PVPG addressing targets of dynamic modeling of a HPS, optimal configuration of WPG or PVPG [1], conversion efficiency improvement of WPG or PVPG, reliable operation by designing suitable controller, pollutant emission evaluation et al [2, 3]. However, there are very few studies with respect to the HPS integrated solar, wind, and PSS, and most of them focus on its optimal system configuration and reliable control of HPS. Hence, it is also important to analyze the operation characteristics and potential risk of the HPS. More importantly, mathematical modeling of PSSs with respect to electric power system performed litter improvements in recent years. Specifically, studies of hydropower models have been divided into two research directions: hydro-turbine governing systems (HTGS) of aspect – oriented electric power systems [4]; and, shaft system of hydro-turbine generator (SSHTG) units regarding aspect – oriented mechanical oscillation analysis [5]. Two main issues are included with these approaches: HTGS models are designed to provide reliable services to the grid by controlling the turbine speed, but ignore shaft axis vibration; conversely, SSHTG modeling attempts to control vibrations rather than speed. Clearly these two models interact with each other, hence a general model coupling both viewpoints is increasingly urgent. Therefore, a detailed model of PPS for HPS considering the two aspects at the same time is also a challenge for engineers and modelers. We present four main contributions in this study. First, by using a novel expression of the hydraulic forces to integrate HTGS with SSHTG we provide a general, unified model of a PSS working in the hydro-turbine condition. Second, using Extended Fourier Amplitude Sensitivity Text method we quantize all the parameter contribution on the contribution of HPS’s output. Third, based on this we validate this model against the existing models. Finally, we verified the feasibility of PSS’s model in integrating of a HPS. 1.1. Modeling of HPS integrated solar-wind and PSS HTGS changes the velocity and direction of water flow through the flow passage under the condition of the hydraulic turbine, and then transfers the energy of flow to the runner in the form of hydraulic forces, so that the rotating runner (an important component of HTGS) is rotated continuously (See Fig.1). It is reasonable that we use the hydraulic forces acting on the runner blades to link the HTGS and SSHTG. Bus_9
Controlled Components Pressure Penstock
Q H
Power Grid
f
y
Guide vane
Turbine scroll
Q
Bearing
PG
O1
Hydro-turbine generating set
H
_
PWM Generator g
Rotor Runner
Controller
Bus_7
Bus_5
VSC1 Control Universal Bridge
+
g
Vdc_mes
Bus_4
+
Three-phases breaker
r0=0.1124, r1=0.045 100km
r0=0.1124, r1=0.045 100km
Hydro Turbine 3 phases 13.8kV 50Hz
r0=0.1124, r1=0.045 100km
f3
Load 2 50Hz P=100MW Q=35Mvar
Uref Iabc_prim
Pulses
PWM Generator 2 kHz2
Universal Bridge1
Feedback module
Load 1 50Hz P=100MW Q=35Mvar r0=0.1124, r1=0.045 100km
+
Setting module
f4
10kV power grid
O
+
Amplification module
230 KV/380V 50Hz Uk=5.86 %
f1
Pulses
O1
_ Main servomotor
Bus_3
r0=0.1124, r1=0.045 100km
m
Stator
Coupling
Bus_8
18KV/230KV 50Hz uk=6.25 %
Qref_pu
y
Rotor
Measuring module
r0=0.1124, r1=0.045 100km
Bus_2
Bus_6
Load 3 50Hz P=100MW Q=35Mvar
380V/230 KV 50Hz uk=5.76 %
D1
Bus_1
O2
D2 D3
Hydro-turbine generating set
Three-phases breaker
Wind Turbine 50Hz 3phases Photovoltaics 50Hz 1phase
f2
(a) A hydro-turbine governing system (b) A hydro-turbine generator set (c) Solar-wind power system (b) Hybrid power system Fig. 1 The two important research directions of the pumped storage station operating in turbine conditions and configuration of solar-wind power system [6] and hybrid power system, e.g. (a) the hydro-turbine governing system (HTGS) [4]; and (b) the hydro-turbine generator set (SSHTG) [5]. The two structure indicate show that HTGS models are designed to provide reliable services to the grid by controlling the turbine speed, but ignore shaft axis vibration; conversely, SSHTG modeling attempts to control vibrations rather than speed. Block of means that the two direction models can be unified by some common factors in the SSHTG. Variables Q, H, y, f, and PG refer to the turbine flow, the head water, the guide vane opening, the rotational frequency, and the generator magnetic power, respectively.
First, we establish a global coordinate system, taking the bottom O of the runner shaft as origin point (O: xyz). The x-axis and z-axis are in line with the direction of water flow and the runner axis. Furthermore, select a horizontal section at height h, and establish a plane coordinate system at the center of the section circle (o: x1y1, see Fig. 2) (b)
(c)
p
y1
z U∞ y1
r
x1
o
H
U
y
h
o
n
p
Blade element
fn
U(
r
U
O
o
V
n
x
Py
m
W
y
x1
(e)
Blade element o
o
(d)
Py ft
x
u ) cos
△h
(a)
n
Fy
p Px
t x
(a) Global coordinate system (b) Plane coordinate system (c) Forces of the blade (d) Body-fixed coordinate system (e) Lift and resistance forces Fig. 2 The coordinate systems of the hydro-turbine runner. Symbols U∞, H, ω, θ, and r refer to the velocity of hydro-turbine flow, turbine height, angular velocity of blade, position angle, radius of locus circle at height h, respectively. The blue line refers to the axis of the blade element in this coordinate system. The two red lines are the axis of the body-fixed coordinate system (Details see Fig. 2d). Symbols U∞, r, ω, θ, t, fn, ft, Ux,
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u, W, V, α, φ, and δ refer to the velocity of hydro-turbine flow, the radius of locus circle at height h, angular velocity of blade, position angle, time, the hydraulic force (Fy, see Fig. 2e) along the radial direction, the hydraulic force along the tangential direction, the velocity of hydroturbine flow in x-direction, induced velocity in x-direction, resultant velocity of hydro-turbine flow and runner, velocity of runner, angle between velocity W and the axis of the blade element (Blue line), angle between velocity V and p-axis of the blade element, and the load angle of blade element (see Fig. 2d), respectively. Variables △h and δ refer to the micro-unit of blade element in p-axis and the load angle of blade element. Symbols m, p, and n are the axis of the body-fixed coordinate system, respectively. Symbols Px, Py, and Fy are the resistance force, the lift force, and the hydraulic force (the resultant force of Px and Py), respectively.
From Fig. 2, the hydraulic force along the radial direction is f n Py cos( ) Px sin( )=
The hydraulic force Fy along the tangential direction is
W 2Ch CL cos( ) CD sin( ) . 2cos
f t Py sin( ) Px cos( )=
The torque caused by force Fy at height h is mt ft r
W 2Ch CL sin( ) CD cos( ) . 2cos
W 2Ch CL sin( ) CD cos( ) r . 2cos
(1) (2) (3)
Assuming that the length of the blade is L, the torque of the hydro-turbine runner caused by flow is L
L
0
0
M t n mt dl n {
0.5W 2Ch CL sin( ) CD cos( )} rdl . cos
(4)
The wind-solar power system and configuration of HPS is presented in Figs. 2b, c. 1.2. Parametric uncertainty on the grid connected PSU
Table 1 describes the definition and parametric uncertainty of the pumped storage model (see Appendix A). Mean values of parameters in SSHTG and HTGS defined in Table 1 is subject to design values of Nazixia hydropower station in China. The model outputs here focus the generator speed (i.e. ω) and the concentric deviation of generator rotor in x-axis (i.e. x11), and the torsional angle of the generator rotor. The random sampling method selects the Monte Carlo method. The EFAST method requires that the sampling times is greater than the number of uncertain parameters multiplied by 65 simulation times. Hence, the number of sampling times is defined as ten thousand times. The main and total sensitivity analysis of the model outputs based on EFAST method is shown in Fig. 3.
(a) Parametric contribution on the generator speed
(b) Parametric contribution on the generator speed
(c) Parametric contribution on x11 (d) Parametric contribution on y11 Fig. 3 Main and total sensitivity results of the pumped storage model integrated into the electric power system. Symbols Si and STi refer to the single parameter’s contribution to the system output uncertainty and the interaction effect of multi-uncertain parameters on the system output uncertainty. Numbers 1 to 67 refer to symbols Us, Xd, Xd1, Xq, Xq1, XL, Td0, θ0, Xad, Xf, ωrated, D, Dt, Tj, Eq1, Ef, r, kp, ki, kd, Wave2, Wave3, bp, KZ, y0, qr, qnl, L0t, L01, L02, D0t, D01, D02, Qr, Hr, Wave1, Ty, ω0, Pm0, ht0, Tj2, e0, m, c1, c3, k1, k3, Ip, R, g0, kr, f0, c0, a0, pp, hg, s1, d1, e00, p, A0, Fjm, Fsm, L, δ1, δ2, and Mrated, respectively. Details see Appendix A. `
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As the generator speed is selected as the model output, the main effect of the initial generator speed (Number 37) is pronouncedly larger than that of other model parameters (see Fig. 3a). Its uncertainty contribution to the generator speed accounts for 76.6% of the contribution of all parameters in model Eq. (4), which means that the initial generator speed directly determines the modeling accuracy of the generator speed. The main effect indexes of parameters except for the initial generator speed changes from 0.47% to 2.19%, meaning that the sensitivity of these parameter interactions are relatively strong. The total effect of uncertainty parameters in the top three are the initial generator speed (2.15%), the bus voltage(1.34%), and the bending stiffness of the shaft in x-axis (0.96%), respectively (see Fig. 3b). The total effect of other parameters is less than 0.3%. This result means that the top ten parameters can indirectly affect the simulation results of generator speed by interacting with other parameters. As the concentric deviation of generator rotor in x-axis (x11 in Eq. (4)) is selected as the model output, the main effect of parameters in the top three is the mass eccentricity of the generator rotor and the excretion coefficient Section headings. Sensitive parameters come from the models HTGS and SSHTG, which indicates that it is correct to propose a unified model both considering the control strategies of HTGS and the shaft vibration of SSHTG. 1.3. Interaction contributions of PSS integration to HPS Parametric interaction contribution analysis of PSS to HPS aims to further quantize the interaction effect of parametric uncertainty to the generator speed.
(a) (b) (c) Fig. 4 Interaction contributions of pumped storage station (PSS) integration to the hybrid power system (HPS). The main sensitive and total sensitive indexes are summarized in the top sixteen. The effect of the leftover fifty-seven parameters to the PSS output is less than 1%. The numbers 5, 22, 24, 33, 36, 38, 40, 42, 46, 50, 52, 55, 56, 57, 58 and 67 refer to Xq1, T, KZ, D02, Wave, ω0, ht0, e, k1, g0, f0, pp, hg, s1, d1, and Mrated.
By comparing the signal and interactions of the sixteen parameters (see Fig. 4a), the deciding factors of the generator speed are more than that of interactions. While the interactions of these parameters are much weaker, which indicates that the coupling effect of parameters for the unified model is relatively weak. This model characterized by this advantage would be helpful to both satisfy the modeling accuracy of vibration responses and generator speed. From Fig. 4c, parameters e, k1, g0, f0, pp, hg, s1, d1 come from the model of SSHTG, indicating that the interaction of SSHTG also has a certain influence on the generator speed. In other words, although coupling effect of parameters for the unified model is relatively weak, the interactions of SSHTG on the generator speed are not to be neglected. Model validation of the unified model about the shaft vibration and the generator speed are verified in Appendix B. 1.4. Dynamic characteristics of HPS in steady and fault states Simulation has been carried out to verify the dynamic characteristics of the HPS integrated PSS, both in steady state and fault A and C of three-phases short-circuit. The terminal voltages and currents of the hybrid power system with the three-phase short-circuit fault of points A and C are shown in Fig. 5.
(a)
(b)
(c)
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(d) (e) Fig. 5 Terminal voltages and currents of the hybrid power system with the three-phase short-circuit fault of point A occurred at 3 seconds, cleared at 3.2 seconds, and the total simulation time is 5 seconds.
From Fig. 5, the HPS works in the steady state from initial to 2 seconds. And at the meanwhile, the SSHTG connects to the HPS, which has little effect on voltage of HPS. The terminal currents of points A and S increase largely and dramatically to be200 times of its rated value when the short-circuit fault occurs at 3 seconds. Note that the terminal voltage (points A, B, and S) reduces substantially. In the fault condition, the three-phase currents of point A spread in a stable periodic motion, but one of the three-phase currents is separated from the others for a moment. Differently, the three-phase current of point B transforms from the stable periodic motion to the stable equilibrium point, and one of the three-phase currents is gradually separated from the others. After the fault is cleared at 3 seconds, the current of point A returns to the stable motion immediately, while it takes some time for point B to restore to stable motion. By comparing the simulation results of points A, B, and S, the nearer the fault location is, the more serious the voltage plunges, especially for the wind power which drops nearly 10% of its rated value. It is thus evident that the current and voltage of PSU can quickly to its normal operation after the three-phase short-circuit fault cleared, while its effect for the current HPS requires certain time to restore. 2. Conclusions In this study, we combined nonlinear mathematical models of the hydro-turbine governing system with the shaft system of a hydro-turbine generator unit. Based on this we proposed and validated the unify model of the PSS integrated to HPS. We perform uncertainty analysis to investigate the interaction effect between the models of SSHTG and HTGS, and investigate the stability of the HPS integrated with solar, wind, and hydro power. Finally, feasibility of the proposed model of PSS integrated to HPS has been verified. Acknowledgements This work was supported by the scientific research foundation of National Natural Science Foundation of China-Outstanding Youth Foundation (No. 51622906), National Natural Science Foundation of China (No. 51479173), Fundamental Research Funds for the Central Universities (No. 201304030577), Scientific research funds of Northwest A&F University (No. 2013BSJJ095), Science Fund for Excellent Young Scholars from Northwest A&F University and Shaanxi Nova program (No. 2016KJXX-55). Appendix A. Specification of parametric uncertainties. Table 1 Specifications of parametric uncertainties in the pumped storage station. Details of physical meanings are obtained from ref. [4, 8]. Nu.
Pa.
Un.
Me.
Va.
Nu.
Pa.
Un.
Me.
Va.
Nu.
Pa.
Un.
Me.
Va.
1 2 3 4 5 6 7 8 9 10 11 12 13
Us Xd Xd1 Xq Xq1 XL Td0 θ0 Xad Xf ωrated D Dt
V Ω Ω Ω Ω Ω
1 1.07 0.34 0.66 0.78 0.3375 5.4 0 0.97 1.29 314 5 0.2
10-3 10-3 10-4 10-4 10-4 10-4 10-4 10-4 10-3 10-3 1 10-1 10-4
24 25 26 27 28 29 30 31 32 33 34 35 36
KZ y0 qr qnl L0t L01 L02 D0t D01 D02 Qr Hr Wave1
-p.u. m3/s m3/s m m m m m m m3/s m m3/s
1 0.95 1 0.15 517 50 30 4.6 2.2 2.2 53.5 312 900
10-3 10-3 10-3 10-4 5 1 10 10 10-2 10-2 1 10 102
47 48 49 50 51 52 53 54 55 56 57 58 59
k3 Ip R g0 kr f0 c0 a0 pp hg s1 d1 k2
N/m kg•m2 m m N/m N•s/m N•s/m rad -p.u. -m N/m
5.76×1010 7.9×107 3.8 10-3 2×108 0.3 6.5×105 0.6 0.5 0.26 1 3.2 5.62×108
1018 1012 10-2 10-8 1014 10-4 109 10-4 10-4 10-4 10-3 0.1 1018
`
N m rad Ω Ω rad/s m --
Beibei Xu et al. / Energy Procedia 158 (2019) 6225–6230 Beibei Xu/ Energy Procedia 00 (2018) 000–000
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14 15 16 17 18 19 20 21 22 23
Tj Eq1 Eft r kp ki kd Wave3 Wave2 bp
s V V -s s s m/s m/s --
0.5 1.4823 2.1847 0.1 0.05 2 0.2 1100 1100 0.04
10-4 10-2 10-2 10-4 10-5 10-2 10-4 102 102 10-5
37 38 39 40 41 42 43 44 45 46
Ty ω0 Pm0 ht0 Tj2 e m c1 c3 k1
s rad/s p.u. p.u. s m kg N•s/m N•s/m N/m
0.5 1 0.5 1.02 0.8 0.8×10-3 3.8×105 7.64×108 2.4×105 7.08×108
10-3 10-3 10-4 10-3 10-3 10-8 108 1014 108 1018
60 61 62 63 64 65 66 67
p A0 Fjm Fsm L δ1 δ2 Pm-rated
-m A A m rad rad kW
3 4π×10-10 2×104 2×104 2.1 π/6 π/7 2.9×104
0.1 10-20 106 106 10-2 10-3 10-4 1016
Appendix B. Model validation
The ability of the PSS containing uncertain random parameters to simulate the HTGS’s responses and SSHTG’s vibration is obtained for some different workiong conditions performed by a hydropower station in China. The key specifications of the hydropower station are given in Tab. 1. Simulations are presented using two conversational models: the HTGS’ model published in ref. 4, and the SSHTG’s model presented in ref. 7. The main difference caused by the interaction effect of SSHTG and HTGS
(a) Dynamic responses of HTGS (b) Structural model of SSHTG (c) Campbell diagram Fig. 6 Model validation of the proposed model. The three dynamic parameters (q, ω, and y) without words “from HTGS” come from simulation results of Eq. (4). The three dynamic parameters (q, ω, and y) with words “from HTGS” come from simulation results of ref. 4. Symbol “ ” refers to the modeling difference from HPS and ref. 6, which indicates that the interaction effect of HTGS and SSHTG changes the responses of q, ω, and y in this part. Model b comes from ref. 7. The software of Pro/E is used to establish the 3D shafting model, and the element solid95 is adopted for its mesh generation. The grid includes 185699 units and 1023789 nodes. Table 2 The comparison of the natural frequencies from Eq. (4) and the model of ref. 38. Source First-order mode (HZ) Eq. (4) 16.85 Ref. (36) 16.62
Second order mode (HZ) 20.45 20.72
From Fig. 6, the main difference in the transient part is caused by the interaction of HTGS and SSHTG. The modeling results of the two models are equal to each other, except for this transient part. Hence, the proposed model in modeling HTGS’s responses is verified. From Fig. 6 and Tab. 2, the natural frequencies calculated from the proposed model correspond closely to the frequencies of the FEW model, which verifies the correctness of the model proposed in modeling the SSHTG’s responses. Therefore, the model proposed in this study is verified.
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