DRPT2008
6-9 April 2008 Nanjing China
1
The Influence of the UHV Transmission Line to the TTCs between Provincial Power Grids in CCG Huimin Yang, Jinyu Wen, Lin Jiang and Shijie Cheng, Senior Member, IEEE
Abstract-- The first 1000kV ultra high voltage (UHV) AC transmission line in China is being constructed from Shanxi province to Hubei province with 645km distance, connecting Central China Grid (CCG) and North China Grid (NCG). Total Transfer Capability (TTC) and Available Transfer Capability (ATC) are two main concerns to reliably transfer power between interconnected power grids. This paper investigates the influence of the UHV transmission line to the TTCs between the provincial power grids in CCG with transient stability constraints. The NCG and provincial grids in CCG are modeled by an equivalent single generator system based on the center of inertia (COI) coordinate. Based on different operation condition of the UHV transmission line continuous load flow method, TTCs between the provincial grids in CCG are calculated. Results show that there is notable change of the values of the TTCs with the operation of the UHV transmission line. A detailed NCG-CCG interconnected power grid model is setup by using the Power System Analyze Software Package (PSASP) and the equivalent threegenerator system (ETS) method is validated. Index Terms -- UHV, COI, TTC, transient stability constraints.
I. INTRODUCTION
T
HE first 1000kV ultra high voltage (UHV) AC transmission line in China is being constructed from Shanxi province to Hubei province with 645km distance. The whole power grid in mainland of China consists of six large scale regional power grid called Northeast China Grid (NEG), North China Grid (NCG), Central China Grid (CCG), East China Grid (ECG), Northwest China Grid (NWG) and South China Grid (SCG). The UHV transmission line is planed to be put into effect in 2009. After that the NCG and CCG will be interconnected via the UHV transmission line, a very large scale synchronous frequency power grid including 12 provincial power grids will be taken into operation. In these 12 provincial power grids, only Shanxi province power grid and Hubei province power grid are interconnected by 1000kV AC transmission line. All the other interconnected provincial power grids are connected by 500kV AC transmisThis work was supported by the National Natural Science Foundation of China (50595410). Huimin Yang, Jinyu Wen and Shijie Cheng are with the College of Electrical and Electronics Engineering, Huazhong University of Science and Technology, Wuhan, 430074, P. R. China (e-mail:
[email protected]). Lin Jiang is with the University of Liverpool, Liverpool, L69 3GJ, UK.
978-7-900714-13-8/08/ ©2008 DRPT
sion lines. According to the present power market operation rules in China, the provincial power grids are the main player of the market, so that the total transmission capacity (TTC) between provincial power grids is a very important parameter for the market. The influence of the UHV transmission line to the TTCs between the provincial power grids in CCG should be studied for the system operation. According to the North American Electric Reliability Council’s definition[1], TTC is defined as the amount of electric power that can be transferred from one area to another over the interconnected transmission network in a reliable manner, while meeting all of a specified set of constraints defined pre and post contingency system condition. The constraints include steady state constraints including voltage quality limits, generation output limits, bus voltage limits, thermal limit of transformer and transmission line, and dynamic constraints such as constraints of transient stability limit. Without the transient stability constraints, the calculated value of TTC is always conservative and the transmission capacity may be overestimated. Calculating TTC with transient stability limit constraints has attracted lots of research efforts [1]. The NCG-CCG power grid will be the largest synchronous frequency one in China after the UHV transmission line in operation. This will result in the change of characteristics of the CCG, mainly the transient stability limits of transmission lines between provincial grids. To operate the transmission line at the old power level may break the new transient stability limit and cause stability problem of grids. This paper investigates the influence of UHV transmission line to TTCs of CCG considering the transient stability limits. The two considered provincial power grids of CCG at ends of transmission lines is modeled as equivalent two-generator system under the COI coordinate[2]. Then NCG is modeled as another generator and connected to CCG, the overall NCGCCG is represented as three-generator system under the COI coordinate. Changing the operation mode of the UHV transmission line, the TTCs are calculated based on the continuous load flow method. The PSASP software package is used. The results show that there is notable change of the values of the TTC and the direction of the power on the transmission line also affects TTC.
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6-9 April 2008 Nanjing China
II. TTC CALCULATION WITH TRANSIENT STABILITY CONSTRAINTS A. The dynamic model of TTC calculation with transient stability constraints The objective function is given as ref. [3] and ref. [4]: min F = − ∑ Pij
(1)
i , j∈SΩ
Where, i and j are bus number, Pij is the active power flow of transmission lines from one area to another; SΩ is the set of transmission lines. Calculation of TTC needs to meet a series of static constraints and dynamic constraints. Static constraints include equality constraints and inequality constraints. Equality constrains are steady state power flow functions of pre and post fault: PG − PL − P (V , θ ) = 0 (2) QG − QL − Q (V , θ ) = 0 The inequality constraints are limits of generator active and reactive power output, limits of bus voltage magnitude, and thermal limits of transmission line: Pgimin < Pgi < Pgimax i ∈ SG min max i ∈ SR Qri < Qri < Qri min max i ∈ SN Vi < Vi < Vi S < S max (i , j ) ∈ S ij CL ij
(3)
Where PG and QG are active and reactive nodal injection vector; PL and QL are active and reactive load flow vector; Pgi and Qri are active and reactive nodal injection; SG is the
set of power source; S R is the set of reactive power source; S N is the set of node; SCL is the set of lines. Equations 2 and 3 are called static model of TTC based on continuation power flow (CPF). Dynamic stability constraints also include equality constraints and inequality constraints. Dynamic stability equality constraints include the dynamic equations of components, for example the rotor equation of the ith generator under the kth fault[5]： d ωk ,i M i dt = Pmi − Pk ,ei (i = 1, 2,", n ) d δ k ,i = ω k ,i dt
(4)
Where i is generator number; k is fault number; M i is inertia time constant of the ith generator; Pmi is input mechanical power; Pk ,ei is output electrical power; δ k ,i and ωk ,i are rotor angle and velocity. Dynamic stability inequality constraints are angle stability constraints that are at the end of the speci-
2
fied calculation interval, the largest rotor angle difference between any generators less than 180 degree, as the following forms [6]: max {[δ i (t ) − δ j (t )]2 } < ρ (5) ∀i , j
Static TTC model augmenting with the dynamic stability constraints constitute the dynamic TTC model. The calculation steps are described as follows. For a special power system, set the growing mode of the load and the corresponding generators’ output, then gradually increase the power level of transmission lines, and check whether the above constraints are broken or not when a serious fault occurs. The largest power transmitted while all constraints are satisfied is the TTC. B. The calculation steps In this paper, continuous power flow (CPF) with transient stability constraints is used to calculate TTC. The CPF uses fixed step size method. Firstly, choose initial power level of the transmission line, and then check whether all of the static constraints are satisfied at each solved point of CPF. If yes, check whether all transient constraints are satisfied under the conditions of the fault. If all constraints are satisfied, increasing the power level and continuing next step calculation, otherwise output result. This method has the merit of simple algorithm and the disadvantage of that the step size will affect the calculation of TTC. Small step size will led to excessive calculation load, while big step size will reduce the accuracy of calculation results, and after large number of constrains be break, we have to shrink step size and calculate again. The calculate procedure is given in Figure 1. III. EQUIVALENT MULTI-GENERATOR SYSTEM UNDER THE COI COORDINATE No matter what kinds of numerical method used for the calculation of TTC, solving the power flow and dynamic equations requires intensive computation at each step of CPF. With the system size expansion, the number of node and the failures will increase a lot and this case become even computing speed will be very slow. Due to the calculation time is very long and this method can only be used in offline analysis. The fault happened at the transmission lines between interconnected power grids is a major reason to influence the system’s transmission capacity. Therefore, power grid at each side of the transmission line can be aggregated to an equivalent generator for the purpose of calculating TTC. When a fault takes place inside the two interconnected power grids, the sending side generators will always wave related to the receiving side generators. Each side of generators has a center of inertia (COI) which relative movement can reflect whether the system is out-of-synchronism. Therefore the whole system can be represented as an equivalent two-generator system under COI coordinate to analyze the TTC shown in Figure 2 [7]. The generator is modeled by using the classic second-order model and the dynamic of excitation system and governor is ignored. The input mechanical power of the prime mover is constant and the transmission network is linear. The load bus
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6-9 April 2008 Nanjing China
and generator’s X d' are incorporated into admittance matrix. The dynamic model with N generators is: dωi M i dt = Pmi − Pei (i = 1, 2," , n) (6) d δi = ω i dt
3 N
δ COI (t ) =
∑ M δ (t ) i
(7)
N
∑M
i
i =1
N
∑ M ω (t ) i
ωCOI (t ) =
i
i =1
∑ Mi i =1
l
Define direction of transmission; Read anticipated fault； CPF Step i=1
'
Equivalent generator’s E is: N
Check the static stability restraints of the safety equilibrium point
'
Satisfied？
∑ M E (t ) '
i
ECOI (t ) =
N
i
i =1
∑M
i
To evaluate the influence of the UHV transmission line to TTC of provincial grids in CCG, the interconnected system is represented as an equivalent three-generator system. Except the two-generator system representing the CCG, the third machine is used to model NCG. The total system is shown in Figure 3.
N
Angle instability？ Y
Check the static stability restraints of post contingency safety equilibrium point
ChuanYu
N
Satisfied？
G
Y
Other Part of CCG
G
j=j+1
Figure 3 the equivalent three-generator system of CCG
Have the all the fault finished？ Y
The above equivalent system has several advantages for the calculation of TTC. It only has a few buses. The investigation can focus on the faults of interconnected transmission line. Due to the small fault number, the calculation time of the power flow and dynamic equation with fixed step size is reduced greatly.
i=i+1
Check the static stability restraints of post contingency Y
Satisfied？ N
IV. SIMULATION
Output TTC
Fig. 1 The calculate procedure of TTC
Henan
Hubei
Jiangxi
Hunan
ChuanYu
G
NCG
G
N
ChuanY u
(9)
N
i =1
Check transient stability restraints under fault j
Transmission line to be investigate
(8)
N
Read the results of power flow
l
i
i =1
Other Part of CCG
G
Figure 2 The equivalent two-generator system of CCG
Equivalent rotor angle δ COI and velocity ωCOI of the system’s COI are calculated as:
As shown in Figure 4, CCG and NCG are interconnected by the UHV transmission line; Chuan-Yu power grid and CCG are interconnected by four 500KV transmission lines called E-Yu lines. Regard this group of lines as the research object, each generator is equivalent to Chuan-Yu power grid, CCG, and NCG under their COI coordinate separately. Adjust the power flow of UHV transmission lines and calculate TTC considering faults on double-circuit parallel transmission line which is the worst fault on E-Yu lines. As ignoring the dynamic characteristics of excitation system and governor in the equivalent process, and just considering the simulation of dynamic in the first swing, the calculation time is often less than 5s. Table 1 show the calculation results of TTC of E-Yu lines based on equivalent three-generator system. Obviously, different power amount that exchange between CCG and NCG have different impact on TTC of E-Yu lines. After the UHV transmission line taking into effect, the TTC of E-Yu lines is reduced, however, as power on UHV transmission lines reduced, TTC of E-Yu line is increased.
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6-9 April 2008 Nanjing China
4
VI. [1]
NCG Henan
[2]
CCG
ChuanY u
Hubei
[3]
Jiangxi
E-Yu line Hunan
Figure 4 The CCG-NCG interconnected power system
Table 1 TTC of the equivalent three-generator system(MW)
Power on UHV line Not work 2800WM 1000MW
TTC 3491 3279 3337
Power on UHV line Not work －2800WM －1000MW
Note: power transfer direction from NCG to CCG is＋.
Table 2 TTC of the original system (MW)
TTC 3684 3485 3612
Power on UHV line Not work －2800WM －1000MW
Chengshan Wang, Xinggang Wang, and Pei Zhang, “Fast Calculation of Probabilistic TTC with Static Voltage Stability Constraint,” in Proc. 2007 IEEE Power Engineering Society General Meeting Conf., pp. 1-7.
[5]
P. Bresesti, D. Lucarella, P. Marannino, R. Vailati and F. Zanellini, “An OPF-Based Procedure for Fast TTC Analyses,” in Proc. 2005 IEEE Power Engineering Society Summer Meeting Conf., pp. 1504-1509.
[6]
Xingbin Yu, Chanan Singh, “Probabilistic Analysis of Total Transfer Capability Considering Security Constraints,” 8th International Conference on Probabilistic Methods Applied to Power Systems, US ,2004
[7]
Yixin Ni, Kenny K.Y. Poon1 Haoming Liu, “Control Frame for Synchronous Stability of Interconnected Power Systems in Deregulated Environments,” in Proc.2006 IEEE Power Engineering Society General Meeting Conf., pp.1-7 CEPRI, PSASP6.24 user Manual, 2003
[8]
To verify the above method the detailed CCG-NCG system, model is established in Power System Analyze Software Package (PSASP). Generators are represented by three/five order model considering excitation system and governor. TTCs are calculated in above different situation [8]. Table 2 show the calculation results of TTC of E-Yu lines based on original system. It is obvious that TTC of equivalent system has the same trend with original system. TTC of other transmission lines can also be calculated by the similar method. Power on UHV line Not work 2800WM 1000MW
[4]
TTC 3491 3347 3408
TTC 3684 3379 3503
V. CONCLUSION In this paper, the interconnected NCG-CCG power grid is modeled as an equivalent three-generator system based upon the center of inertia (COI) coordinate. CPF is used to calculate TTCs of E-Yu transmission lines under different situations considering transient stability constraints. A detailed CCGNCG system model is established in PSASP. The simulation results show that TTCs of the equivalent three-generator system are close to the original system. However, because of restrictions on the equivalent method, the calculated results of TTC will not be fully consistent with the system, further research on equivalence model and improved algorithm should be carried on.
REFERENCES
Kulyos Audomvongseree and Akihiko Yokoyama “Consideration of an Appropriate TTC by Probabilistic Approach,” IEEE Transactions On Power Systems, Vol. 19, NO. 1, February 2004. Liang Min, Ali Abur, “REI-Equivalent Based Decomposition Method for Multi-Area TTC Computation,” in Proc. 2006 PES TD Conf., pp. 506-510 Gengyin Li, Ming Zhou, Yajing Gao “Determination of Total Transfer Capability Incorporating FACTS Devices in Power Markets” IEEE PEDS 2005.
VII. BIOGRAPHIES Huimin Yang was born in Shandong province in the People's Republic of China on April 4, 1983. She has received her B.Sc. degrees in electrical engineering from Huazhong University of Science and Technology (HUST), Wuhan, China, in 2004. Currently she is a PhD student at HUST. Her research interests are power system stability analysis and control. Jinyu Wen received the B.Sc. and Ph.D. degrees in electrical engineering from Huazhong University of Science and Technology (HUST), Wuhan, China, in 1992 and 1998, respectively. He is a full Professor at HUST. He was a Postdoctoral Researcher with HUST from 1998 to 2000, and the Director of Electrical Grid Control Division, XJ Relay Research Institute, Xuchang, China, from 2000 to 2002. His research interests include evolutionary computation, intelligent control, power system automation, power electronics and energy storage. Lin Jiang (M’2001) received the B.Sc. and M.Sc. degrees from Huazhong University of Science and Technology, Wuhan, China, in 1992 and 1996, respectively, and the Ph.D. degree from the University of Liverpool, in 2001 all in electrical engineering. Currently he is a Lecturer at the University of Liverpool. His research interests are power system control, induction motor control and renewable enrgy. Shijie Cheng (M’1986, SM’1987) graduated from the Xi'an Jiaotong University, Xi'an, China in 1967 and received a Master of Engineering Degree from the HUST, Wuhan, China in 1981 and a Ph.D. from the University of Calgary, Calgary, Canada in 1986 all in the Electrical Engineering. He is now a full professor at HUST. His research interests are power system control, stability analysis of power system and application of AI in power systems.
