The 6th International Conference on Renewable Power Generation (RPG) 19 20 October 2017 Situation awareness of power system base on static voltage security region Fei Xiao, Zi-Qing Jiang, Qian Ai, Ran Hao Department of Electrical Engineering, Shanghai Jiaotong University, Shanghai, 200240, People s Republic of China E-mail: xiaofeisjtu@163.com Publishe in The Journal of Engineering; Receive on 12th October 2017; Accepte on 3r November 2017 Abstract: Situation awareness is a key factor in preserving power system security, as it enables effective an timely ecision-making an reactions by the operators to the potential incients. In orer to ientify operating status of large power system integrate with win farms, this stuy presente a metho of situation awareness base on static voltage security region (SVSR). Firstly, inex of voltage security margin is propose base on the limit inuce bifurcation to quantify the level of the power system voltage security. Then, the authors calculate the hyper-planes of SVSR bounary by combination of quasi-steay-state equation an heuristic algorithm. These hyper-planes, obtaine by off-line computation, assist in online assessment of security state an loa margin. Furthermore, a win power forecast technique is use to prouce a new win spee series for a given correlation between two win farms, which support the situation projection. Finally, the correctness an effectiveness of the propose metho is emonstrate by cases stuie in the moifie IEEE 9-bus an IEEE 118-bus system. 1 Introuction Power system situation awareness aims at mastering the security situation of power gri accurately an effectively through three steps, namely, perception, comprehension, an projection. With the growing expansion of the power gri scale an the continuously increase complexity of gri operation, fast an accurate estimation of the system operation state has become the major concern for ispatchers. The security state awareness metho base on precise system component moel is not suitable for the large-scale interconnecte power gri. At the same time, it is ifficult for ispatchers to take preventive measures or emergency control in a timely manner, ue to the ata transmission frequency of monitoring evices an the calculation spee of real-time fault analysis tools. In this case, the static voltage security region (SVSR) is propose to evaluate the power system security status quickly by analysing the relative position of the operating point in the security region space. Its avantages in real-time monitoring are expecte to be applie in the situation awareness, one of the important functions in the control centre. The security region metho was first propose in 1970s by F.F. WU an was efine subsequently as the set of state variables such as injection power, voltage, an phase angle [1]. This metho has been wiely use in some applications, such as line thermal stability, voltage stability, small isturbance stability, an transient stability in recent years [2 5]. A robust master-slave twolevel coorinate SVSR is propose in [2] to protect win units from serious over-voltage an low-voltage problems. A heuristic metho for estimating the shortest raius of power system security region in noe injection space is propose in [3]. In [4], aiming at the real-time ispatch problem, a new concept of effective steay-state security region is propose. Makarov et al. [5] have put forwar the security region framework moel that applies for all essential constraints, incluing thermal, voltage stability, transient stability, an small signal stability. This moel can collect ata by using synchronous phasor measurement unit, an achieve realtime perception an on-line monitoring of the wie area power system. Meanwhile, some problems still remain to be fully explore. For instance, whether the correlation between the capacities of the griconnecte win power woul affect the voltage security margin an the impact of the stochastic an uncontrollable characters of win power with high permeability on gri security status. To solve the above problems, the following research has been carrie out in this paper. Firstly, inex of voltage security margin base on the limit inuce bifurcation (IB) has been propose for the real time evaluation of power system security level. Then, the auto regression moving average moel an time-shifting technique are use to simulate an preict the correlate win spee time series. Moreover, this paper proposes an iterative approach base on heuristic algorithm an constructs a set of secure region moel through offline calculation to meet the nees of online security evaluation. Finally, the correctness an feasibility of the propose metho are prove by the test system. 2 Voltage security margin inex In the analysis of static voltage stability, two types of system instability are usually stuie. One is sale noe bifurcation (SNB), that is, when the system is approaching the bifurcation point, the power flow is often not convergent. The other is the IB, as shown in Fig. 1. P 0 represents base loa capacity. When the generator is in reactive power limit state, i.e. Q Gi = Q lim Gi, the voltage of the system will ecrease graually until the voltage limit is reache, along with the increase of loa. The critical operating point of IB is the reactive/voltage constraine switching point. Then, the generator cannot maintain constant voltage amplitue an the system will suenly collapse, that is IB. The parameters of active power are use to calculate the inex of voltage security margin in this paper. The voltage security margin of loa an generator buses can be calculate as DP = P S max P 0 (1) VSM = DP P 0 100% (2)
where n, m, w i an u j are parameters of ARMA moel; a(t) is gauss white noise sequence. Since the win spee series have a strong correlation when win farms are of close geographic position. Equation (8) gives the calculation metho for correlation coefficient of win spee series of win farms k1 an k2 r = E(SW k1 SW k2 ) E(SW k1 )E(SW k2 ) (8) var(sw k1 ) var(sw k2 ) Fig. 1 PV curves for generator bus where VSM enotes the voltage security margin; P S max is the maximum loa before conitions of IB occurs. where E( ) an var( ) enote the expectation an variance functions, respectively. In aition, the time-shifting technique is use to simulate win spee series with ifferent correlation. Accoring to (9), win spee series at t = K + t 0 can be erive, K an t 0 represent the integer an ecimal part, respectively. Using the linear interpolation technique, the win spee y i can be given by [6] 3 Power system SVSR integrating win farms The SVSR moel is efine as follows: { } f (x) = y, V [ R V V = (P G, P, Q ) V, Q G [ R GQ, I l [ R I (3) y K+i = (1 t 0 )x i + t 0 x i+1 (9) where x i enotes the original win spee series; y i is the shifte win spee series. The actual output of win farm is etermine by the capacity of win turbines [6]. where P G an Q G enote the injection active power an reactive power vector of generator bus, respectively; P an Q enote the injection active power an reactive power vector of loa bus, respectively; f (x) = y represents the power flow equations; V an I l enote the sets of voltage an line currents, respectively; R V, R GQ, an R I represent the bus voltage amplitue constraints, generator reactive power prouction constraints, an line currents limits, respectively. Accoring to SVSR moel, the voltage security margin calculation shoul be extene to the multi-imensional space. Equation (4) efines the minimum 1 norm istance from the operating point to the bounary of the SVSR in the injection power space. Equation (5) efines the voltage security margin l = min P P 0 P [v 1, v i [ V V (4) i VSM = l 100% (5) 1 P 0 where P is the operating point at the SVSR bounary; v i an V V enote the hyper-plane of the security region bounary an sets of bounaries, respectively; 3.1 Preiction moel of win farm output an correlation analysis In the security region moel, the win farm is regare as the PQ bus. Its active power can be obtaine from the mechanical power, which is relate to win spee, regarless of the slip effect. The win spee series can be calculate by (6) with the consieration of the ranomness of the actual win spee [6] SW k (t) = m k (t) + s k (t)s k (t) (6) where m k (t) an s k (t) enote the average win spee an the stanar eviation of win spee at the win farm k within the perio of t, respectively; s k (t) is the scale function time series of win spee. Accoring to the autoregressive moving average (ARMA) moel, the scale function is illustrate as follows: s k (t) = n i=1 w i s k (t i) + a(t) m j=1 u j a(t j) (7) 3.2 Calculation of SVSR bounary After the incorporation of win farms into the power system, it is necessary to introuce the partial erivatives of the win power to the terminal voltage as well as the phase angle in the original Jacobi matrix J, as shown J s = J DP W u DQ W u DP W V DQ W V (10) where DP W an DQ W enote the change of win farm active an reactive power prouction, respectively; V an θ enote the voltage an phase angle of the bus, respectively. Base on the quasi-steay-state equation an the inverse matrix of Jacobi matrix, the approximate expressions of voltage variation are obtaine as DV = [ < W < G H i, DP i + S i, DQ i + R i, DP Gi (11) where DV is the variation of voltage amplitue of th bus; H i,, S i, an R i, are sensitive matrix of active power an reactive power of ith bus;, W an G enote the sets of loa, win farm an generator buses, respectively. The variation of the th bus voltage amplitue satisfies the following constraint uner the sth case V min V s + H s i,(p i P s i) + + R s i, (P Gi Ps Gi ) V max S s i,(q i Q s i) [ < W < G (12) where V s is the voltage amplitue of the th bus uner the sth case; Pi s an Q s i enote the injection active power vector an reactive power vector of the ith loa bus uner the sth case, respectively. PGi s is the injection active power of the ith generator bus uner the sth case. Then (12) is transforme to (13) escribing the lower an upper bounary of the SVSR in th bus (see (11))
Consiering the efinition of IB, the lower limitation of the voltage amplitue, namely, the first part of (13), is use to calculate security region in this stuy. Then, put the critical point V s = V min, Pi s = Pi, cr Q s i = Q cr i an PGi s = PGi cr into (13), an obtain Hi,P cr i cr + Si,Q cr cr i + R cr i,pgi cr Hi,P cr i + Si, cr Q i + R cr i, P Gi [ < W < G (14) If the critical operating point is given, then the sensitivity matrix in the critical operating state is known. After normalisation, the approximate range of the security region calculate by the lower boun of voltage amplitue can be obtaine, as a i P i + b i Q i + c i P Gi 1 (15) where a i, b i an c i are the coefficients of the hyper-plane. 3.3 Iterative calculation of critical operating point base on heuristic algorithm Accoring to Section 2.2, the bounary of the SVSR is calculate base on critical operating point. This section proposes a metho for obtaining critical operating point by heuristic algorithm. In this metho, the growth of generation an loa towars the irection where bus voltage ecreases the fastest, until the critical point is obtaine. The steps of the propose metho are as follows: Step 1: Initialise a secure operation point an etermine the system topology an security constraints. Set iteration steps Sp = 1. Step 2: Take the inverse of the Jacobi matrix in (10) an obtain voltage-sensitivity matrix, as shown in (16). The number of generator buses an loa buses incluing win farms are enote as m an n X Sp = [R, H, S ] [ = Du,..., Du, Du,... Du, Du,..., Du ] P G1 P Gm P 1 P n Q 1 Q n (16) Step 3: Determine the worst power increasing irection to lower the u, i.e. the amplitue of th bus. X Sp g X Sp l = min ( Du ) i P { Gi Du = min, Du } i P i Q i (17) Observing (17) the worst loa-generation increasing irection for eteriorating voltage security of the system is that the gth generation an the lth loa increase power. Therefore, the worst loageneration increasing irection at iteration step Sp is as follows: P Sp G P Sp Q Sp = PSp 1 G + k + h = PSp 1 = QSp 1 + k Sp h + k SP h h (18) Fig. 2 Situation awareness base on SVSR where k Sp G = [0, 0,..., 1,...0] an k Sp = [0, 0,..., 1,...0]; gth lth h enotes the power increments for each step; h enotes the ratio of reactive power an active power of loa buses. Step 4: If the operating point is at the security region bounary, the iteration process is terminate. Otherwise, set Sp = Sp + 1 an get back to step 2. It is also worth noting that the operating point is eeme to be at the security region bounary when occurring the following scenarios: (i) The power flow calculation is not convergent; (ii) The bus voltage amplitue is lower than the voltage security limits; (iii) The transfer capacity though power line is greater than its limits. When calculate SVSR critical point of the generator buses, the maximum reactive power of this generator must be guarantee. In the process of approaching the IB critical point, aitionally, the bus voltage must be greater than the secure voltage limits, hence conitions (i) an (ii) are given with the consieration of the SNB. The situation awareness process is illustrate in Fig. 2, which consiste of offline computation an real-time monitoring. The SVSR is obtaine consiering various scenarios, such as contingency sets, unit expansion an line reconstruction. The real-time monitoring is conucte with short-term forecaste ata, i.e. loa eman an renewable sources. V min V s ( V max V s ( H s i,p s i + H s i,p s i + Si,Q s s i + R s i,pgi) s + Hi,P s i + Si,Q s i + R s i,p Gi [ < W < G R s i,pgi) s + Hi,P s i + Si,Q s i + R s i,p Gi [ < W < G S s i,q s i + (13)
4 Case stuy The moifie IEEE 9 bus test system an IEEE 118 bus test system are aopte in this paper to illustrate the correctness an effectiveness of the propose metho. 4.1 Test case base on moifie IEEE 9 bus system The moifie IEEE 9 bus test system is illustrate in Fig. 3, from which we can see that the win farm is connecte to Bus 7. Given that this win farm is consiste of 14 sets of 1.5 MW win turbines with a power factor of 0.9. The bus voltage amplitue limits are V min = 0.9, an the transfer capacity limit of the power line is two times of the rate transfer capacity. Assume that the operating point is iterate to the critical point of the SVSR at the lower limit of the voltage amplitue of the Bus 9. This critical point, base on heuristic algorithm, is [P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9 Q 4 Q 5 Q 6 Q 7 Q 8 Q 9 ] = [1.63 1.35 0.00 0.9 0.00 0.79 0.00 1.75 0.00 0.3 0.00 0.25 0.00 0.9]. Then, the Bus 9 SVSR bounary coefficients are illustrate in Table 1. The coefficient of Q 9 is 0.422, its absolute value is far greater than that of other parameters, inicating the irect correlation between the injection reactive power an the voltage amplitue of Bus 9. Moreover, the greater the injecte reactive power is, the farther the operating point is from the bounary of the voltage security region. These results are consistent with the real power system. Assume that the operation point is iterate to the SVSR critical point of the Bus 2 an Bus 3, then Bus 2 an Bus 3 have been transforme into PQ noes uring the process of approaching the IB an satisfy Q 2 = Q lim 2 = 40 MW, Q 3 = Q lim 3 = 20 MW. The bounary coefficients of the SVSR are shown in Table 2. 4.2 Test case base on moifie IEEE 118 bus system The IEEE 118 bus system is use as the test system to calculate the bounary of SVSR. This bounary expression contains 118 injection power variables an 117 security region hyper-planes of the monitoring bus. Table 3 only shows the power variable with a greater magnitue of the corresponing coefficients of the security region bounary of Bus 95. In power system, the bus which is likely to cause voltage collapse an other security accients are efine as voltage weak bus. Therefore, on-line monitoring voltage weak bus plays an important role in ensuring the security an stability of the power system. Table 2 Hyper-plane coefficients of Bus 2 an Bus 3 SVSR bounary parameters P 2 P 3 P 4 P 5 Bus 2 0.171 0.318 0.134 0.004 Bus 3 0.121 0.057 1.015 0.005 parameters P 6 P 7 P 8 P 9 Bus 2 0.077 0.027 0.099 0.120 Bus 3 0.147 0.074 0.357 0.064 parameters Q 2 Q 3 Q 4 Q 5 Bus 2 0.079 0.098 0.184 Bus 3 0.713 0.013 0.423 parameters Q 6 Q 7 Q 8 Q 9 Bus 2 0.098 0.254 0.017 0.168 Bus 3 0.089 0.198 0.002 0.182 Table 3 Hyper-plane coefficients of Bus 95 SVSR bounary parameters P 82 Q 82 P 83 Q 93 coefficients 0.027 0.084 0.059 0.087 parameters P 94 Q 94 P 95 Q 95 coefficients 0.052 0.162 0.143 0.381 parameters P 96 Q 96 P 97 Q 97 coefficients 0.054 0.171 0.024 0.086 Fig. 4 shows the closest 1 norm istance from the current operating point to the bounary of the SVSR. It also can be seen from Fig. 4 that the shortest istance between the system operating point an the voltage security bounary is calculate by voltage limits of Bus 21 an Bus 53, inicating these two buses uner the current operating state are more prone to voltage security incients. Base on the offline calculation of SVSR, the average time to estimate the VSM is merely 0.013 s. Since the heuristic algorithm is use in the bounary computation, the istance between the operating point an the security region bounary coul reflect the VSM of each bus. In accorance with the moal analysis metho, the voltage stability weak bus of IEEE 118 bus system is etermine by the value of participation factors [7]. Moreover, the four most unstable moes are shown in Table 4. The voltage stability weak buses etermine by moal analysis metho are basically similar to weak buses calculate by propose metho. The ifference comes from the fact that the moal analysis of weak buses is mainly relate with the topological structure, an moreover the security region metho consiers the current operating status of power system too. For system ispatchers, the VSM can be quantifie accoring to the security region, an this margin can provie strong support for the eman response policy implementation. In the moifie IEEE 118 bus system, win farms are connecte to buses 26, 59, 73, 77, an 92. The rate capacity of win farm is 200, 150, 75, 100 an 120 MW. The sample ata of 24 hours win Fig. 3 IEEE 9 bus system integrate win farm Table 1 Hyper plane coefficients of Bus 9 SVSR bounary parameters P 2 P 3 P 4 P 5 P 6 coefficients 0.093 0.075 0.005 0.150 0.011 parameters P 7 P 8 P 9 Q 4 Q 5 coefficients 0.122 0.071 0.048 0.072 0.082 parameters Q 6 Q 7 Q 8 Q 9 coefficients 0.082 0.104 0.076 0.422 Fig. 4 1-norms istance from operating point to the SVSR bounaries
Table 4 Bus participation factors uner ifferent moes Moe I l = 0.17 Table 5 Correlation coefficients an shifting time of win power in ifferent cases Case Capacity of win farms, MW Moe II l = 0.31 Bus 73 Bus 77 Moe III l = 0.83 Correlation coefficient Moe IV l = 1.14 Bus P ki Bus P ki Bus P ki Bus P ki 20 0.22 43 0.32 51 0.24 117 1.00 21 0.43 44 0.50 52 0.41 22 0.34 45 0.18 53 0.22 23 0.01 58 0.13 l enotes the magnitue of eigenvalue [7]. Shifting time, h 1 75 100 0.2 13 2 75 100 0.5 4.5 3 75 100 0.9 0.5 4 30 50 0.9 0.5 voltage instability in the light of mechanism analysis. The ranomness an uncontrollability of the win power give rise to the increase of the power flow uncertainty an ecrease of situation awareness capability. Taking power system integrate win farms as an example, this stuy uses the VSM to reflect the operating status of the power system. Besies, the application of the propose metho can be extene by incorporating the istribute energy sources an spatial loa forecasting metho. By putting preicte ata into the security region moel, the VSM in a near future can be calculate. As an important part of system situation awareness, the propose inex coul provie information for operators to master the power gri statue. 5 Conclusion In orer to master the operating status of power gri, a SVSR base situation awareness metho is propose. First of all, the inex of voltage security margin, base on the IB conition, is put forwar for real-time evaluation of power system security status. Then, the ARMA moel an the time shift technique are use to preict the win spee series with correlation. Finally, the bounary of the SVSR is obtaine by integrating quasi-steay-state equations with heuristic algorithm. The numerical results show that the propose metho is applicable to weak bus monitoring an security evaluation. The results of the moifie IEEE 118 bus system inicate that the higher the correlation between win farms outputs, the larger the fluctuation range of VSM. On the other han, the voltage security margin will increase when the win farm capacity is reuce. Aitionally, the application of the situation awareness metho to the eman response will be iscusse in the following research. 6 Acknowlegments This stuy is partly supporte by the Development Program of China (2016YFB0901304) an the National Natural Science Founation of China (51577115). 7 References Fig. 5 VSM of IEEE 118 case from 01:00 24:00 spee were selecte from the ata collecte by National Renewable Energy aboratory. As shown in Table 5, there is a certain correlation between the win spee series at the Bus 73 an Bus 77, an the win spee series with ifferent correlation coefficients can be simulate by (6) (9). The voltage security margin inex from 01:00 24:00 can be calculate by (4) an (5), as shown in Fig. 5. The istribution of VSM uner four cases are [1.04%, 1.29%], [0.97%, 1.34%], [0.76%, 1.47%] an [1.55%, 2.63%]. The comparison between cases 1, 2 an 3 emonstrates that the greater the correlation between win farm outputs, the bigger the fluctuation range of VSM is. By comparing cases 3 an 4, it can conclue that the VSM increases along with the ecrease of the capacity of win farm. The reactive power, absorbe by win farms, fluctuates with the win spee, an the reactive power transfer is likely to cause [1] Wu F.F., Kumagai S.: Steay state security regions of power systems, IEEE Trans. Circuits Syst., 1982, 29, pp. 703 711 [2] Ding T., Bo R., Sun H., ET A.: A robust two-level coorinate static voltage security region for centrally integrate win farms, IEEE Trans. Smart Gri, 2016, 7, pp. 460 470 [3] iu K., He G., Chang N.: Estimating the shortest raius of power system security region in noe injection space, Eng. Technol., 2012, 15, pp. 1 7 [4] Cheng F., Yang M., Han X., ET A.: Real-time ispatch base on effective steay-state security regions of power systems. PES General Meeting-Conference & Exposition, National Harbor, MD, USA, 27-31 July 2014; pp. 1 5 [5] Makarov Y.V., Du P., u S., ET A.: PMU-base wie-area security assessment: concept, metho, an implementation, IEEE Trans. Smart Gri, 2012, 3, pp. 1325 1332 [6] Xie K., Billinton R.: Consiering win spee correlation of WECS in reliability evaluation using the time-shifting technique, Electr. Power Syst. Res., 2009, 79, pp. 687 693 [7] Gao B., Morison G. K., Kunur P.: Voltage stability evaluation using moal analysis, IEEE Trans. Power Syst., 1992, 7, pp. 1529 1542