On-line Voltage Stability Monitoring Using Var Reserves

1

On-line Voltage Stability Monitoring Using Var Reserves Lixin Bao, Zhenyu Huang, Member, IEEE, Wilsun Xu, Senior Member, IEEE

Abstract-- For many years, system operators have noticed that the var reserves of key generators can indicate the degree of controllability of key bus voltages in a system. This observation has lead to the development of a few var reserve monitoring systems. In this paper, a rigorous investigation on the subject is conducted. Using the correlative relationship between generator var reserves and the system voltage stability margin, a practical and systematic method for on-line voltage stability monitoring is proposed. The method has been thoroughly tested on two real-life power systems with promising results. Index Terms-- Voltage Stability Management, On-line Voltage Stability Monitoring, Var Reserve.

I. INTRODUCTION

O

n-line voltage stability management attempts to predict and control the voltage stability of an operating power system on a real time basis. It is an essential component to ensure the stable operation of a power system. Although various efforts have been made in the area, reliable and easyto-implement techniques for on-line voltage stability applications are still at large. Based on capability and complexity, on-line voltage stability management techniques can be broadly classified into three types as follows: 1) On-line monitoring: The goal of these techniques is to provide reliable indictors on the voltage stability level of a power system. The basic idea behind the technique is to monitor the generator var reserves and, as a result, the system is simple to understand and implement; 2) On-line assessment: This type of techniques attempts to determine the voltage stability level of a power system for the current as well as the anticipated operating conditions. A typical idea for these techniques is to implement the off-line techniques (e.g. PV curve calculation.) in an online environment. Consequently, the scheme requires the support of advanced energy management system (EMS). Many utility companies are unable to capitalize on such technologies. 3) On-line control: The tools are expected to automatically find the best solutions to prevent voltage collapse under normal and contingency conditions. This scheme is still a vision at present. The authors would like to thank the strategic grant support from the Natural Science and Engineering Council of Canada for this project. L. Bao, Z. Huang and W. Xu are with the Department of Electrical and Computer Engineering, the University of Alberta, Edmonton, AB T6G 2V4 (e-mail: [email protected], [email protected] and [email protected]).

The main objective of this paper is to present a practical and systematic method for on-line voltage stability monitoring. Over the years, system operators have relied on generator var reserves to gauge the voltage stability level of a power system. This understanding has led to several research efforts on the subject. For example, Reference [3] showed that the impact of var reserves on voltage stability is area-dependent. Reference [4] suggested the use of switched capacitors to maintain var reserves in a system. Reference [5] proposed the use of generator rotor heating level as an indicator of system voltage stability. BPA developed a system that monitors many key generators [1]. This work introduced an index that measures the total reserve level of a system. A small index value would mean that the system is short of var reserve (and hence is close to voltage collapse). To our knowledge, this is the first reallife implementation of a var reserve monitoring system. The method, however, does not quantify the relationship between the var reserve level and the voltage stability level. It is not clear, for example, how close the system is to voltage collapse if a small index value is obtained. The work presented in this paper was motivated by the various efforts cited above. In view of the fact that all published var reserve monitoring systems are based on ad hoc engineering experiences, we believe that a systematic investigation on the phenomenon is warranted. It is only through such an investigation that one can develop and use a var reserve based on-line voltage stability monitoring system with confidence. There is also a need to quantify the relationship between the var reserves and the system margin, since just knowing the reserve level, not the associated stability level, can be either conservative or pessimistic. Eventually, such an investigation could lead to the establishment of a systematic procedure to develop a voltage stability monitoring system using commonly available SCADA structure and many utilities can benefit from it without acquiring advanced EMS features. II. CORRELATION BETWEEN VAR RESERVE AND SYSTEM MARGIN The main postulation behind voltage stability monitoring systems is that the var reserves can predict system margin. It is therefore necessary to check and to determine the correlation between the reserves and margin. This section investigates the subject in several steps. A. System with one dominant var source The simplest case to investigate the correlation between voltage stability margin and var reserves is the systems with

2

one dominant var source and one load center. For this purpose, a hypothetical system shown in Fig. 1 is created. The system has a condenser G1 near the load center. G2 and G3 are generators that provide active power to the load center. G4 serves as the slack generator. It is far from the load center and has little impact on voltage stability. 5 P4 =0.0 V4=1.03 θ4 =0.0

4

1

0.05j

P1, V1=1.0

0.6j

1.5j

2 P2, V2=1.0

0.9j

3 P3, V3=1.0

P5+jQ5 =330+j160MVA (Load Center)

Fig. 1 Simple illustration system I

Such a system can have many operating scenarios. For example, one of the lines connecting G2 to the load center may be out of service. Generation needs to be re-dispatched so that active or reactive loss is minimized for the operating condition. Let’s assume that the system has five different operating scenarios as shown in Table I. # 1 2 3 4 5

Therefore, it is sufficient to monitor only the key generator, i.e. G1, for the sample system, since the reserve of G1 exhibits the most consistent correlation with the system margin. A physical explanation for this result is that there is one load center in the system and G1 is very close to the load center as compared to other generators. B. System with multiple key var sources The task can become more complicated if there are multiple load centers or the distances of the var sources to the load centers are comparable. However, the correlation technique used in Section II.A can still be utilized to find if any correlation exists. For this purpose, a two-load-center system is created, see Fig. 3. Table II lists the scenarios used for this study. 1

0.05j 7 P7 =0.0 V7 =1.03 θ7 =0.0

3.0j

P8+ jQ8 =330+j160MVA (Load Center 1) 2.0j

TABLE I TYPICAL OPERATING SCENARIOS OF THE SIMPLE SYSTEM I P2 (MW) P3 (MW) Out-of-service line(s) P1 (MW) 0 198 132 None 0 165 165 1 line 2-5 0 110 220 2 lines 2-5 0 228.6 101.6 1 line 3-5 0 270 60.1 2 lines 3-5

P1, V1=1.0

0.6j

2 P2, V2=1.0

0.9j

3 P3, V3=1.0

8 4

0.05j

P4, V4=1.0

0.6j

5 P5, V5=1.0

P9 + jQ9 =330+j160MVA (Load Center 2)

0.9j 9

6 P6, V6=1.0

Fig. 3 Simple illustration system II

For all scenarios, the condensers and generators are expected to have different amount of var output. The voltage stability margin of each scenario can be different as well. What is of interest here is to determine if there is any relationship between the margins and the var reserves. To this end, the PV margins of the scenarios are computed and plotted against the var reserve of each var source. The results are shown in Fig. 2. In the figure, each generator has five var reserve levels. Each level corresponds to one of the operating scenarios. It can be seen that an almost linear relationship exists between the margin and the reserve of G1. This observation confirms the belief that the reserves of some var sources could be used as a voltage stability indictor. If the var reserve of G1 is monitored, one could get a good ‘feel’ about the voltage stability condition of the system. The results also show that the reserves of G2 and G3 are not good indicators for stability monitoring. 70% 60% G1 PV Margin

50% 40%

G2 G3

The var reserve versus PV margin plot is shown in Fig. 4. At the first glance, there seems to be no correlation exists for any of the var sources. If examining the dots associated with G1 and G4 in more detail, however, one can notice that the scenarios can be divided into two groups. Good linear relationship exists for scenarios in Group 1. Further analysis of the results shows that G1 has a good correlation with scenarios 2, 3, 4 and 5 in Group 1. They are associated with the load center 1. G1 is therefore the key generator to monitor for these scenarios. A similar conclusion can be drawn for G4. These are load center 2 associated scenarios 6, 7, 8 and 9 in Group 1. G4 is the key generator that should be monitored. One can also note that the reserves of G1 and G4 are almost constant for scenarios in Group 2. This is because the generators are not sensitive sources for the respective scenarios. For example, G1 is not a sensitive source for scenario 6. But for the same scenario, G4 is more sensitive and the scenario dot associated with G4 is in Group 1 and it has helped to select G4 as the monitoring source.

30% 20%

#

10% 0% 500

600

700 800 Reactive reserve(MVar)

900

1000

Fig. 2 PV margin vs. reactive power reserve for each generator

To be precise in measuring system stability, one can use curve-fitting techniques to determine the relationship between the margin M and the reserve of G1, Qr1. If a linear correlation is assumed, the relationship can be found as M = 0.0027Qr1 – 1.4818

(1)

1 2 3 4 5 6 7 8 9

TABLE II TYPICAL OPERATING SCENARIOS OF THE SIMPLE SYSTEM II P2 P3 P4 P5 P6 Out-of-service P1 (MW) (MW) (MW) (MW) (MW) (MW) line(s) 0 198 132 0 198 132 None 0 165 165 0 198 132 1 line 2-8 0 110 220 0 198 132 2 lines 2-8 0 228.6 101.6 0 198 132 1 line 3-8 0 270 60.1 0 198 132 2 lines 3-8 0 198 132 0 165 165 1 line 5-9 0 198 132 0 110 220 2 lines 5-9 0 198 132 0 228.6 101.6 1 line 6-9 0 198 132 0 270 60.1 2 lines 6-9

3 W eighting fac tor fitting

70%

0.7

4.5

x 10

-3

W eight fac tors of eac h var s ourc e

Base case

60% G1

50%

3.5

G2

0.5 3

G3

Group1

G4

30%

G5 Group2

20%

Weight Factors

40%

PV margin

PV Margin

4

0.6

0.4

0.3

G6

2.5 2 1.5

0.2

10%

1 0.1

0% 600

700

800

900

1000

0.5

0 5.6

Reactive reserve(MVar)

5.7

5.8

5.9 E quivalent Q res erve

6

6.1

0

6.2

0

2

4 var s ourc es

6

Fig. 4 PV margin vs. reactive power reserve for each generator

Fig. 5 (a) System margin vs. equivalent reserve and (b) weighting factors

One intuitive approach to deal with multi-load-center systems is, therefore, to identify key generators for each load center and to find out the corresponding correlation curves, one for each scenario group. This method has practical limitations, however, since it requires associating certain generators with load centers and scenario groups. It is not easy to choose which correlation curve to use for a given operating condition, either. An alternative approach to is to assume that the overall system margin is linearly related to an ‘equivalent’ var reserve as follows:

The idea of equivalent var reserve has been further investigated using a real-life power system – the 1000-bus BC Hydro system. Operating scenarios for the system were formed by removing a few key transmission lines (one line for one scenario) and by re-dispatching generation with optimal power flow (OPF). For each scenario, the var reserves of all plants were recorded and the corresponding system margin was found by using the PV curve method. Fig. 6(a) and (b) give two examples of the relationship between the system margin and the reserve of a specific var source in the system. Similar to the earlier case, no single generator shows strong correlation with the margin for all scenarios, although a general pattern of correlation exists. Using the figure of JOR as an example, one can see that the scenarios in group A have poor correlation with the margin. If one examines the figure of VIT, however, these scenarios almost line up perfectly on a straight line. This means that the reserve of VIT should be monitored for these scenarios. A similar situation exists for the group B scenarios. The best var source to monitor them is JOR as the JOR reserve shows a linear relationship with the margins of these scenarios. In conclusion, none of the var reserves can be used alone to monitor all scenarios. It is necessary to combine the ‘strength’ of all var sources. This can be done using the concept of equivalent var reserve described earlier. The results are shown in Fig. 6 (c) and (d). It can be seen that a good linear correlation now exists between the margin and the equivalent var reserve.

(3)

where w1 and w4 are the weighting factors. This equation can be understood as follows: For certain scenarios, the reserve of G1 is important, and for other scenarios the reserve of G4 is important. The relative importance of the reserves can be characterized using weighting factors. Since the linear relationship between the reactive power reserves of G2, G3, G5 and G6 and PV margin is not good, their weight factors are supposed to be zero. If one could determine the weighting factors in a way that takes into account all scenarios in a consistent manner, the equivalent source could be expected to yield useful information on the system margin. Note that there is no requirement for (2) to be a linear equation. Other forms can also be used. The linear equation is selected here for its simplicity. Using the data obtained from all scenarios, parameters for (2) and (3) can be determined with a least square fitting method. Fig. 5 shows the relationship between the PV margin and the equivalent var reserve. It can be seen that the margin has a strong linear correlation with the reserve. There are a total of 9 dots in the figure with each dot corresponding to one scenario. The figure further indicates that the margin versus equivalent reserve curve is applicable to all scenarios. Fig. 5(a) can also be understood as a linear mapping of Fig. 4. In other words, the position of every scenario dot in Fig. 4 have been mapped to a new location in Fig. 5(a) through the weighting factors. This mapping has caused the dots to line up in a straight line.

0.22

0.22 JOR

0.2

0.18 0.16

0.18 0.16 0.14

0.14

A

A

0.12 0.1 62.1

B

VIT

B

0.2

PV Margin

Q R = w1 Q r1 + w4 Qr 4

62.2

62.3

0.12

62.4

62.5

62.6

62.7

0.1 150

62.8

200

Q reserve(MVar)

250

300

350

400

450

Q reserve(MVar)

(a) Margin vs. JOR reserve

(b) Margin vs. VIT reserve

Weighting factor fitting 0.22

0.0006

0.2

0.0005 Weighting factor

where QR is the equivalent system var reserve, k is the slope of the margin-reserve correlation line and b is a constant. It is further assumed that the equivalent var reserve is linearly related to the physical reserves as follows:

PV Margin

(2)

0.18 PV margin

M = kQ R + b

0.16

0.14

0.0004 0.0003 0.0002 0.0001

0.12

0 0.1 0.13

0.14

0.15

0.16

0.17 0.18 0.19 Equivalent Q reserve

0.2

0.21

0.22

0.23

BUT

VIT

DMR ASH SCA

JOR

JHT

GMS MCA REV

Var source

(c) Margin vs. equivalent reserve (d) Weighting factors Fig. 6 Correlation between PV margin and var reserve for a real-life system

C. Effect of switched shunts In the previous analysis, switched shunts have been locked when creating scenarios and calculating margins. For real power systems, however, switched capacitors always exist. It has been a common operating practice to use switched shunts

4

to boost the var reserves of key var sources. This practice can be viewed as ‘positioning’ the system dynamic var sources for anticipated contingencies. Accordingly, one can expect that the switched shunts will have a significant impact on the var reserve level of the system. If one only monitors the dynamic var sources such as condensers and generators, it would be impossible to know the true reserve level and hence the real stability condition of the system. As an example, the BC Hydro system is analyzed by allowing the adjustment of switched shunts. The switched shunts were grouped in 4 areas – Lower Mainland, Vancouver Island, Peace and Columbia. It can be seen from Table III that the total var reserves of generators and condensers have increased significantly when switching on the shunts. The increase is more than the total var of the switched-on shunts. The switched shunts therefore have two effects. One is to increase the var reserve level and the other is to compensate the system var losses. Fig. 7 shows the reactive reserves of major dynamic var sources in the system as different groups of switched shunts are switched on. All sources have shown increased var reserve level over the base case where the shunts are off. It is important to note that the impact of switched shunts is local, namely, plants in the area of switched shunt actions experience larger increase in reserves than other plants, e.g. BUT in the Lower Mainland area, and VIT and DMR in the Vancouver Island area. TABLE III EFFECT OF SWITCHED SHUNTS ON REACTIVE RESERVE Area of switched-on Shunts switched on Total plant reserve shunts (MVar) increase (MVar) 692.32 1009.30 Lower Mainland 509.76 809.29 Vancouver Island 615.87 893.29 Peace 490.00 711.73 Columbia 1600 Base Case

Low er Mainland

Vancouver Island

Peace

Columbia

Reactive reserve (MVar)

1400

switched shunts. An effective approach to take into account the wide variety of var sources is to create an equivalent var reserve. In this section, a rigorous analysis is conducted on this basic idea. It leads to the development of a systematic method for on-line voltage stability monitoring.

A.

Formulation of the problem Without losing generality, the equivalent reactive reserve for a system can be defined as the weighted summation of the reactive power reserves of all variable var sources: NQ

QR − j = ∑ wi Qr −ij

M j = kQ R − j + b,

NQ

M j = k ∑ wi Qr −ij + b

* ∑ (M j − M j )

DMR

KMO

GMS Plant

PCN

MCA

REV

SEV

KCL

Fig. 7 Plant reactive reserve with the effect of switched shunts

We therefore propose to monitor the ‘reserves’ of key switched shunts in addition to those of the dynamic var sources. In view of the local nature of the impact of the switched shunts, one can expect that the correlation between the system margin and the reserves of switched shunts will not be uniform. There is a need to find an equivalent source that can take into account the reserves of both static and dynamic var sources and some switched shunts could be selected as monitoring points. III. A SYSTEMATIC METHOD FOR VOLTAGE STABILITY MONITORING The results shown in the previous section have confirmed that var reserves can indeed be used as an effective voltage stability indicator, if the relationship between the system margin and the var reserves can be identified. It is important to monitor all types of variable var sources including the

(7)

NS

200

VIT

2

j =1

E= BUT

(6)

Equation (6) shows that the PV margin of scenario j could be estimated from the reactive reserves of all var sources. The estimation error can be defined as the RMS error between the actual PV margin and the estimated PV margin: NS

CMS

(5)

j = 1, 2, ..., N S

i =1

800

0

j = 1, 2, ..., N S

where Mj is the PV margin of scenario j, k is the slope of the correlation line and b is a constant. Parameters k and b define the correlation line. Combining (4) and (5), we can obtain

1000

400

(4)

where QR−j is the equivalent reactive reserve for scenario j, NQ is the total number of var sources, NS is the total number of scenarios, wi is the weighting factor for var source i. It is required that wi ≥ 0, and Qr-ij is the reactive reserve of var source i for scenario j. Assuming a linear relationship between the system PV margin and the equivalent reactive reserve, the following equation can be established:

1200

600

j = 1,2,..., N S

i =1

where Mj* is the actual PV margin for scenario j. If a set of scenario data (Mj*, Qr-ij) is available, parameters wi, k, and b can be determined by minimizing the error in (7). This optimization problem can be formulated as follows. NS

E=





NQ



* ∑ M j −  k ∑ wi Qr −ij + b  j =1   i =1   

NS

2

=

min{E (v i )} Subject to vi ≥ 0

NS



j =1



N Q +1



i =1



* ∑  M j − ∑ vi Qr −ij 

2

(8)

NS

(9)

kwi , i = 1, 2, ..., N Q where vi =  , and Qr −( NQ +1 ) j = −1 . vi b, i = N Q + 1 is the combined weighting factor for var source i. The above problem can be solved with standard optimization routines. The results are parameters vi and b, which are sufficient for estimating PV margins of new operating scenarios. The combined weighting factors vi represent the relative importance of various var sources. Case

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study results of Section IV will show that most var sources will be assigned to a zero value of vi. Only those with non-zero weighting factors need to be monitored. This small number of var sources is the key sources of the system. The on-line monitoring procedure can be summarized as follows: 1. Prepare a set of operating scenarios. They can be created, for example, according to system operation guide. 2. Determine the PV margin and var reserves for each scenario. 3. Solve the problem (9) to determine the parameters vi and b and identify key var sources. 4. Collect var reserve information from common SCADA system. 5. Apply (6) to determin the system margin for the current operating point. The RMS error defined in (7) characterizes the overall performance of the monitoring method: the smaller the error, the better the performance. However, the prediction accuracy for individual scenarios, which is desired for on-line applications at current operating moment, is unknown from this definition. The prediction error for an individual scenario j can be defined as the percentage of the difference between the predicted PV margin and the actual PV margin with respect to the actual PV margin. Err j =

M j − M j* M j*

j = 1,2,..., N S

(10)

B. Pre-filtering of small var sources Theoretically speaking, all var sources should be included in (8) no matter how insignificant they are. For practical implementation, there is a need to use only a selected number of sources for curve fitting. This is due to two considerations. Firstly, the actual implementation of the monitoring system becomes more manageable if only a few sources need to be monitored. Secondly, there is a need to condition the curving fitting data so that the final results are more meaningful. This situation can be understood by considering the following hypothetical situation: if a system has 5 scenarios and 10 var sources. The unknowns would be more than the equations so multiple solution sets would be found. The basic idea for pre-filtering is to determine which sources have better correlation with and are more sensitive to the system margin. We can assume that each var source attempts to predict system margin using a linear equation as follows: M j = k i Qr −ij + bi , i = 1,2,..., N Q , j = 1, 2 , ..., N S

(11)

Using the scenario data sets and the least square method, we can determine the parameters ki and bi. The inverse of ki (ai=1/ki) can be considered as the sensitivity of the ith var reserve with respect to the system margin. If ai is large, the source is more sensitive to margin variation. In other words, if such a source is selected for monitoring, a larger range of reserve variation can be measured. One of the pre-filtering criteria is, therefore, to identify the sensitive sources, i.e. If ai > a 0 , select var source i. i = 1,2,..., N Q

(12)

where a0 is the pre-filtering threshold. Case study results show that a larger a0 gives a larger least square error (defined in Eqation (8)). On the other hand, if the pre-filtering threshold a0 is lowered many var sources will be selected. There is, therefore, a need to make a trade-off between the fitting error and the number of monitored sources. These conflicting requirements can be illustrated by Fig. 8. With the increase of threshold a0, the error E increases, but the number of var sources selected, L, decreases. The best threshold will be the one considering both factors. More details on this topic are provided in Section IV. E,L

E

L

Pre-filtering threshold a 0

Fig. 8 Illustration on determining the best pre-filtering threshold

C. Adaptive learning procedure The proposed method can be implemented using the SCADA system available in many utilities. The main effort is to perform off-line scenario studies and to determine the weighting factors. It is possible that the initial scenario set does not cover all credible system operating conditions. The system itself is evolving constantly too. A procedure is therefore needed to update the monitoring system so its accuracy does not deteriorate over time. A practical adaptive learning procedure is proposed to address this concern. This procedure is summarized as follows: 1. Assume that monitoring system is created using an initial set of scenarios. This set may just include a small number of scenarios. It can be called as the fitting set; 2. As time goes by or more efforts are made, new scenarios have emerged. These scenarios are called test set; 3. Estimate PV margins of the test set using the monitoring formulas and parameters; 4. Identify the first few scenarios that have the largest estimation errors, using the definition in (10). These are critical scenarios; 5. Add the critical scenarios to the fitting set. Re-calculate the weighting factors using the expanded fitting set; 6. Repeat 3 to 5 until the estimation error is less than a prespecified tolerance or the estimation error is less than the fitting error. IV. CASE STUDIES Two large-scale real-life power systems have been used to test the proposed method. One is the 1000-bus BC Hydro system and the other is the 1800-bus Alberta system. Only the result of the BC Hydro system is presented because of space limitations. The results obtained from both systems are similar. For the BC Hydro system, there is a total of 90 credible scenarios prepared for establishing the monitoring system. Among them, 44 are associated with out-of-service of transmission lines. 45 are associated with generator out-ofservice.

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A. Performance of the proposed method All scenarios are used as the fitting set to find the weighting factors. The results are given in Fig. 9-11. More than one set of weighting factors are obtained by changing the pre-filtering threshold a0.

B. Determination of the best pre-filtering threshold The best pre-filtering threshold is a trade-off between the fitting error and the number of monitored sources. Fig. 12 gives the fitting error E and monitored var source number L for different pre-filtering threshold a0. When a0>80, error E increases significantly. L corresponding to a0 = 80 is small. Therefore, 80 is the best pre-filtering threshold in this case. It gives 8 var sources for monitoring (Fig. 10(b)). 100

80 70 60

Weighting factor fitting

9.0

0.42

8.0

0.4

7.0

PV margin

0.38 0.36 0.34

10

5.0

0 0

3.0

0.3

2.0 1.0

0.26

3.6

Var source

Equivalent Q reserve

(b) Weighting factors (a) Optimization result (E=0.0030) Fig. 9 Optimization result and weighting factors when a0 = 0 Weighting factor fitting 0.44

0.0012

0.42

Plant Shunt

0.0010

0.0006

0.26

0.56

0.58

0.6

0.62 0.64 0.66 Equivalent Q reserve

0.68

0.7

0.72

K LY500

0.0000 VIT

0.0002

0.28

N IC 500

0.0004

0.3

ING 230

0.32

D M R 500

0.34

M D N 230

0.36

0.0008

MCA

0.38

JO R

W eig h t in g fact o r

0.4

10

20

30

40 50 60 70 Pre-filtering threshold a0

80

90

100

Fig. 12 Determination of the best pre-filtering threshold

0.0

0.24 3.4

PV margin

20

6.0

0.28

0.24 0.54

30

4.0

0.32

50 40

Plant Shunt

W eig h t in g facto r

0.44

L 7000*E

90

L and E

The sensitivity parameters ai of the var sources are found according to the method described in Section III.C. Var sources DMR500, MCA, CKY500, NIC500, VIT and ING230 have the largest ai. It indicates they are large-capacity and sensitive var sources in the system. MCA is a generator, VIT is a synchronous condenser and others are switched shunts.

Var source

(b) Weighting factors (a) Optimization result (E=0.0066) Fig. 10 Optimization result and weighting factors when a0 = 80 (best)

C. Error analysis When the best pre-filter threshold is applied (see Fig. 10), the error of each scenario is calculated and plotted in Fig. 13. It is clearly shown that the result is satisfactory and all the errors are within ±10% range. The largest error is about 8.24% conservative and it is corresponding to the scenario of the VIT out-of-service. Synchronous condenser VIT in the Vancouver Island has the largest weighting factor because of its importance. When VIT is out of service, the lost reactive support will be taken by other reactive sources with smaller weighting factors in the surrounding area. This may cause large error and be the reason of being conservative.

Weighting factor fitting

0.0014

0.38

0.0012

0.34 0.32 0.3

0.0010 0.0008 0.0006 0.0004

0.66

0.68

0.7

NIC 500

D M R 500

0.58 0.6 0.62 0.64 Equivalent Q reserve

C KY500

0.56

M CA

V IT 0.54

0.3

2

0.25

0 -2

1

6

11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86

Var source

(b) Weighting factors (a) Optimization result (E=0.0096) Fig. 11 Optimization result and weighting factors when a0 = 100

Fig. 9(b)-11(b) plot non-zero weighting factors only. Most var sources have weighting facotors of zero. Note that only those var sources with non-zero weighting factors need to be monitored. The larger threshold, the less generators are selected, while the fitting error increases. With the best prefiltering threshold (Fig. 10), the fitting error is quite acceptable and the number of monitored var sources is reduced. In addition, some small var sources are filtered out, such as GPT12B, GIB25 and FMT25. A good balance is reached between the accuracy and the number of monitored var sources. Fig. 10 also shows a good correlation between the equivalent var reserve and the PV margin. Important var sources such as VIT, JOR and ING230 have been selected for monitoring. VIT is a large synchronous condenser located in the Vancouver Island. JOR, also in the Vancouver Island, is a large generator (170MW output) with strong reactive support capability to the local area. ING230 is a large switched shunt located in the main load center of the system.

0.1

-6

0.05

-8 -10

0.2 0.15

-4

0.0000

0.4 0.35

4

0.0002

0.24 0.52

PV margin

6

0.28 0.26

0.45

8

Error (% )

PV margin

0.36

10

Plant Shunt

PVm argin

0.0016

0.4

W eig h t in g fact o r

0.42

Sce nario

0

Fig. 13 Error of each scenario with the best pre-filtering threshold

D. Adaptive learning procedure To evaluate the performance of the adaptive learning procedure, only part of the scenarios are selected as the fitting set and the rest as the test set. Repeat the adative learning procedure described in Section III.C. Each time the first two scenarios with the largest errors are identified as new critical scenarios and added to the fitting set. Fig. 14 and 15 show the results when applying the adaptive learning procedure. Note that the test error has been reduced much. PVO132 is added into the monitoring list. PVO132 is an important shunt with 100MVar capability in the Vancouver Island. The weights of other selected var sources are adjusted to include the effect of new critical scenarios. It is worth noticing that the established learning procedure needs only smaller number of scenarios to obtain good performance, compared with the case using all the scenarios in the previous subsections.

0

0.24 0.7

0.75

0.8 Equivalent Q reserve

0.85

0.9

Fitting error

0.001

0.000

Test error

(a) Margin vs. equivalent reserve (b) Error comparison Fig. 14 Performance of the adaptive learning procedure

0.0015

N IC500

KLY500

ESQ 12

G LD 132

DM R500

IN G 230

PVO 132

RE V

VIT

N IC 500

K LY500

ES Q 12

D M R 500

ING 230

G LD 132

R EV

M D N 230

MCA

0.0000

VIT

0.0005

0.0000

M D N230

0.0010

0.0002

Var source

Var source

(a) Before adaptive learning (b) After adaptive learning Fig. 15 Weighting factors

V. SENSITIVITY STUDIES As it can be seen from the case study results, the performance of the proposed monitoring method could be affected by two factors – pre-filtering threshold and the data set used for fitting. Furthermore, all the case studies are conducted at only one load level, which is the peak load. There is also a need to examine if the weighting factors can be applied to other load levels. A. Sensitivity to pre-filtering threshold This study investigates the impact of the pre-filtering threshold on the weighting factors. The weighting factors in Fig. 9-11 are compared in Fig. 16(a). Although the number of the monitored var sources has changed for different thresholds, the most important var sources are always selected. A larger pre-filtering threshold only filters out var sources. It does not result in the addition of new var sources to the monitoring list. More cases are studied with the adaptive learning procedure by choosing different pre-filtering thresholds. The weighting factors are shown in Fig. 16(b). “a0 = 35” is the same case shown in Fig. 14. The conclusion is similar: the proposed method possesses good robustness and consistency with respect to the pre-filtering threshold. 0.005

0.004

best a0

a0 = 0

a0 = 50

a0 = 35

a0 = 50

0.004

0.003 Weighting factor

Weighting factor

a0 = 0

0.002

0.001

0.003

0.002

0.001

0.000

0.000

Var source

It can be seen that there is a good consistency between the results of data sets 1 and 2. The weighting factors of data set 3 have large difference from the other two. This is likely caused by the random nature of the scenarios selected in data set 3. This set missed some critical scenarios. So a “good” fitting set is necessary for good performance. The adaptive learning procedure is one way to improve the scenario selection. It is found that once the critical scenarios are included in the fitting set, the list of the var sources to be monitored is similar and weighting factors are consistent among the sources. C. Sensitivity to load level In this investigation, the BC Hydro system with ±2% and ±4% load variations is considered. The load variation results in a number of new scenarios. The monitoring system created at the base case load level is then used to predict the system margins for other load levels. The results are shown in Fig. 18. This figure also shows the estimation error for each load level. It is noted that the monitoring system has larger errors for other load levels. 0.5

0.08

0.45

0.07 0.06

0.4 0.35 PV margin

0.0020

MCA

0.0004

Plant Shunt

0.0025

JOR

0.0006

JO R

W eig h t in g fact o r

0.0008

W eig h t in g facto r

Plant Shunt

0.0010

Var source

Fig. 17 Weighting factors for different data selections (AB system)

0.0030

Error

0.0012

G ENE

0.001

0.26

0.002

SH EE

0.002

Part scenarios

LAM O UR EU

0.003

0.3 0.28

Self-learning

0.003

C BAR

0.004

R O SS

0.32

All scenarios W eig h t in g f acto r

0.34

0.004

LANG

0.005

procedure.

After learning

J AN ET

0.006

0.36

Before learning

EN M AX38S

0.007

0.38

M ET ISKO W

0.008

0.4

ST R ACH AN

0.42

RM S erro r

PV margin

7

0.3 0.25

0 -4.00%

0.45

0.5

0.55 0.6 Equivalent Q reserve

0.65

0.7

0.75

-2.00%

0.00% Load level

2.00%

4.00%

(a) Margin versus equivalent reserve (b) Estimation errors Fig. 18 Performance of the proposed method at different load levels

In order to consider the effect of load level variations, it is necessary to select some scenarios at different load levels for fitting. An example is given in Fig. 19. The results are obtained by adding only one scenario at the –2% load level to the fitting set. Performance of the system has been improved a lot. Although including scenarios associated with other load levels is one way to construct the monitoring system, one can also develop several sets of weighting factors for a system. Each set could be used for one specific load level.

Var source

Test of fitting results

??????

0.5

(a) All scenarios (b) With adaptive learning Fig. 16 Weighting factors with different pre-filtering thresholds(AB system)

0.45

0.4

PV margin

B. Sensitivity to data set The weighting factors obtained from three different data sets are compared. The first one is the result of using all scenarios as the fitting set. The third one is the result of selecting part scenarios as the fitting set. In the second case, the fitting set contains those scenarios in the third case and those critical scenarios identified by the adaptive learning

0.03 0.01

0.15 0.1 0.4

0.04 0.02

base -4% -2% 2% 4%

0.2

0.05

0.35

0.3

0.25

0.2

0.15 0.45

0.5

0.55

0.6 0.65 Equivalent Q reserve

0.7

0.75

0.8

(a) Margin versus equivalent reserve (b) Estimation errors Fig. 19 Fitting and test results with the information of other load levels

8

VI. CONCLUSION An easy-to-implement and practical method for systematic on-line voltage stability monitoring has been proposed in this paper. This method is based on the correlative relationship between var reserves and system PV margins. Main contributions of this paper are: 1. The correlation between var reserves and system margins has been thoroughly investigated on sample and real-life systems. It is found that var reserves of individual sources do not exhibit consistent correlation with the system margin. The concept of equivalent var reserve is introduced and the index has a good correlation with the system margin. 2. A set of methods and procedures has been developed to determine the equivalent var reserve and its relationship with the system margin. 3. Based on the findings, a systematic method for constructing an on-line voltage stability method was proposed. The method was further enhanced with an adaptive learning procedure for practical applications. 4. Extensive case studies and sensitivity analysis have been conducted to assess the proposed method. Promising results have been obtained. The case studies have indicated that this method has good accuracy and is able to accomplish the task of monitoring voltage stability. The monitoring system can be used as an independent tool for voltage stability management or as a complementary tool for the on-line assessment methods. In addition to its simplicity, another strength of the proposed method is that the results are derived from a multitude of case study results. They are therefore less sensitive to data errors as compared to the on-line assessment method. Although this paper has covered many issues on the proposed method, we believe the following topics deserve further investigation: 1. Alternative methods to capture the correlation between the system margin and var reserves could be explored. For example, nonlinear equations could be used to model the margin-reserve correlation. Data mining tools could be used to find different ways to represent the relationship. 2. Since most scenarios have large margins, it could be useful to treat each scenario differently when calculating the weighting factors. For example, scenarios of small margins could be given more weight. The experience of the system operators could also be incorporated. 3. Some form of field test verifications of the proposed method would be useful. Real operating scenarios can be used to check the performance of the proposed method. VII. REFERENCES [1]

[2]

[3]

C. W. Taylor and R. Ramanathan, "BPA Reactive Power Monitoring and Control Following the August 10, 1996 Power Failure", VI Symposium of Specialists in Electric Operational and Expansion Planning, Salvador, Brazil, May 24-29, 1998. E. Vaahedi, A. Y. Chang, S. Mokhtari, N. Muller and G. Irisarri, “A Future Application Environment for B.C. Hydro’s EMS”, IEEE Trans. on Power Systems, vol. 16, no. 1, pp. 9-14, Feb. 2001 B. Avramovic and L. K. Fink, “Real-time Reactive Security Monitoring” , IEEE Transactions on Power Systems, Volume: 7, Issue: 1 , Feb. 1992, Page(s): 432-437

[4]

[5]

[6]

L. Sandberg, K. Roudén and L. Ekstam, “Security Assessment Against Voltage Collapse Based on Real-time Data Including Generator Reactive Capacity,” CIGRÉ, paper 39/11-03, 1994 W. R. Lachs and D. Sutanto, “Rotor Heating as an Indicator of System Voltage Instability”, IEEE Transactions on Power Systems, Volume: 10, Issue: 1 , Feb. 1995, Page(s): 175 –181 W. Xu and Z. Feng, “Assessment of Reactive Power Constraints and Deficiencies of the Alberta Interconnected Electric Transmission System,” Project Report prepared for the ESBI Alberta Limited, November 1998

VIII. BIOGRAPHY Lixin Bao Zhenyu Huang (M’01) received his B. Eng. from Huazhong University of Science and Technology, Wuhan, China, and Ph.D. from Tsinghua University, Beijing, China, in 1994 and 1999 respectively. From April to October of 1998, he was a research assistant in the University of Hong Kong. From September 2000 to September 2001, he worked at McGill University as a post-doctoral fellow. He is presently a post-doctoral fellow at the University of Alberta. His research interests are in power electronics, power system stability and power quality. Wilsun Xu (M'90, SM'95) received Ph.D. from the University of British Columbia, Vancouver, Canada in 1989. He worked in BC Hydro from 1990 to 1996 as an engineer. Dr. Xu is presently a professor at the University of Alberta. His main research interests are power quality and voltage stability. He can be reached at [email protected].