OMR lWl, E L S E V I E R Electric Power Systems Research 33 (1995) 119-124

Implementation of enhanced network sensitivities in rule based systems for line flow security analysis--case studies for a

practical power system

Ying-Yi Hong Department of Electrical Engineering, Chung Yuan Christian University, Chung Li 320, Taiwan

Received 8 November 1994

Abstract

This paper presents the use of network sensitivity factors for alleviating line overflow. The network sensitivity factors are enhanced to consider multiple circuits between two adjacent buses. Associated with the sensitivities, a rule based system is presented for correcting the line overload after a contingency occurs. The accuracy of the sensitivities, selection of the swing bus and impact of multigenerators at a common bus are discussed. The IEEE 30-bus system and a practical 265-bus system in Taiwan are used as samples to show the applicability of the rule based system proposed in this paper.

Keywords: Security analysis; Sensitivity factors; Rule based systems; Control strategies; Line overload

1. Introduction

Owing to the fast growth of power system loads, system security is becoming increasingly important nowadays. When the system suffers from contingencies such as generator or line outages, the line flow and voltage security are the two main problems that con- cern operators. The lines may become overloaded and then tripping occurs. Generally, operators should make fast and accurate decisions to reschedule MW genera- tion, switch line structures or shed parts of system loads. On the other hand, the system may support a reactive power problem for a longer time. Complex control actions involving generator voltages, on-load tap changers (OLTCs) and compensators can be achieved to alleviate low or high voltage magnitudes. Generally, the real and reactive power problems are de- coupled. The real power problem is stressed in this paper.

It is known that the network sensitivity factors provide sufficient accuracy with respect to the megawatt flows but a full AC load flow analysis is required for voltage problems [1,2]. Network sensitivity factors have been used to determine the ranks of contingencies [1 4] and have been incorporated with functional (security) constraints in mathematical programming for eliminat- ing line overflow [5-12]. The solutions obtained from

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the network sensitivity factors retain a good accuracy compared with those from AC models [1-12].

Expert systems have also been applied to solve many practical power engineering problems [13-16], such as voltage control [14], var planning [15], customer restoration [16], etc. In this paper, a rule based system incorporating network sensitivity factors is proposed to solve the line overflow problem. The generator shift factor (GSF), line outage distribution factor (LODF) and compensated generator shift factor (CGSF) [1] are used in this rule base. The following points are ad- dressed in this paper:

(1) accuracy and limitations of network sensitivity factors;

(2) a rule based system for alleviating line overflow; (3) impact of different swing buses on solutions; (4) impact of multigenerators at a common bus on

network sensitivity factors; (5) modification of network sensitivity factors to deal

with multiple circuits between two adjacent buses.

2. Network sensitivity factors

2.1. Review of network sensitivity factors

The GSF and LODE in Ref. [1] are used to correct the line overflow. The GSF, denoted as ali, is the

120 Y.Y. Hong/Electric Porter Systems Research 33 (1995) 119 124

sensitivity of the MW line flow variation at line l to the MW generation change at generator i; the LODF, represented as dlk, is the sensitivity of the MW line flow variation at line l to the MW line flow change at line k. The line l (k) locates between buses m and n (p and q). The formulation of the GSF and LODF is as follows [1]:

all - ( 1 ) Xl

dlk = xk (Xpn -- Xqn -- xpm -~ Xqm ) (2) x l x k -- X l (Xnn + Xmm -- 2X.m )

where xtCk) is the line reactance for line l(k), and Xp, is the (p, n) element of matrix X; X is the inversion of matrix B where B has the following elements: B p p = z ( 1 / X p q ) where Xpq is the reactance between buses p and q, bus p is not the swing bus, and q are all buses connected to bus p; Bpp=O when p is the swing bus; Opq = - 1/Xpq when neither p nor q is the swing bus; and Opq = 0 when p or q is the swing bus.

In network analysis, it is often required to analyze an outage case with line tripping. It is inconvenient to recompute the GSF for each outage case because of inversion of the matrix. Therefore, another useful network sensitivity factor is the compensated gener- ator shift factor (CGSF) which can be derived as follows:

A f~ = al~ APgi q- dzk Afk

= ati APgi + dtk[aki APgi]

= (all + dtkaki)APgi

= CGSFti APg~ (3)

where Af/¢k) denotes the variation of the MW line flow at line l (k) and APgz represents the variation of the MW generation at generator i. CGSF/i means the sensitivity of the MW line flow variation at line I to the MW generation change at generator i when line k is tripping. GSF, LODF, and CGSF are all obtained via a FOR- TRA N program in this research.

2.2. Modified network sensitivity factors

For many practical power systems, there are several possible circuits between two adjacent buses. Hence, Eqs. (1) and (2) should be modified because xt is a single reactance between two adjacent buses. A modified GSF concerning the variation of MW flow in one of the circuits between two adjacent buses m and n to the MW change at generator i is presented first in this section.

For easy presentation, assume that there are two circuits between buses m and n. Let the two circuits have reactances x n a n d x~ and an equivalent reactance

of xl. X,, and X,,, are elements of X based on x I. Because

f/new =f/old _~_ ali APgi (4)

the MW flow on circuit I (with xtl) is

f/new Xl2 _f/old Xt2 t- ali XZ--I-L----2 APgi (5) xll + xz2 Ytl + xz2 xzl + xt2

Therefore, the modified GSF between the circuit with xz~ and generator i becomes

xl: X,,~- X.., all i = a l i - (6)

Nil -}- Xl2 Nil

Generally, the GSF concerning the j th circuit between two adjacent buses m and n to generator i is

X. , - X.,, aoi -- (7)

X(/

For the same reason, the LODF considering the multicircuit can be obtained. Suppose there are multi- ple circuits between two adjacent buses p and q; there are also multiple circuits between two adjacent buses m and n. The equivalent reactances for the above circuits are x~ and xl. Let Xp,, Xqn , Xpm , Xqm , Xnn , Xmm , and Xm, be the elements of matrix X based on xk and xt. Then the modified LO D F between the circuit with reactance xk, between buses p and q and the circuit with reactance xr between buses m and n is

dl,k,= Xk ' (XPn- ~ fqn - Xpm-~- Xqm) (8) Xl ,Xk , - Xl,(Xnm .Jr- Xmr n -- 2X.m )

3. Rule base

3.1. General description

The network sensitivity factors cannot be used on their own. Associated with these factors, rules have been developed to eliminate line overloads using the experience of the author and senior engineers. Rules for eliminating overloaded lines using the corrective mode are developed in this paper. The corrective mode means that the MW line overflow is corrected by ad- justing the MW generation among generators after the line tripping.

There are about 150 PDC P RO LO G rules for elimi- nating the MW line overflow. They are classified into the following essential modules.

Task A. Identify the most severely overloaded line. Task B. Identify the generator with the largest maxi-

mum correction. Task C. Reschedule the MW generation for the gen-

erator identified in Task B. Task D. Evaluate all line flows by GSFs or CGSFs. Task E. Examine if the reasoning should stop.

Y.Y. Hong / Electric Power Systems Research 33 (1995) 119-124 121

3.2. Rules for eliminating line overloads

The rule based system focuses on the most severely overloaded line at each 'iteration'.

Rule I. IF there are overloaded lines, T H E N deter- mine the severity according to the amounts of violation.

Rule 2. IF the severity of the overloaded lines has been determined, THEN select the most severely over- loaded line.

Rule 3. IF the most severely overloaded line has been identified, T H E N sort the maximum corrections for all generators.

If the value of a GSF (CGSF) is negative (positive), then the MW output at the generator should be in- creased (decreased) for the most severely overloaded line. The largest absolute value (say at generator i) among all the GSFs (CGSFs) does not mean generator i is the most efficient. The most efficient generator is the one with the largest maximum correction. For example, the maximum correction is defined as [(pg~in _Pgi)ajil for aj~>0 or I(AiPgmiaX-Pg~)ajil for aji<O in Task B where a~i is the GSF related to generator i and line j, Pgi is the MW generation at generator i, At is a ratio smaller than unity to avoid generating the maximum amount, and the superscripts min/max denote the mini- mum/maximum MW generations. In other words, the available margin should be considered in conjunction with the GSF (CGSF). Only the generator with the largest maximum correction is identified to be resched- uled at each iteration.

Rule 4. IF the maximum corrections for all genera- tors have been sorted, T H E N identify the generator with the largest maximum correction.

Rule 5. IF the generator with the largest maximum correction has been identified, T H E N compute the adjusted amount of MW generation.

The adjusted amount of MW generation is essen- tially computed from the following equation:

AMW/= a~i AUi (9)

where AMW/is the amount of violated line flow on line j. AUi denotes the adjusted amount of generator output (MW) at generator i.

In Task C, the MW generation limits and the swing bus should be taken into account in addition to the amount of overload to get the adjusted MW amount. Rules 6 - 9 below are rules for the generator which has been identified as requiring increased MW generation. The term 'new MW generation' below means po!a - - g t + AUi.

Four similar rules were also developed to decrease MW generation for the identified generator.

Rule 6. IF the new MW generation of the identified generator is less than its maximum generation and this increased generation does not make the swing bus lower its minimum MW generation, T H E N adjust the MW generation according to the computation.

Rule 7. IF the new MW generation for the identified generator is less than its maximum generation and this increased generation makes the swing bus lower its minimum generation, T H E N increase the MW genera- tion such that the MW output of the swing bus equals its minimum MW generation.

Rule 8. IF the new MW generation for the identified generator is greater than its maximum generation and this increased generation does not make the swing bus lower its minimum generation, TH EN adjust the MW generation to its maximum generation.

Rule 9. IF the new MW generation for the identified generator is greater than its maximum generation (say over A~ MW) and this increased generation makes the swing bus lower its minimum generation (say under A 2 MW), T H E N initiate the 'result' of Rule 7 or Rule 8 depending on the larger of A~ and A 2 MW.

For implementation of Rules 6 9, an approximate system MW loss should be estimated to check whether the real power is balanced in the system.

After the MW generation is adjusted, all line flows are computed for the system. The line flows can be computed via the power flow simulation or by using the GSFs (or CGSFs) in Task D. There are two possibili- ties for ceasing the reasoning (Task E): no overloaded line exists or all generators reach their limits.

For all iterations, the identified generator can only be adjusted in one direction (up/down) in order to avoid cyclic iterations.

Rule I0. IF the MW generation of the identified generator has been increased, and it has to be decreased in the present iteration, T H E N select the generator with the next largest maximum correction.

4. Test results

In this section, the IEEE 30-bus system and a practi- cal 265-bus system in Taiwan are used as samples. The total system load of the 265-bus system is 15 669 MW which is the peak load. The 265-bus system includes 56 generators, 465 lines, 52 compensators, 205 OLTCs, and 13 EHV transformers.

4. I. Accuracy of the network sensitivity ,/'actors

The accuracy of the network sensitivity factors is discussed first to demonstrate the performance of the rule base. Because of GSFs, LODFs and CGSFs are derived from the matrix X, only GSFs are verified in this section.

The 56 generators are assumed to trip individually. The line flows obtained from the GSF and AC power flow methods are examined. The comparison is sepa- rated into two groups: nuclear generators and others (Tables 1 and 2; only errors greater than 15 MW are illustrated). From these tables, the following arise.

122 Y. Y. Hong // Electric' Power Systems Researeh 33 (1995) 119-124

Table 1 Errors greater than 15 MW for nuclear generators

Generator Generation Lines Line flow Line flow Error (MW) by GSF (MW) by AC (MW) (MW)

Nuclear- 1 st- 1 5 7 4 . 6 5 ChinShan-KuGuan2 640.72 665.94 25.22 CbinShan-ChinShanH 649.76 669.29 19.53

Nuclear-2nd-2 929.89 ChinShan-KuGuan2 995.95 1049.02 53.05 ChinShan-ChinShanH 996.00 1057.52 61.52

Nuclear-3rd-2 8 8 9 . 5 5 TieLune-KuGuan 1 561.18 537.76 23.42 TieLune-KuGuan2 391.63 370.80 20.83

Table 2 Errors greater than 15 MW for other generators

Generator Generation Lines Line flow Line flow Error (MW) by GSF (MW) by AC (MW) (MW)

HseiHo-1 4 7 6 . 3 1 ChinShan-KuGuan2 542.36 559.85 17.49 ChinShan-ChinShanH 542.41 562.20 19.79

HseiHo-3 487.36 ChinShan-KuGuan2 553.42 571.49 18.07 ChinShan-ChinShanH 553.47 573.94 20.47

TaLin-5 5 0 5 . 5 0 TieLune-KuGuanl 368.54 353.48 15.06

(i) All of the lines listed in Tables 1 and 2 are near the swing bus. In other words, larger errors for line flow calculation occur at the lines near the swing buses. The errors result from numerical errors, ignorance of MW loss, the linear model, etc.

(ii) The errors from nuclear unit tripping are large, as shown in Table 1. In the above tests, the changes of output are from 889.55 and 929.89 MW to 0 MW for Nuclear-3rd-2 and Nuclear-2nd-2, respectively. There- fore, if GSFs are used to study the contingency screen- ing problem, misleading results may be obtained. However, the nuclear units are not used to alleviate the line overflow in this paper because their outputs are generally fixed.

(iii) The three generators listed in Table 2 are all thermal units and are the three largest thermal units in this system. The largest error is 20.47 MW because Hseiho-3, with the whole 487.36 MW, is tripping, as shown in Table 2. It is expected that the error should be smaller than 20.47 MW if the generator is rescheduled only for alleviating the overflow.

Comparison of the line flow calculation between the GSF and AC model methods for a typical thermal unit (TaLin-1) is shown in Table 3. Only the line flows related to GSF absolute values greater than 0.1 are shown in Table 3. From Tables 1-3, we see that GSFs can be used to reschedule the MW generation.

4.2. Elimination of line overflow

4.2.1. Elimination of line overflow for the IEEE 30-bus system

In this section, the IEEE 30-bus system is used as the sample. To demonstrate the performance of the rule

base in eliminating the line overflow, the line between buses 22 and 24 is assumed to be tripping. Suppose that the maximum line flow limit for each line is 25 MW except for the lines between buses 1-3, 1-2, 9-11, and 12 13 that are generator output paths. The maximum line flow limit for each of these special lines is 150 MW.

The reasoning of the expert system for this case is as follows.

(1) There are five lines overloaded: between buses 2-5 , 2-6 , 3-4, 4 -6 , and 9-10.

(2) The most severely overloaded is the line between buses 3 and 4. The line flow is 32.46 MW.

(3) The largest absolute value of the CGSFs is for the generator at bus 13 (-0.3656). The most efficient generator is also the generator at bus 13' with a maxi- mum correction of 40.2153 MW.

(4) The MW generation at bus 13 is increased from 30 MW to 50.418 MW just to eliminate the overflow.

(5) There are two transmission lines overloaded after adjustment of the MW generation at bus 13. The line

Table 3 Line flow comparison between GSF and AC models for TaLin-I unit

Lines Line flow Line flow Error by GSF (MW) by AC (MW) (MW)

TeiLun-ChunLiao 722.774 730.292 7.518 LungChi-JaMin 939.827 943.528 3.701 ChunLiao-JaMin 352.474 354.035 1.561 LungChi-JaMin 439.906 442.870 2.964 LungChi-HsiTar 1255.968 1258.237 2.269 TeiLun-KuGuan 265.832 255.642 10.178 ChinShan-KuGuan 367.309 356.315 10.994 TaLin-NanGon 458.155 458.754 0.599 KauKan-NanGon 226.892 229.536 2.644

Y. E Hong / Elect ric Power Systems Research 33 (1995) 119 - 124 123

flows for lines between buses 4 and 6 and buses 9 and 10 are 30.822 MW and 25.363 MW, respectively.

(6) The largest absolute value of the CGSFs is for the generator at bus 8 ( -0 .5022) . The most efficient generator is also the generator at bus 8 with a maxi- mum correction of 37.6652 MW.

(7) The MW generation at bus 8 is increased from 15 MW to 26.593 MW just to eliminate the overflow of the line between buses 4 and 6.

(8) There is one transmission line overloaded after adjustment of MW generation at bus 8. The line flow for the line between buses 9 and 10 is 25.539 MW.

(9) The largest absolute value of the CGSFs is the generator at bus 11 (0.3704), whereas the most efficient generator is the generator at bus 13 with a maximum correction of 17.441 MW.

(10) The MW generation at bus 13 is increased from 50.418MW to 53.187MW just to eliminate the overflow.

(11) No overloaded line exists.

4.2.2. Elimination o f line overflow for the TPC system--- Approach I

The Taiwan Power Company (TPC) system is used to illustrate the capability of the rule based system to eliminate the line overflow. The TPC system is a longi- tudinal system. Its length is about 400 km from north to south. The line (circuit 1) between buses Panchiao and Shuter in the northern area is assumed to be tripping. The swing bus for this case study is ChinShan that locates in the central area in the TPC system. The reasoning from the rule base system is as follows.

(1) There are five lines overloaded. (2) The most severely overloaded is the line between

buses Panchiao and Shuter (circuit 2). The line flow is 371.35 MW (remark: the maximum limit is 364.74 MW).

(3) The largest absolute value of the CGSFs is for the generator at Linko-1 ( -0 .122) . The most efficient generator is also the generator at Linko-1 with a maxi- mum correction of 5.6981 MW (remark: Linko-1 is in the northern area).

(4) The MW generation at Linko-1 is increased from 253.50 MW to 300.00 MW (maximum limit).

(5) There is one transmission line overloaded. The line flow for the line (circuit 2) between buses Panchiao and Shuter is 365.87 MW.

(6) The largest absolute value of the CGSFs is for the generator at Linko-2 ( -0 .122) . The most efficient generator is the generator at Hseiho-3 with a maximum correction of 4.729 MW (remark: Hseiho-3 is in the northern area).

(7) The MW generation at Hseiho-3 is decreased from 487.36 MW to 400.23 MW just to eliminate the overflow of the line beween buses Panchiao and Shuter (circuit 2).

(8) The line flow between Panchiao and Shuter is 364.41 MW (circuit 2).

(9) No overloaded line exists.

4.2.3. Elimination o f line overflow for the TPC sy s t em- - Approach H

The same contingency is studied in this section but the swing bus is changed to Hseiho-1 (in the northern area). The reasoning from the rule base system is as follows.

(1) There are five lines overloaded. (2) The most severely overloaded is the line between

Panchiao and Shuter (circuit 2). The line flow is 371.35 MW (remark: the maximum limit is 364.74 MW).

(3) The largest absolute value of the CGSFs is for the generator at Linko-1 ( -0 .136) . The most efficient generator is also the generator at Linko-1 with a maxi- mum correction of 6.340 MW (remark: Linko-1 is in the northern area).

(4) The MW generation at Linko-1 is increased from 253.50 MW to 300.00 MW (maximum limit).

(5) There is one transmission line overloaded. The line flow for the line (circuit 2) between buses Panchiao and Shuter is 365.41 MW.

(6) The largest absolute value of the CGSFs is for the generator at Linko-2 ( -0 .136) . The most efficient generator is the generator at MinHu-2 with a maximum correction of 3.06 MW (remark: MinHu-2 is in the central area).

(7) The MW generation at MinHu-2 is increased from 75.00MW to 126.87 MW just to eliminate the overflow of the line between buses Panchiao and Shuter (circuit 2).

(8) The line flow between Panchiao and Shuter is 364.27 MW (circuit 2).

(9) No overloaded line exists.

4.3. Discussion o f the test results for the TPC system

The proposed rule based system and modified net- work sensitivity factors have been used for studying many single and double contingencies for the TPC system. The contingency described in Section 4.2 is a typical test case. The following points are made after examination of many tests on the TPC system.

(i) Selection of the swing bus influences the values of the GSFs, LODFs, and CGSFs. The swing bus is expected to locate in the area near the contingency because (a) the MW losses are ignored in the sensitivity model and (b) the identified generator with the largest maximum correction would exchange its MW genera- tion with MW generation from the swing bus. For example, if the contingency occurs in the northern area, the swing bus is expected to locate in the northern or central area in the TPC system. The southern area is

124 Y.Y. Hong / Electric Power Systems Research 33 (1995) 119 124

bus 1 bus 2 bus 3 bus 4

I (common bus)

Lines to the syste~

Fig. 1. Four generators connected to a common bus.

not a proper candidate in this case. For this reason, the swing bus generally locates in the central area of the TPC system.

(ii) Selection of the swing bus is insensitive to the proposed rule based system if its selection is reasonable. The reason is that the identified generator for rescheduling is the one with the largest maximum cor- rection; in other words, the available margin is signifi- cant in the proposed rules.

(iii) When many generators are connected to a com- mon bus, we should avoid selecting one of these gener- ators to be the swing bus. As shown in Fig. 1, generators 1 - 4 are connected to bus 5. Let us assume that generator 1 is the swing bus. Theoretically, the values of the GSFs for generator 2 to the step-up transformers 1 and 2 (modeled as lines XF1 and XF2) are - 1 and 1, respectively. Moreover, the values of the GSFs for generator 2 to any other lines are zero. This means that generator 2 cannot be used to eliminate line overflow occurring in another part of the system be- cause increase/decrease of MW generation from genera- tor 2 would be directly absorbed/supplied from the swing bus. The same phenomena occur for generators 3 and 4. The remedy can be achieved by modeling these four generators as one generator if all installed genera- tions for the four generators are the same.

5. Conclusions

A rule based system incorporating network sensitiv- ity factors for eliminating line overflow is presented in this paper. The network sensitivity factors are enhanced to consider multiple circuits between two adjacent buses. The accuracy/limitations of the sensitivities, se- lection of the swing bus, and the impact of multigener-

ators at a common bus are discussed. The rule based system was tested with many scenarios. The test results based on the IEEE 30-bus system and a practical 265-bus system in Taiwan show the proposed rule based system is useful for large-scale systems.

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