An Artificial Intelligence Framework for On-Line - IEEE Xplore

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and corresponds to the top node of the DT; the most refined subsets correspond to terminal nodes. To each level of the DT corresponds a partition of the LS.
Testing of any load forecast algorithm on historical load and weather data produces better results than that can be obtained under on-line conditions. In this study, we have tried to identify the factors that affect the accuracy of our rulebased algorithm, after it was tested on historical data. This was done by repeating the load forecast using weather variables as forecasted, and other data collected under online conditions. In addition to the natural differences in electric demand from one day to another, there are several factors that can affect the accuracy of the load forecast. The most important factors affecting the accuracy are: * Bad data in the database; * Inaccuracy in on-line load data measurements; * Unplanned sale/purchase of power between utilities; * Weather forecast errors; and * Direct load control impacts. The rule-based load forecast program takes 20 seconds of CPU time on the IBM-RT/PC for generating a 24-hour load forecast. The 24-hour load forecast is automatically checked for possible direct load control (DLC) effects. Then the forecasts with and without DLC are released for display. The load forecast software has been tested for load and weather data (historical) for the Virginia Power service area. A summary of forecast errors for all days of all seasons of the year (1986) is presented in Table 1. Similar analysis has been performed for 1983 as well. The absolute annual average of errors for 1983 and 1986 are 1.437% and 1.298% respectively. These are obtained by averaging the seasonal averages of all hours of the day. Discussers: S. S. Ahmed, N. D. Reppen, and R. Mukerji

TABLE 1 24-hour Load Forecast Error (%) Statistics for 1986 Hour 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Winter Summer Fall Spring Aver. Aver. St.Dev. St.Dev Aver. St.Dev. Aver. St.Dev

0.162 0.118 0.572 0.485 0.479 1.119 1.110 1.323 1.296 1.254 1.140 1.066 1.036 1.242 1.265 1.276 1.372 1.314 1.217 1.108 1.130 1.152 1.116 1.378

0.114 0.117 0.401 0.463 0.405 0.566 0.584 0.578 0.541 0.580 0.651

0.575 0.624 0.786 0.801 0.854 0.780 0.782 0.738 0.710 0.736 0.822 0.865 1.073

Aver. 1.030 n.a.

0.243 0.261 0.552 0.666 0.708 0.936 1.378 1.696 1.719 1.549 1.837 1.778 1.636 1.746 1.837 2.097 1.970 1.987 1.837 1.513 1.573 1.664 1.732 1.655

0.151 0.186 0.298 0.453 0.545 0.979 0.943 0.867 0.880 0.914 1.112 1.105 1.279 1.281 1.234 1.371 1.332 1.289 1.243 1.118 1.025 0.972 0.987 0.927

1.440 n.a.

0.250 0.278 0.451 0.597 0.752 0.755 1.133 1.287 1.277 1.262 1.328 1.429 1.399 1.919 1.983 1.855 1.965 1.914 1.778 1.754 1.693 1.732 1.774 1.467

0.208 0.237 0.374 0.417 0.521 0.619 0.571 0.633 0.568 0.603 0.664 0.582 0.666 0.779 0.749 0.871 1.041 1.042 1.028 0.928 0.971 0.928 0.860 0.792

1.334 n.a.

0.171 0.183 0.653 0.601 0.740 0.874 1.207 1.327 1.416 1.536 1.611

1.713

1.701 1.953 1.970 1.909 1.951 1.877 1.604 1.545 1.801 1.837 1.647 1.502

0.127 0.136 0.472 0.442 0.544 0.672 0.716 1.209 1.127 1.653 1.688 1.666 1.616 1.871 1.892 1.820 1.897 1.826 1.160 1.184 1.204 1.331 1.360 1.143

1.389 n.a.

88 SM 699-1

May 1989

An Artificial Intelligence Framework for On-Line Transient Stability Assessment of Power Systems L. Wehenkel, Th. Van Cutsem and M. Ribbens-Pavella Dept. of Electrical Engineering University of Liege, Inst. Montefiore-B28 B 4000-Liege, Belgium

Keywords: On-line transient stability assessment, artificial intelligence, transient stability analysis and preventive control, inductive inference.

Summary Transient stability assessment (TSA) of a power system pursues a twofold objective: first to appraise the system's capability to withstand major contingencies, and second to suggest remedial actions, i.e. means to enhance this capability, whenever needed. The first objective is the concern of analysis, the second is a matter of control. For the time being, the on-line TSA is still a totally open question. Indeed, none of the existing two broad classes of methods (the time domain and the direct methods) are able to meet the on-line requirements of the analysis aspects, nor are they in the least appropriate to tackle control aspects. The methodology we are introducing aims at solving the above stated on-line problem by making use of decision rules, preconstructed off-line. To this end, an inductive inference method is developed, able to provide decision rules in the form of binary trees expressing relationships between static, pre-fault operating conditions of a power system and its robustness to withstand assumed disturbances. This paper concentrates on this latter problem, which is the most difficult task, and also the kernel of the overall

methodology. The proposed inductive inference (II) method pertains to a particular family of Machine Learning from examples. It derives from ID3 by Quinlan [11, tailored to our problem, where the examples are provided by numeric (load flow and stability) programs [2, 3]. According to the method, a decision tree (DT) is built on the basis of a preanalyzed learning set (LS), composed of states or operating points (OPs). Each state characterizes the steady-state (pre-fault condition) of a power system; it is analyzed with respect to (w.r.t.) a given disturbance. The ultimate goal is to discover the static attributes upon which depends essentially the stability behaviour of the states composing the LS; by static attribute we mean some simple algebraic combination of components of the state vector. A DT is a hierarchical organization of this LS into a collection of subsets. The most general subset is the LS itself and corresponds to the top node of the DT; the most refined subsets correspond to terminal nodes. To each level of the DT corresponds a partition of the LS. The lower the level, the more refined the corresponding partition. Hence, generating successors of a given node amounts to reducing the uncertainty (or entropy) about the degree of stability of the corresponding states, or equivalently, to increasing the information about it. The automatic building of a DT proceeds in a top down fashion beginning with the design of the top node and ending up with the terminal nodes. On the basis of an information theory measure, appropriate dichotomic tests on the attributes of the OPs are associated with the intermediate nodes. The terminal nodes, on the other hand will correspond to the different stability classes or degrees. Conversely, the use of a preconstructed DT to classify an OP may conform to the following pattern: starting at the top node, apply the test corresponding to it; progress down the tree by applying at the successor nodes successively met, the appropriate test and by directing the OP according to the outcome of the test; stop when a terminal node is reached:

IEEE Power Engineering Review, May 1989.

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the OP will be declared to belong to the class of this node. Note that although extremely straightforward, the above way of using a DT is not unique [4]. The proposed 11 method has been applied to a 14-machine system. DTs relative to a given disturbance have been constructed in three different classifications, corresponding to 2-class (where the OPs are merely labelled stable or unstable) 3-class and 4-class patterns, the latter providing a more refined stability assessment. Among the many results obtained, we briefly observe that: * .he complexity of the DTs in terms of number of nodes and hierarchical levels is overall rather low; for the 2-, 3and 4-class DTs constructed, the total number of nodes is respectively 15, 21 and 27; * the reliability is very satisfactory; moreover the larger the number of classes the better the stability appraisal; note that increasing the number of classes scarcely affects the overall computing time, which anyhow is spent offline; * hence, from the user's point of view the multi-class DTs should be preferred: they ensure very good reliability, without affecting on-line computational performances. Although at an early stage of its development, the 11 method proposed in this paper provides extremely encouraging results. Overall, the artificial intelligence methodology we propose for the transient stability analysis and preventive control of power systems, differs in many respects from other approaches. From the artificial intelligence point of view, it relies much on expertise acquired via numerical methods appropriately exploited, unlike other logic- or heuristic-based methods. From the domain application standpoint, of particular interest is the possibility offered by our method to combine freely the generally contradictory objectives of arbitrary modelling sophistication and of on-line performances. Another essential merit of the method is to replace the "black box" type approaches traditionally used in transient stability studies, by a "transparent box": the DT, which relates explicitly the characteristics of the power system and its stability. Hence, the very electrical process can be followed and better understood. In turn, for the first time, this paves the way towards transient stability control. Discussers: M. A. Pai, S. S. Ahmed, C. Liu, S. Wang, A. Debs, E. Nascimento and B. J. Cory

88 SM 727-0 May 1989

A Method for Identifying Weak Nodes in Nonconvergent Load Flows M. Dehnel and H. W. Dommel, Fellow, IEEE

This paper presents the "Weak Node Method" for identifying weak areas in power system scenarios for which the Newton-Raphson load flow method does not converge. Nonconvergent load flows often present program users with the task of implementing corrective measures with little or no information as to the source of nonconvergence, especially for cases which diverge outright. For slow-converging load flows modifications of the basic Newton-Raphson load flow method [11, better initial guess estimates [21, and modifications in the data specification [31 have been used to achieve convergence. For divergent cases, the Weak Node Method provides meaningful trouble indicators which enable load flow program users to more easily identify problem areas, as well as the nature of the weakness (active or reactive power problem). The Weak Node Method requires a converged minimum mismatch solution [41 for load flows that would normally diverge. This is obtained by a damped Newton-Raphson method which calculates a damping multiplier Xmin to be used in arriving at the next iteration's approximate solution i+ 1x+XminA

where x is the approximate solution to the nonlinear load flow equations, Ax is the Newton correction vector, and i is the iteration count. Xmin is found in such a way that a mismatch function is minimized in the direction of A' from xi [5]. This mismatch function is defined as f=

where Pk and qk

are

the mismatches

Pk=Re

qk=

-I

(1p2p+Zq2q)1/2

m

{

V {

Vg

Ykm Vm }

Ykm

Vm }

Ppecified

Qspecified

Xmin approaches zero as the minimum of the mismatch function is reached. It can therefore be used to indicate that the minimum mismatch solution has been found. The Weak Node Method processes the information at the minimum mismatch solution in three procedures:

References [11 J. R. Quinlan, "Induction of decision trees," Machine Learning, Vol. 1, No. 1, pp. 81-106, 1986. [21 L. Wehenkel, Th. Van Cutsem, M. Ribbens-Pavella, 1 ) List the highest and lowest voltage magnitudes VkI. "Artificial intelligence applied to on-line transient stability 2) List the largest active (Pk) and reactive (qk) power assessment of electric power systems," Proc. of the mismatches. 10th IFAC World Congress, pp. 308-313, Munich, July 3) Obtain sensitivity vectors of the form AX/AUk [61 with 1987. the largest Euclidean norm, where the scalar uk is either [31 L. Wehenkel, Th. Van Cutsem, M. Ribbens-Pavella, the specified active (pspecified) or reactive (Qspecified) "Inductive Inference applied to on-line transient stability power at node k. assessment of electric power systems," Submitted for publication on AUTOMATICA, 1988. (41 L. Wehenkel, Th. Van Cutsem, M. Ribbens-Pavella, The nodes k which are associated with the quantities listed in "Decision trees applied to on-line transient stability procedures 1 to 3 are the weak nodes of the nonconvergent assessment of power systems," IEEE Int. Symp. on scenario. To test the Weak Node Method, a weak node or a number Circuits and Systems, Helsinki, Finland, June 1988. of weak nodes were artificially created in power system scenarios to see whether they could be identified. This was achieved by increasing specified active or reactive power loads at a single node or a number of nodes until the NewtonRaphson method no longer converged. At this point, the minimum mismatch solution vector was obtained. In each the Weak Node Method identified the altered specified loads as being the weak nodes of the nonconvergent system. The Weak Node Method was used to analyze an actual nonconvergent scenario from industry. This scenario was provided by West Kootenay Power and Light Co., Trail, B.C. Canada. The Weak Node Method successfully identified the case

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IEEE Power Engineering Engineering Review, Review, May May 1989