Overload Alleviation With Preventive-Corrective Static ... - IEEE Xplore

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 24, NO. 1, FEBRUARY 2009

Overload Alleviation With Preventive-Corrective Static Security Using Fuzzy Logic Laurent Lenoir, Student Member, IEEE, Innocent Kamwa, Fellow, IEEE, and Louis-A. Dessaint, Senior Member, IEEE

Abstract—This paper presents a concept overview of an automatic operator of electrical networks (AOEN) for real-time alleviation of component overloads and increase of system static loadability, based on state-estimator data only. The control used for this purpose is real-power generation rescheduling, although any other control input could fit the new framework. The key performance metrics are the vulnerability index of a generation unit (VIGS) and its sensitivity (SVIGS), accurately computed using a realistic ac power flow incorporating the AGC model (AGC-PF). Transmission overloads, vulnerability indices and their sensitivities with respect to generation control are translated into fuzzy-set notations to formulate, transparently, the relationships between incremental line flows and the active power output of each controllable generator. A fuzzy-rule-based system is formed to select the best controllers, their movement and step-size, so as to minimize the overall vulnerability of the generating system while eliminating overflows. The controller performance is illustrated on the IEEE 39-bus (New England) network and the three-area IEEE-RTS96 network subjected to severe line outage contingencies. A key result is that minimizing the proposed vulnerability metric in real-time results in increased substantial loadability (prevention) in addition to overload elimination (correction). Index Terms—Automatic operator, fuzzy logic control, generation dispatch, overload alleviation, preventive/corrective security, sensitivity factors, vulnerability index.

I. INTRODUCTION

P

OWER system insecurity refers to the system’s inability to meet all or part of the load. Insecurity can be due to: transient stability limits or voltage collapse limits; total available generation smaller than the demand and component (line and/or transformer) overloads [1], [2]. Overloads can result in component outage, which translates into either an immediate load outage (if the component is radial), or subsequent stability limit or voltage collapse limit leading to an outage. It can also trigger subsequent cascading overloads. To maintain the state of the system within acceptable and secure operating conditions, especially after a contingency or during fast ramps of loads or intermittent generation [3], operators must make rapid decisions and apply preventive or emergency/corrective actions. Manuscript received December 28, 2007; revised July 21, 2008. Current version published January 21, 2009. This work was supported by the Hydro-Québec TransÉnergie Chair on Simulation and Control of Power Systems. Paper no. TPWRS-00969-2007. L. Lenoir and L.-A. Dessaint are with the Département de génie électrique, École de Technologie Supérieure, Montreal, QC H3C 1K3, Canada (e-mail: [email protected]; [email protected]). I. Kamwa is with the Institut de recherche d’Hydro-Québec (IREQ), Varennes, QC J3X1S1, Canada (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org Digital Object Identifier 10.1109/TPWRS.2008.2008678

With deregulation of the electricity markets, overload-alleviation (or flow-limit enforcement) has come to be known as congestion management, which is about controlling the transmission system so that transfer limits are observed at the lowest cost [4], [5]. Congestion is indeed manageable using market redispatch tools if it occurs in a forward market situation. In real time, however, it becomes an emergency situation that the dispatcher needs to deal with as quickly as possible using his experience, often supplemented with a heuristically-based decision support system [6]. Generally speaking, security problems can always be relieved by load reduction [7]. This kind of control action affects all system limits but it is triggered reluctantly and infrequently, generally by way of automatic load-shedding systems, producing undesirable impacts on service quality [8]. From the dispatcher’s standpoint, the generation pattern is comparatively easier to control than the load pattern and this has motivated a lot of recent work on congestion management through generation market redispatch [9]. However, “optimal market clearing” is not the prime concern when an emergency occurs in real time and the dispatcher has to resort to fast out-of-merit redispatch to control generation pattern so as to avoid the system limit violations [1]. Although less easy to automate than generation control, line switching with a busbar breaker reconfiguration [10] is another option. Basically, two approaches could be used to design a redispatch-aided corrective security system (so-called out-of-sequence dispatch): a security-constrained OPF (SCOPF) with a security index as an objective function [9], [11], and a sensitivity-based heuristic controller, which closely mimics the operator heuristics [12]. The AC-SCOPF tool is now felt to be robust enough for use in the CaISO forward market dispatch [13]. However, despite the progress made in recent years in this area [14], [15], security constrained DC OPF is still the standard in off-the-shelf applications [16] and it is not clear at present if the deterministic convergence and speed of solution required by a minute-to-minute corrective security system could be achieved using an AC-SCOPF. This is especially true when the objective function is a security margin measure, generally a strongly nonlinear function of the parameters such as the Static Severity Index (SSI) in [9] or the Static Vulnerability Index (SVI) in [17]. Even the classical overload factor (OF), termed static overload severity function in [18], which is the actual quantity of prime interest in relation to congestion management is a steep nonlinear function of the generation to be redispatched. To circumvent this numerical intractability

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LENOIR et al.: OVERLOAD ALLEVIATION WITH PREVENTIVE-CORRECTIVE STATIC SECURITY USING FUZZY LOGIC

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critical contingency in power system security assessment. For the th generator, the VI is given by the square of the ratio of the actual generation to the maximum active-power output as follows:

(1)

where is the number of generators. Similarly, the th transmission line VI is defined as the square of the ratio between the actual apparent power line flow and the maximum power line flow as follows:

Fig. 1. AOEN implantation.

in real time, sensitivity-based iterative schemes have been suggested, some based on intelligent systems [12], [19], [20], others on linear [21] or greedy optimization [9]. Fig. 1 summarizes our view of the security control problem. It is basically a new look at Di-Lyacco’s vision of an “automatic operator” [1] for rapid contingency analysis and intelligent minute-by-minute decision-making. The Automatic Operator of Electrical Networks (AOEN) computes the global vulnerability index and the security margin every time the state estimator updates the network data. If the security margin is not sufficient, AOEN is in preventive mode. If the system is overloaded, AOEN is in curative mode. In both cases, AOEN analyzes the VI sensitivity first and suggests actions required to increase the security margins. Then it validates the actions by performing an AGC-PF, followed eventually by a security-unconstrained maximum loadability assessment using continuation power flow [9]. Although AOEN is automated, the final decision at this early stage of development is taken by human operators. This paper is divided as follows. Section II presents the vulnerability index concept. Section III develops the fuzzy-logic-based rescheduling algorithm embedded in the AOEN scheme for real-time transmission-flow limit enforcement. Lastly, Section IV presents the encouraging results, using detailed simulations of the IEEE-39 bus network [10], [22] and the three-area 73-bus IEEE RTS96 network [23] with additional AGC and dispatch data from [24].

II. STATIC VULNERABILITY INDEX Many static severity functions or indices have been proposed which could well serve as a basis for increased security. However, their analytic expression is non-smooth and their derivatives are difficult to insert into a sensitivity-based controller. This paper will instead use the Vulnerability Index (VI) [17] to specify the safety allowance factor of the individual power system components and of the whole power system under static conditions. The VI expression is based on the so-called Performance Index (PI) [25] used in the past to select the most

(2)

and is the number of lines. where While (1) and (2) deal with individual units of equipment, the aggregate generation and line VI is given by

and

(3)

The larger the VI value, the more vulnerable the system. Also, as VI is a quadratic function, it is relatively easy to find its derivative formulas analytically and use them as sensitivity factors. III. FUZZY-LOGIC BASED GENERATION RESCHEDULING In [12] and [19], fuzzy-logic controllers making use of the generator shift sensitivity factor (GSSF method [2]) with respect to the line flows were designed to enforce flow limits through generation control. One of these methods [19], used in the sequel as benchmark, mimics operator heuristics quite closely and can efficiently eliminate equipment overloads but the security margin of the resulting generation and global system is not guaranteed. Consequently, to enhance the safety margins, the VI and its sensitivity are combined here with the GSSF method. Other security objectives, such as the voltage stability margin or the system maximum loadability index, could be considered within the same framework, using reactive power redispatch together with active power. The controller block diagram presented in Fig. 2 shows three inputs and one output. For simplicity, the picture is valid for only one generator, in an aim to alleviate a single overloaded line. The definition of the input-output variables and the base rule are detailed in the following sections, assuming is the generator index and , the overloaded line index. All membership functions are chosen linear because a nonlinear function such as the Gaussian is more complex to use in real-time and the results more difficult to study, especially at the defuzzification stage.

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Fig. 4. Membership functions of generator shift sensitivity factor.

ation gives the GSSF ( generator as follows:

Fig. 2. Overview of the fuzzy-logic-based controller.

, MVA/MW) of lines for that particular

(6) This process is repeated for all generators yielding a matrix , where is the number of (GSSF matrix) of dimension transmission lines and , the number of generators in the system. The corresponding membership functions are defined in Fig. 4: LS (low sensitivity), MS (medium sensitivity), HS (high sensitivity). Again, these membership ranges are arbitrarily chosen to suit a smooth network control strategy. The last input is the sensitivity of the generation vulnerability index SVIGS as follows:

Fig. 3. Membership functions of overloading factor.

(7)

A. Inputs of Fuzzy Inference System and Fuzzification The first input of the fuzzy inference system (FIS) is the overload factor as follows:

Equation (1) shows that the generator with the greatest sensitivity is the smallest. It is therefore convenient to normalize the SVIGS vector by the rating of the smaller generator as follows:

(4) is the flow of line (in p.u.) and , the loading where limit of line in p.u. Only the lines for which OFs exceed 0.9 are considered for overload alleviation. Therefore (8) (5) The associated fuzzy sets are provided in Fig. 3: NFL (nearly fully loaded), MOL (moderately overloaded) and HOL (heavily overloaded). The range of the different categories is arbitrarily chosen and it can be changed with a different strategy of network operation. The second input is the GSSF which gives the change in line flow for a given change in generation at a generator bus. are First, a base load flow is obtained and the line flows computed. and the line flows Then, one generator is disturbed by repeating the AGC-PF algoare computed again rithm. The ratio of the change in line flow to the change in gener-

The normalized SVIGS take values between 0 and 1 and the corresponding fuzzy sets are given in Fig. 5. The heuristic behind this range selection is simply to get three balanced categories. B. Fuzzy Inference System and Output Definition The output is derived on the basis of rules defined by an inference matrix (see the FIS block in Fig. 2). The number of rules depends on the number of inputs and input states, as seen in Table I. Three inputs (OF, GSSF and SVIGS) with three states rules for the FIS. each a total of Its output is defined as the level of generation rescheduling , the for one generator and one overloaded line and is named


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respectively, were chosen heuristically to modulate the output is increased by 50% when is L. so that for instance, C. Aggregation and Defuzzification The result of each rule evaluation must first, in a so-called aggregation stage, be converted to a value that lends itself to is defined as defuzzification. In our system,

.. .

(9)

Fig. 5. Membership functions of SVIGS.

TABLE I SUMMARY OF FUZZY INFERENCE SYSTEM RULES

From this aggregate value, applicable to each generator, a complete dispatch is built in order to maintain the demand-production equilibrium while enforcing generator limits and AGC constraints. For this purpose, let us consider the following exfrom (6) as follows: pression of

(10) If that

is considered the overloaded line flow, it results from (4)

(11) If

is considered as the corrected line flow, then from (5)

(12) In the limit case

(13) If (11) and (13) are bootstrapped in (10), we obtain

(14) Therefore, must be converted into which in turn and can be categorized in two separate sets of increasing corrections for each generator as follows: decreasing

result of the th rule, matching the behavior of generator with can respect to the line . As evident from Table I, the output have up to four states: Z (zero), S (small), M (medium) and L (large). The corresponding numerical values, 0, 0.5, 1 and 1.5,

(15) (16)

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Taking row in the GSSF matrix for the overloaded line , the sensitivity factor is given for all generators. The GSSF can be , put them in a list called positive or negative. If several the GD (generator decrease) list. If several , put them in a GI (generator increase) list. For each list, the data must be sorted so that the most sensitive generator is ranked 1. We can for generators in the GI list based on (15). now compute If we applied the directly to the power flow equation, a must be balanced by power mismatch would occur, so , from the generators in the GD list. This is an equivalent done according to (16), so as to obtain

(20) where and are, respectively, the number of increased generator output and the number of decreased generator output. value, the generators with the highest In order to lower the SVIGS values will be chosen as a matter of priority. To limit the number of rescheduled generation output, we use the GSSF to compute the flow in the overloaded line, by reformulating (6) as follows: (21)

is the overloaded line and is the number of genwhere erators to be redispatched. The latter is defined such as Fig. 6. Iterative algorithm for reinforcing line flow limits.

(22) With the weighting factor

defined as

``

''

(17)

and are, respectively, the maximum and minimum changes in generation that are permitted as follows: (18) (19) D. Overall Processing Algorithm for Alleviating Overload The scheme summarized in Fig. 6 runs as soon as the state estimator is refreshed or the topology of network changed. First, using the operational power flow and for a given operating configuration, all vulnerability indices are computed ( and ). Next, the GSSF matrix is determined by disturbing all participating generators by a small amount. The network is then checked for an overloaded line. If none, the algorithm is stopped; otherwise it continues.

The threshold value, , where is the thermal limit of the overloaded line, is the margin between the trans, an mission flow prior and after correction. To compute incremental “while” loop is performed until the condition on is met. If several line overloads are detected, a sort in descending [overload factor is defined in (4)] is created. In order of the first step, the highest overload is corrected and validated by AGC-PF. Then, the new configuration is used to recompute all VI and SVIGS vector and to check the security state of the new network. This loop finishes when all overload lines are alleviated. IV. SIMULATION RESULTS The fuzzy-logic-based generation redispatch approach described above was prototyped in Matlab. In addition, an improved, more operator-minded ac power flow, has been developed within the framework of PSAT [26] to model in detail the frequency-bias-based automatic generation control (AGC), which, in addition, to solving the slack-bus issue, incorporates frequency-governing droop and static-frequency-voltage dependent load models.


A. Review of AGC-PF

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and the tangent vector can be approximated by

In the conventional ac load flow, the system load generation imbalance is assumed to be regulated by the swing bus, whose voltage magnitude is fixed assuming a sufficient reactive regulating range at the bus, which is not true. The entire imbalance of real power in the system is met by the swing bus generator only, although sufficient regulation is available at the other generators in operation. Finally, loads are not constant, as they change continually due to variations in the system voltage and frequency at the load buses [20], [27], [28]. The AGC power flow (AGC-PF) algorithm avoids these limitations by incorporating load regulation characteristics and generation controls. The proposed AGC-PF implementation was successfully benchmarked against a step-by-step AGC model embedded in an operator training simulator [29]. In the sequel, the AGC mode will be the flat frequency control, i.e., the real power imbalance is dispatched on each generator under the AGC proportionally to its rating.

B. Review of the Perpendicular Intersection CPF To compare the new and the conventional schemes, we elected to use loadability margin as the main figure of merit which is computed using a continuation power flow (CPF). Start by reformulating the power flows equations as follows: (23) where is the function of the net active and reactive power injections, the algebraic variables (voltage amplitudes and angles) and is the loading parameter, i.e., a scalar variable which multiplies generator and load directions, as follows:

(26) From (25) and (26)

(27)

A step size control has to be chosen for determining the increand , along with a normalization to avoid large ment is large, as follows: step when

(28) where , and its sign determines the increase or the decrease of . equa2) Corrector Step: In this corrector step, a set of tions is solved, as follows:

(29)

where the solution of must be in the bifurcation manifold and is an additional equation to guarantee a non-singular set at the bifurcation point. In case of perpendicular intersection, the expression of becomes

(30) where (24)

In (24), are the “base case” generator and load powers. Giving a continuously increasing , the solution of (23) can be obtained quite efficiently up to the maximum loadability , by alternating a predictor step based on the compoint putation of the tangent vector and a corrector step based on a perpendicular intersection of it. Our implementation of this method follows broadly that in PSAT [30] and is summarized below. 1) Predictor Step: At a generic equilibrium point, the following relation applies:

(25)

and

are corrected values.

C. Results With New England Network A stress configuration was built from a 20% system load increase and the outage of line 7 (dotted line in Fig. 20). This configuration generates one overload on line 22 (dashed line L22 in Fig. 20) According to [10], reclosing line 7 with the load still at 20% above normal resulted in two overloaded lines (L9 and L22), although one of the lines was only marginally overloaded. The new method (GSSF+VI) is benchmarked, in different tables and figures, against a conventional GSSF-based method [19], with reference to the post-contingency (P-C) state of network. For each configuration studied, we computed the vulnerability index, the losses, the maximum unconstrained loadability and the reactive reserve . 1) One Overloaded Line: Table II summarizes the flow on the overloaded line 22 (dashed line L22 in Fig. 20) while Table III summarizes the flow on the same line after the dispatch rescheduling. Figs. 7 and 8 illustrate, respectively, the change in transmission line flows and generation dispatch before and after correction by the GSSF or GSSF combined with

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Fig. 9. Losses and loadability versus overload alleviation method. Fig. 7. New England network with one overloaded line (cf. Table XIII in the Appendix for the line nomenclature).

Fig. 10. Loadability and reactive margin versus overload alleviation method. TABLE V POWER FLOW RESULT FOR RECLOSING LINE 7 Fig. 8. New England generator dispatch with one overloaded line. TABLE II POWER FLOW RESULT FOR LINE 7 OUTAGE

TABLE III POWER FLOW RESULT AFTER REDISPATCH

TABLE IV VI ON NEW ENGLAND NETWORK WITH ONE OVERLOADED LINE

SVIGS methods. While in Fig. 7, the two methods alleviate the overload in line 22, the GSSF correction induces three new overloaded lines (dashed lines L3, L17 and L18 in Fig. 20).

Figs. 9 and 10 demonstrate that, compared to the standard GSSF, the GSSF VI method lowers the losses (7.5 MW) and increases the loadability (446 MW) and reactive reserve (119 and are MVAR). Moreover, Table IV shows that reduced by 7% and 6.14%, respectively. Compared to post-contingency state, we see that removing and the overload with GSSF+VI method improves by 3.13% and 6.91% respectively. The losses and loadability are increased by 8 MW and 286 MW, respectively, but the reactive reserve remains near the same value. Thus, the GSSF+VI method alleviates the overloading of the New England network while enhancing its security margin in terms of an increased loadability only. Since this grid is already highly loaded, there is less room left for additional enhancement with respect to losses and reactive power margin. 2) Two Overloaded Lines: Table V summarizes the flow on the overloaded lines 22 and 9 (dashed line L9 and L22 in Fig. 20) while Tables VI and VII summarize the flow on the lines 9 and 22 after the dispatch rescheduling. Figs. 11 and 12 illustrate, respectively, the change in transmission line flows and generation dispatch before and after correction by the GSSF or GSSF combined with SVIGS methods. Figs. 14 and 15 illustrate the change in the losses of line, in the loadability of system, and in the reactive margin versus the overload alleviation method. In


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TABLE VI POWER FLOW RESULT AFTER GSSF REDISPATCH

TABLE VII POWER FLOW RESULT AFTER GSSF+VI REDISPATCH

Fig. 13. First step to alleviate two overloaded lines.

Fig. 11. New England network with two overloaded lines (cf. Table XIII in the Appendix for the line nomenclature).

Fig. 14. Losses and loadability versus overload alleviation method.

Fig. 15. Loadability and reactive margin versus overload alleviation method. Fig. 12. New England network with two overloaded lines.

Fig. 11, only the new method is able to enforce the flow limits while the GSSF is unable to find a solution even for the highly overloaded line 22. To alleviate the two overloads, the GSSF algorithm proceeds in a loop. In the first step, it tries to alleviate the highest overload, i.e., on line 22 (dashed line L22 in Fig. 20). Fig. 13 shows that the line 22 overload was indeed fixed after the first stage. Consequently, the algorithm was successful in this respect but it creates another overload on line 3 (dashed line L3 in Fig. 20). This brings the number of overloads to two, with line 3 becoming the most overloaded. In trying to alleviate line 3, we compute the line flows of Fig. 11 and the generation dispatch of Fig. 12, where the GSSF method has brought back the overload of line 22. In contrast, the proposed GSSF+SVIGS method generalizes

TABLE VIII VI ON NEW ENGLAND NETWORK WITH TWO OVERLOADED LINES

well, proving its ability to remove the two overloads at the expense of an increase in total transmission losses. Table VIII summarizes the VI values and confirms that GSSF+VI method does better than GSSF method and improve the post-contingency VI values.

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D. Optimal Dispatch With VIGS

TABLE IX POWER FLOW RESULT AFTER FOUR LINE OUTAGES

The optimal dispatch with VIGS (OD) is a nonlinear constrained optimization problem and consists of an objective function and a set of equality and inequality constraints, as follows:

(31) are the control variables (i.e., the active power where as production) and and , the generation units lower is defined and upper bounds. The objective function as follows:

(32) where (32) represents the quadratic sum of active power margin of generation units. Minimize permits to keep an optimal production margin for all units. represents the The set of equality constraints balance between the supply and demand without the losses in the transmission line as follows:

Fig. 16. Line flows in region 1: 230-kV transmission lines. (cf. Table XII in the Appendix for the line nomenclature). TABLE X POWER FLOW RESULT AFTER REDISPATCH

(33) is the sum of all scheduled loads. where The OD tends by design to make a more intensive usage of generators with the most generation margin. The case of RTS96 is singular because the required load increase is such that the generators are very stressed. In this context, the huge generators will be used more intensively because of the limits constraints. Contrary to New England network, the RTS96 power plants are divided in several generation units and a lot of units have a small real power rating. The OD will permit to study the impact of VI on the rescheduling dispatch after a contingency. E. Results With RTS96 Network Similar studies as in the previous section were conducted with the IEEE RTS96 network in order to check the generality of the results obtained on New England network. A modified IEEE RTS 96 network [24] with three regions (Fig. 21 in the Appendix) is used as the initial test case. To create an overloaded line, we had to increase the load in the base system by 10% and subsequently open four lines (in dotted line in Fig. 21). Table IX summarizes the post-contingency state of the overloaded line (Bus 115—Bus 121). Table XIV in the Appendix presents the generation units of the RTS96 network for each region. There are a total of 96 such units in the three regions. To complete the study we use the optimal dispatch with VIGS (OD) in addition to the GSSF+VI method already tested on the New England network. The OD problem is solved within the GAMS framework, properly interfaced to Matlab.

Fig. 17. Losses and loadability versus overload alleviation method.

Table X and Fig. 16 show the change in transmission line flow for the “post-contingency” state, as well as after a redispatch with the plain GSSF method or the GSSF combined with SVIGS method and the GSSF combined with SVIGS and OD. The overloaded line is between bus 115 and bus 121 (dashed line in Fig. 21). We observe in Table X that as more features are added to redispatch algorithm, the flow in the corrected line is increasing, in contrast to the losses which are decreasing according to Fig. 17. Furthermore, Fig. 18 shows that the loadability and reactive margins increase substantially with the GSSF+VI and GSSF+VI+OD methods. The same observations can be done and indexes with the Table XI which show the decreasing with the algorithm being more and more complete.


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Fig. 18. Loadability and reactive margin versus overload alleviation method.

TABLE XI AOEN PERFORMANCE ON THE RTS96 Fig. 20. IEEE 39-bus New England network.

used in real time operation with little further optimization. This rule based system will be suitable for online use. Based on the compelling evidence described in this section, we can safely conclude that the proposed GSSF+VI+OD trio is the best combination to alleviate an overload while enhancing the security margin in terms of reduced losses, increased loadability and reactive reserve margin. The optimal dispatch results in an optimal production margin system-wide. With the active power production being better dispatched, each generator can ultimately produce more reactive power under contingencies, which is one of the prime reasons for the improved security margins after an OD. V. CONCLUSION

Fig. 19. Generation vulnerability index by unit size for one region: stressed case after redispatch. TABLE XII TIME REQUIREMENT FOR COMPUTING THE RESCHEDULED DISPATCH

Fig. 19 summarizes the generation redispatch performed in order to alleviate the overloaded line. Only the units size of 12, 20, 50, and 100 MW are shown because the other generation . We can see that, in contrast to units product have the proposed scheme, the GSSF method draws more power from small generators (in the range of 12 and 50 MW). Therefore, the two schemes result in opposite generation allocation strategies. On an Intel Q6600 Core2 Quad running at 2.4 Ghz, the time requirement to compute the GSSF matrix and the rescheduled dispatch is very modest and detailed in the Table XII. Despite the fact that the algorithms are developed in the Matlab framework which known for its slowness, we can notice the algorithm is fast with the three tested methods and it can be conceivably

The advent of intermittent generation has recently brought about a robust trend toward improvement in systems operation tools and a sharp increase in the amount of intra-hour transactions-based activities [31]. It is expected that, unless comprehensive technical tools such as the proposed Automatic Operator of Electrical Networks are provided to assist in timely decision-making, human operators will be under increased stress during more frequent emergency situations. However, at this prospective stage, the AOEN’s purpose is rather modest, consisting primarily in helping the operator alleviate line overloads, although our approach pays due attention to the static vulnerability index of the system components. Other security objectives, such as the voltage stability margin or the system maximum loadability index, could be also considered within the same framework, using reactive power redispatch together with active power. In addition, an improved, more operator-minded, ac power flow, has been developed within the framework of PSAT [26] to model the frequency bias-based automatic generation control (AGC). By doing this, the slack bus issue can be solved while including frequency governing droop and static frequency-voltage-dependent load models. The fuzzy decision system embedded in the AOEN was shown to be relatively effective in recommending generation rescheduling (shift away from economic dispatch) to reinforce

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TABLE XIII LINE IDENTIFICATION FOR FIGS. 7 AND 11

TABLE XIV THE 32 GENERATION UNITS IN AN IEEE RTS96 REGION

systems comprising 39 and 73 buses, respectively. In sharp contrast with previous related work, it appears that a vulnerability-based AOEN tends to alleviate security violations while providing generation and load-flow patterns with more safety margins set aside for preventing the next contingency damages. As the desired results can be obtained quickly based on repeated AGC-PF only, the fuzzy logic-based AOEN is suitable for online application in an EMS with modest optimization for large networks. APPENDIX Figs. 20 and 21 show the IEEE 39-bus New England network and the system diagram IEEE RTS96 network, respectively. Table XIII lists the line identification for Figs. 7 and 11, and Table XIV lists the 32 generation units in an IEEE RTS96 region. ACKNOWLEDGMENT The authors would like to thank F. Levesque and R. Mailhot of Hydro-Québec TransEnergie for fruitful discussions during the planning stage of this research work. REFERENCES Fig. 21. System diagram IEEE RTS96 network.

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Laurent Lenoir (S’06) received the B.Sc. degree in electrical engineering from the École Supérieure d’Ingénieurs en Électrotechnique et Électronique d’Amiens (ESIEE-Amiens), Amiens, France, in 2001 and the M.Sc.A degree at the École Polytechnique de Montréal, Montréal, QC, Canada, in 2004. He is currently pursuing the Ph.D. degree in electrical engineering at the École de Technologie Supérieure, Montréal. His research interests are power system analysis, security, stability, and control.

Innocent Kamwa (S’83–SM’98–F’05) received the B.Ing. degree and the Ph.D. degree in electrical engineering from Université Laval, Québec City, QC, Canada, in 1984 and 1988, respectively. Since then, he has been with the Hydro-Québec Research Institute, where at present, he is a Principal Researcher with interests broadly in bulk system dynamic performance. Since 1990, he has held an Associate Professor position in electrical engineering at Université Laval. Dr. Kamwa is a recipient of the 1998 and 2003 IEEE PES Prize Paper Awards and is currently serving on the System Dynamic Performance Committee, AdCom. He is also the acting Standards Coordinator of the PES Electric Machinery Committee and an associate editor for the IEEE TRANSACTIONS ON POWER SYSTEMS. He is a member of CIGRÉ.

Louis-A. Dessaint (M’88–SM’91) received the B.Ing., M.Sc.A., and Ph.D. degrees from the École Polytechnique de Montréal, Montréal, QC, Canada, in 1978, 1980, and 1985, respectively, all in electrical engineering. He is currently a Professor of electrical engineering at the École de Technologie Supérieure, Montréal. From 1992 to 2001, he was the Director of the Groupe de recherche en électronique de puissance et commande industrielle (GREPCI), a research group on power electronics and digital control. Since 2002, he has been the TransÉnergie (Hydro-Québec) Chair on Power Systems Simulation and Control. He is one of the authors of the SimPowerSystems simulation software of MathWorks. Dr. Dessaint received the “Outstanding Engineer Award” from IEEE-Canada in 1997. He is also an associate editor for the IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY.