VIEWS: 0 PAGES: 12 CATEGORY: Education POSTED ON: 5/10/2010 Public Domain
M. A. El-Kady and M. S. Owayedh FRAMEWORK FOR OPTIMAL POWER FLOW INCORPORATING DYNAMIC SYSTEM SECURITY M. A. El-Kady * and M.S. Owayedh King Saud University Saudi Electricity Company Riyadh, Saudi Arabia اﻟﺨﻼﺻﺔ: ً ً ً ﻳﻘﺪم هﺬا اﻟﺒﺤﺚ إﻃ ﺎرا ﻋﻤﻠﻴ ﺎ ﺟﺪﻳ ﺪا وﻃ ﺮق ﻣﻌﺎﻟﺠ ﺔ ﻧﻈﺮﻳ ﺔ وﺗﺤﻠﻴﻠﻴ ﺔ ﻟﻠﺘﻌﺎﻣ ﻞ ﻣ ﻊ اﻟﻤ ﺸﻜﻠﺔ اﻟﻤﻌﻘ ﺪة اﻟﺘ ﻲ ﺗﺘﻄﻠ ﺐ اﻟﻤﻮازﻧ ﺔ ﺑ ﻴﻦ اﻻﻋﺘﺒ ﺎرات اﻻﻗﺘ ﺼﺎدﻳﺔ واﻷﻣﻨﻴ ﺔ ﻓ ﻲ ﺗ ﺸﻐﻴﻞ ﻧﻈ ﻢ اﻟﻄﺎﻗ ﺔ اﻟﻜﻬﺮﺑﺎﺋﻴ ﺔ. وﻟﻤﺠﺎﺑﻬ ﺔ ه ﺬا اﻟﺘﺤﺪي ﺑﻄﺮﻳﻘﺔ ﻋﻤﻠﻴﺔ وﻓﻌﺎﻟﺔ ﺗﻘﺘﺮح هﺬﻩ اﻟﻮرﻗﺔ دﻣﺞ ﺗﻘﻴﻴﻢ اﻷﻣﻨﻴﺔ ﻟﻠﺸﺒﻜﺎت اﻟﻜﻬﺮﺑﺎﺋﻴﺔ ﻣ ﻊ ﻣﺘﻄﻠﺒ ﺎت اﻟﺘ ﺸﻐﻴﻞ اﻻﻗﺘ ﺼﺎدي اﻷﻣﺜ ﻞ وذﻟ ﻚ ﺑﻮﺳ ﺎﻃﺔ اﺳ ﺘﺨﺪام اﻟﻄﺮﻳﻘ ﺔ اﻟﻤﻌﺮوﻓ ﺔ ﺑﺎﺳ ﻢ داﻟ ﺔ اﻟﻄﺎﻗ ﺔ اﻟﻌ ﺎﺑﺮة ﻣ ﻊ إدﺧ ﺎل ﺗﻜﻠﻔ ﺔ اﻟﺘﺸﻐﻴﻞ اﻟﻜﻠﻴﺔ ﻟﻠﻨﻈﺎم آﺪاﻟﺔ رﺋﻴﺴﻴﺔ ﻳﺘﻢ ﺗﻘﻠﻴﻠﻬﺎ ﺑﻘﺪر اﻹﻣﻜﺎن ﻣﻊ اﻻﺣﺘﻔﺎظ ﺑﺎﻷﻣﻨﻴ ﺔ اﻟﺤﺮآﻴ ﺔ ﻟﻠ ﺸﺒﻜﺔ. وﻓ ﻲ ه ﺬا اﻹﻃﺎر ﺗﻘﺪم اﻟﻮرﻗﺔ ﻣﺒﺪأﻳﻦ ﺟﺪﻳﺪﻳﻦ ﻟﻠﺘﻌﺎﻣﻞ ﻣﻊ اﻟﻤﺸﻜﻠﺔ وﻟﻠﺤﺼﻮل ﻋﻠ ﻰ وﺻ ﻒ أدق ﻷداء اﻟﻨﻈ ﺎم اﻟﻜﻬﺮﺑ ﺎﺋﻲ ﺗﺤﺖ ﻇﺮوف اﻟﺘﺸﻐﻴﻞ اﻟﻤﺨﺘﻠﻔﺔ. :* Address for correspondence Professor M. A. El-Kady Electrical Engineering Department King Saud University 008 P. O. Box 12411 Riyadh Saudi Arabia E-mail: melkady@ksu.edu.sa .5002 Paper Received 14 September 2004; Revised 28 February 2005; Accepted 18 June 6002 October The Arabian Journal for Science and Engineering, Volume 31, Number 2B 991 M. A. El-Kady and M.S. Owayedh ABSTRACT This paper introduces a novel framework and methodologies which are capable of tackling the complex issue of power system economy versus security in a practical and effective manner. At heart of achieving such a challenging and far-reaching objective is the incorporation of the Dynamic Security Assessment (DSA) into production optimization techniques using the Transient Energy Function (TEF) method. In addition, and in parallel with the already well- established concept of system security, two new concepts pertaining to power system performance will be introduced in this paper, namely the concept of system dynamic susceptibility, which measures the level of system weakness to a particular contingency and the concept of system consequent restorability, which measures the extent of contingency severity in terms of the required subsequent system restoration work should a particular contingency occur. Key words: Economy, security, optimization, transient stability, dynamic security assessment, transient energy margin, transient energy function method, optimal power flow, power flow 200 The Arabian Journal for Science and Engineering, Volume 31, Number 2B October 2006 M. A. El-Kady and M. S. Owayedh FRAMEWORK FOR OPTIMAL POWER FLOW INCORPORATING DYNAMIC SYSTEM SECURITY 1. INTRODUCTION Due to the critical importance of electric energy and the rising cost of its production, power utilities around the world are compelled to minimize production cost while, at the same time, operating within acceptable security limits [1–3]. The complexity of the overall problem and the multi-disciplinary nature of the research involved have resulted in division of the research into two main areas, namely power system security and operational economy. The objective in the operational economy area is to determine the optimum schedule of utility generating units that minimizes the total operation cost subject to equipment and system constraints [4,5]. On the other hand, the objective in the power security domain is to ensure the system's ability to withstand some unforeseen, but probable, disturbances with the minimum disruption of service or reduction of service quality [6,7]. Basically, power system security assessment can be broadly divided into two sub-areas: Static Security Assessment (SSA) and Dynamic Security Assessment (DSA). The term “static security” means that all limit violations reflect steady-state quantities such as steady state bus voltage violations and steady-state transmission line over-loading. The analysis tools required are those related to steady-state analysis (i.e. load flow and related sensitivity analysis methods). DSA, on the other hand, corresponds to the investigation of disturbances, which may lead to transient instability (loss of synchronism among machines). Over the past two decades, the loading of transmission network and the amount of power transfer between interconnected systems, in many power systems worldwide, has increased to the point where power system security constraints start to influence the generation commitment and loading decisions. This has led researchers [2,8,9] to develop techniques suitable for incorporating static security constraints into production optimization procedures known as Optimal Power Flow (OPF). In real power systems, however, any re-distribution of generator power output to minimize fuel cost (economic dispatch) would also influence the system dynamic behavior (stability) when a contingency occurs (for example, a fault at a given bus of the network which is cleared by tripping a transmission line). The proper inclusion of dynamic security constraints in the OPF formulation has so far been limited, mainly because of the inherent problem complexity and the lack of appropriate methodologies This paper will introduce framework and methodologies for incorporating dynamic security constraints in the production optimization techniques. In addition, and in parallel with the already well-established concept of system security, two new and far-reaching concepts pertaining to power system performance will be introduced, namely the concept of ‘system dynamic susceptibility’ and the concept of ‘system consequent restorability’. 2. ECONOMY-SECURITY INTEGRATION In general, and depending on the philosophy and mandate of the utility, there are basically two possible scenarios. The first is to try to minimize the operating cost subject to minimum reliability requirements. The second is to maximize reliability subject to a maximum cost (budget ceiling). Of course, the two solutions are theoretically and practically different. Therefore, in theory, there are two possible formulations involving the integration of both economy and security functions in the power utility business. These alternative formulations are [1]: Alternative 1: Minimize: Production Cost Subject to: Minimum Security (Reliability) Requirements Alternative 2: Maximize: Security (Reliability) Subject to: Maximum Cost (Affordability Constraint). In practice, however, all power utilities are adopting the first formulation. That is, to focus primarily on minimizing operating costs as long as the minimum acceptable security level is met. The above dilemma exists essentially because the economy and security functions have totally different mandates. The economy group in the power utility is concerned, in principle, with making money and generating profit by minimizing costs. It is their job mandate to minimize the production cost to the extent possible. On the other hand, the group concerned with system security October 2006 The Arabian Journal for Science and Engineering, Volume 31, Number 2B 201 M. A. El-Kady and M.S. Owayedh functions attempts, in most cases, to limit the freedom available to the economy group by raising concerns relating to system security issues. Indeed, the utility cannot have it both ways. If it opts for higher reliability, it must then pay more and, conversely, if it opts for less cost, then it would have to relax the reliability standards (i.e. take the risk) and lower the level of service quality offered to its customers. This, in essence, is the main reason for regulating the power utility business by local governments in some parts of the world, even though they may lose some advantages of the free market economy. Depending on the organizational structure of the power utility and the technology available, there are basically three possible scenarios for integrating economy and security functions these over listed follows: 2.1. Loosely-Integrated Security and Economy Functions: In this case, it is assumed that both economy and security functions are totally separate in terms of individual decision making processes. Here, the economy group develops a production costing plan, say for the next 48 hours, and pass it on to the security group to check if it would violate any of the system security (static and/or dynamic) limits. If some security limits are violated, then the production plan is rejected and returned to the economy group for modifications. In technical terms, this would degrade the plan from optimal to sub-optimal status. The cycle is repeated until an acceptable plan is developed. We note here that the only signal that is given back from the security to the economy group is a ‘Yes / No’ signal and, therefore, this scenario reflects a measure of weak integration between the two functions. This scenario is depicted in Figure 1. Economy Function Yes / No Operating Parameter Security Function Figure 1. Loosely-integrated economy and security functions. 2.2. Semi-Integrated Security and Economy Functions In this scenario, the utility tries to achieve more integration between the two functions, which, because of the technology and software limitations that may exist, can only be done partially. Instead of the ‘Yes / No’ signal, the security function would also give sensitivity information to the economy function to indicate how much the security margin is sensitive to changes in operating parameters. This information would tremendously decrease the number of iterations between the two groups as the economy group would, in this case, be able to estimate the impact of variations in system operating parameters (for example, a power plant output) on the security. This scenario is shown in Figure 2. Economy Function Sensitivities of Dynamic Security Margin Security Function Figure 2. Semi-integrated economy and security functions. C) Fully-integrated Security and Economy Functions: In this scenario, which is demonstrated in Figure 3, a full integration would be attempted between economy and security functions. Here, the problem is usually formed as a conventional economy function in which security constraint(s) are added to ensure that the resulting plan satisfies the security constraints as well. An example of this scenario would be the minimization of the total fuel cost subject to the system being stable. 202 The Arabian Journal for Science and Engineering, Volume 31, Number 2B October 2006 M. A. El-Kady and M. S. Owayedh Economy-Security Function Minimize: Production Cost w.r.t: Operating parameters Subject to: Power Flow Equations Voltage and Flow Constraints Dynamic Security Requirements Figure 3. Fully integrated economy and security functions. 3. MATHEMATICAL FORMULATION The OPF problem was defined in the early sixties as an extension of the traditional economic dispatch to determine the actual setting for control variables in a power system representing various constraints. Traditional scheduling fails to take the precise operating conditions of the network into account. In the conventional OPF problem formulation [10], a total cost function is minimized with respect to optimization variables and subject to system constraints representing steady-state load-flow equations as well as upper and lower bounds on system variables. The optimization variables include a set of control variables u that are adjusted to obtain the optimal operating point defined in terms of the state variables x. The Transient Energy Function (TEF) method [11,12] has been used for many DSA studies as an alternative to the conventional time-domain simulation. Recent developments in the TEF and the related sensitivity analysis have made it a position candidate to meet the speed and dependability required for incorporation into production optimization techniques. The avoidance of a lengthy step-by-step time domain solution and the provision of quantitative measure (Energy Margin) are features that make the TEF method very attractive. In addition the TEF has also the flexibility to obtain analytical sensitivity information on how the energy margin is affected by variations in system parameters and conditions. The proposed formulation will utilize the TEF method to produce an analytic measure (energy margin) of the system transient stability. Using proper formulations and advanced sensitivity analyses, both economy and security requirements will be integrated and included in one routine of optimization. Without loss of generality, the control variables are assumed to contain voltage magnitude and active power generation at generator buses. In addition, upper and lower bounds are imposed on the control variables. It should be noted that other control variables, including transformer tap and phase-shifter settings, controlled VAR sources, and even demand powers (load shedding) could be incorporated in the computational scheme. When the objective function represents the total fuel cost, the resulting Dynamically-Constrained Optimal Power Flow (DCOPF) problem can then be stated as follows: Minimize C (PGi ;i=1,2,..., NG) (1) with respect to |Vi|, PGi; i=1,2,..., NG Subject to: Equality constraints (load flow equations) (2) Upper & lower bounds on problem variables (static security constraints) (3) EM ≥ EMM in (dynamic security constraint) (4) If the objective is to maximize dynamics security, then, the overall Cost Constraint Maximum Dynamic Security (CCMDS) problem, which maximizes the transient energy margin, can then be stated as follows: Minimize EM (|VGi|, PGi ; i=1,2,..., NG) (5) with respect to |VGi|, PGi ; i =1,2,..., NG Subject to: Equality constraints (load flow equations) (6) October 2006 The Arabian Journal for Science and Engineering, Volume 31, Number 2B 203 M. A. El-Kady and M.S. Owayedh Upper and lower bounds on problem variables (static security constraints) (7) C ≤ CMAX (Production cost constraint) (8) The production cost represents the sum of fuel costs associated with various dispatched generators. Mathematically, the objective function is as follows: NG C = ∑C i (PGi ) i =1 (9) where Ci ( PGi ) = Ci 0 + Ci1 * PGi + Ci 2 * PGi is a cost function for generator. 2 The energy margin is a non-linear function of the control variables of the form EM = f ( PG,VG ) (10) The TEF can be formulated directly using the Center of Inertia (COI) frame of reference. Converting loads to constant shunt admittances and transforming rotor angles and speeds to the COI reference, the swing equation of the NG generators, which represent the system equilibrium condition, can be written in the following compact form [12,13] • M f (V ,θ , δ ) = M i ω i = Pm i − PG i − i PCOI = 0 (11) MT • where θi is the generators bus voltage angle, δi is the generator internal angles, ωi and ωi are the generator speed and its time-derivative, Mi is the moment of inertia, Pmi and PGi are the mechanical power input and generation power output respectively, ⏐Vi⏐ is the bus voltage magnitude and NG MT = ∑ M i i =1 (12) NG PCOI = ∑ ( Pmi − PGi ) i =1 (13) The equilibrium points of the system are the points representing various solutions of the nonlinear swing equations (11). Among such equilibrium points, the Stable Equilibrium Point (SEP) and the controlling Unstable Equilibrium Point (UEP) are of interest for the purpose of the transient stability analysis. The only difference between the determination of the SEP and the UEP is the initial condition provided to the solution algorithm. For the SEP, the condition at fault clearing is used while, for the UEP, the ray point [12], which maximizes the position energy along the ray from post disturbance point to the controlling UEP, is normally used unless for stressed systems in which more robust techniques are needed to solve for the UEP [10]. Having solved for the SEP and the UEP, the transient energy function V (θ,ω) is expressed as NG NG V ( θ , ω ) = 0.5 ∑M i =1 iωi - 2 ∑P i =1 mi ( θ i −θ s ) i N G θi + ∑∫P i =1 θ s Gi dθ i (14) i in which the three RHS terms represent the kinetic energy, position energy, and magnetic and dissipation energy of the system, respectively. The stability assessment is done by comparing two values of the transient energy V. These are the values of V computed at fault clearing Vcl and the critical value Vcr which is the position energy at the controlling UEP, for the particular disturbance under investigation. Substituting for Vcr and Vcl in (14) and using the concept of kinetic energy correction [12], the energy margin can be obtained as 204 The Arabian Journal for Science and Engineering, Volume 31, Number 2B October 2006 M. A. El-Kady and M. S. Owayedh NG NG EM = 0.5 ∑ M eq (ω cl ) 2 - ∑ Pmi ( θ iu - θ icl ) i=1 i=1 NG θ iu (15) +∑ ∫θ cl PG i dθ i , i =1 i in which ωcl and θcl are calculated using either the step-by-step method or directly assuming constant acceleration. The dissipation energy term can be evaluated only if the system trajectory is known. The fairly accurate approximation, assuming linear angle path as suggested by Athay [14], is used in the present analysis. The security constrained optimal power flow problem has been solved by different techniques in the literature [15–17]. In the present work, the above optimization problem is solved using standard non-linear programming techniques [18]. In this paper the Gradient Projection method of Rosen is adopted for the solution of the optimization problem. 4. ECONOMY-SECURITY INTEGRATION APPLICATIONS In this section, practical applications of DCOPF and CCMDS are presented. The power system used in the applications is the interconnected Saudi Electricity Company (SEC) power grid. This power system consists of two main regions, namely the SEC-C (Central Region) and SEC-E (Eastern Region). The two SEC systems are interconnected through two 380 kV and one 230 kV double-circuit lines. In the original (unreduced) load-flow system model, the interconnected SEC bulk electricity system comprises 150 generator buses, 637 load buses, a total of 1168 transmission lines, and transformers. In order to prepare a number of meaningful system models, which are suitable for the present stability studies, the original base-case underwent a series of carefully performed static network reductions. The first reduced network model comprises 119 buses (19 generators, 100 loads), 334 lines, and 122 transformers. This system model will be referred to as the 19-Generator model. The nineteen generators are distributed as 11 in the SEC-C area, 8 in the SEC-E area, as shown in Figure 4. The system under investigation is the reduced 3-Generator system model created from the 19-Generators SEC model. The contingency considered is a 3-phase fault at bus #30 on the SEC-E side of the 380 kV tie-line between SEC-E and SEC-C, cleared after 0.08 seconds by tripping the double-circuit 380 kV line (between bus #1 and bus # 30). Table 1 summarizes the results of five different operating objectives, namely: (1) Original base-case; (2) Cost minimization without dynamic security constraints (conventional OPF); (3) Cost minimization with dynamic security constraints (DCOPF); (4) CCMDS (maximize un-normalized EM with an upper bound on production cost of 370 kSR/hr; (5) DCOPF with the EM fixed at the initial base case value; and (6) CCMDS with total production cost fixed at the initial base case value. 6 SEC CENTRAL 83 81 SEC EAST PP8X 12 112 110 111 41 47 82 44 2 4 1 87 85 84 48 GAZLAN 45 46 40 8 7 15 14 5 23 BERI 51 103 JSWCC 34 NORTH AREA 49 QPP2 77 PP8B 61 62 38 75 74 63 89 92 68 67 PP8A 119 78 39 37 90 91 PP5 80 78 9 RIYADH AREA 50 93 79 114 86 107 106 105 104 94 113 19 73 115 PP9 DAMMAM 116 56 108 DAMAMAM AREA 88 26 30 98 97 96 95 99 SHEDGUM 35 109 21 71 100 29 28 43 PP4 66 QPP3 65 59 42 76 64 20 57 60 16 36 PP7B PP7A 54 10 55 70 69 17 QURAIAH QASSIM AREA 117 102 101 27 18 58 13 LAYLA 53 33 32 31 24 118 25 11 22 72 SOUTH AREA 3 AL-KAHARJ AREA 52 FARAS Figure 4. SEC 19-Generators System Model. October 2006 The Arabian Journal for Science and Engineering, Volume 31, Number 2B 205 M. A. El-Kady and M.S. Owayedh Table 1. Security/Economy Applications # Objective P. Cost (kSR/hr) Energy Margin 1 Initial Base Case 362.78 3.203 2 OPF 346.89 <0.00 3 DCOPF 356.58 0.000 4 CCMDS 370.00 29.84 5 DCOPF (Initial EM) 358.16 3.203 6 CCMDS (initial P. Cost) 362.78 10.42 The optimization was performed by adjusting six operating parameters representing the real power and voltage at three major power plants (Qurraiah, PP8X, and Qassim). The results of Table 1 show that, for the operating scenarios considered, a mere cost minimization would lead to an unstable system if the anticipated contingency occurred. It is also shown from Table 1 that, while the CCMDS solution produces a very stable system with EM value close to 30, the resulting production cost is about 3.7 percent higher than the DCOPF solution. The Study Scenarios #5 and #6 represent interesting scenarios, which underline the importance of using advanced optimization methodologies in the modern system operation environment. The Study Scenario #6, for example, demonstrates that it is possible to increase dynamic system security without necessarily incurring any additional operating costs. In this case, the energy margin was improved from 3.2033 to 10.424 per-unit while maintaining the total production cost at 362.78 kSR/hr. On the other hand, the Study Scenario #5 demonstrates that it is possible to reduce the system operating cost without necessarily reducing the level of the dynamic system security. In this case, the total production cost was reduced from 362.78 kSR/hr to only 358.16 kSR/hr while maintaining the energy margin at its base-case value of 3.2033. Table 2 shows the values of some key control variables for both the conventional OPF (without security constraint) and the cost minimization with dynamic security constraints (DCOPF) solutions. 5. SYSTEM DYNAMIC PERFORMANCE System performance assessment is not, and should not be, confined to only the transient stability analysis and the dynamic security assessment, which has so far been the case. In this respect, it is well known in the literature that a traditional time-domain transient stability run would provide a basic stable/unstable answer. A dynamic security assessment, on the other hand, would extend the information provided by also giving the associated degree (or level) of system stability (or instability). This is done, in essence, by computing the value energy margin corresponding to the operating scenario under consideration. An advancement to the state-of-the-art is made by extending further the above two concepts to serve two very important objectives in the practical power system operation, namely: (i) To determine the rate of deterioration in the dynamic security with respect to certain contingencies, and (ii) To determine the true severity of a particular contingency in terms of its consequent impact on system restoration. In the present work, the first objective will be termed dynamic susceptability, while the second objective will be termed as consequent restorability. These two new far-reaching concepts, together with the more classical term of “probability of contingency” should complete, to a large extent, the general domain of power system dynamic performance assessment. Because of the nature of such an advancement, as conceptual rather than methodological, a comprehensive definition and an associated practical example would be sufficient to explain each concept, as in the following two subsections. An application is then presented to demonstrate the overall assessment of system dynamic performance on a particular operating scenario in the SEC-C power system. 206 The Arabian Journal for Science and Engineering, Volume 31, Number 2B October 2006 M. A. El-Kady and M. S. Owayedh Table 2: Application of OPF and DCOPF VARIABLE POWER BASE OPTIMIZATION PLANT CASE OPF DCOPF PP8X 1.035 1.050 1.050 QUR 1.020 1.030 1.041 QPP3 1.020 1.050 1.050 GAZ 1.015 1.050 1.050 PP5 1.000 1.004 1.009 PP7A 1.000 1.034 1.011 VG (PU) SHED 1.015 1.050 1.044 FARAS 1.000 1.028 1.022 PP9 1.020 1.050 1.033 PP8A 1.020 1.050 1.031 QPP2 1.045 1.050 1.050 PP7B 1.000 1.050 1.011 PP8B 1.020 1.050 1.032 PP8X 795.4 498.2 685.0 QUR 1792.4 2400.0 2143.0 QPP3 313.5 54.0 63.9 GAZ 3903.5 469.1 4139.1 PP5 406.6 60.0 270.3 PP7A 840.0 644.1 752.1 PG (MW) SHED 874.4 985.0 985.0 FARAS 549.6 725.0 725.0 PP9 398.4 110.7 285.1 PP8A 302.4 289.4 273.3 QPP2 72.0 90.0 90.0 PP7B 846.0 329.1 311.9 PP8B 302.4 115.3 221.3 ENERGY MARGIN 19.0775 < 0.0 3.000 TOTAL COST (kSR) 316.724 291.81 303.328 5.1. Dynamic Susceptibility Dynamic susceptibility of a given power system with respect to a particular contingency is defined as the combined effects of: (1) how far the system operating point is from the insecurity boundary; and (2) how fast the deterioration in dynamic security would be as one of the operating parameters changes. The key difference between dynamic security and dynamic susceptibility concepts is that the former deals with incidental value of system security level (for example, a value of the energy margin describing the degree of system stability, or instability), while the latter deals with the trend (sensitivity) of the system security to varying parameters. For example, a higher gradient of energy margin with respect to a particular operating parameter (e.g., power output from a particular generator) would indicate that the system is susceptible to that parameter. A demonstration of this concept is given in Figure 5, which depicts the EM as a function of the East-Center tie-line flow for four contingency scenarios representing faults at buses number 1, 24, 43, and 51, respectively, in the 19- Generator system model. Based on the above definition, it is clear that the system is more dynamically susceptible to the first and second contingency for increasing levels of the tie-line flow, and to the third contingency for decreasing levels of the tie-line flow. October 2006 The Arabian Journal for Science and Engineering, Volume 31, Number 2B 207 M. A. El-Kady and M.S. Owayedh SCENARIO I SCENARIO II SCENARIO III SCENARIO IV 30.0 ENERGY MARGIN (UN-NORMALIZED) 25.0 20.0 15.0 10.0 5.0 0.0 -5.0 800.0 900.0 1000.0 1100.0 1200.0 1300.0 1400.0 1500.0 1600.0 EAST-TO-CENTER FLOW (MW) Figure 5. Demonstration of Dynamic Susceptibility. 5.2. Consequent Restorability Consequent restorability of a given power system with respect to a particular contingency is defined as the degree of difficulty which is encountered in attempting to restore the system, or its supplied load, to its initial state should the contingency occur. A demonstration of this concept is best provided through a practical operating case scenario in the SEC power system. This case scenario involves a fault close to bus 78 in the Qassim area as shown in Figure 4. The fault is cleared by, in one contingency case by disconnecting the double circuit line between buses 78 and 79 while, in the second contingency case, the fault is cleared by disconnecting the double circuit line between buses 78 and 80. The load lost in the two contingency cases is practically the same, that is 17 MW and 20 MW, respectively. The ease of load restorability is, however, very different in the two cases. It is possible to restore the lost load in the first contingency case within hours, through the 33 kV network, using the normally opened circuits. For the second contingency case, on the other hand, the load restoration might take up to several days, depending on the extent of the circuit damage. Note, in this case, that there are no low voltage network links to other generation sources due to the remoteness of the substation involved. 5.3. Example of Dynamic Performance Assessment An example is presented here, which demonstrates a comprehensive assessment of the power system dynamic performance. The purpose of this example is to explain how different, and often contradicting, criteria could be analyzed to assess the overall dynamic performance of the system more comprehensively. In this case the following contingency and performance criteria are considered: (i) Severity of contingency in terms of amount of load lost, (ii) Probability of contingency, (iii) Difficulty of consequent load restoration. The case study under consideration pertains to the Al-Kharj area of the SEC-C power gird. The load for the Al-Kharj area is about 119 MW and only one power plant (Layla) is located in the area according to the 19-Generator system model of Figure 4. As the production cost of the Layla power plant is the most expensive in the network, it is economical to generate the minimum possible power from this plant. Now, consider the following two fault scenarios: 208 The Arabian Journal for Science and Engineering, Volume 31, Number 2B October 2006 M. A. El-Kady and M. S. Owayedh (i) Fault on circuit 13-33 cleared by disconnecting that circuit, (ii) Fault on transformer 101-102 cleared by disconnecting that transformer. The analysis of the system for the above two fault scenarios reveals the following interesting facts concerning the dynamic system performance: 1. The severity of second fault scenario is less than the severity of the first fault scenario, according to the severity criterion described before (the load lost is 13 MW for the second fault scenario as compared to 119 MW for the first fault scenario). 2. The consequent restoration of the second fault scenario is less difficult than the first fault scenario, as it is always possible to restore the lost load for the second scenario case within half an hour (the time required to synchronize and load the gas turbine generating unit). On the other hand, it would not be possible to restore the full lost load for the first fault scenario since the amount of the load lost is more than the maximum capacity of the power plant (90 MW). 3. In addition, it is well known that the probability of the first fault scenario, which represents a common faults on an overhead transmission line, is much higher than the probability of the second fault scenario, which represents a rare internal failure in a transformer. The above assessment is summarized in Table 3. On the basis of this assessment, it can safely be concluded that the dynamic performance of the system is more degraded in the first fault than in the second in regard to the criteria of contingency severity, consequent restorability, and probability of contingency. Table 3. Assessment of Dynamic System Performance FAULT FAULT SCENARIO 1 FAULT SCENARIO 2 SEVERITY HIGH LOW RESTORABILITY DIFFICULT EASY PROBABILITY HIGH LOW 6. CONCLUSION This paper introduces a framework and methodologies, which are capable of tackling the complex issue of economy versus security in a practical and effective manner. In this regard two formulation were presented, namely the DCOPF and its dual formulation, the CCMDS. This frame work can be further developed in integration of dynamic security constraints into other cost-based planning and operation algorithms and computer programs such as unit commitment, seasonal maintenance schedules and fuel inventory. In addition, and in parallel with the already well-established concept of system security, two new and far-reaching concepts pertaining to power system performance were introduced, namely the concept of system dynamic susceptibility, and the concept of system consequent restorability. The concepts of dynamic susceptibility and consequent restorability could be extended further to form quantitative measures which can easily be implemented in operation and planning studies, provided that the required data is available. October 2006 The Arabian Journal for Science and Engineering, Volume 31, Number 2B 209 M. A. El-Kady and M.S. Owayedh REFERENCES [1] M.A. El-Kady and M.S. Owayedh, “Advanced Modeling of Power System's Cost of Security”, Proceedings of IASTED International Conference on Modelling, Simulation and Optimization, Gold Coast, Australia, 1996, Paper #242-183,. [2] M.S. Owayedh, “Optimal Energy Production with Dynamic Security of Power Systems”, Ph.D. Thesis, King Saud University, 1998. [3] S.K. Chakravarthy, “Characteristic Multipliers for Assessing Stability of Electrical Power Systems”, IEEE Transactions on Power Systems, 22(1) (2002), pp. 55–58. [4] M.A. El-Kady, B.D. Bell, V.F. Carvalho, R.C. Burchett, H.H. Happ, and D.R. Vierath, “Assessment of Real Time Optimal Voltage Control”, IEEE Transactions on Power Systems, PWRS-1 (2) (1986), pp. 98-107. [5] D.A. Alves and G.R.M. da Costa, “An Analytical Solution to the Optimal Power Flow”, IEEE Transactions on Power Systems, 22 (3) (2002), pp. 49–51. [6] F.P. Demello, “Power system Dynamic Overview” Proceedings of the Symposium on Adequacy and Phelosophy of Modeling: Dyanamic System Performance, 1975 IEEE Publication 75CH0970-4-PWR. [7] C. Concordia, “Power System Stability”, Proceeding of the International Symposium on Power System Stability, Ames, Iowa, 1985. CIGRE (WG 38/02). [8] R.C. Burchett and H.H. Happ, “Large Scale Security Dispatching: An Exact Model”, IEEE Transactions on Power Apparatus and Systems, PAS-102 (9) (1983), pp. 2995–2999. [9] Z.Q. Wu, “Single Machine Equal Area Criterion for Multimachine System Stability Assessment Based on Time Domain Simulation”, IEEE Transactions on Power Systems, 21 (11) (2001), pp. 51–52. [10] M.E. El-Hawary, “Optimal Power Flow: Solution Techniques, Requirements and Challenges”, IEEE Tutorial Course No. 96, (1996), TP 111-0. [11] M.A. El-Kady, C.K. Tang, V.F. Carvalho, A.A. Fouad, and V. Vittal, “Dynamic Security Assessment Utilizing the Transient Energy Function Method”, IEEE Transactions Power Apparatus and Systems, PWRS-1 (1986), pp. 284-291. [12] G.A. Maria, C.K. Tang, J. Kim, A.A. Fouad, V. Vittal, and M.A. El-Kady, “On-Line Transient Stability Calculator. ”, Final Report, EPRI Project Report RP-2206-1, 1994. [13] M.M. Abu-Elnaga, M.A. El-Kady and R.D. Findlay, “Sparse Formulation of the Transient Energy Function Method for Applications to Large-Scale Power Systems”, IEEE Transactions on Power Systems, 3 (4) (1988), pp. 1648-1654. [14] T. Athay, R. Podmore, and S. Virmani, “A Practical Method for the Direct Analysis of Transient Stability”, IEEE Transactions on Power Apparatus and Systems, PAS-98 (2) (1979), pp. 573–580. [15] L. Chen, Y. Tada, H. Okamoto, R. Tanabe, and A. Ono, “Optimal Operation Solutions of Power Systems with Transient Stability Constraints”, IEEE Transactions on Circuits and Systems - I: Fundamental Theory and Applications, 48 (3) (2001), pp. 327–339. [16] D. Gan, R.J. Thomas, and R.D. Zimmerman, “Stability-Constrained Optimal Power Flow,” IEEE Transactions on Power Systems, 15 (2) (2000), pp. 535-540. [17] Y. Yuan, J. Kubokawa, and H. Sasaki, “A Study Of Transient Stability Constrained Optimal Power Flow With Multi- Contingency, ” T. IEE Japan, 122-B (7) (2002), pp. 798-804. [18] M.S. Bazzara, H.D. Sherali, and C.M. Ahetty, Nonlinear Programming Theory and Algorithm, Second Edition, John Wiley & Sons Inc., New York, (1993). 210 The Arabian Journal for Science and Engineering, Volume 31, Number 2B October 2006