199 framework for optimal power flow incorporating dynamic system ...

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 

M. A. El-Kady and M. S. Owayedh 

: ﺔﺻﻼﺨﻟا 

ﻲﺘﻟا ةﺪﻘﻌﻤﻟا ﺔﻠﻜﺸﻤﻟا ﻊﻣ ﻞﻣﺎﻌﺘﻠﻟ 

ﺔﻴﻠﻴﻠﺤﺗو ﺔﻳﺮﻈﻧ ﺔﺠﻟﺎﻌﻣ قﺮﻃو ًاﺪﻳﺪﺟ 

ًﺎﻴﻠﻤﻋ 

ًارﺎﻃإ 

ﺚﺤﺒﻟا اﺬه مﺪﻘﻳ 

اﺬه ﺔﻬﺑﺎﺠﻤﻟو . ﺔﻴﺋﺎﺑﺮﻬﻜﻟا ﺔﻗﺎﻄﻟا ﻢﻈﻧ ﻞﻴﻐﺸﺗ ﻲﻓ ﺔﻴﻨﻣﻷاو ﺔﻳدﺎﺼﺘﻗﻻا تارﺎﺒﺘﻋﻻا ﻦﻴﺑ ﺔﻧزاﻮﻤﻟا ﺐﻠﻄﺘﺗ 

ﻞﻴﻐﺸﺘﻟا تﺎﺒﻠﻄﺘﻣ ﻊﻣ ﺔﻴﺋﺎﺑﺮﻬﻜﻟا تﺎﻜﺒﺸﻠﻟ ﺔﻴﻨﻣﻷا ﻢﻴﻴﻘﺗ ﺞﻣد ﺔﻗرﻮﻟا ﻩﺬه حﺮﺘﻘﺗ ﺔﻟﺎﻌﻓو ﺔﻴﻠﻤﻋ ﺔﻘﻳﺮﻄﺑ يﺪﺤﺘﻟا 

ﺔﻔﻠﻜﺗ لﺎﺧدإ ﻊﻣ ةﺮﺑﺎﻌﻟا ﺔﻗﺎﻄﻟا ﺔﻟاد ﻢﺳﺎﺑ ﺔﻓوﺮﻌﻤﻟا ﺔﻘﻳﺮﻄﻟا ماﺪﺨﺘﺳا 

ﺔﻃﺎﺳﻮﺑ 

ﻚﻟذو ﻞﺜﻣﻷا يدﺎﺼﺘﻗﻻا 

اﺬه ﻲﻓو . ﺔﻜﺒﺸﻠﻟ ﺔﻴآﺮﺤﻟا ﺔﻴﻨﻣﻷﺎﺑ ظﺎﻔﺘﺣﻻا ﻊﻣ نﺎﻜﻣﻹا رﺪﻘﺑ ﺎﻬﻠﻴﻠﻘﺗ ﻢﺘﻳ ﺔﻴﺴﻴﺋر ﺔﻟاﺪآ مﺎﻈﻨﻠﻟ ﺔﻴﻠﻜﻟا ﻞﻴﻐﺸﺘﻟا 

ﻲﺋﺎﺑﺮﻬﻜﻟا 

مﺎﻈﻨﻟا ءادﻷ قدأ ﻒﺻو ﻰﻠﻋ لﻮﺼﺤﻠﻟو ﺔﻠﻜﺸﻤﻟا ﻊﻣ ﻞﻣﺎﻌﺘﻠﻟ ﻦﻳﺪﻳﺪﺟ ﻦﻳأﺪﺒﻣ ﺔﻗرﻮﻟا مﺪﻘﺗ رﺎﻃﻹا 

. ﺔﻔﻠﺘﺨﻤﻟا ﻞﻴﻐﺸﺘﻟا فوﺮﻇ ﺖﺤﺗ 

* Address for correspondence: 

Professor M. A. El-Kady 

Electrical Engineering Department 

King Saud University 

P. O. Box 800 

Riyadh 11421 

Saudi Arabia 

E-mail: melkady@ksu.edu.sa 

Paper Received 14 September 2004; Revised 28 February 2005; Accepted 18 June 2005. 

October 2006 The Arabian Journal for Science and Engineering, Volume 31, Number 2B 199

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 wellestablished 

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


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


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. 

Yes / No 

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. 

Sensitivities of Dynamic 

Security Margin 

Economy Function 

Operating Parameter 

Security Function 

Economy Function 

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. 


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) 

with respect to |VGi|, PGi ; i =1,2,..., NG 

Subject to: 

(5) 

Equality constraints (load flow equations) (6) 



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 

2 

( ) 0 1 * 

2 * i 

G 

C i PG 

i = Ci 

+ Ci 

PG 

i + Ci 

P 

M i 

f ( V , θδ , ) M i ωi Pmi PGi PCOI 

0 

M 

• 

where is a cost function for generator. 

The energy margin is a non-linear function of the control variables of the form 

EM = f( P G,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] 

= = − − = 

(11) 

N G N G 

V( θ, ω) = 0.5 2 s 

∑M i ω i - ∑P 

m ( i θ i −θ 

i ) 

i=1 i=1 

N G θ i 

+ ∑∫ PG 

i d θ i 

i=1 s 

θ i 

T 

where θi is the generators bus voltage angle, δi is the generator internal angles, ωi and 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 

T = ∑ i 

i= 

1 (12) 

M M 

NG 

PCOI = ∑( Pm i − PG 

i ) 

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 

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 

ωi • 

(9) 

(14)

EM = 0.5 

+ 

NG 

∑ 

i= 

1 

NG 

∑ 

i=1 

∫ 

M 

u 

i 

cl 

i 

θ 

θ 

eq 

P 

G 

i 

cl 

( ω ) 

2 

dθ 

i , 

- 

NG 

∑ 

i=1 

P 

m 

i 

( θ -θ 

) 

u 

i 

cl 

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. 

78 

80 

79 

40 

36 

QPP2 

78 

35 

34 

41 

75 

39 

QPP3 

QASSIM AREA 

43 

6 

38 

37 

42 

8 

12 

77 

PP8B 

PP8A 

PP7B 

76 

13 33 

3 

74 

114 

115 

98 

PP8X 

2 

7 

97 

PP7A 

64 

96 

PP4 

SEC CENTRAL 

4 

95 

15 

RIYADH AREA 

88 

113 

116 

100 

117 102 101 

118 

AL-KAHARJ AREA 

14 

19 

9 

LAYLA 

Figure 4. SEC 19-Generators System Model. 

5 

1 

20 

10 

October 2006 The Arabian Journal for Science and Engineering, Volume 31, Number 2B 205 

23 

63 

27 

32 31 

PP5 

73 

PP9 

21 

BERI 

112 

47 

87 

26 30 

29 28 

25 

16 

17 

QURAIAH 

18 

56 

24 

52 

86 

111 

53 

54 

83 

GAZLAN 

51 

11 

50 

55 

110 

22 

107 

108 

99 

109 

66 

72 

70 

81 

106 

57 

SEC EAST 

105 

65 

60 

82 

85 84 

48 

45 46 

103 

JSWCC 

NORTH AREA 49 

61 62 

89 92 68 

119 

90 91 

FARAS 

104 

DAMAMAM AREA 

59 

69 

71 

58 

44 

93 

67 

94 

DAMMAM 

SHEDGUM 

SOUTH AREA 

(15)


Table 1. Security/Economy Applications 

# Objective P. Cost (kSR/hr) Energy Margin 

1 Initial Base Case 362.78 3.203 

2 OPF 346.89

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. 



ENERGY MARGIN (UN-NORMALIZED) 

30.0 

25.0 

20.0 

15.0 

10.0 

5.0 

0.0 

SCENARIO I SCENARIO II 

SCENARIO III SCENARIO IV 

-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: 



(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 

6. CONCLUSION 

FAULT FAULT SCENARIO 1 FAULT SCENARIO 2 

SEVERITY HIGH LOW 

RESTORABILITY DIFFICULT EASY 

PROBABILITY HIGH LOW 

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. 



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