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Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
1
CHAPTER X
STATİC SECURİTY CONSTRAİNED OPTİMAL ECONOMİC
DİSPATCH (SSCOED) – AN OVERVİEW
M. EL-Shimy
Professor of electric power systems. Electric power and machines
department, faculty of engineering, Ain Shams university, Cairo, Egypt.
Emails: shimymb@yahoo.com; Mohamed_bekhet@eng.asu.edu.eg;
Phone: +201005639589
Table of Contents
Abstract ................................................................................... 1
Keywords ................................................................................. 2
1. Introduction ......................................................................... 2
2. Effect of load Uncertainty on Power System Operation ... 17
3. Spinning Reserve Requirements ....................................... 18
4. Formulation of the economic dispatch with static security
constraints (SSCOED) .......................................................... 21
5. Solution of the SSCOED .................................................. 26
6. Conclusions ....................................................................... 30
Abstract
Avoiding power interruptions is among the main requirements of
sustainable energy sources. The chapter presents a brief summary of the
security requirements, and operational states of power systems. In
addition, a detailed comparison between the optimization formulations of
the classical OED, OPF, and SSCOED is presented. Linear programming
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
2
is used for solving the linearized formulation of the SSCOED. The
generator scheduling of the IEEE 30 bus system using the SSCOED shows
the capability of the linear programming of solving the considered
problems.
Keywords
Optimal economic dispatch (OED); power system security; security
programmes; contingency analysis; static security constrained optimal
economic dispatch (SSCOED)
1. Introduction
Power system security may be defined as1,2 the continuous ability
of the power system to keep all the system limits not violated with
minimum interruption to the supplied loads. The main target of the power
system security is to keep the system intact under normal and disturbed
conditions. Therefore, the successful security system should minimize the
impact of disturbances on the operation, economics, and power quality of
power systems. In addition, an acceptable system security level guarantees
the immunity of power system to disturbances and makes the system
defensive. Therefore, secure operation of power systems requires the
integration of all practices designed for keeping acceptable system
operation when components fail.
Power system security covers both static and dynamic
phenomena. Therefore, the security analysis is usually categorized to static
1 Wood AJ, Wollenberg BF. Power generation, operation, and control. Canada:
John Wiley & Sons; 2012.
2 Mohamed EL-Shimy: Dynamic Security of Interconnected Electric Power Systems -
Volume 1. 05/2015; Lap Lambert Academic Publishing / Omniscriptum Gmbh & Company
Kg; Germany., ISBN: 978-3-659-71372-9, DOI:10.13140/RG.2.2.19425.71520
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
3
(or adequacy) and dynamic security3,4. The static security considers the
impact of static or slow changes in the system limits while the dynamic
security considers the dynamical impacts of disturbances (or
contingencies) on the system. It is known that the static security studies
are performed by neglecting the dynamical impcats of changes or
disturbances. Consequently, it is assumed that the transients associated
with the motion of the operating conditions from one state to another are
neglected. Therefore, the static security may be considered as a sub-study
of the dynamic security. It is assumed the system transients associated
with disturbances are stable, while the post-disturance steady state
operating conditions are evluated in the static security studies where the
focus on the loading levels, and voltage magnitudes.
Fig. 1: Operational constraints
The core definition of the dynamic security and stability is the
same, but the security is a wider term than stability. The stability is
3 Eremia M, and Shahidehpour M, (eds). Handbook of Electrical Power System
Dynamics: Modeling, Stability, and Control, John Wiley & Sons, Inc., Hoboken,
NJ, USA. 2013.
4 Mohamed EL-Shimy: Dynamic Security of Interconnected Electric Power
Systems - Volume 2: Dynamics and stability of conventional and renewable
energy systems. 11/2015; Lap Lambert Academic Publishing / Omniscriptum
Gmbh & Company Kg; Germany., ISBN: 978-3-659-80714-5,
DOI:10.13140/RG.2.2.36832.07683
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
4
defined as5 “the ability of an electric power system, for a given initial
operating condition, to regain a state of operating equilibrium after being
subjected to a physical disturbance, with most system variables bounded
so that practically the entire system remains intact”; however, “Security
not only includes stability, but also encompasses the integrity of a power
system and assessment of the equilibrium state from the point of view of
overloads, under- or overvoltages and underfrequency”6.
The system limits define the normal operation of power systems.
These limits or constraints can be classified into two categories; the
equality and inequality constraints as illustrated in Fig. 1, while the
definations of the input (or independent) and state (or dependent) variables
are shown in Fig. 2. In addition, the system limits may be classified
according to their origin into intrinsic and operating range limits. The
equality constraints basically represent the load flow equations while the
inequality constraints represent the allowable range of acceptable
operation of various components in the system.
In fact, the intrinsic and operating range limits elaborates the
inequality constraints associated with a specific component. The intrinsic
limits of an equipment are determined basically from the design and
characteristics of the equipment. The operating range limits are generally
less than the intrinsic limits and they are limited by the fulfilment of the
overall operational requirements of the system.
For example, consider a simple hypothetical system where an off-
grid generating plant supplies a load center via a short transmission line
with negligible impedance.The generator is capable of producing a voltage
5 Kundur P, Paserba J, Ajjarapu V, Andersson G, Bose A, Canizares C, et al.
Definition and classification of power system stability IEEE/CIGRE joint task
force on stability terms and definitions. Power Systems, IEEE Transactions on.
2004;19(3):1387-401.
6 Machowski J, Bialek J, Bumby J. Power system dynamics: stability and control:
John Wiley & Sons; 2011.
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
5
magnitude at its terminal in the range 85% - 115% while the load requires
a voltage magnitude in the range 95% - 105%. In this case, the generator
voltage limits present the intrinsic limits of the generator and they are
mostly related to its design. Successful operation requires that the voltage
magnitude at the load bus should not be violated. Therefore, the operating
range limits of the generator bus-voltage magnitude becomes equal to the
load requirements (i.e. 95% - 105%). It is worthy to be mentioned that the
95% - 105% voltage limits present an intrinsic limit as viewed from the
load perspective. It is also important to know that the operating range
limits should not violate the intrinsic limits of any component within a
system. Otherwise, the system will be incapable of fulfilling the
operational requirements.
Both intrinsic and operating range limits are not absolute
constants. The intrinsic capability limits usually decline with time due to
degradation of the equipment. For example, the annual output degradation
rate7 of specific technologies of solar-PV systems is about 0.7%/year. The
degradation may be attributed to the aging, operational stresses, and
maintenance quality. The operating range limits are also variable. For
example, the ampacity (or ampere capacity or current limits) of a cable are
highly dependent on the temperature of its surroundings. The ampacity
limits are usually increased during the winter and decreased during the
summer. This is for avoiding over-temperature of the cable insulation.
Recalling that in the normal operation of a power system, all the
inequality and equality constraints as well as the security constraints of the
system are satisfied. For example, the system security requires a minimum
available, reserve margin (see Fig. 3).
7 EL-Shimy M. Analysis of Levelized Cost of Energy (LCOE) and grid parity for
utility-scale photovoltaic generation systems. 15th International Middle East Power
Systems Conference (MEPCON’12), Dec. 23-25, 2012, Alexandria, Egypt, pp. 1-
7
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
6
(a)
(b)
Fig. 2: Defination of variables. (a) Input variables; (b) state variables
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
7
Fig. 3: Chrnological load curve showing daily load flucations, energy mix
requirements, and the generation reserve8
Again, power system security may be also defined as the ability
of the system to withstand credible contingencies without violating the
normal operation limits. A system operating under normal conditions is
also said to operate in the normal state. The security strength of the system
is usually defined by the maximum number of time-independent, and
simultaneous disconnection of major system components (such as
generators, transformers, and line) without affecting the normal operation
of the system. Defining N as the number of available components
(generation, transmission, and distrubition) to supply and can supply the
8 Mohamed EL-Shimy: Dynamic Security of Interconnected Electric Power
Systems - Volume 1. 05/2015; Lap Lambert Academic Publishing / Omniscriptum
Gmbh & Company Kg; Germany., ISBN: 978-3-659-71372-9,
DOI:10.13140/RG.2.2.19425.71520
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
8
system peak load (see Fig. 3). A system with an N-k security criterion is a
system in which k random components may be simultaneously
disconnected and the system will be able to fulfil the normal state
requirements in the post-contingencies. Due to investment constraints,
power systems are usually designed according to the N-1 security
criterion. The normal state is a secure state and a system operating in the
normal state is said to be intact.
Fig. 4: State transition diagram
Deviations from the normal state requirements cause the system
operation to move to insecure operating states. These deviations are
mainly caused by contingencies which are stochastic and unexpected
events; however, the rate of contingencies may be reduced for example by
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
9
proper maintenance of components. Four insecure operating states can be
realized9. These states are the alert, emergency, extreme (or collapse), and
restoration states. Fig. 4 illustrates the main operational characteristics of
these states, and the interrelations between them. This figure is usually
called the state transition diagram. Table 1 summarizes the characteristics
of various states, some causes of state transitions, and examples of the
corrective actions for each state. The nomenclature used in the table is
illustrated in Fig. 4.
It is worthy to be mentioned here that any intact system is capable
of providing power balance; however, not all intact systems are secure. If
the power balance could not be achieved, then the system becomes not
intact. Consequently, the synchronization of generators upsets. Therefore,
the system frequency protection devices will split the system into parts or
islands; the situation is called islanding and it is within the extreme state.
The frequency and power balance conditions in each island are
different and abnormal. Therefore, system blackout or unintentional
brownout is usually detected. Delay is activating the possible corrective
actions while the system is in the emergency state may be the main cause
of the transition to the extreme state.
Generally, delayed or unsuccessful corrective actions during the
operation in any state may lead to severe consequences. Therefore, any
security programme (Fig. 5) includes a contingency analysis block.
The contingency analysis is an investigative simulation of
hypothesized contingency for evaluating their impact on the system
security. On the other hand, the corrective action analysis is the process of
figuring the possible actions that may be taken for overcoming the
consequences of security upsetting contingencies.
9 Fink LH, Carlsen K. Operating under stress and strain. IEEE Spectrum;(United
States). 1978;15(3).
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
10
Table 1: Summary of operating states and state transitions
State
E
I
N-
1
N
Intact
Causes of
transition from
normal state
Corrective
actions
Normal
-
-
Alert
Constraints are
near their limits.
Examples,
reduction in the
reserve margin
or bus voltage
close to the
limits.
Preventive control.
Examples, startup of
non-spinning reserve
or switching on
compensators
respectively.
Emergency
Severe
disturbances.
Example, short-
circuit faults or
cascaded
ouages.
Emergency control
actions (heroic
measures).
Example: fast fault
isolation or
operation of
reclosers.
Extreme
Delayed or
unsuccessful
emergency
control actions.
Severe power
imbalance.
Heroic and remedial
actions such as load
shedding, generator
trip, or intentional
islanding for
keeping power
balance.
Restoration
Attempt of
restoring the
system to the
normal state or
at least to the
alert state.
Manual or
automated
reinsersion of
generators and
loads. The inequality
constraints should
be kept satisified
during the entire
restoration process.
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
11
Fig. 5: Main functions of a security programme
The corrective action analysis works in two distinct modes. The
first mode operates for solving the problems found by the contingency
analysis. Therefore, this mode is offline while the second mode operates in
real time operation for securing the system during its real-time operation.
The contingency analysis and the corrective action analysis require the
simulation of the system. Therefore, an accurate system model should be
available. In addition, the results obtained from these analyses are highly
dependent on the accuracy of the system model.
Real-time models of a power system require centralized real-time
data collection available from local measuring and monitoring devices at
each system component. Therefore, telemetry is required for
communication within the system and for estimating its state.
In the conventional static security studies, the post-contingency
state is related to the pre-contingency (or the base case) through linear
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
12
senstivity factors (LSF)10,11. These are the generation shift factors, and line
senstivity factors shwon in Fig. 6.
Fig. 6: Linear senstivity factors for continegency analysis
where al,i represents the generation shift factor that relates the change in
the flow on line l (fl) to the change at the generation at bus i (Pi). The
line outage distribution factor dl,k relates the change in the flow on line l
due to the outage of line k. This is also illustrated in Fig. 7. The LSF are
based on the DC power flow model where all the resistances are neglected,
and the voltage magnitudes are assumed constant. Therefore, this approach
10 Wood AJ, Wollenberg BF. Power generation, operation, and control. Canada:
John Wiley & Sons; 2012.
11 EL-Shimy M. Improved Evaluation of ATC with Line-thermal Limits and Bus-
voltage Quality Constraints. Scientific Bulletin - Faculty of Engineering - Ain
Shams Uni. 2005;40(1):619 - 30.
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
13
only accounts for the active power loadings, while the reactive power
effects cannot accurately calculated. In this figure, Xij is the element (i, j)
in the X matrix of the network, while xn is the reactance of line n.
(a)
(b)
Fig. 7: Defination of the LSF. (a) Line outage; (b) Generation shift
As shown in Fig. 6, the post-contingency flow
can be
determined based on the initial base flow (fo) on any line using the LSF.
The post-contingency flow on a line are then compared with the rated flow
on the line for determining the condition of the contingency. If all the
flows are less than or equal to the rated values
, the the
contingencu is safe. Otherwise
, the contingency is unsafe
and the contingency analysis module transfer the found problem(s) to the
corrective action analysis for finding proper corrective actions. İt should
be noted that if
is very close to , then the continegency analysis
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
14
provides an altert of insecure condition. For N-1 static security analysis,
the continegncy analysis id performed according to the flowchart shown in
Fig. 8.
Fig. 8: Continency analysis algorithm
The optimal economic dispatch (OED) is essential for real time
control of power system operation. It is a computational process
whereby the total generation required to be allocated among the
available generating units so that the constraints imposed are satisfied
and the cost of energy requirements to be minimized; however, the
standard OED does not consider the security requirements of power
systems.
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
15
Security of power system12,13 operation has a considerable
influence on the secure economic dispatch problem. The system operator
is responsible for the minute-by-minute control of the system where
several problems arise such as load variations, and component outages.
These include outage of generation, and network components. If the
new system state has any overloaded transmission lines, the system
operator must take appropriate actions to alleviate this problem by, for
example, redispatching the real power generation in the system. The
nonlinear load flow provides power flows and voltages for a new power
system state; however, the nonlinear iterative load flow techniques are
relatively slow and prone to convergence problems. Sensitivity
analysis14 is developed to compute the power flow in each line, the load
voltage and the power generation redispatch as well as quick solution of
the new power system state without the need of recalculations of load
flow and power generation dispatch techniques; see Fig. 6, and 7.
System contingencies should also be considered in the generation
scheduling (or dispatch) for satisfying various secure operational
constraints. A simple example that illustrates the OED and the static
security constrained OED (SSCOED)is shown in Fig. 9.
This chapter presents the fundaments of SSCOED for educational
purposes.
12 Mohamed EL-Shimy: Dynamic Security of Interconnected Electric Power
Systems - Volume 1. 05/2015; Lap Lambert Academic Publishing / Omniscriptum
Gmbh & Company Kg; Germany., ISBN: 978-3-659-71372-9,
DOI:10.13140/RG.2.2.19425.71520
13 El-Shimy M. Dynamic Security of Interconnected Electric Power Systems-
Volume 2: Dynamics and stability of conventional and renewable energy systems.
Lap Lambert Academic Publishing/Omniscriptum Gmbh & Company Kg. 2015
Nov.
14 Wood AJ, Wollenberg BF, Sheblé GB. Power generation, operation, and control.
John Wiley & Sons; 2013 Dec 18.
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
16
(a)
(b)
Fig. 9: Comparison between the impact of contingencies on the
traditional OED, and the SSCOED.
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
17
2. Effect of load Uncertainty on Power System Operation
Since the basic requirement of a power system is to supply
electric power and energy in a secure and economic manner, load
forecasting methods15 have been used to determine the generation
capacity requirements in advance. If the hourly variation in load demand
is not accurately predicted, the actual demand may be either greater or
less than the predicted values. For a greater demand than its predicted
value, the new system state exists which may include overloaded
components, such as generators or lines. In addition, there are
possibilities of voltage magnitude problems, such as over-voltage, or
under-voltage as well as under-frequency problems. Therefore, there is
a necessity of generation reserve to be in service quickly for avoiding
service interruption.
The reserve in this case in very expensive and its amount is
limited. On the other hand, if the demand value is than its predicted
value, there will be a surplus of power reserve which results in an
increase in the operating cost, and possible over-frequency problems. As
a result, the capability of accurately predicating the system load several
hours in advance is essential for secure operation, and correct economic
scheduling of power generation.
A precise short term load forecasting is essentially for
monitoring and controlling power system operation. Short-term load
forecasting deals with the hourly load forecast for few hours in advance.
It can be mainly divided according to the time frame to:
15 Hahn H, Meyer-Nieberg S, Pickl S. Electric load forecasting methods: Tools for
decision making. European journal of operational research. 2009 Dec
16;199(3):902-7.
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
18
1. Hourly load forecast: the hourly forecast of load demand is
necessary for on-line operation and control of the power
system.
2. Four hour load forecast: Forecasting the system load 4-hours
ahead or less is needed for the economical load dispatch and for
real time state monitoring and security programs.
3. One day ahead load forecast: the 24-hours ahead load
forecasting is desired for the system generation policy during
the base and peak load intervals and for the provisions of power
reserve.
Decreasing the loss of economy is of the most important
functions of electric utilities. This depends mainly on the accuracy
of load forecasting models and accurate state monitoring. In
addition, the errors in the forecasted loads specially underestimating
the actual load may result in a breach of system security function
since the system risk may exceed the specific value agreed upon for
secure operation. Since, economy, security and reliability are
affected by the load forecast uncertainties, the economical reliability
level is also affect by the accuracy of load forecasting.
3. Spinning Reserve Requirements
As shown in Fig. 3, it is required that a power system at all
times operates an amount of generating capability in excess of its actual
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
19
demand, which is available within a specified interval of time sufficient
to cover the unscheduled loss of generating equipment, or any
unexpected deviation of this demand from the anticipated levels. The
power reserve can be classified16,17,18 as shown in Fig. 10 and Table 2.
Fig. 10: Classification of power reserve
16 Towne HW, inventor; AT&T Corp, assignee. Alternating current power reserve
system. United States patent US 1,951,482. 1934 Mar 20.
17 Frunt J, Kling WL, Myrzik JM. Classification of reserve capacity in future
power systems. In2009 6th International Conference on the European Energy
Market 2009 May 27 (pp. 1-6). IEEE
18 Frunt J, Kling WL, Van den Bosch PP. Classification and quantification of
reserve requirements for balancing. Electric Power Systems Research. 2010 Dec
1;80(12):1528-34.
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
20
Table 2: Spinning reserve classification
Reserve
type
Duration
Description
Momentary
Mean access time to
fast reserve (EZ1= 1
to10 min)
The momentary power reserve is the
result capacity of primary governor
action of all interconnected units of
all partner systems.
Fast
Mean access time to
the slow reserve
(EZ2 = 0.5 to 8
hours)
It is the total power of a number of
generating unite operated at
minimum or on-load conditions.
These units are mainly gas turbine,
pumped storage and hydro units.
Slow
Operates till the end
of the repair time.
The mean repair
time (ET) equals to
30 to 250 hours
It is the total power of a number of
generating units operated when
required. These units are mainly
thermal units
Fig. 10 shows the reserve application procedure after an outage of a
generating unit. The power deficiency for the first few minutes after an outage
is covered by the momentary reserve of all partners of the interconnection
system. This is provided by the primary governor action of all operating units.
Within a short time (1-10) minutes it is needed to cover the power deficiency
by the fast reserve. So, a fast reserve with a mean access time of (1-10)
minutes should be available. The previous types of reserve should be replaced
by the fast reserve as soon as possible (on the average this takes about 0.5 to 8
hours). This because the operating cost of the fast reserve is significantly
expensive with respect to the slow reserve. In addition, the fast reserve has a
limited capacity and it should also be available for any upcoming random
contingencies that cause power deficiencies.
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
21
4. Formulation of the economic dispatch with static
security constraints (SSCOED)
The popular formulation of the Optimal Economic Dispatch
(OED) is given as:
minimize
n
i
ii PCC
1
)(
the objective function (1)
subjected to:
0)(
1
iLD
n
i
iPPPP
equality (or power balance) constraint (2)
maxmin iii PPP
ınequality (or generator limlits) constraints (3)
where C is the total cost function of the committed generating units in
$/h, Ci(Pi) of the cost function of the generating unit number i, n is the
number of committed generating units, Pi is the net power output of unit I
in MW, PD is the power demand in MW, PL(Pi) is the power loss in MW,
Pimax is the maximum net output power of generating unit i, and Pimin is
the minimum net output power of generating unit i.
This classical formulation did not take into account the
operational and security requirements (see Fig. 1, 2, Table1, and Fig. 10).
Therefore, it cannot provide generation allocation (or scheduling) that
ensure secure operation of the power system; however, it provide the
allocation of generators for minimum costs19. Extension to this
19 Wood AJ, Wollenberg BF. Power generation, operation, and control. Canada:
John Wiley & Sons; 2012
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
22
formulation can take into consideration the intrinsic as well as the
operational limits, and minimization of the GHG emissions20, but again
the security requirements cannot be guaranteed.
The operation cost function of conventional units (thermal, and
hydro) takes the approximate quadratic function form21,
Ci (Pi) = i + i Pi + i Pi2 $/hr (4)
Therefore, the initial operating point (Pio) obtained from the classical
OED results in the initial cost,
This operating point has to be modified for considering the operational
and security requirements of the system i.e. the solution obtained from the
classical OED is considered as the initial guess for the SSCOED. For
simplification, the common factor cost function is used in the following
formulations for the SSCOED.
or
20 A. N. Afandi, A. P. Wibawa, SyaaPadmantara, Goro Fujita, W. Triyana, Yunis
Sulistyorini, H. Miyauchi, Nedim Tutkun, M. EL-Shimy Mahmoud, X. Z. Gao,
"Designed Operating Approach of Economic Dispatch for Java Bali Power Grid
Areas Considered Wind Energy and Pollutant Emission Optimized Using
Thunderstorm Algorithm Based on Forward Cloud Charge Mechanism",
International Review of Electrical Engineering (IREE), Vol 13, No 1 (2018). DOI:
https://doi.org/10.15866/iree.v13i1.14687
21 Stevenson WD. Elements of power system analysis. New York: Mcgraw-hill;
1982 Jan.
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
23
where
This form of the cost function is linearized because the SSCOED
constitutes a non-linear programming problem with convergence
difficulties if the non-linear cost functions are adopted.
Static Security Constraints Optimal Economical Dispatch
(SSCOED) is a computational process whereby the total generation
required is allocated among the available generating units so that the
constraints imposed are satisfied and the objective cost function is
minimized i.e. its formulation takes the form of equations (8) to (??)
simultaneously.
The system total power generation should meet the system load
demand and network transmission losses
The generator output power must be within its maximum and
minimum generation limits
The generating units cannot ramp their output instantaneously, but
takes a specified time () to meet the load demand. Therefore, the
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
24
ramping capabilities of generating units are constraints that have to
be met in following the load changes. The range of actual operation
of online generating unit is restricted by its ramp rate limits22 as
shown in equation (11).
(a)
(b)
Fig. 11: Ramp rate limit constrains. (a) Increased demand; (b) Reduced
demand
22 Benhamida F, Ziane I, Souag S, Salhi Y, Dehiba B. A quadratic programming
optimization for dynamic economic load dispatch: Comparison with GAMS. In3rd
International Conference on Systems and Control 2013 Oct 29 (pp. 625-630).
IEEE.
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
25
These limits have impacts on the operation and maneuverability of
generating units. In other words, the power schedule of a given unit
in a given hour is affected by the previous hour schedule of the same
unit and affects the upcoming hour schedule. This is due to the ramp
rate limit.
where PDi is the ramp rate limit of generating unit i to meet load
reduction; PUi is the ramp rate limit of generating unit i to meet load
increase; Pi(t) is the output power of generating unit i at time step t. This
constraint is explained in Fig. 11 considering linearized ramp rate
characteristics, which is valid for small deviations of the output power.
Among the main constraints is to maintain the power flow in each
line of the transmission network to be within specified limits.
Therefore, the active power flow on a transmission link k is PTk, and
then
It can be seen from Fig. 6 that the LSF can be used to linearly link the
change in the flow on a specific line l with either the change in the power
generation at bus i, or the change of the power flow on another line. These
LSF will be used in evaluating the impacts of the change of the power
generation schedule from the initial values (obtained from the OED) for
security reasons. Till this point, the classical OED is now formulated as
an optimal power flow (OPF) problem. The following additional
constraints present the spinning reserve constraints for security
requirements. The spinning reserve constraints can be written as,
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
26
where
the minimum allowable value of total required spinning
reserve ;
the maximum available spinning reserve that can be
contributed from unit i in less than or equal to 10 minutes when the
system operates in the emergency state; Yi is the amount of spare capacity
of the unit i that is unavailable due to, for example, bad weather
conditions, or low state of health.
5. Solution of the SSCOED
Fig. 12 shows of the linear programming iterative approach for
solving the considered problem. The presented example is not a complete
solution of the SSCOED formulation and its objective is only the
demonstration of the differences between OED, OPF, and SSCOED
problems. For simplification and due to the incomplete required data, the
ramp rate limits of equation (11) are neglected, while the output power
limits are considered i.e. . The consideration of the
constraints of equation (11) converts the OED, OPF, and SSCOED to
dynamic problems as the time is included.
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
27
Fig. 12: Solution algorithm of the SSCOED
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
28
The presented algorithm23 is applied to the IEEE 30 bus system shown in
Fig. 13 with a total load of 296.28 MW, and the losses are neglected for
demonstration purpose of the method. The results are shown in Table 3.
The change in the power schedule due to the application of the SSCOED
w.r.t the OPF is shown in Fig. 14. The load flow results ensure the
satisfaction of the operational and internsic limits, while the contingency
analysis ensures the satisfaction of the spinning reserve requirements and
security constraints.
Fig. 13: IEEE 30 bus test system
23 http://www.fglongatt.org/Test_Systems/IEEE_30bus.html
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
29
Table 3: OED, OPF, and SSCOED of the IEEE 30 bus system
i
Initial OED
SSCOED iterations
1
2
3
1
138.28
152.48
152.48
152.48
2
56.56
65.56
49.56
65.56
3
24.1
17.06
32.06
17.06
4
35
35.00
31.41
31.41
5
26.15
13.43
13.43
17.77
6
16.19
12.75
17.34
12.00
Total Gen. (MW)
296.28
296.28
296.28
296.28
Total cost ($/h)
822.12
832.80
824.47
Fig. 14: Change of the power schedule of the SSCOED w.r.t the OPF
Static security constrained optimal economic dispatch (SSCOED) – an overview.
M. EL-Shimy
30
6. Conclusions
It is essentially important for system secure operation to not only
considers the operational and intrinsic limits for enhancing the scheduling
obtained from the classical OED problem, but security constraints must
be considered. This chapter presents a linearized SSCOED and the
formulation is solved using the linear programming.
The results show that efficiency of the method for fulfilling all
the constraints under normal and abnormal states of power systems.
