International Journal of Engineering Trends and Technology (IJETT) – Volume 8 Number 7- Feb 2014
Optimization Based on Reactive Power in Frequency
AC Generating System
T.Yuvaraja1, Somnath Mazumder2, Dr.M.Gopinath,3
1
Research Scholar, & Department of EEE, Meenakshi Academy of Higher Education & Research, Chennai, India,
2
Lecturer, & Department of ECE, Shirdi Sai Engineering College, Bangalore, India,
3
Professor, & Department of EEE, Dr.N.G.P. Institute of Technology, Coimbatore, India,
Abstract— This approach calls for the nonlinear fore bay level,
tailrace level, penstock loss, and hydropower production functions to
be replaced with their piecewise linear approximations. In this
generating system, the power winding produces the VFAC electricity
to feed loads, and the control winding is connected to a static
excitation converter to keep the output voltage stable. Based on the
change law of the reactive power provided by the control winding, an
improved instantaneous slip frequency control strategy both with the
load active and reactive power feed forward is proposed to improve
the system dynamic performance. However, the effects of the
linearization of the nonlinear functions and related constraints on
solution feasibility have not been fully discussed in the literature. The
information of the load active and reactive power is employed
through two feed forward loops to rapidly change the reactive power
provided by the control winding, so as to quicken the regulation of
the slip frequency and excitation reactive power. The simulations
show that the system using the strategy has a good dynamic
performance with inductive and capacitive loads, and demonstrate
the correctness and validity of the proposed control strategy.
I. INTRODUCTION
The past four decades, computer scientists have systematically
developed theories of correctness and safety in different aspects,
such as methodologies, techniques, and even automatic tools for
correctness and safety verification of computer systems (see, for
example, [1], [5], [11]. Of these, model checking has been
established as one of the most effective automated techniques to
analyze correctness of software and hardware designs [2], [5]. A
model checker checks a finite-state system against a correctness
property that is expressed in a propositional temporal logic such as
linear temporal logic (LTL) or computation tree logic (CTL).
These logics can express safety (e.g., no two processes can be in
the critical section at the same time) and levelness (e.g., every job
sent to the printer will eventually print) properties [1], [10]–[12].
Model checking has been effectively applied to reasoning about
correctness of hardware, communication protocols, software
requirements, etc.
Many industrial model checkers have been developed,
including Simple Promela Interpreter (SPIN) [8] and Symbolic
Model Verifier (SMV). Whereas model-checking techniques
focus on the absolute guarantee of correctness—it is
impossible that the system fails in practice, such rigid notions
are hard, or even impossible, to guarantee. Instead, systems
are subject to various phenomena of an uncertainty nature,
such as message incomplete or garbling and the like, and
correctness—with 99% chance the system will not fail or the
system will not fail most often—is becoming less absolute. To
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handle with the systematic verification which has something
to do with uncertainties in probability, Hart Sharir [7]
investigated the logic of timing sequence in probability
propositions and applied probability theory to model checking
in which the uncertainty is modelled by probability measure.
Baier and Katoen [2] systematically introduced the principle
and method of model checking based on probability.
Fig.1 Frequency voltage controlling system
This will measure and related applications with Markov
chain models for probability systems. On the other hand, since
Zadeh proposed the theory of fuzzy sets in 1965, many
scholars have been devoting themselves to the research in this
theory and its applications. As a branch of the theory of fuzzy
sets, possibility measure (more general, fuzzy measure is a
development of classical measure, which focuses on non
additive cases (cf., [9] and that are different from the cases
focused by probability measure which is additive.
Most problems in real situations are complicated and non
additive. As a matter of fact, fuzziness seems to pervade most
human perception and thinking processes as noted by Zadeh,
especially modelling human-centred systems, for example,
biomedical systems [16], criminal trial systems, decisionmaking systems [6], and linguistic quantifiers. Therefore, it is
necessary to do some research work in the theory and
applications of model checking on nondeterministic systems
of no additive measure, especially, fuzzy measure. In addition,
this paper attempts to initiate an LTL model checking that is
based on possibility measure. In this paper, the notion of the
possibility Kripke structure is introduced by combining the
system with fuzzy uncertainty, and then a possibility measure
is induced by the given possibility Kripke structure.
Linear-time properties specify the traces that a possibility
Kripke structure should exhibit. Informally speaking, one could
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International Journal of Engineering Trends and Technology (IJETT) – Volume 8 Number 7- Feb 2014
say that a linear-time property specifies the admissible (or 1.2 Variable-Size External Repositor
desired) behaviour of the system under consideration. In the
following, we provide a formal definition of such properties.
The external repository is a bounded elite archive used for
This definition is rather elementary and gives an example of preserving the non dominated solutions found along the search
what a linear-time property is. In particular, the possibilities of process. After the initialization of each searching group, the
model checking of reach ability and repeat reach ability are initial repository is determined by the non dominated members
studied, which can be proceeded by solving certain fuzzy obtained in the initial population. For each iterative step of the
relation.
MGSO algorithm, each non dominated individual obtained in
the new generation of the population is checked for dominance
with the solutions in the current repository. The following is
the dominance comparison strategy adopted for updating the
archive:
1) In case the new solution obtained is infeasible or
dominated by other members in the population, the solution
will not be saved into the repository.
2) If a non dominated member in the population cannot be
dominated by any solution in the current repository, the
solution will be saved into the repository.
3) Any dominated solution in the current repository by this
non dominated member will be removed from the repository.
Though a large-size memory of the elite repository tends to
represent the better characteristics of the PF, it would lead to
explosion in the computational burden due to the dominance
comparisons [8]. Therefore, the number of PF solutions saved
in the repository, i.e., the size of the PF, should be limited. In
this paper, a variable-size external repository, which can be
resized on demand, is adopted.
After each iterative step of the algorithm, the repository
will be resized to cover the entire non dominated set, including
new non dominated members and the survival solutions in the
repository. The resized repository could further be shrunk if
the hierarchical clustering was adopted. In (4)–(10), Im is rms
value of the excitation current; Ic(L) and Ic(C) are the rms
values of the control winding current for the inductive load
and the capacitive load, respectively; Ipc is rms value of the
Fig. 2 Systematic Voltage Stability Calculation
auxiliary excitation capacitor current; Ip and Ir are rms values
of the power winding current and the rotor current,
1.1 Algorithm Framework
respectively; ILp and ILq are the rms values of the active and
reactive currents of the load, respectively; Em is the rms value
In the proposed MGSO, various stochastic global searching of the back EMF; Up is the rms value of the power winding
and probability selection techniques have been integrated for voltage; Rp,Rc , and Rr are the equivalent resistances of the
different types of swarm members. Firstly, the population of power winding, the control winding, and the rotor,
MGSO consists of multiple searching groups, and each group is respectively; Xm is the magnetization reactance;Xlp andXlr are
designed based on producer-scrounger model [18] for each the leakage reactance of the power winding and the rotor,
objective of the MOPD problem. For each searching group, respectively; P is the real power transmitted for the rotor to the
there are four categories of swarm members for four different stator; ω is the angular synchronous frequency; s is the slip.
searching strategies as follows:
Using (9) and (10), the control winding reactive current under
1) Producer: this member is designated to the member different speeds and loads can be calculated. Because the
conferring the best single-objective fitness for each iteration, control winding current phasor and the excitation current
and it is the group leader which has a critical impact on the phasor is the same or opposite, the calculation results from (9)
overall searching direction of the group.
and (10) actually has indicated the situation of the reactive
2) Scroungers: except for the producer, 80% of the remaining power provided by the control winding.
feasible members are selected randomly as scroungers which
If the calculation result is positive, the control winding
constitute the main searching force in the algorithm. Thus, the
should supply some inductive reactive power for the DWIG.
update policy of this swarm should take all the objectives into
At this time, the SEC on the control-winding side is
account through social cooperative mechanism among groups.
equivalent to a capacitor, and plays a role in excitation. The
3) Rangers: the remaining feasible members in the group are
larger the calculation result is, the more inductive reactive
rangers, and they can move in an unpredictable dispersion to
power the control winding provides. If the calculation result
discover resource globally.
is negative, the control winding should provide some
4) Infeasible members: the update policy of this swarm
capacitive reactive power for the DWIG. At this moment,
should be a constraint satisfaction process for handling the
the SEC on the control-winding side is equivalent to an
complex constraints. Also, every individual in the
inductance, and plays a role in demagnetization.
population has a current position
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International Journal of Engineering Trends and Technology (IJETT) – Volume 8 Number 7- Feb 2014
The smaller the calculation result is, the more capacitive approach. Several demonstrators have been realized for the
reactive power the control winding provides. The 13-point different modelling approaches. Table I gives an overview of
linearization technique is applied by employing the procedure the state of the art.
presented in Section II-C. Hence, 13 steady-state operating
points are determined under 13 different output power
conditions of wind generation. The values of stability indices (x1.4 Objective
axis) and their sensitivities with respect to the firs wind power
output (y-axis) are calculated at each steady-stat operating point
This work is dedicated to AC emulation, the most recent
by deterministic analysis and plotted in Fig.3 as an example. It power emulation approach. As an extension of the author’s
can be seen from Fig. 3 that the sensitivity of stability indices previous work, the first hardware demonstrator is presented.
has a noticeable change with the increase of wind power
At this early stage of development, we focused on the
penetration level. This explains that the conventional method speed aspect. Thus, the scope is to prove the high-speed
based on one-point linearization may not provide accurate capabilities of AC emulation with simple models, in fact, the
result.
models used at the beginning of power system simulation
development. This permits to clearly separate microelectronic
influences and power system theory aspects leading to
precious conclusions for going a step further with less
implementation risks.
This paper is divided into 7 sections: general approach to
keep the modularity of analog emulators, general description
of AC emulation emphasizing the differences between the two
emulation approaches, specific description of the first AC
demonstrator, behavioural model validation, microelectronic
implementation with scaling issues, results of hardware testing
and conclusion.
II. FLEXIBILITY
Fig. 3 Linearized Stability Analysis
1.3 State of the Art
Currently, three different implementations of power system
dynamic simulation using analog emulation are under
development. Their progress can be found in the literature [4]–
[11]. These implementations are based on two different
modelling approaches called “Phasor emulation approach” and
“AC emulation approach”, respectively. The Phasor emulation
approach [1], [4]–[7] is based on a mathematical representation
of the grid. It uses a complex representation of voltages and
currents in the grid. Two isolated and resistive networks are thus
realized in order to emulate separately the real and imaginary
part of the grid’s current and voltages.
It provides the downscaled envelopes of the real power
system signals. The power grid is implemented with analog
components, whereas the generator and load models can be
implemented using purely analog, mixed or purely
numerical implementations. AC emulation [8]–[11] is
instead based on a one-to-one mapping of the components
of the real power system by emulating their behaviour on
dedicated analog (micro)-electronics.
Frequency dependence of the elements is preserved and the
signals propagating on the emulated grid are the shrunk and
downscaled current and voltage waves (AC signals) of the real
power system. As such, this approach is termed AC emulation
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One main consideration for simulators is their modularity.
Analog emulation approaches are often seen as too rigid
compared to numerical simulators. Indeed, in numerical
simulators, the topologies, the characteristic of the elements
and the models used to characterize the different power system
components can simply be changed through the software. No
hardware changes are needed. The authors developed a
concept called Field Programmable Power Network System
(FPPNS) [12] in order to enhance the flexibility of antilog
emulation approaches.
The concept is based on an array of reconfigurable basic
blocks called power system Atoms (PSA). Each PSA is
composed of the basic elements of a power system. Hence it
contains at least a generator model (GM), a load model (LM)
and some analog transmission line models. The analog
transmission lines are used to interconnect the atoms. Fig. 2
shows a possible PSA topology. Each element of a PSA is not
only reprogrammable but is also equipped with switches.
Therefore it is possible to emulate different power system
topologies and scenarios without changing the hardware. A
possible PSA array is depicted in Fig.2. It includes PSA atoms
connected through their transmission lines and a
communication bus A user flow example is depicted in Fig. 3.
The power system topology under investigation and the
system parameters are set through the UI (i.e., a personal
computer). This information is then converted into the
corresponding emulated network parameters and transmitted to
the PSA array through the communication bus.
Once the initial values are set, the operating point of the
network (known as the steady state of the power system) is
automatically reached and the system is ready to emulate the
response of the power system to a particular perturbation event
data is extracted and evaluated on-chip.
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Therefore, only a limited amount of information has to be
depends entirely on the implementation of the generator and
sampled and transmitted to the UI for monitoring. With such
load models. Pure analog implementations are thus more rigid
an approach, the flexibility of emulation becomes
in terms of models than mixed-signal implementations such as
comparable to the flexibility of numerical simulators in term
proposed.
of topology and configurability of the elements.
The authors are aware of the fact that FPPNS does not
guarantee the flexibility in terms of models. This flexibility
Fig. 4 Output Voltage and Resistance of OTA
2.1 Optimization Model Formulation Concept
Phase emulation provides the downscaled envelopes of the
real power system signals. Frequency dependence of the
elements is thus lost. AC emulation aims to keep frequency
dependence of the elements. Theoretically, it becomes possible
to simultaneously analyze various types of stabilities with
different time constants after the occurrence of a contingency.
Practically, of course, this depends additionally on the models
that are implemented. A high-speed, multiple-phenomena-inone simulator would be a very powerful tool for upcoming
power system challenges which could be achieved using AC
emulation. While large-scale PEVs can bring significant
benefits, there are costs in the coordination of PEV charging
and discharging. The cost-benefit analysis (CBA) of a
coordination strategy for the optimal coordination of large scale
PEV charging and discharging is crucial for power system
planning or supporting PEV-related decision or policy making.
In this section, we present how to calculate the benefits and
costs of a coordination strategy for optimal control of charging
states of large scale PEVs as a part of power system planning
from a social welfare perspective.
Some assumptions are made based on the Similar to the
benefits, we conduct the cost calculation in CBA as a part of
power system planning with a focus on social welfare. The
costs that can be incurred in implementing a coordination
strategy for large scale PEVs in a power grid come from
various aspects, as shown in Table II. The method of
calculating the costs is concerned with the costs of
construction, maintenance, and the upgrade of the
charging/discharging infrastructure, including the control
systems and the cost of energy consumed for the
coordination of PEV charging and discharging.
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The annual cost, denoted by , is composed of a fixed annual
cost for the building and maintenance of the infrastructure, such
as the power electronic devices, the communication systems and
IT devices, and a variable cost resulting from energy loss and
battery degradation.
III FORMULATION
The key question addressed by the formulation is how to
optimally invest in capacity enhancement to mitigate seismic
risk on power networks. We measure the performance of the
power network as the sum of the power generating costs and
load shed costs under a set of consequence scenarios, that model
the seismic hazard in the region and vulnerability of the network
to that hazard.
The electric power transmission system investment planning
model is formulated as a two-stage stochastic program. A two
stage stochastic program is an optimization model formulation
that incorporates uncertainty in the parameters of the model. The
two-stage structure assumes that all decisions are made at one
time instant prior to the resolution of all uncertainty. In this case,
the uncertainty revolves around what damage will occur to each
component in the electric power system.
This uncertainty is expressed through the use of a
number of consequence scenarios, where each consequence
scenario gives the damage to each component. The
decisions are made in what is termed the “first-stage” of the
model. In our formulation, the first-stage is the
identification of what components in the electric power
system should be enhanced. The consequences of those
decisions, under each consequence scenario, occur in the
“second-stage” of the model. In this problem formulation,
the second-stage is the power flow across each component
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International Journal of Engineering Trends and Technology (IJETT) – Volume 8 Number 7- Feb 2014
including what demands for power are not satisfied under
transformers is 6 months. For low voltage transformers, we
each consequence scenario.
assume that the operator would have access to spares within a
We first introduce the topology of the power network. Let D month.
be the set of transmission lines. Let be the set of substations. Let
be the set of generators. Let be the set of buses. Let be the set of
3.2 Small Signal Rotational Angle
generators connected to bus . We define the first-stage binary
decision variables as follows. Let take integer values 0, 1 or 2
Therefore, all the components in substations under complete
representing the number of capacity increments to add to the damage are back to normal within a month with the exception of
capacity of power generator. The cost to add a discrete medium and high voltage transformers which is 6 months. For
increment to the existing capacity of generator.
transmission lines we only model two levels of damage:
Let take integer values from 0 to 4 representing the number extensive and complete. Extensive damage for a transmission
of increments to add to the transmission capacity for line The line corresponds to a damage ratio of 50% of the total cost of the
cost to add a discrete capacity increment to the existing capacity line and complete damage results in costs totalling the full cost
of transmission line is . We assume that the total available of the line. Transmission lines under extensive damage can be
budget for transmission capacity and power generation repaired within 3 days and under complete damage within a
enhancement is . Since the total investments to add capacity to week. This implies that by the end of 6 months, in the worst
the components cannot exceed the available budget, In practice, case, the system is back to normal. The analysis focuses on
transmission line and generation enhancement increment units damage to transformers not damage to other substation
and maximums are specific to each component.
components because transformers typically drive the restoration
When available, the proposed model can be easily adjusted to process due to their long repair lead-times.
include the specific incremental units for each component. In
The analysis does not include damage to generators because
the absence of the exact information we propose to use the total they generally perform better than the rest of components in
component’s capacity as reference to the incremental unit. The power networks. From a modelling perspective, this implies that
percentage of the capacity and maximum capacity to add for the repair process is composed of 4 time periods. The first period
transmission lines and generators were selected to reflect the extends from the event to the end of the third day. By then
sense that there are more variations in the transmission line transmission lines that have experienced extensive damage have
upgrade. Transmission line enhancement is modelled as discrete been restored. Also, substations under moderate damage have
increments of a quarter of total original capacity of the line.
been repaired. The second time period extends from the
beginning of day four to the end of the first week.
3.1 Voltage Buffer
By then transmission lines that have experienced complete
damage have been repaired as well as substations under
Generation enhancement is modelled as discrete increments extensive damage. The third time period extends from the end of
of a fifth of initial capacity. The cost of the enhancement is the first week to the end of the first month. By the end of this
modelled as a percentage of the total cost of the line or time period, low voltage transformers will have been replaced.
generator. Capital costs and operational unit cost of generation The final time period extends from one month to six months. Six
unit were obtained from [20]. Line capacity enhancement costs months after the event, medium and large voltage transformers
were extracted from [21]. All the costs were converted to 2002 will have been replaced.
U.S. dollars and adjusted to make them consistent among
The following notation encapsulates these time period
sources. Requiring the enhancements to be discrete is more definitions. Let, days, week, month, and months, then is the time
widely representative of practically feasible upgrades such as length in days of period. It is important to observe that the
re-conduct ring, changes in operational limits with improved uncertainty in the repair times could have been integrated into
coordination or controls, or adding another generating unit.
the scenario definitions. This would likely lead to more than four
Based on the HAZUS seismic risk assessment
time periods.
methodology [19], five damage states are defined for
electric power components: none, minor, moderate,
3.3 A & B System
extensive and complete. Of those five, we disregard minor
because the damage is not significant in this context.
The second approach, referred to as the introduces some
Moderate damage generates a repair cost of 40% of
approximation. In fact, many solvers are built on a compromise
substation cost and does not affect any of the transformers in
between speed and accuracy. In stability studies, even the
the substation. Extensive damage is assumed to imply
integrated scheme with small time steps but too demanding
damages costing 70% of the value of the substation
electromagnetic transient simulation. A similar trade off is
including impacting 50% of the transformers in the
accepted when resorting to dynamic equivalents. The localized
substation.
Newton scheme presented in this paper exploits the fact that, in a
Complete damage causes the complete loss of the substation
large-scale system, many components have little participation in
including all the transformers. presents restoration curves for
the dynamic response and hence can be replaced by a less
substations, lines and generators for different damage stages
demanding simplified model.
[19]. The mean time for repair is 3 days for moderate damage
and a week for extensive damage. For substation restoration
That replacement is controlled by a single tolerance
under complete damage, the mean value is 30 days; however,
parameter. The computational effort is thus localized on the
repairs can vary depending on the difficulty with which some
components with significant response. The BBD structure is
components such as transformers can be replaced. We assume
further exploited to this purpose. Localization concepts have
that the average lead-time for medium and high voltage
been used in time-domain simulation in the multi rate method
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International Journal of Engineering Trends and Technology (IJETT) – Volume 8 Number 7- Feb 2014
[12]. They have been also applied to static security analysis
to two buses, such as HVDC links, TCSCs, etc. is
[13]. Similar techniques have been used in the simulation of
considered.
VLSI circuits [14], where components little affected by a
The state vector and the matrix can be split into and , relative
disturbance are called latent.
to the th injector. Without loss of generality, it is assumed that
the first two (out of ) components of are and , the rectangular
components of the complex current injected into the network,
The idea behind localization is to detect injectors with low
dynamic activity (classified as latent) and replace their original
models with much simpler mathematical relations. The rest of
the injectors (classified as active) continue being solved without
approximation. The resulting algorithm is referred.
3.4 Newton scheme.
Fig. 5 Integrated Scheme of Transmission
Equation (4) has a structure that reflects the physical
structure of the system, i.e., a set of injectors interacting
through the network only, as illustrated in Fig. 1. In this
paper, the term “injector” designates any equipment
connected to the network, such as a synchronous machine
with its controllers, an induction motor, a dynamic or static
load, or a static var compensator. The generic model
considered hereafter is illustrated in an example in
Appendix B, while the extension to components connected
Thus, an active injector is solved with the same accuracy as in
a detailed simulation. The techniques detailed in Section IV-B
apply to those injectors and allow performing less iterations on
injectors with lower dynamic response. For a latent injector, on
the other hand, (13) are not solved at all. Its vector is even not
computed.
Fig. 6 Probabilistic Measurement on Switching Frequency
IV Identifying Latent Injectors
Which injectors are latent and which ones are active
cannot be decided a priori because it depends on the
simulated disturbance. Furthermore, an injector may change
from active to latent after some transients have died out and
then switch back to active under the effect of the system
evolving. The linearization instant is defined as the last time
the injector changed from active to latent. At the beginning
of the simulation, is initialized to zero for all injectors. After
extensive tests, the following latency identification rules
were found the most satisfactory by the authors.
1) For a “probationary” period after the initial
disturbance, all
injectors are active, in order to
collect information about their level of dynamic activity.
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2) At the end of each time step, say at time : an injector
switches from active to latent if its current components have not
changed by more than a threshold.
In this paper, we studied several important possibility
measures of LT properties and LTL formulas corresponding to
them. Concretely, we introduced the notions of LT properties;
several particular LT properties such as reach ability and
repeatedly reach ability were introduced. More generally, LT
properties such as regular safety properties and regular
properties using automata theory were studied.
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[16] Y. Hu, L. Zhang, W. Huang, and F. Bu, “A fault-tolerant
V Conclusion
This model checking that is based on possibility measure and
fuzzy measure extension of classical model checking. emulators
aim to complete nowadays high-performance and highprecision numerical simulators by proposing solutions to their
speed, cost and size bottlenecks. Such high spec emulators
would certainly contribute to the operation security of the
emerging Smart Grids. Moreover, the here presented work has
shown that the AC emulation approach is ready to b
implemented as FPPNS to go a step further and prove the
suitability of such simulator for large-scale topologies Both the
possibilistic and probabilistic model checking solve certain
uncertainty of error or other stochastic behaviour occurring in
various real-world applications. This paper presents the
successful achievement of the first step in the development of a
large-scale, multi-phenomena, high-speed power system
simulator based on AC emulation.
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