Paper Code: 01A8
Security Constrained Unit Commitment in Deregulated Power Systems by Seeker Optimization Algorithm Sahar S.Kaddah
Ragab A. El Sehiemy
Electrical Power& Machines Engineering, Department University of Mansoura, Egypt
[email protected]
Alaa A. Zaky
Electrical Engineering Department University of Kafrelshiekh, Egypt
[email protected];
[email protected] that minimizes the commitment and dispatch costs of meeting the forecast system load, taking into account various physical, inter-temporal constraints for generating resources, transmission, and system reliability requirements[8-12] . During the normal real-time operation, system operator dispatches the committed generation resources to satisfy the actual demand and reliability requirements. In the event that the actual system condition significantly deviates from the expected condition in emergency situation, system operator needs to take certain corrective actions such as committing expensive fast-start generator or load shedding in emergency
Abstract - Security constrained unit commitment (SCUC) is becoming a strategic scheming in modern deregulated electric energy markets. This calculation extends the conventional unit commitment (UC) problem to incorporating the power transmission network constraints for pre- and post-contingency operating conditions. Such constraints complicate the problem considerably, and much work remains to be done to implement them satisfactorily. This paper concerns with solving the SCUC problem using the seeker optimization algorithm at normal and abnormal operating conditions. Abnormal (Emergency) operating conditions may occur due to increased power transactions and continuing postponement of transmission reinforcements. The SCUC is solved considering the transmission losses. Different case studies are employed to show the capability of the proposed procedure. .
situation to maintain system security. In this paper, the main causes of the unexpected events come from the uncertainties associated with the load forecast error, changes of system interchange schedules, generator’s failure to follow dispatch signals, and unexpected transmission and generation outages . In recent years, higher penetration of renewable energy resources (such as wind power, solar power, and distributed generators) and more price-responsive demand participation have posed new challenges to the unit commitment process, especially in the independent system operator (ISO) managed electricity markets. It becomes important for the ISOs to have an effective methodology that produces efficient unit commitment decisions that ensure the system reliability in the presence of increasing real-time uncertainty[13-17]. Recent developments in restructured electric power systems provide an opportunity for electricity market participants, such as GENCOs, TRANSCOs, and DISCOs, to exercise least-cost
Index Terms - Deregulation, Electricity Market, Profit Based Unit Commitment, Generation Companies (GENCOs, and Seeker Optimization Algorithm (SOA).
I. INTRODUCTION Unit commitment is one of the most critical decision processes and tasks performed by system operators in deregulated electricity markets as well as in vertically integrated utilities[1-7]. UC faces new challenges as the supply and demand uncertainty increases dramatically due to the integration of variable generation resources and price responsive demand. The objective of the UC problem is to find the units schedule
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Sahar S.Kaddah et. Al. – International Conference on New Trends for Sustainable Energy 2016 [ICNTSE] or profit-based operations. However, the system security is still the most important aspect of the power system operation. In restructured markets, the ISO, as the key market entity, has the authority and responsibility to commit and dispatch system resources and curtail loads for maintaining the system security (i.e., balance load demands and satisfy fuel, environmental, and network security requirements). Consequently, the ISO must be equipped with powerful tools to fulfill unit commitment and dispatch in open markets by optimizing a set of objectives at steady state while satisfying pre- and postcontingency security constraints [18]. In this paper, the seeker optimization algorithm (SOA) for solving (SCUC) problem is proposed. The critical constraints such as network constraints, ramp rate constraints and transmission security constraints are incorporated into the proposed model. The main contributions of the proposed model can be summarized as: 1) Developing a seeker optimization model for the SCUC problem for normal and abnormal operating conditions. 2) Proposing the maximum pricing strategy that provides an alternative option for ISO to cover the shortage in power demand from other connected networks at maximum pricing level. If the ISO fails to achieve the first option, the load shedding is carried out. 3) Conducting extensive numerical experiments on standard test systems with different scales. I.
and a step length aij (t) are computed separately for each ith seeker on each jth variable at each step t, where aij (t) ≥ 0 and dij Є {-1, 0, 1}. Here, i represent the population number and j represents the optimizing variable number. Calculation of search direction It is the natural tendency of the swarms to reciprocate in a cooperative manner, while executing their needs and goals. Normally, there are two extreme types of cooperative behaviour prevailing in swarm dynamics. The first, egotistic, is entirely pro-self and the other, altruistic, is entirely pro-group. Every seeker, as a single sophisticated agent, is uniformly egotistic. Each one should go towards his historical best position according to his own judgment. This attitude of the ith seeker may be simulated by an empirical direction vector di,ego(t) as: di ,ego (t ) sign pi ,best t xi t
(1) In altruistic behaviour, seekers try to communicate with each other, cooperate explicitly and adjust their behaviours in response to the other seeker in the same neighbourhood region for achieving the desired goal. Here, the seekers exhibit entirely pro-group behaviour. The population then exhibits a self-organized aggregation behaviour in which the positive feedback takes the form of attraction towards a given signal source. These two optional altruistic directions are:
di ,alt1 (t ) sign pg ,best t xi t
NOMENCLATURE
(2)
di ,alt 2 (t ) sign pl ,best t xi t
PF RV xk,t
Profit of GENCO ($). Revenue of GENCO ($). Specifies the consecutive time that the unit has been on (+) or off (-) at the end of the hour t. Sk(xk,t) Start-up cost, which for thermal units depends on the prevailing temperature of the boilers K Represent the generator number Pkmax Maximum output of generator k Pkmin Minimum output of generator k tkdn The time that generator should be stay off when shutdown tkup The time that generator should be stay on when start up. II. SEEKER OPTIMIZATION ALGORITHM
(3)
In equations (2) and (3), pg, best t represents neighbours' historical best position and p l, best t means neighbours' current best position. Moreover, seekers having the properties of pro-activeness seekers do not simply act in response to their environment but they are able to exhibit goal-directed behaviour. In addition, the future behaviour can be predicted and guided by the past behaviour. As a result, the seeker may be pro-active to change his search direction and exhibit goaldirected behaviour according to his past behaviour. Hence, each seeker is associated with an empirical direction called “pro-activeness direction” given as:
The SOA is a population-based heuristic search algorithm, which simulates the act of humans’ intelligent search with their memory, experience, and uncertainty reasoning. Each individual of this population is called a seeker. SOA regards the optimization process as an optimal solution obtained by a seeker population. The total population is randomly divided into n-subpopulations. These subpopulations search over several different domains of the search space. All the seekers in the same subpopulation constitute a neighbourhood. This neighborhood represents the social component for the social sharing of information. In the SOA, a search direction dij (t)
d i, pro (t ) signxi t1 xi t 2 (4) where, t1 and t2 t , t 1, t 2 and it is assumed that xi (t1) is better than xi (t2). The Abovementioned four empirical directions, presented in equations (1-4), are considered to take a rational search direction decision. If the j th variable of the ith seeker goes towards the positive direction of the coordinate axis, the value of dij(t) is taken as +1. If the j th variable of the ith seeker goes towards the negative direction of the coordinate
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Sahar S.Kaddah et. Al. – International Conference on New Trends for Sustainable Energy 2016 [ICNTSE] axis, the value of dij(t) is assumed as -1. The value of dij (t) is assumed as 0 if the jth variable of the ith seeker stays at the current position. Every variable j of dij (t) is selected by applying the following proportional selection rule as stated in the following equation:
0 d ij 1 1
if r j p j if p j
(0)
if p j
(0)
Subpopulations learn from each other Each subpopulation is searching for the optimal solution using its own information. It hints that the subpopulation may trap into local optima yielding a premature convergence. Subpopulations must learn from each other about the optimum information so far they have acquired in their respective domain. Thus, the position of the worst seeker of each subpopulation is combined with the best one in each of the other subpopulations using the following binomial crossover operator:
( 0)
rj p j
(0)
pj
(1)
(5)
p j rj 1 (1)
where, rj is a uniform random number in [0,1],
p jm m 1,0,1 is the percent of the numbers of “m”
Xlj , best X K j ,worst X K j ,worst n n
from the set {dij, ego, dij,alt1, dij,alt2, dij,pro} on each variable j of all the four empirical directions, that is,
p jm the numberof m 4
i max
S Ii ( max min ) S 1
Problem formulation
(6)
In equation (6), Ii is the sequence number of xi (t) after sorting the fitness values; µmax is the maximum membership degree value that is equal to or a little less than 1.0. Here, the value of µmax is considered as 0.95. Thus, a minimum value of µ, µmin = 0.0111, is set. Moreover, the Bell membership function parameter, δ, is determined by:
abs( xbest xrand )
where, abs (.) operator refers to the absolute value of the input vector and the parameter ω is used to decrease the step length with increasing time step so as to gradually improve the search precision where is linearly decreased from 0.9 to 0.1 during a run. The x best and x rand are the best seeker and a randomly selected seeker respectively, from the same subpopulation to which the ith seeker belongs. In the same subpopulation, x rand is different from x best and δ is shared by all seekers. A uniformly random real number within the range [µi, 1] is returned by: µij= rand (µi, 1) Equation (7) denotes the action part of fuzzy reasoning and gives the step length α ij for every variable j as:
ij j ln(ij )
j else
0.5 (8)
Where, randj is a uniformly random real number within [0, 1], X knj, worst is denoted as the jth variable of the nth worst position in the kth subpopulation and Xlj,best is the jth variable of the best position in the lth subpopulation. Here, n, k, l = 1, 2, ..., K-1, k ≠ l..The abovementioned steps of SOA can be summarized in the flow chart shown in Figure 1.
Calculation of step length The fitness function of SOA considers the fuzzy system to turn all the seekers into sequence numbers from 1 to S as the inputs of fuzzy reasoning. The membership function is used in the conditional part since the universe of discourse is a given set of numbers, that is, 1, 2, ..., S, as:
if rand
(7)
Updating each seeker In a population of size S, for each seeker i (1 ≤ i ≤ s), the position update of each seeker j is given by:
xij t 1 xij t ij t dij t
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Sahar S.Kaddah et. Al. – International Conference on New Trends for Sustainable Energy 2016 [ICNTSE] P(i,t 1) P(i,t) Ridown for i 1,.N and t 1,.T -Minimum up/down time limits,
Figure 1 Flow chart of the proposed SOA The UC solution is implemented for calculating the optimal dispatch of generators, minimizing the bid-based operating cost at steady state, and preventing system violations when contingencies occur. In restructured power systems, GENCOs and TRANSCOs submit to the ISO their preferred schedules. The ISO uses the proposed model to examine and adjust the preferred schedules for maintaining the minimum operation cost and transmission security. These constraints are summarized as follows : 1) Generation constraints: these constraints involve generating unit capacity, System spinning and operating reserve requirements, ramping up/down limits, minimum up/down time limits, maximum number of simultaneous on/offs in a plant and maximum number of on/offs of a unit in a given period. 2) Power balance constraints. 3) Transmission constraints: these constraints involve AC network security constraints, Transmission maintenance resource and crew availability (including the maximum number of lines and the total transmission line capacity that is to be on maintenance simultaneously including transmission flow and bus voltage limits SCUC can provide an hourly commitment of generating units with minimum bid-based dispatch cost considering the transmission constraints. The objective function of UC problem in the deregulated power system as mentioned previous is composed of bid-based fuel costs for producing electric power and startup and shutdown costs of individual units for the given period. Equation 6.1 explains the problem objective as:
Max v k ,t , Pk ,t
on X on (i, t - ) - Ti U (i, t -) U it
off X off U it - U (i, t -) (i, t - ) - Ti
-Unit generation limits.
Pi min P(i ,t ) Pi max The security constraints are related to steady state conditions and it should be considered in the post-contingency states. To guarantee secure operation of units and network, terms like voltage constraints and power flow constraints are used.
Vmin V Vmax PFi t PFimax where,
Vmin
and Vmax - minimum and maximum voltage magnitude limit at bus i (pu), respectively.
PFit
PFimax
- Maximum flow limits for branch i (MVA). Proposed Methodology The proposed solution methodology is carried out through the following strategy. 1- Modeling the system under study. 2- For normal operating condition, solving the SCUC problem using seeker optimization algorithm considering transmission constraints. 3- For abnormal operating condition, solving the SCUC problem for each abnormal condition then check the following constraints: a- The power flow constraints for security requirements. b- The capability of GENCO to provide the loading condition under emergency conditions. If the GENCOs isn't able to fed the total power demand requirements, we are proposing anew index to decide feeding the excess demand requirements from neighbouring networks or shed it based on the value of the maximum pricing level. The maximum pricing level can be obtained using
T M { [mt Pk ,t -CFk (Pk ,t ) S k (x k ,t )(1 v k ,t 1 )]v k ,t } t 1 k 1
The hourly UC constraints listed below include the system power balance PGi t PDit Vit Vjt (Gij CosBij Bij SinBij)
QGit – QDit Vit Vjt (Gij SinBij Bij CosBij)
where,
PGit, QGit are the active and reactive power generation at bus (i) at time respectively.
PDit, QDit are the active and reactive power demand at
MPL=
bus (i) at time (t) respectively.
G ij , Bij
where, Fc is the total generation costs for pre-emergency or at normal operating conditions.
Vit
Fc past is the committed generation costs after the occurrence
- Voltage magnitude of bus(i) at time (t) pu. -System spinning and operating reserve requirements,
R itU it SR t'
of emergency events.
t 1, , T
Psh
i 1
-Ramping up/down limits,
P(i,t) P(i,t 1) R i up
Fc pre Fc past Psh pre
- Conductance and susceptance between bus (i) and bus (j) respectively.
N
- power flow through branch i at time t (MVA).
for i 1,.N and t 1,.T
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is the accumulated planed shedded power.
Sahar S.Kaddah et. Al. – International Conference on New Trends for Sustainable Energy 2016 [ICNTSE] Hour
Load (MW)
Unit1
Unit2
Unit3
Unit4
Fuel cost ($)
1
450
300
2
530
300
3
600
4
540
5
Transition cost ($)
150
0
0
9145.36
0
205
25
0
10892.2
150
300
250
30
20
12570.5
0
300
195
25
20
11079.4
0
400
300
0
80
20
8532.18
60
6
280
255
0
25
0
5845.57
85
7
290
265
0
25
0
6024.79
0
8
500
300
200
0
0
10066.4
220
Total cost
74841.4
Total Profit
18968.28
Table 2 UC schedule and their OPD for 4-unit test system for outage unit (3) at hour (5) Figure 2 shows the proposed strategy to solve the SCUC considering various options.
If, the pricing level PL
