Optimal power flow problem with the integrated renewable energy sources: A survey 1
Sundas Shafiq1 , Nadeem Javaid1,∗ , Sakeena Javaid1 , Khursheed Aurangzeb2
Department of Computer Science, COMSATS University Islamabad, Islamabad 44000, Pakistan sundasshafi
[email protected], {nadeemjavaidqau, sakeenajavaid}@gmail.com 2 College of Computer and Information Sciences, King Saud University, Riyadh 11543, Saudi Arabia
[email protected] (K.A.) ∗ Correspondence:
[email protected]; www.njavaid.com
Abstract—In a transmission network, optimal power flow (OPF) is considered as one of the most widely studied non-linear, non-convex and highly constrained problem. While solving the conventional OPF problem, power generation system mainly consists of fossil fuel thermal generators; however, with the increased energy demand, renewable energy sources like wind turbines, solar photovoltaic panels and hydro plants are also introduced. OPF problem is solved using traditional and heuristic approaches to attain the stated objectives that mainly include fuel cost reduction, power loss minimization and emission reduction. These objectives are either optimized individually or in combination where two or more objectives are optimized simultaneously to achieve multi-objective optimization. Further, this study gives an overview of how these economical, environmental and technical objectives are achieved. Index Terms—Optimal power flow, Optimal scheduling, Optimization, Emission, Renewable energy sources, Heuristic.
1. I NTRODUCTION Optimal power flow (OPF) is an important optimization problem that determines the best operating levels for an electric generation system. The basic functions of an electric power system are carrying out the optimal operations of the system and meeting the load demand efficiently and economically [1]. Due to the increased demand for electricity, supply side management may face the challenges of maintenance, reliability and sustainability [2]. Various constraints, objectives and challenges for the OPF are mentioned in Fig. 1. Recently, throughout the world, the problem of OPF has received more attention, as it is a highly constrained, large-scale, non-convex and non-linear optimization problem [3]. In a transmission network, an OPF problem is formulated and solved for providing the generated electricity efficiently with the following basic objectives: 1) Minimize the total electricity generation cost. 2) Reduce the total power loss in a transmission network. 3) Reduce the carbon emission from the thermal units. 4) Minimize the voltage deviation. In other words, optimization is basically the minimization or maximization of the stated objective functions. The basic OPF optimization process is shown in Fig. 2. Various optimization techniques are proposed and implemented to find an optimal solution for the OPF problem. In 1968, Dommel and Tinney present a simplified gradient method; the first algorithm to
solve an OPF problem [4]. Optimization solution for an OPF problem is then provided by using many conventional methods such as Newton method [5], quadratic programming [6], reduced gradient method [7], Lagrangian relaxation [8], interior point method [9], semi-definite programming [10] and linear programming [11]. Other than this, heuristic and evolutionary algorithms are also proposed and used to find an optimum solution for an OPF problem. The fundamental categorization is given in Fig. 3. All of these methods and techniques are used to solve the OPF problem for both singleobjective optimization (SOO) and multi-objective optimization (MOO). Classic OPF problem only considers the conventional thermal generators that consume fossil fuel for the generation of electricity. However, with the increase in energy demand and environmental concerns, renewable energy sources (RESs) are used to reduce fossil fuel usage. Electricity generation through fossil fuel plays a crucial part in increasing carbon emission and global warming effect. Integration of RESs such as wind turbines and solar photovoltaic (PV) panels is a complicated task, as they possess uncertainty in their generation due to their dependence on wind speed and solar irradiance. RESs are a challenge for system operators or planners not only because of variability in their output power; however, also due to inability of their output power to be scheduled like normal thermal generators. With increasing penetration of RESs, it becomes necessary to incorporate these resources optimally into the electricity generation system. SOO and MOO are done to solve the OPF problem for RESs integrated systems. In this survey, comparative analysis is presented for the optimization of various single and multi-objective OPF problems that incorporate RESs. List of abbreviations and symbols used in this study are given in Table I and Table II. The structure of the paper is organized as follows: Section 1 gives a brief introduction while Section 2 summarizes literature survey and our contribution. Section 3 presents the SOO while MOO is discussed in Section 4. Finally, Section 5 summarizes the conclusion of the study. 2. R ELATED W ORK , M OTIVATION AND O UR C ONTRIBUTION Numerous researchers present surveys and review articles in the domain of OPF. These surveys differ from each
OPF extended versions x x x x x x x x x x x
Applications x x x x x x x x
Static OPF Dynamic OPF Transient stability constrained OPF Security constrained OPF Deterministic OPF Stochastic OPF Probabilistic OPF Multi-objective OPF AC OPF DC OPF Mixed AC/DC OPF
Base case development Reactive planning Volt/VAR tuning FACTS network dispatch Voltage instability Contingency response ch Constrained economic dispatch Seasonal adjustment
Optimal power flow Constraints x x x x x x x x x x x
Challenges x x x x x x x x x
Active power Reactive power Voltage Current Voltage angle Tap position Capacitor bank Curtailment Reserve Flowing AC power to grid Security
Increased computational complexity Increased problem dimension Unbalanced networks at low voltage level Integration of storage devices F problem Decomposition of OPF ronization Computational synchronization Application of MILP neration Modeling load and generation uncertainties mization x Applying robust optimization
Fig. 1: Applications, constraints and challenges of OPF other as few of them focus on the OPF problem solving methodologies while some highlight the effect of distributed generations in the power system. Authors in [12] present a comprehensive survey on OPF problem solving methods. The main categorization is done on the basis of traditional and artificial intelligence (AI) techniques. Then, authors discuss in detail few approaches from both traditional and AI methods. However, a concluding statement is made that the AI methods are able to find the optimal solution in less time and with a better convergence rate. Another study is presented in [13], where OPF problem is discussed with flexible alternating current transmission system (FACTS) devices. AI methods, hybrid methods and multi-objective OPF are discussed. An observation is stated that the power system’s complications increase by including more FACTS devices. A technical review is given in [14] for the optimal allocation of the distributed generators in the power system; satisfying the system constraints. The authors give a brief description about the stated objectives, mentioned equality and in-equality constraints, SOO and MOO. Also, conventional, nature inspired, society inspired and hybrid algorithms are analyzed for solving the OPF problem. Furthermore, the comparison of the optimization algorithms is also presented. Another analysis is presented in [15] with the distributed resources. Power conversion and delivery components like RESs, storage systems, transformers and shunt capacitors are
described in detail. Then, the deterministic and probabilistic approaches are explained for solving the problems in the load flow. Furthermore, a brief information is given about the simulation tools for planning and analysis. At the end, a case study for the distribution networks is also included. Zeineb et al. present an overview of the optimization techniques applied for the integration of distributed generations from the RESs [16]. At first, various drivers and challenges related to the distributed generations are highlighted. Later, the optimization techniques are compared under the categorization of conventional methods, intelligent search methods and hybrid heuristic optimization methods. Another comprehensive review is presented in [17], where various scheduling problems are discussed. These briefly discussed scheduling problems are associated with the problem formulation type, objective functions, problem solving techniques, control and automation, emission, demand response and MOO. In addition, a comparison analysis is also provided among the selected set of papers on the basis of optimization methods and objectives. A brief review of OPF approaches is given in [18] related to smart grid and micro grid. These approaches are measured in terms of objective functions, constraints, challenges and their methodologies. A comprehensive analysis is presented to identify and categorize the techniques used to solve the OPF problem under the conventional generation sources and RESs
2
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Fig. 2: Basic OPF steps [19]. Integration and planning for the renewable distributed generations in the transmission system is over-viewed by the authors in [20]. Various conventional and meta-heuristic approaches are analyzed and discussed in detail. Availability of RESs and their uncertain power generation is also highlighted.
traditional and heuristic techniques are applied to solve the SOO OPF problem. The techniques applied to attain the stated objectives are enlisted in Table IV. Few of the single-objectives considered while solving the highly constrained OPF problem are: • Fuel cost reduction for thermal generators • Direct, reserve and penalty cost minimization of RESs • Active and reactive power loss reduction • Voltage deviation minimization and carbon emission reduction Fuel cost reduction is the optimization objective in most of the studies. However, various other objectives are used to form single and multi-objective fitness functions for solving the optimization problem. These objective functions are discussed in the sub-sections below.
For the better understanding of the research work done in any domain, a survey paper is written that summarizes, organizes and often categorizes the work done in that specific domain. A survey paper must provide a brief overview of the respective selected domain and it should include both recent and previous literature work. According to our knowledge, number of surveys are published for distributed energy resources and OPF problem solving techniques; however, no particular survey work is found for RESs integrated within the OPF problem. Therefore, this proposed work is presented to highlight some points according to the above mentioned particular aspect. This survey incorporates the latest work published till 2018 that includes the optimization of different objective functions. Other than that, it provides the basic overview of the optimization categorization that mainly focus on SOO and MOO. Furthermore, a comparative analysis is presented that illustrates the basic objective functions and the techniques implemented to achieve those objectives.
3.1. Cost Reduction The most common and basic function for solving an OPF problem is the reduction in power generation cost. This cost minimization function includes the individual cost of all the generators producing electrical energy. Thermal generators are mostly used by the power grid systems; however, to save more cost and to keep the environment clean, RESs like wind turbines and solar PV panels are also introduced. Among the 14 papers that solved the OPF problem for SOO, all of them incorporate the basic direct fuel cost reduction function. The cost reduction equation including all of the thermal, solar PV and wind generators is given in Eq. 1. This cost reduction function refers to the different equality and inequality constraints.
3. SOO The desired solution for an OPF problem is obtained by implementing the proposed methodology for different objective functions. Main steps to solve the RESs integrated OPF are given in Fig. 4. Various articles from the literature solve the OPF problem with the integration of RESs to achieve the individual objective optimization. From the few selected articles, 14 provide the solution for SOO as shown in Table III. The taxonomy for the SOO is illustrated in Fig. 5. Both
F1 = M in [CT G + CP V + CW T ].
(1)
Where, CT G is the direct cost for thermal generators, CP V is the total combined cost for PV panels and CW T is the com-
3
Optimal power flow optimization methods
Quadratic methods
xReduced gradient xConjugate gradient xGeneralized reduced gradient
Gradient methods
Simplex methods Evolutionary algorothms xQuasi-newton xNewton raphson
Newton methods
Conventional Optimization
Probabilistic Optimization Nature inspired algorithms
Non-linear methods
Society inspired algorithms
Mixed integer M linear programming
xPrimal dual xPredictor-connector xMultiple centrality corrections xTrust region
Hybrid intelligent algorithms
Interior point methods
Swarm based d algorithms
Linear methods L
xArtificial immune system xDifferential evolution xEvolutionary programming xGenetic algorithm
xAnt colony xFirefly xArtificial bee colony
xSimulated annealing xHarmony search xTabu search xImperialist competition xFuzzy set based
xGenetic algorithm & Tabu search xCuckoo search and firefly xHarmony search with fuzzy based xParticle swarm and genetic algorithm xFirefly and tabu search
Fig. 3: Methodologies for OPF Where, Cs,k (Pss,k ) is the direct cost for solar PV, PSS,k is scheduled solar output power and hk represents the cost co-efficient for solar PV.
bined cost for wind turbines. Further detail for the evaluation of these cost functions is given below. 3.1.1. Direct Cost Function for Thermal Generators Thermal generators require fossil fuel to produce electricity. The cost minimization function for thermal generators is direct cost function as used in [1-24]. Various heuristic, metaheuristic and traditional approaches are proposed and implemented to achieve the basic objective for cost minimization. Mathematically, this particular objective function is depicted in a quadratic form as mentioned in Eq. 2 [1-24]: CT G = ai + bi PT Gi + ci PT2 Gi .
As, the RESs are uncertain and stochastic in nature, so a situation may arise where the estimated power is more than the actual power provided by the PV panel. This situation is known as overestimation and the reserve cost associated with this scenario is calculated as [27]: CRs,k (Pss,k − Psav,k ) = KRs,k ∗ fs (Psav,k < Pss,k )∗ (4) [Pss,k − E(Psav,k < Pss,k )].
(2)
Where, Pss,k is the scheduled and Psav,k is the actual available power from the k th power plant, CRs,k is the reserve cost for solar PV panel, KRs,k is the reserve cost co-efficient of k th solar power plant, fs (Psav,k < Pss,k ) is the probability of solar power shortage occurrence than the scheduled power Pss,k and E(Psav,k < Pss,k ) is the expectation of solar PV power below Pss,k .
Where, CT G is the fuel cost for ith thermal generator, PT Gi is the total generated output power, whereas, ai , bi and ci are the cost co-efficients for ith thermal generator. 3.1.2. Combined Cost Function for Solar PV Panels For the generation system where RESs are integrated, the cost function for solar PV panels is also incorporated to calculate the total operational cost. Unlike thermal generators, these power generation resources do not require any fuel. Direct cost for the k th PV panel is evaluated as [27]: Cs,k (Pss,k ) = hk .Pss,k .
On contrary, if the actual power delivered by the PV panel is higher than the estimated power, this is known as underestimation and the penalty cost function for this situation is given as [27]:
(3)
4
TABLE I: Acronyms Abbreviation ACO AI BBO DE DSOPF FAAPO FACTS FPA GA GWO ICA MAC MBFA MOEA/D MOO MPSO OPF PV RESs SHADE SMODE SOO SF TEP
Description Ant colony optimization Artificial intelligence Biogeography based optimization Differential evolution Dynamic stochastic optimal power flow Fuzzy adaptive artificial physics optimization Flexible alternating current transmission system Flower pollination algorithm Genetic algorithm Grey wolf optimization Imperialist competitive algorithm Mean adjustment cost Modified bacteria foraging algorithm Multi-objective evolutionary algorithm based on decomposition Multi-objective optimization Modified particle swarm optimization Optimal power flow Photovoltaic Renewable energy sources Success history based adaptation technique for differential evolution Summation based multi-objective differential evolution Single-objective optimization Superiority of feasible solution Transmission expansion planning
TABLE II: Symbols Symbol δij α, β, γ, μ ai , bi , ci CT G Cs,k (Pss,k ) CP V CW T CRs,k (Pss,k − Psav,k ) CP s,k (Psav,k − Pss,k ) Cw,j (Pws,j ) CRw,j (Pws,j − Pwav,j ) CP w,j (Pwav,j − Pws,j ) E(Psav,k < Pss,k ) E(Psav,k − Pss,k ) fs (Psav,k < Pss,k ) fs (Psav,k > Pss,k ) gj Gij hk KRw,j KP w,j nl NL Pws,j Pwr,j PT G Pss,k Pwav,j
Description Difference in voltage angles between bus i and bus j Co-efficients for emission Cost co-efficient for ith thermal generator Direct cost for thermal generators Direct cost for solar PV panel Total combined cost for PV panels Total combined cost for wind turbines Reserve cost for the solar PV Penalty cost for the solar PV Direct cost of wind power plant Reserve cost for the wind turbine Penalty cost for the wind turbine Expectation of solar PV power below scheduled power Expectation of solar PV power above the scheduled power Probability of solar power shortage occurrence than the scheduled power Probability of solar power surplus than the scheduled power Cost co-efficient for each wind farm Transfer conductance at the buses i and j Cost co-efficient for solar PV Reserve cost co-efficient Penalty cost co-efficient Total number of lines in a network Number of load buses in a transmission network Scheduled wind power Rated output power Total generated output power Scheduled solar output power Actual available wind power
be written as: CP V = Cs,k (Pss,k ) + CRs,k (Pss,k − Psav,k )+ CP s,k (Psav,k − Pss,k ).
CP s,k (Psav,k − Pss,k ) = KP s,k ∗ fs (Psav,k > Pss,k )∗ (5) [E(Psav,k − Pss,k ) − Pss,k ].
(6)
3.1.3. Combined Cost Function for Wind Turbines Where, CP s,k is the penalty cost for PV panel, KP s,k is the penalty cost co-efficient of k th solar power plant fs (Psav,k > Pss,k ) is the probability of excess solar power than the scheduled power Pss,k and E(Psav,k − Pss,k ) is the expectation of solar PV power above Pss,k . The final combined cost function for the solar PV panel can
The cost function for wind turbines is similar to that of solar PV panel, as no fuel is required to generate the electricity from these sources. The direct cost for the j th wind power plant is modeled as [27]: Cw,j (Pws,j ) = gj .Pws,j .
5
(7)
Start
Thermal generator power
Thermal generator
End
Input initial system data Wind generator
Solar PV generator
State the optimal solution
Forecasted wind power
Weibul density function
Lognormal probability density function
Forecasted solar power
Run initial power flow to get the base case solution
Optimization method
No
Constraint violation?
Optimized output
Yes
Load demand
Rayleigh probability density function
Select the desired objective function
Forecasted load demand
Determine control and decision variables
System data
Run power flow and check the constraints
Select the method for optimization
Fig. 4: Steps to solve an OPF problem Here, Cw,j (Pws,j ) represents direct cost of wind power plant, Pws,j is the scheduled wind power and gj is the direct cost co-efficient for each wind farm. Reserve cost for wind turbines associated with the overestimation scenario can be written as [27]: CRw,j (Pws,j − Pwav,j ) = KRw,j
Pws,j 0
(Pws,j − Pwj )
3.2. Voltage Deviation Reduction In the literature [21-24], [29], [33], [36], [39], [43] and [44] reviewed earlier, the OPF problems for voltage deviation reduction and voltage profile improvement according to objective function are addressed. However, the system inequality constraint for voltage is to be satisfied for all the techniques while solving an OPF problem. Voltage deviation is basically the measure of a voltage quality in any electric transmission network. While solving the non-linear OPF problem for any other objective, the voltage might deviate or violate the stated constraints. Therefore, an individual objective function is required to enhance the voltage profile. Mathematically, it is represented as [27]:
(8)
fw (Pwj )dpwj .
Where, CRw,j (Pws,j − Pwav,j ) is the reserve cost for wind turbine, KRw,j is the reserve cost co-efficient and Pwav,j is the actual available power from the same plant. Penalty cost function in case of wind farm is written as [27]: CP w,j (Pwav,j − Pws,j ) = KP w,j
Pwr,j Pws,j
(Pwj − Pws,j )
V oltage deviation =
|Vi − 1.0|.
(11)
i=1
(9)
Where, N L is the number of load buses in a transmission network and Vi is the voltage at the ith bus.
fw (Pwj )dpwj . Where, CP w,j (Pwav,j − Pws,j ) is the penalty cost for wind turbine, KP w,j is the penalty cost co-efficient and Pwr,j is the rated output power from the same farm.
3.3. Power Loss Minimization The OPF problem is also solved for achieving the objective of power loss minimization from the transmission lines. It is impossible to avoid the power loss as there exists a resistance between transmission lines. However, this power loss can be minimized by reducing both active and reactive power loss while transmission of electricity. A linear losses models to develop a computational efficient model for large-scale transmission expansion planning (TEP) applications is presented in [34]. The majority of researches only focused on total real or
The combined final cost function for the wind turbines is given by: CW T = Cw,j (Pws,j ) + CRw,j (Pws,j − Pwav,j )+ CP w,j (Pwav,j − Pws,j ).
NL
(10)
6
TABLE III: Comparative analysis for the single and multi-objective functions Ref. No.
Singleobjective -
[21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44]
Multiobjective
Solar plant
Wind plant
Hydro plant
Direct cost
Reserve cost
Penalty cost
-
-
-
-
20 $/ton tax rate is assumed in [27]. The emission cost along with the carbon tax (Ctax ) can be calculated as:
active losses in power systems [22-25], [27-30], [32], [34], [36], [39], [43] and [44]. However, reactive power loss is also minimized by [23], [24], [34] and [43]. The mathematical formulation for power loss can be written as [27]: Ploss =
nl nl
Gij Vi2 + Vj2 − 2Vi Vj cos(δij ).
CE = Ctax .Emission. 4. MOO
(12)
As observed from the literature, an OPF problem is solved for various single and combined objectives. SOO is being implemented by various authors; however, in realistic scenarios more than one objective needs to be optimized simultaneously. The objectives for the MOO might be similar to the basic objectives for an OPF problem, therefore, solving them simultaneously might give different results. The multiobjective functions tend to find a better model which provides the best solution for contradicting objectives. As, during the implementation of cost reduction in [26], the voltage limits might violate. On contrary, while solving the problem in multiobjective scenario, both of these objectives are minimized and a balanced solution is achieved. MOO is usually solved by assignments of weights to each objective function; however, this approach has a limitation that it is not able to find the appropriate trade-off between different objective functions in a single run. OPF problem is solved for multi-objective scenario in [23-26], [29], [32], [37], [39], [42] and [44]. Reduction of emission, voltage deviation and fuel cost is considered in [23]. Three different scenarios are considered in [44]: minimization of power loss along with the voltage deviation and fuel cost reduction, minimization of power loss with voltage deviation and emission reduction, minimization of power loss and cost reduction.
i=1 j=1
Where, nl is the total number of lines in a network, Gij is the transfer conductance at the buses i and j, Vi and Vj are the voltage magnitude at the ith and j th buses, whereas, δij is the difference in voltage angles between bus i and bus j written as δij = δi − δj . 3.4. Emission Reduction One of the most significant and emerging problem in the power system is to control and reduce the harmful effect of emissions on the environment. As, thermal generators burn fossil fuel to generate electricity which is the major cause for emission of pollutants like carbon dioxide CO2 , nitrogen oxides N Ox and sulfur oxides SOx . So, the use of RESs automatically minimize the carbon emissions up to some level. For the scheduling problem of OPF, various articles from the literature work consider the objective of emission reduction as in [24-27], [32] and [37]. Carbon emission in ton/h can be evaluated as [27]: Emission =
N TG
(14)
[(αi +βi PT Gi +γi PT2 Gi )∗0.01+ωi e(μi PT Gi ) .
i=1
(13) Here, αi , βi , γi and μi are all co-efficients of emission. Due to the increased amount of emissions and changing environmental conditions like global warming, various countries are taking some effective measures to insure the reduced emissions by imposing the tax for per unit emission. For this purpose,
5. C ONCLUSION OPF is an emerging and highly constrained non-linear optimization problem that can be solved by a variety of different
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TABLE IV: Comparison of optimization methods in existing literature Technique Genetic algorithm (GA) and modified bacteria foraging algorithm (MBFA) [21] Gbest guided artificial bee colony (GABC) optimization algorithm [22] Ant colony optimization (ACO) and MBFA [23] Hybrid ACO-ABC algorithm [24]
Objectives Cost minimization, two objective functions for cost: with and without reactive power violation cost Fuel cost reduction, power loss reduction and voltage profile improvement
Test system IEEE 30-bus test system
Minimization of generation cost, voltage enhancement and reduction in system loss Minimize total loss, minimize carbon emissions, reduce energy cost and improve voltage stability
IEEE 30-bus test system
Hybrid GA-BFA algorithm (HA) [25] Biogeography based optimization (BBO) algorithm [26] Success history based adaptation technique for differential evolution (SHADE) algorithm [27] Grey wolf optimization (GWO) algorithm [28] GA, HA and MBFA [29]
Operational cost minimization, emission reduction and real power loss minimization Cost and emission reduction while considering correlated wind power and load uncertainty Fuel cost reduction and emission reduction
Modified particle swarm optimization (MPSO) [30] Fuzzy adaptive artificial physics optimization (FAAPO) algorithm [31] Multiobjective evolutionary algorithm based on decomposition (MOEA/D), summation based multiobjective differential evolution (SMODE) and superiority of feasible solution (SF) [32] Differential evolution (DE), flower pollination algorithm (FPA) and MBFA [33] Linear losses models [34]
Open loop optimal control model [35] PSO, GA, and imperialist competitive algorithm (ICA) [36] Adaptive immune GA [37]
Chance constrained dynamic stochastic OPF (DSOPF) model [38] Framework based on a fusion of multi-objective optimization and decision analysis [39] GA and two point estimate method [40] OPF and unit commitment (UC) frameworks integrated with large scale ESS units [41] FPA [42] FACTS devices are modeled and incorporated with Newton Raphson load flow algorithm [43] PSO [44]
IEEE 30-bus test system
IEEE 33-bus and IEEE 69-bus distribution system IEEE 30-bus system IEEE 30-bus system IEEE 30-bus system
Fuel cost minimization and power loss reduction
IEEE 30-bus system
Cost minimization, voltage stability and power loss reduction Generation and operational cost reduction and power loss minimization Reduce generation cost for both thermal and wind generators
IEEE 30-bus system IEEE 30-bus system
Cost minimization and emission reduction
IEEE 30-bus system and Indian 75-bus practical system IEEE 30-bus system
Cost reduction and voltage stability
IEEE 30-bus system
To develop an adequate and computational efficient losses model for large-scale TEP (transmission expansion planning) applications
Standard Garver’s 6-bus test system, IEEE 118bus system and Spanish bus test system NA
Minimize the operational cost of hybrid system Reduction of system losses, cost reduction of distributed generators and the improvement of voltage profile To conduct the economic operation optimization and minimize the generation cost considering carbon trading and spare capacity variation Minimize the total generation cost, including conventional generators and wind farms
34-bus electrical system and 13-bus radial distribution system IEEE 30-bus test system
Minimize the regulation costs, power distribution losses and voltage deviation
IEEE 30-bus system and IEEE 37-node test feeder
Minimize the deterministic mean adjustment cost (MAC) Operational cost minimization with startup and shutdown cost reduction
IEEE 30-bus system
Operational cost minimization
IEEE 30-bus and Indian utility 30-bus system Benchmark 5-bus test system
Power loss minimization and voltage profile improvement Minimization of network power losses, minimization of the total costs of distributed energy resources, improvement of voltage stability and minimization of greenhouse gas emissions
8
IEEE 14-bus system
IEEE 24-bus reliability test system
13-bus radial distribution system
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Fig. 5: Hierarchal representation of the objective functions in OPF methods and techniques. With the integration of RESs into the system, the problem becomes more complex and it becomes difficult to satisfy operational and physical constraints. Various objective functions are formulated and optimized to attain the balanced power generation system. These objective functions could be achieved through SOO and MOO. In the presented study, some of the objectives are discussed; however, MOO is more efficient and accurate as it provides a balanced and realistic results between two or more optimization functions.
R EFERENCES [1] Mandal, B. and Roy, P.K., 2014. Multi-objective optimal power flow using quasi-oppositional teaching learning based optimization. Applied Soft Computing, 21, pp.590-606. [2] Khalid, A., Javaid, N., Guizani, M., Alhussein, M., Aurangzeb, K. and Ilahi, M., 2018. Towards dynamic coordination among home appliances using multi-objective energy optimization for demand side management in smart buildings. IEEE Access, 6, pp.19509-19529. [3] Buch, H., Trivedi, I.N. and Jangir, P., 2017. Moth flame optimization to solve optimal power flow with non-parametric statistical evaluation validation. Cogent Engineering, 4, pp.1-22. [4] Dommel, H.W. and Tinney, W.F., 1968. Optimal power flow solutions. IEEE Transactions on Power Apparatus and Systems, 10, pp.1866-1876.
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[5] Maria, G.A. and Findlay, J.A., 1987. A Newton optimal power flow program for Ontario hydro EMS. IEEE Transactions on Power Systems, 2(3), pp.576-582. [6] Grudinin, N., 1998. Reactive power optimization using successive quadratic programming method. IEEE Transactions on Power Systems, 13(4), pp.1219-1225. [7] De Carvalho, E.P., Dos Santos Junior, A. and Ma, T.F., 2008. Reduced gradient method combined with augmented Lagrangian and barrier for the optimal power flow problem. Applied Mathematics and Computation, 200(2), pp.529-536. [8] Santos, A.J. and Da Costa, G.R.M., 1995. Optimal-power-flow solution by Newton’s method applied to an augmented Lagrangian function. IEEE Proceedings-Generation, Transmission and Distribution, 142(1), pp.3336. [9] Yan, W., Yu, J., Yu, D.C. and Bhattarai, K., 2006. A new optimal reactive power flow model in rectangular form and its solution by predictor corrector primal dual interior point method. IEEE transactions on power systems, 21(1), pp.61-67. [10] Bai, X. and Wei, H., 2011. A semidefinite programming method with graph partitioning technique for optimal power flow problems. International Journal of Electrical Power & Energy Systems, 33(7), pp.13091314. [11] Mota-Palomino, R. and Quintana, V.H., 1986. Sparse reactive power scheduling by a penalty function-Linear programming technique. IEEE Transactions on Power Systems, 1(3), pp.31-39. [12] Khamees, A., Badra, N. and Abdelaziz, A., 2016. Optimal power flow methods: A comprehensive survey. International Electrical Engineering Journal (IEEJ), 7(4), pp.2228-2239. [13] Alkhayyat, M.T. and Bashi, S.M., 2016. A new survey for optimum power flow with facts devices. Journal of Electrical & Electronic Systems, 5(209), pp.2332-0796. [14] HA, M.P., Huy, P.D. and Ramachandaramurthy, V.K., 2017. A review of the optimal allocation of distributed generation: Objectives, constraints, methods, and algorithms. Renewable and Sustainable Energy Reviews, 75, pp.293-312. [15] Joshi, K. and Pindoriya, N., 2017. Advances in distribution system analysis with distributed resources: Survey with a case study. Sustainable Energy, Grids and Networks, doi, 10.1016/j.segan.2017.12.004, pp.1-15. [16] Abdmouleh, Z., Gastli, A., Ben-Brahim, L., Haouari, M. and Al-Emadi, N.A., 2017. Review of optimization techniques applied for the integration of distributed generation from renewable energy sources. Renewable Energy, 113, pp.266-280. [17] Nosratabadi, S.M., Hooshmand, R.A. and Gholipour, E., 2017. A comprehensive review on microgrid and virtual power plant concepts employed for distributed energy resources scheduling in power systems. Renewable and Sustainable Energy Reviews, 67, pp.341-363. [18] Abdi, H., Beigvand, S.D. and La Scala, M., 2017. A review of optimal power flow studies applied to smart grids and microgrids. Renewable and Sustainable Energy Reviews, 71, pp.742-766. [19] Khan, B. and Singh, P., 2017. Optimal power flow techniques under characterization of conventional and renewable energy sources: A comprehensive analysis. Journal of Engineering, 2017, pp.1-16. [20] Ehsan, A. and Yang, Q., 2018. Optimal integration and planning of renewable distributed generation in the power distribution networks: A review of analytical techniques. Applied Energy, 210, pp.44-59. [21] Panda, A. and Tripathy, M., 2014. Optimal power flow solution of wind integrated power system using modified bacteria foraging algorithm. International Journal of Electrical Power and Energy Systems, 54, pp.306-314. [22] Roy, R. and Jadhav, H.T., 2015. Optimal power flow solution of power system incorporating stochastic wind power using gbest guided artificial bee colony algorithm. International Journal of Electrical Power and Energy Systems, 64, pp.562-578. [23] Panda, A. and Tripathy, M., 2015. Security constrained optimal power flow solution of wind-thermal generation system using modified bacteria foraging algorithm. Energy, 93, pp.816-827. [24] Kefayat, M., Ara, A.L. and Niaki, S.N., 2015. A hybrid of ant colony optimization and artificial bee colony algorithm for probabilistic optimal placement and sizing of distributed energy resources. Energy Conversion and Management, 92, pp.149-161. [25] Panda, A. and Tripathy, M., 2016. Solution of wind integrated thermal generation system for environmental optimal power flow using hybrid algorithm. Journal of Electrical Systems and Information Technology, 3(2), pp.151-160.
[26] Shargh, S., Mohammadi-ivatloo, B., Seyedi, H. and Abapour, M., 2016. Probabilistic multi-objective optimal power flow considering correlated wind power and load uncertainties. Renewable Energy, 94, pp.10-21. [27] Biswas, P.P., Suganthan, P.N. and Amaratunga, G.A., 2017. Optimal power flow solutions incorporating stochastic wind and solar power. Energy Conversion and Management, 148, pp.1194-1207. [28] Siavash, M., Pfeifer, C., Rahiminejad, A. and Vahidi, B., 2017, May. An application of grey wolf optimizer for optimal power flow of wind integrated power systems. In 18th International Scientific Conference on Electric Power Engineering (EPE), Kouty nad Desnou, Czech Republic, held on 17-19 May, 2017. [29] Panda, A., Tripathy, M., Barisal, A.K. and Prakash, T., 2017. A modified bacteria foraging based optimal power flow framework for hydro-thermalwind generation system in the presence of STATCOM. Energy, 124, pp.720-740. [30] Khaled, U., Eltamaly, A.M. and Beroual, A., 2017. Optimal power flow using particle swarm optimization of renewable hybrid distributed generation. Energies, 10(7), pp.1013. [31] Teeparthi, K. and Kumar, D.V., 2018. Security-constrained optimal power flow with wind and thermal power generators using fuzzy adaptive artificial physics optimization algorithm. Neural Computing and Applications, 29(3), pp.855-871. [32] Biswas, P.P., Suganthan, P.N., Qu, B.Y. and Amaratunga, G.A., 2018. Multiobjective economic-environmental power dispatch with stochastic wind-solar-small hydro power. Energy, 150, pp.1039-1057. [33] Panda, A., An efficient scenario based optimal generation scheduling of hydro-thermal system incorporating wind power. International Journal of Recent Trends in Engineering and Research, 4(4), pp.1-7. [34] Fitiwi, D.Z., Olmos, L., Rivier, M., De Cuadra, F. and Perez-Arriaga, I.J., 2016. Finding a representative network losses model for large-scale transmission expansion planning with renewable energy sources. Energy, 101, pp.343-358. [35] Tazvinga, H., Zhu, B. and Xia, X., 2015. Optimal power flow management for distributed energy resources with batteries. Energy Conversion and Management, 102, pp.104-110. [36] HassanzadehFard, H. and Jalilian, A., 2016. A novel objective function for optimal DG allocation in distribution systems using meta-heuristic algorithms. International Journal of Green Energy, 13(15), pp.1615-1625. [37] Wang, Z., Shi, Y., Wang, X., Zhang, Q. and Qu, S., 2016. Economic dispatch of power system containing wind power and photovoltaic considering carbon trading and spare capacity variation. International Journal of Green Energy, 13(12), pp.1267-1280. [38] Sun, G., Li, Y., Chen, S., Wei, Z., Chen, S. and Zang, H., 2016. Dynamic stochastic optimal power flow of wind power and the electric vehicle integrated power system considering temporal-spatial characteristics. Journal of Renewable and Sustainable Energy, 8(5), pp.053309. [39] Vaccaro, A., 2016. A reliable methodology for multi-objective voltage regulation in the presence of renewable power generation. Electric Power Components and Systems, 44(12), pp.1357-1370. [40] Reddy, S.S., 2017. Optimal power flow with renewable energy resources including storage. Electrical Engineering, 99(2), pp.685-695. [41] Hemmati, R., Saboori, H., Dehghan, S. and Ghiasi, S.M.S., 2017. Evaluating and comparing profitability of bulk storage systems in unit commitment and optimal power flow operation frameworks. Journal of Renewable and Sustainable Energy, 9(2), pp.024101. [42] Kathiravan, R. and Kumudini Devi, R.P., 2017. Optimal power flow model incorporating wind, solar, and bundled solar-thermal power in the restructured Indian power system. International Journal of Green Energy, 14(11), pp.934-950. [43] Khaled, U., Eltamaly, A.M. and Beroual, A., 2017. Optimal power flow using particle swarm optimization of renewable hybrid distributed generation. Energies, 10(7), pp.1013. [44] HassanzadehFard, H. and Jalilian, A., 2018. Optimal sizing and siting of renewable energy resources in distribution systems considering time varying electrical/heating/cooling loads using PSO algorithm. International Journal of Green Energy, 15(2), pp.113-128.
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