Genetic Algorithm Approach to Generation Expansion Planning under Deregulated Environment

This paper presents an application of Improved Genetic Algorithm (IGA) with the support of Optimal Power Flow (OPF) algorithm for the least cost Generation Expansion Planning (GEP) problem under deregulated environment of power system. The proposed GEP model includes the presence of firm bilateral transactions, multilateral transactions and Independent Power Producers (IPP) in the system. The optimal location and size of new generators have also been determined using this model. The performance of the proposed algorithm has been illustrated for 6-year planning period with modified IEEE-30 Bus system. The results of IGA is compared and validated with Dynamic Programming (DP) solutions. Nomenclature Cj is the objective function value of the j individual attached to the expansion plan t is the time in years (1, 2 . T) T is the length of the study period (total number of years) I is the capital Investment cost S is the Salvage value of investment cost M is the Maintenance cost of the unit O is the Outage cost (Cost of the energy not served) [Kt] is the vector containing the number of all generating units which are in operation in the year t [At] vector of committed addition of units in year t [Rt] vector of the retirements of generating units in year t [Ut] vector of candidate generating units added to the system in year t. U t, max maximum construction capacity [MW] vector by unit types in year t Dt annual demand in the year t in MW R min lower bound of reserve margin R max upper bound of reserve margin ∈ reliability criterion expressed in LOLP Pg is the real power of the generating bus PL is the real power of the load bus Qg is the reactive power of the generating bus QL is the reactive power of the load bus S. Kannan et al/Journal of Energy & Environment 3 (2004) 1 13 2 P (V,θ) is the real power as a function of voltage and phase angle Q (V,θ) is the reactive power as a function of voltage and phase angle Vi is the minimum voltage limit of the i bus Vi is the maximum voltage limit of the i bus fj is the fitness function value of the j individual α1 is the penalty factor for reserve margin constraint Ψ1 is the amount of reserve margin constraint violation α2 is the penalty factor for LOLP constraint Ψ2 is the amount of LOLP constraint violation δ is the penalty value added for the power flow constraint violation ν represents the degree of satisfaction P is the vector of online generating capacities of each generating unit a, b and c constants (Fuel cost) Introduction In developing countries like India, which has one of the largest electrical networks, it is the right time to think about effective utilization of electrical network [1] along with deregulated market developments. The government policy changes permit the Independent Power Producers (IPP) to enter into the bulk transmission network. Furthermore in the wake of pollution arising from usage of oil and coal for the power generation, the non-conventional energy sources (especially wind and solar) are entertained. A large number of private parties are entering into the electrical network by connecting their miniature units at sites selected for non-conventional energy sources and utilizing the power at remote places; known as firm transactions. Some private concerns are interested in utilizing the transmission network alone for their power transactions. In these circumstances, the utility shall have to focus their concentration on the effective utilization of transmission line, to reduce the power cost of the utility consumers. The Generation Expansion Planning (GEP) problem concentrates mainly on ‘When’, ‘Where’, and ‘Which’ generating units to be committed on line. In the deregulated environment, ‘when and where to allow the transactions’ is an important question remains to be answered. This problem is another form of GEP, with both firm bilateral and multilateral wheeling transactions. The necessity to coordinate both long term and short term planning in thermal systems is illustrated in [2]. The necessity of composite generation and transmission expansion planning has been explained in [3]. An attractive work has also been carried out for optimization of generating unit’s location in [4]. A modeling framework is developed which comprises of investment planning, unit commitment and OPF modules for generator bid selection in [5]. The Genetic Algorithm (GA), iterative GA and advanced evolutionary programming are also applied to simple GEP problem successfully [6-8]. In this paper, the GEP for 6 years planning period considering the IPPs, firm purchases and other multilateral transactions without violating transmission constraints is explained considering the methods suggested in [2-6]. The planning problem is solved by running Optimal Power Flow (OPF) including the various transactions with load growth. The solving technique includes Dynamic Programming (DP) and Improved Genetic Algorithm (IGA). S. Kannan et al/Journal of Energy & Environment 3 (2004) 1 13 3 Problem Formulation A. Objective function The least cost GEP problem is a stochastic, nonlinear, dynamic optimization problem with many constraints [9]. The GEP problem determines a set of best decision vectors over a planning horizon that minimizes the cost (objective function) under several constraints. The cost function for the GEP problem has been formulated by considering the capital cost of the unit to be installed, energy generated by the new units, the capacity charge of the IPPs and the operation and maintenance cost of the existing and the new units. This problem is started with the addition of IPPs for the various transactions. The various transactions used in this paper are firm transactions, multilateral transactions and multilateral transaction with firm purchase. In all types of transactions, the private parties use only the transmission lines of the utility. In firm purchase, the private parties operate over a longer period. They inject power at one bus and draw in some other bus. Bilateral transactions can be either firm or non firm. In non-firm transactions, the supplier are not bound to transmit the fixed power all the time and it will vary depending upon system congestion. In multilateral transaction, the private parties inject and/or they may draw the power from more than one point. The objective function (cost function) for each type j is calculated by the following expression [ ] (1) O M S I C Min T 1 t t t t t j ∑ = + + = The maintenance cost of the unit includes the fixed cost for the maintenance as well as the variable cost. Normally probabilistic production costing method is used to find the expected energy produced by each unit. Equivalent energy function method may be used to find the probabilistic production cost. The generating units are scheduled for operation according to their economic merit order and the energy produced by each generating unit can be calculated. But this method ignores the transmission losses. So in the proposed model, to get an exact cost, the OPF method is used, which include, the generation required (economic dispatch) to meet the load demand as well as the transmission losses. So this proposed method provides better result than the probabilistic production costing method. B. Constraints The various constraints that are used in this paper for DP and IGA algorithms are reserve margin, reliability criterion and power flow constraints. If [Kt] is a vector containing the number of all generating units which are in operation in year t for a given expansion plan, then [Kt] must satisfy the following relationship (2) ] [U ] [R ] [A ] [K ] [K t t t 1 t t + + = [At] and [Rt] are given data, and [Ut] is the system configuration vector which is the vector of newly added units. [At] is the committed addition of units in year t. The committed addition of units implies the already selected units in the previous expansion plans which are going to be constructed in the year t. [Rt] is the retirement of the generating units. In this paper, both [At] and [Rt] are not considered. (3) ] [U ] [U 0 max t, t < < S. Kannan et al/Journal of Energy & Environment 3 (2004) 1 13 4 i) Reserve margin The selected units along with the existing units should satisfy the annual demand. To carry out the maintenance activities of the generators and to compensate for the unexpected outage of units, the reserve margin of 20 % to 60 % is used. The selected units should satisfy the minimum and maximum reserve margin given by equation (4). If it is not met, then the error (ψ1) is calculated by using the equation (5). (4) D ) R (1 ] [K D ) R (1 t max t t min × + ≤ ≤ × + ∑ (5) ) ) D ) R (1 [K ( , ) [K D ) R (1 ( max( t max ] t ] t t min 1 × + × + = Ψ ∑ ∑ If the minimum or maximum reserve margin is violated, then the proportional penalty value is added with the original objective function value. If the minimum reserve margin is violated, ((1+Rmin) × D Σ[Kt]) of equation (5) becomes positive and ((Σ[Kt]) – (1+Rmax) ×D) becomes negative. The maximum of the two terms results in positive value and corresponds to the shortage value of reserve margin. Similarly for maximum reserve margin, if the margin is exceeded, then ((Σ[Kt]) – (1+Rmax) ×D) becomes positive and ((1+Rmin) × D Σ[Kt]) becomes negative. The positive value corresponds to the excess of generation capacity. This error term Ψ1 is used in the penalty function approach. ii) Reliability criterion The reliability criterion includes the Loss of Load Probability (LOLP) and the Expected Energy Not Served (EENS). If LOLP (Kt) is the LOLP, every acceptable configuration must satisfy the following constraint. (6) ) (K LOLP t ∈ ≤ (7) ) (K LOLP t 2 ∈ = Ψ Both LOLP and EENS are calculated by the Equivalent energy function method [9]. iii) Optimal power flow constrains In this paper, in addition to the above constraints, the power flow constraints are also checked and if it satisfies the optimal power flow, then the cost obtained, is included as variable cost. The location of generating units is also considered by assuming the availability of generators at the specified buses. To check the MVA limits of transmission lines alone, it is enough to use a D.C power flow algorithm. To include additional constraints such as real power flow, reactive power flow, voltage magnitude at each bus, etc A.C power flow algorithm can be used. The various constraints used to check the optimal power flow are as follows: The active power balance equation is (8) 0 θ) P(V, P P Li gi = S. Kannan et al/Journal of Energy & Environment 3 (2004) 1 13 5 The reactive power balance equation is (9) 0 θ) Q(V, Q Q Li gi = The apparent power flow limit of lines, (from side) is (10) S S ~ max ij f ij ≤ The apparent power flow limits of lines, (to side) is (11) S S~ max ij t ij ≤ The bus voltage limits is (12) V V V i i i max min ≤ ≤ The active power generation limits is (13) P P P max gi gi min gi ≤ ≤ The reactive power generation limits is (14) Q Q Q max gi gi min gi ≤ ≤ The selected units should satisfy all the constraints from (8) to (14). If it satisfies all the constraints, OPF is satisfied, the cost from this OPF is taken as a variable cost. If the constraints are not met, then the OPF is not satisfied and a penalty value (δ) is added to the objective function value. III. IGA implementation GA emphasizes the models of chromosome selections as observed in nature, such as crossover and mutation. Each variable used is assumed to be one chromosome and the crossover and mutation are likely to takes place in these chromosomes. The populations are generated and their fitness values are calculated. Then by crossover and mutation, offspring are formed and fitness function values for these offspring are also calculated. GA uses the Darwin principle “Survival of the Fittest”. The best individual among the parents and the offspring are selected for the next generation. In GA, ‘penalty function approach’ and ‘elitism’ are introduced to improve the effectiveness of the approach.