A distribution generation (DG) multiobjective optimization method based on an improved Pareto evolutionary algorithm is investigated in this paper. The improved Pareto evolutionary algorithm, which introduces a penalty factor in the objective function constraints, uses an adaptive crossover and a mutation operator in the evolutionary process and combines a simulated annealing iterative process. The proposed algorithm is utilized to the optimize DG injection models to maximize DG utilization while minimizing system loss and environmental pollution. A revised IEEE 33bus system with multiple DG units was used to test the multiobjective optimization algorithm in a distribution power system. The proposed algorithm was implemented and compared with the strength Pareto evolutionary algorithm 2 (SPEA2), a particle swarm optimization (PSO) algorithm, and nondominated sorting genetic algorithm II (NGSAII). The comparison of the results demonstrates the validity and practicality of utilizing DG units in terms of economic dispatch and optimal operation in a distribution power system.
With the increasing demand for clean and renewable energy, the issue of distribution generation (DG) is drawing more attention worldwide. DG provides voltage support to largescale distribution power systems, which results in reliability improvements and reduction loss in the power grid. DG technology has become a hot research topic, given the increasing global concerns about environmental protection, energy conservation, and the increasing sophistication of wind power, photovoltaic power generation, and other renewable energy technologies. After DG is connected to a distribution network, the distribution network’s structure, operation and control mode will tremendously change, and the distribution system automation and the demandside management must consider the coordination between DG and distribution network control. Deciding the optimal DG output is a challenging research problem, especially considering the multiple optimal objectives associated with cases of multiple DG unit injections.
Traditionally, multiobjective DG optimization has been treated as a singleobjective optimization problem using suitable weighting factors to form a weighted sum of single objectives. This approach has the disadvantage of finding only a single solution that does not express the tradeoffs with different weighting factors. Generating multiple solutions using this approach requires several runs with different factors, which leads to long running times [
The literature includes several DG output studies that examined multiple objectives and applied evolutionary optimization techniques. From the perspective of mathematical optimization, DG unit injection is a complex multiobjective optimization problem that presents a challenge to the optimization analysis of a distribution power system. The objectives include optimal energy consumption, the minimum power consumer’s electricity purchasing cost, and the minimum power loss based on the constraints of power grid security and DG power output. Multiobjective economic/emission dispatch algorithms were investigated in [
In this paper, a DG multiobjective optimization method based on an improved evolutionary algorithm was investigated for a distribution power system. Adaptive crossover and a mutation operator were used in the evolutionary process, and simulated annealing was combined in the iterative process. A fuzzy clustering algorithm was applied to manage the size of the Pareto set. The rest of the paper is organized as follows. In Section
Three objectives are considered in the optimization model, which includes the fuel cost and the pollutant emission penalty, reducing consumer costs on electricity bills when DG units are injected into the distribution network and reducing transmission line losses. The first optimization objective is minimum energy consumption and a pollutant emission model, which is mainly based on government requirements. There will be more penalties if the system emits more pollutants and exhibits greater fuel consumption. The second objective is consumer related, where the consumer uses DG to maximize savings on their bills. The third objective is to lower system line losses, which is the demand objective of the power supply provider. The three objectives involve perspectives based on government requirements, consumer needs, and power supply enterprise needs, and the objectives can conflict. For example, when a consumer utilizes a micro gas turbine to maximize their savings on their energy bill, there is a subsequent increase in fuel cost and pollutant emission. In addition, the extra power from the micro gas turbine will increase or decrease the line losses, depending on the size and placement location of the micro gas turbine.
The first objective is to minimize the fuel cost and the pollutant emission penalty, which reflects the impact of energy utilization on the environment. It can be expressed as follows:
The fuel cost
The pollutant emission quantity can be obtained based on DG output. Then, based on the penalty standard, the environmental penalty for pollutant emission is calculated as follows:
The second objective is to maximize the cost savings on electricity user bills when the DG is injected into the distribution network. The savings in electricity, which should have been purchased from the power supply enterprise, are the total power output of the DG units. Utilizing DG output and timeofuse (TOU) rate, consumer electricity purchasing costs could be reduced as follows:
The third objective is to minimize the system line losses after DG injection into the distribution network. This objective can be expressed as follows:
In the previous three optimization models, the fuel cost and the pollutant emission penalty function
Three constraint conditions are considered in the optimization model, which includes constraints of power flow equations, nodal voltage, and DG capacity.
The constraint of power flow equations is described as follows:
Generation limits:
Load bus voltage constraints:
Thermal limits:
In the inequality constraints,
There is always a limit on penetration of DG for a distribution power system to ensure reliability. Different countries have different penetration factor values. The penetration factor indicates the aggregated DG rating on an electric power system (EPS) feeder, divided by the peak EPS feeder load. If we assume that the maximum DG penetration factor is 25%, then the maximum injected DG capacity should be limited to 25% of the maximum total load in the distribution network, which can be described as follows:
Aggregating the objectives and constraints, the problem can be formulated as a nonlinear programming problem as follows:
Multiobjective optimization can be expressed as
A solution
For
Assume that set
The traditional Paretobased evolutionary algorithm is shown in Figure
Flowchart of traditional Paretobased approach.
To solve the difficulties in traditional optimization techniques, a new evolutionary populationbased searching technique is proposed to solve the multiobjective optimization problem based on SPEA2 [
In the improved SPEA2, an individual
The objective of each solution
The individual’s fitness
The selection of crossover probability
In this paper, fuzzy set theory is used to select the optimal solution set among the obtained multiobjective solution sets. Fuzzy sets are sets whose elements have degrees of membership. Fuzzy set theory permits the gradual assessment of the membership of elements in a set. This membership is described with the aid of a membership function valued in the real unit interval
First, define a linear membership function
The dominant function
Because the value of
The best Pareto optimal solution is the one achieving the maximum membership function
Simulated annealing (SA) is a generic probabilistic metaheuristic for the global optimization problem of locating a good approximation to the global optimum of a given function in a large search space. It is often used when the search space is discrete. Here, SA is utilized in the individual selection.
Based on the individuals after selection, crossover and mutation steps, the simulated annealing operation is performed on the individuals of the population. The two genes in each individual will be selected and disturbed randomly. Then, the new individual will be evaluated to form new fitness values. If the fitness value of a new individual is larger than the old value, then the old individual will be replaced by the new individual. If the fitness value of the new individual is smaller than the old value, the new individual can also be accepted using the following probability:
The iterative procedure can be terminated when any of the following conditions are met: (1) the true Pareto front is obtained, and (2) the iteration number of the algorithm reaches the predefined maximum number of iterations. However, the true Pareto front will not be known in advance in most practical multiobjective problems, so the convergence condition is to iterate to a predefined maximal iteration number.
The flow chart of the proposed algorithm is illustrated in Figure
Flowchart of improved Paretobased evolutionary algorithm.
Generate an initial set
Establish the penalty function to constrain each objective function, and then form new objective functions.
Compute the fitness of individual in both the populationbased set
Duplicate the nondominated individuals in both the population and nondominated archive set to a new archive set
Evaluate if the nondominated set
Copy the superior dominated individual to
Evaluate the convergence criteria. If the iteration number
Perform adaptive crossover and mutation operation on the individuals of
Perform a simulated annealing operation, and then go to Step
To demonstrate the effectiveness of the proposed method, the algorithm in Section
Schematic diagram of the IEEE 33bus system with 4 DG units.
Among the four DG units, only the two diesel turbine DG units have fuel cost. Because it would be difficult for market players to accept/implement a central costbased dispatch in the distribution system including DG units, the cost of fossilfuel consumed by micro diesel turbine is calculated as follows:
As global environmental pollution is growing, optimizing power generation and pollutant emission costs are two conflicting goals. These goals present a restrictive and coordinated relationship. Environmental cost mainly refers to the fines related to pollutant emission. Tables
The pollutant emission rate of DG units (g/kWh).
Pollutant emission  Coal generation  Diesel engine  PV panel  Wind turbine 


6.46  4.3314  0  0 
CO_{2}  1070  232.0373  0  0 
CO  1.55  2.3204  0  0 
SO_{2}  9.93  0.4641  0  0 
Standard pollutant emission penalties ($/kg).
SO_{2} 

CO_{2}  CO 

0.75  1.00  0.002875  0.125 
Using the optimization model developed in Section
The optimized output of four DG units in 24 hours.
The power system loss before and after DG unit injection.
As shown in Figure
The forecasted and optimized solar power outputs based on the computed results are shown in Figure
The comparison of forecasted PV value and the computed optimal PV value.
The comparison of forecasted wind values and the computed optimal value.
Assuming that the coal consumption from the power plant is 0.35 kg/kWh and the highest coal price is 0.124 $/kg, the cost savings for coal consumption by using clean energy is illustrated in Figure
Hourly cost savings on coal consumption.
A pollutant emission penalty reduction curve was obtained based on data from Tables
Hourly penalty reduction for pollutant emission.
Assuming that the timeofuse price is 0.095 $/kWh for peak time from 6:00 am to 22:00 pm and 0.054 $/kWh in other period, the cost saving for the electrical bills of users per hour is shown in Figure
Hourly bill saving for consumers with DG unit injection.
The proposed algorithm was compared with the SPEA2 [
Table
Comparison of different algorithms.
Iterations  Time  Min 
Max 
Min 


Proposed algorithm  200  34 s  $1535.3  $86.0  114.5 kW 
SPEA2  200  42 s  $1568.5  $84.5  129.0 kW 
PSO  200  39 s  $1589.6  $82.6  131.2 kW 
NSGAII  200  36 s  $1573.9  $83.2  125.2 kW 
This paper presented an improved Paretobased evolutionary algorithm, which increases the global optimization ability with a simulated annealing iterative process and fuzzy set theory, to solve the multiobjective optimization problem for a distribution power system. The proposed algorithm was utilized to optimize a model of DG unit injection with objectives of maximizing the utilization of DG while minimizing the system loss and environmental pollution. The results indicate that the proposed optimization is applicable to practical multiobjective optimization problems that take into considering the requirements from utilities, consumers, and the environment.
With respect to the state of the art, the improvements from this new multiobjective optimization method can be listed as follows: (1) the ability to search an entire set of Pareto optimal solutions is enhanced by using SA, which is proven by the comparison experiments, and (2) the Pareto front converges to better optimum set of solutions using the proposed algorithm. Future work will be focused on probabilistic evaluation and optimization that considers multiple DG units and load profile in distribution systems.