Essay: Minimizing of power losses for distribution system

Introduction
Statement of the Problem
With the concern on increasing load demand that makes increasing in power losses, and the voltage profile of the system will not be improved to the required level, distributed generation (DG) units are used as an alternative energy solution to meet required load demand. DG units are integrated in distribution network to improve voltage profile, reliable and to achieve economic benefits such as minimum power losses (REF 1).
DG acts as a small share of the electricity network to play a key role in improvement the distribution power system performance. Although a big benefits of DG in distribution network, inappropriate sizing and sitting of DG lead to increase power losses and weaken voltage profile (REF 2). So the allocation of DG in an optimal way is interested to study.as shown in the figure 1 and 2, the difference between the traditional utility response and the effect of using distributed generation in the utility when demand increased.
Figure 1 Traditional utility response when demand increase
Figure 2 the effect of using DG
Thesis objectives
The main goal of this thesis is to solve an optimization problem defined as minimizing of power losses for distribution system in a single objective function. In the multi-objective function, the aim also is to minimize power losses, and to maximize of voltage stability index and to minimize the cost of distributed generation (DG). These two cases are applied to IEEE69-bus. The aims of thesis are achieved through different ways as follows:
Single objective function
Analytical methods, like voltage stability index , is used to define the optimal location of DG and by gradually changing the size of DG then the optimal size has minimum power losses.
Genetic Algorithm (GA) solves the optimization problem automatically to find a suitable location and size of DG.
Multi-objective function
A comparison between different applications of DG will be presented in this thesis using more than optimization method like Multi-Objective Genetic Algorithm (MOGA), Particle Swarm Optimization (PSO) and Biogeography Based Optimization (BBO) without consideration of load curve overall the day where the type of DG that used in this part is non-dispatchable DG.
When the load curve of distribution system is considered, the dispatchable DG is used in this case. For each hour all the day, the size of DG is changed to find the optimal size of DG by using MOGA. The dispatchable DG units can meet the increasing loads demand while improving system reliability and reducing the overall investment cost.
Outline of the thesis
A brief description about the content of the remaining chapters is given below:
Chapter 2 is a literature review providing an overview on definition of DG and various optimization techniques that used earlier for allocation DG.
Chapter 3 discusses the proposed optimization techniques problem.
Chapter 4 provides the problem formulations that used in the thesis and how they applied to allocate DG.
Chapter 5 discusses the effect of placement of DG in radial distribution system by using analytical and heuristics methods for minimizing the total power losses and improving the voltage profile. The comparison between different application of DG and The allocation of dispatchable DG is also discussed in this chapter.
Chapter 6 provides conclusion and presents conclusion for future work.
Chapter 2
Review
Definition of Distribution Generation
Distributed Generation (DG) is defined as electric power generation within distribution networks or close to the point of use in the network [1]. DG is also known as embedded or dispersed generation.
DG units are modeled as synchronous generators for small hydropower, geothermal power, combined cycle and consumption turbines. They are considered as induction generators for wind and micro hydro power. DG units are considered as power electronic inverter generators for micro gas turbines, solar power, photovoltaic power and fuel cells [2]. DG in buildings includes renewable and non-renewable energy generators as outlined in Table 1 [3].
Table 1 Distributed generation technologies by sector
Residential Commercial
Renewable Solar photovoltaic
Wind Solar photovoltaic
Wind
Hydroelectric
Wood
Municipal solid waste
Non-renewable Neutral gas-fired fuel cell Neutral gas-fired fuel cell
Neutral gas-fired reciprocating engines
Neutral gas-fired turbines
Neutral gas-fired micro turbines
Diesel reciprocating engines
Coal
In general, DG can be classified into four types:
Type 1 : DG capable of injecting constant active power.
Type 2 : DG capable of injecting both active and reactive power.
Type 3 : DG capable of injecting active power but consuming reactive power.
Type 4 : DG capable of injecting or delivering reactive power only.
A distributed generation unit also can be categorized into
A dispatchable DG
A non dispatchable unit.
Dispatchable generation refers to “sources of electricity that can be dispatched at the request of power grid operators or of the plant owner; that is, generating plants that can be turned on or off, or can adjust their power output accordingly to an order” [5]. The output power of a dispatchable DG unit can be controlled according to the daily load shedding. In contrast, the output power of nondispatchable DG is normally controlled based on the optimal operating condition of its primary energy source [7].
Dispatchable DG units are considered to be extremely reliable and flexible in operation, whereas non-dispatchable DG units require a significant amount of long term storage to be considered reliable due to the lack of availability of renewable energy resources [8].
Distributed Generation Benefits:
DG can provide several different benefits to the distribution system as follows [4]:
Reduces dependence on major power plants. This results in eliminating the need to erect new big power generation and deferral of new capacity
Reduces dependence on long-distance national transmission grid (releasing transmission lines capacities). This reduces cost of installing new transmission lines and reduces transmission congestion.
Reduces transmission and distribution line losses.
Reduces environmental impacts and greenhouse-gas emissions. This is because lots of DG units are renewable or low emission generators based sources.
Reduces price volatility in energy markets.
Enhances or preserve system reliability by having a back-up generation.
Deferral of new capacity (postpone upgrading the T&D infrastructure).
Enhances flexibility for system operators.
Accelerates retirement of old units.
Increases energy security by diversifying energy sources and reducing dependence on complex large systems.
Increases personal, business and regional self-sufficiency.
Well adapted to alternative and renewable energy sources.
Distributed Generation Issues:
In the following, several issues results from the impact of DG on distribution networks [6]:
If large DG is inserted in the network, energy losses may be increased.
The level of short circuit capacity is increased.
DG connection via interfaces like power electronic converters may cause power quality issues like voltage fluctuations (flickers) and distortions (harmonics)
Operation of DGs suffers with the unbalancing of loads in the phases. Their performance destroys due to unbalancing.
Cost
Literature Review
An analytical method is used in [9] to define the optimum size and location of DG unit to reduce only the power loss. Willis in [10] presented the rule called 2/3 rule for optimal DG placement for loss reduction. The optimal DG size with uniformly distributed load was 2/3 of the total load and the optimal location was 2/3 of the total distance.
In (1) used evolutionary programming approach for optimal placement and size of DG in radial distribution feeder. In (2) and (3), they explained a various objective function to find optimal sitting and sizing of DG.
The improvement of voltage and loss minimization is used as objective function in (4). The proposed techniques based on multiobjectives for optimal location of DG units in radial distribution. Ref (5) studied the effects of the significant parameter such as reliability, loss reduction and efficiency to optimize losses and improve voltage profile.
Genetic algorism is methodology that used in (6) to find optimal placement and size of CHP and PV generation in order to minimize the power losses. In (7), a novel optimization approach applied an Artificial Bee Colony (ABC) algorithm to find the optimum DG size, power factor and location to minimize the total power loss.
Particle swarm optimization (PSO) algorithm is applied to determine the placement and sizing of distributed generation in (10). Minimizing total cost system and minimizing power losses is considered as objective functions. The effect of sitting and sizing DG on power system network reflected on improving voltage profile, minimizing power losses and increasing power transfer capacity.
Reference (11) showed the comparison between PSO and Genetic Algorithm (GA) in solving DG allocation. The result indicated the perfection of PSO compared to GA in terms of solution quality and number of iteration optimization methods. Moreover in (12), presented combined methods with GA as well as PSO. Multiobjectives optimization problem was formulated to obtain the optimal size and location for DG in distribution system. The proposed objectives were to minimize the power losses, maximize the voltage stability and improve voltage regulation in radial distribution. GA was used for sitting of DG while PSO is solved for sizing of DG.
Biogeography Based Optimization (BBO) is presented to define the location and size of DG and capacitors in (15). Reducing active and reactive losses is an objective function taking into consideration the value reduction of losses at different load levels.
In Reference (16), A hybrid algorithm PSO & HBMO is used for optimal placement and sizing of distributed generation (DG) in redial distribution system to reduce the total power loss and improve voltage profile. objective function is cost over profit. Costs consist of charge of active and reactive power production and the advantage is obtained from reduction of losses and variance of voltage.
Conclusion
All the above described researches present solutions on the peak demand load using different optimization problem. This these will present the comparison between various heuristic approaches for finding optimal location and size of radial distribution system within the different distributed generation technologies such as biomass, solar, wind… etc. Where studying of allocation of DG at one hour (Peak load) is not a practical solution, the dispatchable DG is also discussed in this thesis taking into consideration the different loads, whether residential, industrial or commercial.
Chapter 3
Optimization Techniques for DG Allocation
The placement of distributed generation and sizing will be discussed by different methods. Several optimization techniques have been presented by researchers in determining the optimal location and size of DG. Such optimization methods can be classified into deterministic methods such as analytical and SQP methods and heuristic methods such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Biogeography Based Optimization (BBO), etc., based on the number of objectives. The major objective of DG placement techniques used in the literature is to minimize power system losses. However, other objectives, like improving the voltage profile and cost minimization have also been considered.
**-3-1 Analytical Method
The objective function here will be the total active power loss of distribution system.
a- Placement of DG using voltage stability index (VSI)
The loads generally have a role in voltage stability analysis and therefore the voltage stability is known as load stability. The optimal allocation and sizing of DG improves voltage regulation, reduces the system losses and improves of the reliability of supply.
To get the optimum locations of DG by placing the DG at the node that VSI value is less compare to all the nodes. The amount of active power supplied from DG varies from 0% to 100% of the total active power load with consideration of constraints.
Allocation DG and sizing algorithm using VSI
Perform load flow to calculate the bus voltage magnitudes and the total power loss.
Compute the VSI for each bus.
VSI(n_2 )=(V_1 )^4-4(P_2 R_1+Q_2 X_1)(V_1 )^2-4(P_2 X_1-Q_2 R_1 )^2 (**.20)
Select the bus having the lowest value of VSI and place DG
Run power flow and find losses again
Change the size of DG to small step and calculate losses
Find the size of DG which leads to the lowest power system losses.
b- Placement of DG using power stability index (PSI)
DG in the distribution system will reduce the active line component of the current. The power stability index (PSI) is derived for finding the most optimum site of DG based on the most critical bus in the system that can lead to system voltage instability when the load increases above certain limit (7).
The PSI is given by:
PSI=(4r_ij (P_L-P_G))/([|V_i |Cos(θ-δ)]^2 ) ≤1 (**.25)
Where,
rij Resistance between two buses i and j
PL Active power load
PG Active generated power
Vi Voltage at bus i
θ Phase angle
Under stable operation, this value should be less than unity; closer the value of PSI to zero, more stable will be the system.
Allocation DG and sizing algorithm using PSI
Perform load flow to calculate the bus voltage magnitudes and the total power loss.
Compute the PSI for each line in the given system and arranged from high to the lowest value.
The line whose PSI value is higher, DG is placed at the receiving end node.
Figure 3 flow chart of allocation DG using PSI (REF)
a- Genetic Algorithm
Genetic Algorithm is a general-purpose search techniques based on principles inspired from the genetic and evolution mechanisms observed in natural systems and populations of living beings. Their basic principle is the maintenance of a population of solutions to a problem (genotypes) as encoded information individuals that evolve in time (8). The present work has two control variables such as location and size of DG. The suggested algorithm is programmed under MATLAB software (2014b) using Genetic Algorithm Toolbox (GA)
Figure (**.4) Genetic Algorithm Method
Algorithm for Optimal Placement and Sizing of DG using GA (8)
1- Start: create random population of m chromosomes.
2- Fitness: Find the fitness of each chromosome in the population.
3- New population:
(a) Selection-it is based on the fitness function.
(b)Recombination -crossover chromosomes
(c) Mutation -mutate chromosomes
4- Acceptation: accept or reject the new one
5- Replacing the old: replace the old population by new.
6- Test: test for problem standard
7- Loop: carry on with step 2, 5 until the standard is fulfilled.
In this study the following parameters were set and the rest are default by the GA:
Population Size: 100
Generations: 200*no of variables
Selection Function: Tournament
Crossover Function: Intermediate
Crossover Fraction: 0.7
Penalty Factor: 50
b- Particle swarm Optimization
Particle swarm optimization (PSO) is a population based stochastic optimization technique developed by Dr. Eberhart and Dr. Kennedy in 1995, inspired by social behavior of bird flocking or fish schooling.
PSO shares many similarities with evolutionary computation techniques such as Genetic Algorithms (GA). The system is initialized with a population of random solutions and searches for optima by updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation. In PSO, the potential solutions, called particles, fly through the problem space by following the current optimum particles.
Compared to GA, the advantages of PSO are that PSO is easy to implement and there are few parameters to adjust. PSO has been successfully applied in many areas: function optimization, artificial neural network training, fuzzy system control, and other areas where GA can be applied (9).
In conventional PSO, particles change their positions (states) with time. Let ‘u’ and ‘v’ denote a particle coordinates (position) and its corresponding flight speed (velocity) in a search space respectively. The position vector ui and the velocity vector vi of the i th particle in the n dimensional search space can be represented as (10).
u_i=(u_i1,u_i2,……..,u_in) (**.26)
v_i=(v_i1,v_i2,……..,v_in) (**.27)
The best previous position of the I the particle is recorded and represented as
P_best=(u_i1^pbest,u_i2^pbest,…….,u_in^pbest)
(**.28)
The index of the best particle among all the particles in the group is represented by
G_best=(u_i1^Gbest,u_i2^Gbest,…….,u_in^Gbest)
(**.29)
The modified velocity and position of each particle can be calculated as per following formulas
v_i^((k+1) )=ωv_i^((k) )+c_1 r_1×(〖Pbest〗_i^((k) )-u_i^((k) ) )
+c_2 r_2×(〖Gbest〗_i^((k) )-u_i^((k) )) (**.30)
u_i^((k+1))=u_i^((k))+v_i^((k+1)) (**.31)
Where,
ω,c1, c2 ≥0, k is the iteration number.
ω: is the inertia weight factor
c1 and c2 : are the acceleration coefficients.
r1 and r2 : are two random numbers within the range [0,1].
v_i^((k) ),u_i^((k) ): are the velocity and the current position of particle i in the search space at iteration k , respectively.
The proposed PSO-based technique for optimal allocation of DG units in the power systems is as follows (11):
Input data of the system and busbar voltage limits
Calculate the system power loss
Randomly generate an initial population of particles with random positions and velocities on dimensions in the solution space. Set the iteration counter k=0, each particle consisted of 2 parts, n for sizes and anther n for location of DG units.
For each particle, if the bus voltage is within limits calculate the total system power loss. Otherwise, that particle is infeasible.
For ach particle, compare its objective value with the individual best , if the objective value is lower than Pbest, set this value the current Pbest and record the corresponding particle position
Choose the Particle associated with the minimum individual best Pbest of all particles and set the value of this Pbest as the current overall best (gbest ).
Update the velocity and position of particle using (**.30).
If the iteration number reaches the maximum limit, got to step 9 , otherwise set iteration index k=k+1 and go back to step 4.
Print out the optimal solution, the best position includes the optimal location and size of DG units.
C- Biogeography Based Optimization
BBO is inspire from the theory of island biogeography that is based on mathematical models that describe the emigration, immigration, and distribution of species among islands .The suitability of an island for life is quantified by habitat suitability index (HSI. An island with a high HSI has a high emigration rate (), and the immigration rate () of the island is low. In BBO, a good individual (candidate solution) is analogous to an island with a high HSI, and poor individual is analogous to an island with a low HSI. The sharing of features (independent variables) among individuals is analogous to migration between islands.
BBO is initialized with a random population. Based on the cost values, and values are assigned to each individual, which are the emigration rate and immigration rate, respectively. Good individuals have a larger and a smaller compared to poor individuals. If an individual is probabilistically selected for immigration, then the emigrating individual is chosen by roulette wheel selection on the basis of all of the values in the population (12). The immigration and emigration rates are the functions of the number of species in the habitat and defined for a habitat containing k -species as (13)
μ_k=1/2 (1+cos⁡((πr_k)/N) ) (**.32)
λ_k=1-μ_k (**.33)
Where N is the population size and rk is the cost rank of the k-th individual,
Figure (**.4) Migration models for BBO
After migration between individuals, mutation is used to diversify the population. Also, the best solutions are kept as elites for the next generation. Mutation rate, the number of elites, and the population size need to be tuned to achieve good optimization performance.
The Pseudo-Code for the BBO Algorithm
**-4 Fuzzy Decision Making
The fuzzy sets are defined by equations called membership functions. These functions represent the degree of membership in fuzzy sets using values from 0 to 1. The membership value ‘0’ indicates incompatibility with the sets, while ‘1’ means full compatibility. Fuzzy membership functions which assign a degree of satisfaction to each objective are defined based on which the best solution can be found out of the available pareto-optimal solutions.
Here, it is assumed that μ(Fi) is a strictly monotonic decreasing function defined as (14):
μ(F_i )={█(1 ;F_i≤F_i^min@(F_i^max-F_i)/(F_i^max-F_i^min ) ;F_i^min≤F_i≤F_i^max@0 ;F_i^max≤F_i )┤ (**.34)
Where,
Fimin and Fimax are the expected minimum and maximum values of ith objective function. The best solution can then be selected using fuzzy min-max proposition.
μ_(bestsolution )=Max{min⁡[μ(F_j ) ]^k} (**.35)
Where,
j is number of objectives to be minimized and k are number of pareto-optimal solutions obtained.
Chapter (**)
Modeling and Problem Formulation
**-1 Introduction
Installing DG in an electrical distribution system has numerous positive impacts, but these impacts can be further enhanced if the DG units are installed at a proper place and in a proper size. Non-optimal placement and sizing of DG units can cause significant negative repercussions on distribution systems. In this chapter, the optimal DG sitting and sizing problem is reviewed using a different methods of the optimization techniques that is subjected to equality and inequality constraint equations. The optimal DG size problem is solved via the bus-injection to branch-current (BIBC) and branch-current to bus-voltage (BCBV) matrices method and by performing this method at all candidate buses (1). The bus with a minimum losses will be selected as the optimal location to install the DG. The proposed technique succeeds in solving single and multiple DG installations for both radial distribution systems.
**-2 Problem Formulation
A basic single-objective optimization problem can be formulated as follows:
〖Min/Max〗_(x∈R^n ) : f(x) (**.1)
subject to: h(x)=0 ,i=1,2,…,n
(**.2)
g_i (x)≤0 ,i=1,2,…,m
(**.3)
x^min≤x≤x^max (**.4)
Where,
f(x) : The objective function, a function of x that we want to maximize or minimize.
h(x), g(x) : The vectors of equality and inequality constraints that the unknowns must satisfy.
x : The vector of n decision or unknown variables and x=[x1, x2, … , xn].
The multi-objective optimization problem can be mathematically formulated as follows:
〖Min/Max〗_(x∈R^n ) : F(x)=[ f_1 (x),f_2 (x),…,f_k (x)] (**.5)
subject to: h_i (x)=0 ,i=1,2,…,n
(**.6)
g_i (x)≤0 ,i=1,2,…,m
(**.7)
x^min≤x≤x^max (**.8)
Where, F(x) is a vector of k objective functions.
**-2-1 Objective Functions
The objective functions utilized in the optimization problem are the total real power losses function, the total cost of DG installation cost and voltage stability index. All objective functions are subjected to equality and inequality constraints.
1- Power Losses
min⁡〖f_1 (x)=〗 Plosses
The total power losses will be formulated as a function of the power injections based on the equivalent current injection. The formulation of total power losses will be used for determining the optimum size of DG and calculation of the system losses. The total active and reactive losses (i.e Pl and Ql) in the distribution system with N buses can be calculated by (2),
Pl=∑_(b=1)^N▒〖|I_b |^2 R_b 〗 (**.9)
Ql=∑_(b=1)^N▒〖|I_b |^2 X_b 〗 (**.10)
Where,
Rb and Xb are respectively the resistance and reactance of branch b.
Ib is the current magnitude.
At each bus b, the equivalent current Injection is determined by
I_b=(P_b-〖jQ〗_b)/(V_b^* ) (**.11)
Where,
Vb is the node voltage, Pb + jQb is the complex power at each bus b, n is the total number of buses.
The branch current B is calculated with the help of BIBC matrix. The BIBC matrix is the result of the relationship between the bus current injections and branch currents. The elements of BIBC matrix consist of ‘0’s or ‘1’s
[B]_(nb*1)=[BIBC]_(nb*(n-1)).[I]_((n-1)*1) (**.12)
Where,
nb is the number of the branch, [I] is the vector of the equivalent current inject ion for each bus except the reference bus.
The total power losses can be obtained as a function of the bus current injection:
Ploss=∑_(b=1)^nb▒〖|B_k |^2.〗 R_k=[R]^T |[BIBC].[I]|^2 (**.13)
The voltage drop from each bus to the reference bus is:
[∆V]_((n-1)*1)=[BCBV].[BIBC].[I] (**.14)
Where,
BCBV matrix is the relations between branch currents and bus voltages. The elements of BCBV matrix consist of the branch impedances (1).
Algorithm of BCBV matrix
Read BIBC matrix, Zb branch impedance vector
Convert Zb vector to a diagonal matrix (Z).
Multiply transpose of BIBC matrix with Z matrix ([ BCBV] = [BIBC] . [Z])
Algorithm for Distribution System Load Flow
Figure **.1: Flowchart for load flow solution for radial distribution networks.
Algorithm for Distribution Networks Load Flow with DG
The algorithm steps for load flow solution of distribution networks are given below (3):
Step 1: Read the distribution networks line data and bus data.
Step 2: Calculate DG power for each nodes and update the system bus data.
Step 3 Calculate the total power demand with DG, [S]=[S_(D_b ) ]-[S_(〖DG〗_b ) ].
Step 4: Calculate the each node current or node current injection matrix.
Step 5: Calculate the BIBC matrix.
Step 6: Evaluate the branch current by using BIBC matrix and current injection matrix.
Step 7: Form the BCBV matrix.
Step 8: Set Iteration k = 0.
Step 9: Iteration k = k + 1.
Step 10: Update voltages.
I_b^k=((P_b+〖jQ〗_b)/(V_b^k ) )^* (**.15)
[∆V^(k+1) ]=[BCBV].[BIBC].[I^k ] (**.16)
[V^(k+1) ]=[V^0 ]+ [∆V^(k+1) ] (**.17)
Step 11: If max (([V(k+1)-|V(k)| > tolerance) go to step 5.
Step 12: Calculate branch currents, and losses from final node voltages.
Step 13: Display the node voltage magnitudes and angle, branch currents and losses.
Step 14: Stop
2- Cost of Installation DG.
min⁡〖f_2 (x)=〗 〖DG〗_Cost
The total cost of DG installation can be mathematically formulated as (3):
Cost= ∑_(i=1)^nDG▒〖(C_Cap*P_i^DG )+8760 X ∑_(t=1)^T▒μ_t ∑_(i=1)^nDG▒〖((C_(M&O)+C_var×n)X P_i^DG)〗〗 (**.18)
presentworth:μ_t=1/((1+d)^t ) (**.19)
Where,
Ccap Investment Cost (M$/kW)
CM&O Maintenance and Operation Cost ($/kwh)
Cvar Variable Cost ($/kwh-year)
PiDG Generated power by DG source installed in bus i (Mw)
d Discount rate
t
Planning period (year)
nDG Number of DG placements in the network
The following parameters are set according to the type of DG (4).
Table 1 : Constant parameter of the studied cases
(C1)
$/kw (C2)
$/KWH (C3)
$/KWH.Y (n)
Biomass 3830 15 95 20
Micro turbine 2250 3.67 6.31 20
Solar 3180 0 48 20
Wind 1980 0 60 20
Hydrothermal 3500 6 15 20
CHP 1647 16 6.5 20
Fuel Cell 2334 35 6.5 20
3-Voltage Stability index
max⁡〖f_3 (x)=〗 〖VSI〗_min
VSImin : Voltage stability index at node that has minimum voltage instability
The voltage instability index (VSI) is used for finding the most critical collapse (5). VSI for each node is calculated by:
VSI(n_2 )=(V_1 )^4-4(P_2 R_1+Q_2 X_1)(V_1 )^2-4(P_2 X_1-Q_2 R_1 )^2 (**.20)
Where,
n2 Receiving end node
V1 Voltage of node n1
P2 Total real power load fed through node n2
Q2 Total reactive power load fed through node n2
R1 Resistance of branch i
X1 Reactance of branch i
**-2-2 Constraints
Equality Constraints:
Load balance
The constraint of power flow equation is described as follows.
P_g+∑_(i=1)^N▒〖P_(〖DG〗_i )=∑_(i=1)^N▒〖P_(D_i )+P_L 〗〗 (**.21)
Where,
Pg Injected generation power at slack bus
PDG Real power of distributed generation
PD Demand power
PL Losses Power
Inequality Constraints:
Voltage limits
For each bus, there should be an upper and lower voltage bounds (6)
|V_i |^min ≤ |V_i |≤|V_i |^max (**.22)
Where,
|V_i |^min = 0.95 pu , and |V_i |^max=1.05 pu.
Generation Limit
P_(〖DG〗_i)^min≤P_(〖DG〗_i )≤ P_(〖DG〗_i)^max (**.23)
Q_(〖DG〗_i)^min≤Q_(〖DG〗_i )≤ Q_(〖DG〗_i)^max (**.24)
Where,
P_(〖DG〗_i)^min, P_(〖DG〗_i)^max: The lower and upper active generating unit limits respectively.
Q_(〖DG〗_i)^min, Q_(〖DG〗_i)^max: The lower and upper reactive generating unit limits respectively.
Thermal constraint
**-5 Results and Discussions
**-5-1 Software Tools and Test System
In this thesis, the study tools, which were presented in the previous chapter, including methodologies and algorithms have been developed for distributed generation. These tools have been coded in MATLAB environment. A test distribution system from 69 buses has been employed throughout in this thesis. A brief description system is provided below.
69-Bus Test System
A single line diagram of the 12.66 kV, 69-bus test radial distribution system is shown in Figure. It has one feeder with eight laterals, 68 branches, a total peak load of 3800 kW and 2690 kVAr and its corresponding loss of 224.93 kW. Its complete load data are provided in Table A.2 (Appendix A) (15)
Normal Case:
This case is without distributed generation
Ploss=224.98 and Qloss=102.16
minVoltage= 0.90919 at bus 65
Figure 4 Voltage Profile without DG
Figure 5Current Branch Magnitude
**-5-2 Single Objective Function:
In this section, it’ll be discussed the results of different ways to placement the DG using one objective function power losses.
Results of placement of DG using voltage stability index
By using (equation (**.20)) it found that the minimum voltage stability is 0.6834 at bus 65. As discussed, DG is located in the bus that has minimum VSI at 65. When the amount of the power supplied from DG varies, the parabolic curve is obtained as a relation between DG size and losses, first decreases, and then increases (Fig)
Figure 6 The relation between size and power losses , DG installed at bus 65
Suitable size of DG to get min PLosses= 1.4 MW
Figure 7 Voltage Profile Before and After Installing DG
Figure 8 Current Branch Magnitude
PTloss=112.1 kw
QTloss=55.148 kw
Results of placement of DG using Power Stability Index
By using (equation (**.25)) it found that the max PSI is 0.0234 between bus 60 and bus 61.alllocate DG at bus 61. The relation between DG size and losses as shown (Fig)
Figure 9 The relation between size and power losses DG installed at bus 61
Suitable size of DG to get min PLosses= 1.8 MW
Figure 10 Voltage Profile Before and After Installing DG
Figure 11 Current Branch Magnitude
PTloss=83.213 kw
QTloss=40.547 kw
(Add comparison between result of considering bus or branch voltage)
Results of placement of DG using Heuristic Methods
As shown in the table (), the comparison between different optimization tools GA, PSO and BBO. A single optimization function is used when the objective function is minimizing the power losses in case of unity PF.
Title Parameter for each method needed
methods GA PSO BBO
Location of DG 61 61 61
Size (MW) 1.9 1.9 1.88
ما سبق تم اختيار المكان بناء على اقل معامل اتزان و السعة بناء على القدرة المفقودة
**-5-3 Multi-objective functions
In this section, the objective functions are minimizing power losses, minimizing cost and maximizing the minimum value of voltage stability index. A multi-objective optimization problem is applied to obtain the Pareto optimal set of non-dominated solutions and the compromise solution among them. Single and multiple DG installation cases are considered in the test, which ended with comparative study with different units of DG.
Installing a single DG
By using multi-objective genetic algorithm, the Pareto optimum front consists of 50 solutions. The Pareto optimal is obtained as a figure;
Figure 12 Pareto Front
The best compromise solutions can be obtained by applying the fuzzy decision-making method to the generated Pareto optimal front.
The result that obtained in matlab
Location PDG Losses Cost minVSI
Sol 1 61 1900 28.32856 7.6844 0.8915
Sol2 65 1254 70.76672 5.0703 0.8731
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Compromise solution 58 655 133 3.1461 0.7585
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Sol 49 25 98 215.9682 0.3973 0.6859
Sol 50 58 637 134.7728 2.5747 0.7563
Comparison between optimization techniques
As discussed that the different ways of heuristic methods that used to determine the location and size of the distributed generation such as multi-objective genetic algorithm (MOGA), Particle Swarm Optimization(PSO) and Biogeography Based Optimization(BBO). Table () is define the time execution of each optimization technique in case of installing one DG. The specification of PC that used is Intel core i5 with ram 6 GB.
Time execution (sec)
MOGA 492.75
PSO 153.23
BBO 20.39
As shown that the execution time of BBO is less valuable than other methods while MOGA has the highest value.
Voltage Profile of Optimization Techniques
Figure 13 Voltage Profile Optimization Techniques
Figure 14 Voltage Profiles in without and with DG Application using BIBC and BCBV load flow method
Comparison between a compromise solutions of Heuristic Methods for Different Power Plants
Conclusion
In this thesis, a comparative between the optimization techniques used for optimal distributed generation Allocation and sizing of Distributed generation Systems using different based artificial intelligence techniques. After case study it can be concluded that different methods used for this optimization techniques are MOGA, PSO and BBO. The proposed techniques are applied to IEEE 69 bus system radial distribution system. Based on the results, the proposed algorisms have the capability to allocate the distribution generation; the results also illustrate the efficiency of these approaches for the voltage profile improvement and power losses reduction. Also depending on the characteristics of the demand, the dispatchable DG is implemented and affected in the power losses.