Application of Honey Bee Mating Optimization on Distribution State Estimation Including Distributed Generators Jia-Xian Zhu

Introduction Distribution State Estimation (DSE) Distributed Generators (DGs) Load Static Var Compensators (SVCs) Voltage Regulators (VRs) Under Load Tap Changer (ULTC)

Introduction Online monitoring of power distribution systems plays a key role in this part of power systems and improve efficiency and reliability of the power distribution system. The performance of online monitoring highly depends on the quality of load data and DG outputs.

Introduction A number of DSE methods have been developed in distribution systems, which are divided into two main categories. –Statistical methods, which usually use an iterative convergence method. –Load adjustment state estimation, which usually utilize sensitivity analysis. It is assumed that the objective functions and constraints should be continuous and differentiable. Due to the existence of distributed generation, as well as SVC and transformer tap changers with discrete performance.

Introduction Recently, a new optimization algorithm based on honey bee mating has been used to solve difficult optimization problems such as optimal reservoir operation and clustering. In this paper, a new approach based on HBMO for a practical distribution state estimation including DGs, SVC and VRs is presented. The proposed approach is compared with the methods based on neural networks, Ant Colony Optimization (ACO), and genetic algorithms for two test systems.

Distribution State Estimation Including Distributed Generators The state variables vector including the loads’ and DGs’ outputs. zizi The i th measured values. wiwi The weighting factor of the i th measured variable. hihi The state equation of the i th measured variable. mthe number of measurements. NgNg The number of DGs with variable outputs. NLNL The number of loads with variable outputs. PiGPiG The active power of the i th DG. P i load The active power of the i th load.

Distribution State Estimation Including Distributed Generators The absolute power flowing over distribution lines. The maximum transmission power between the nodes i and j. Tap i The current tap positions of the i th transformer. NtNt The number of transformers and VRs installed along feeder. ViVi the actual voltage magnitude of the i th bus. QicQic The reactive power of the i th capacitor. NcNc The number of capacitors installed along feeder.

Distribution State Estimation Including Distributed Generators In order to have a unique solution, these assumptions should be made: –Status of distribution lines and switches is known. –A contracted load and distributed generation values are known at each node. –Voltage and current at the substation bus (main bus) are known. –If outputs of DGs and loads are fixed, the outputs and power factors will be available. –If outputs of DGs and loads are variable, the average outputs, the standard deviations and the power factors can be obtained. –Set points of VRs and local capacitors are known.

Distribution State Estimation Including Distributed Generators Objective function

Distribution State Estimation Including Distributed Generators Constraints –Active power constraints of DGs: –Distribution line limits: –Tap of transformers:

Distribution State Estimation Including Distributed Generators Constraints –Bus voltage magnitude: –Active power constraints of loads: –Reactive power constraint of capacitors:

Honey-bee modeling A colony may contain one queen or more during its life- cycle, which are named monogynous and/or polygynous colonies. Broods arise either from fertilized or unfertilized eggs. –The former represent potential queens or workers, whereas the latter represent prospective drones. A queen is the only member of a colony capable of laying eggs which are fertilized by spermatozoa. –A queen life time is 6-7 years. Drones' sole function is to mate with the queen. –They live about eight weeks. –Any drones left at the end of the season are considered non- essential and will be driven out of the hive to die.

Honey-bee modeling Worker bees do all the different tasks needed to maintain and operate the hive. –Workers born early in the season will live about 6 weeks while those born in the fall will live until the following spring. Mating flight. Only the queen bee is fed ‘‘royal jelly”. ‘‘Nurse bees’’ secrete this nourishing food from their glands and feed it to their queen.

Honey-bee modeling

Application of the HBMO to Distribution State Estimation Step 1: Define the input data –The speed of queen at the start of a mating flight (S max ). –The speed of queen at the end of a mating flight (S min ). –The speed reduction schema (  ), the number of iteration, the number of workers (N Worker ). –The number of drones (N Dreone ). –The size of the queen's spermatheca (N Sperm ). –The number of broods (N Brood ).

Application of the HBMO to Distribution State Estimation Step 2: Transfer the constraint DSE to the unconstraint DSE – f(X) is the objective function values of DSE problem. –N eq and N ueq are the number of equality and inequality constraints, respectively. –h i (X i ) and g i (X i ) are the equality and inequality constraints. –K 1 and k 2 are the penalty factors, respectively.

Application of the HBMO to Distribution State Estimation Step 3: Generate the initial population

Application of the HBMO to Distribution State Estimation Step 4: Calculate the augmented objective function value Step 5: Sort the initial population based on the objective function values Step 6: Select the queen

Application of the HBMO to Distribution State Estimation Step 7: Generate the queen speed –The queen speed is randomly generated as: Step 8: Select the population of drones –The population of drones is selected from the sorted initial population as:

Application of the HBMO to Distribution State Estimation Step 9: Generate the queen's spermatheca matrix (Mating flight) –At the start of the mating flight, the queen flies with her maximum speed. –A drone is randomly selected from the population of drones. –The mating probability is calculated based on the objective function values of the queen and the selected drone. Prob(D) is the probability of adding the sperm of drone D to the spermatheca of the queen,  (f) is the absolute difference between the fitness of D and the fitness of the queen and S(t) is the speed of the queen at time t. The probability of mating is high when the queen is with the high speed level, or when the fitness of the drone is as good as the queen's.

Application of the HBMO to Distribution State Estimation –A number between 0 and 1 is randomly generated and compared with the calculated probability. If it is less than the calculated probability, the drone's sperm is sorted in the queen's spermatheca and the queen speed is decreased. Otherwise, the queen speed is decreased and another drone from the population of drones is selected until the speed of the queen reaches to her minimum speed or the queen's spermatheca is full.

Application of the HBMO to Distribution State Estimation Step 10: Breeding process –Where β is a random number between 0 and 1. Brood j is the j th brood.

Application of the HBMO to Distribution State Estimation Step 11: Feeding selected broods and queen with the royal jelly by workers –Improve the newly generated set of solutions employing different heuristic functions and mutation operators according to their fitness values. Step 12: Calculate the augmented objective function value for the new generated solutions –The augmented objective function is to be evaluated for each individual of the new generated solutions by using the result of distribution load flow. If the new best solution is better than the queen replace it with queen. Step 13: Check the termination criteria –If the termination criteria satisfied finish the algorithm, else discard all previous trial solutions and go to step 3 until convergence criteria met.

Simulation results It is assumed that the following information is available. –Value of output for constant loads and DGs. –Average value and standard deviation for variable DGs and loads. –Values of measured points –Power factor of Loads and DGs –Set points of VRs and local capacitors

Simulation results For this system it is assumed that there are three DGs connected at buses 6, 17 and 29.

Simulation results Comparison of measured and estimated values for DGs DG No HBMOACOGANN actualestimatedactualestimatedactualestimatedactualestimated G G G

Simulation results Comparison of execution time Comparison of average and standard deviation for different executions MethodHBMOACOGANN Execution time(s) ~0 MethodAverageStandard Deviation (%) ACO GA NN HBMO

Simulation results Maximum Individual Relative Error Maximum Individual Absolute Error where X est and X true are the estimated and actual values, respectively.

Simulation results Comparison of errors for estimated loads ACOHBMONNGA MIRE(%)value location MIAE(%)value location

Simulation results Comparison of errors for estimated DGs ACOHBMONNGA MIRE(%)value locationDG2DG1 DG3 MIAE(%)value locationDG2DG1DG3

Simulation results A single line diagram of 80-bus test system

Simulation results Comparison of execution time Comparison of average and standard deviation for different executions MethodHBMOACOGANN Execution time(s) ~0 MethodAverageStandard Deviation (%) ACO GA NN HBMO