Instantaneous Wind Penetration Using Particle Swarm Engineering Essay

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Abstract- In this paper a new algorithm and methodology have been proposed for attaining the maximum safe instantaneous wind penetration model by the optimization of Grid Control Parameters based on neuro Particle Swarm Optimization. The developed algorithm has been tested on modified IEEE 14 bus test system. The results shows the maximum safe instantaneous wind energy penetration limit in percentage and also maximum safe bus loading point explicitly beyond which system drives into instability.

Keywords - Wind power generation, Wind Penetration, Weibull distribution, Particle Swarm Optimization


Eigen Value of the state Jacobian Matrix

Violated Constraint Index, No: of Violated Constraints

Total Number of Wind Turbines, Farms

Total No: of Buses , Generators

Active Power , Reactive Power

Penalty Factor & Violation of constraint k.

Real Power Delivered by turbine wt of wind Farm

Total real Power Output of all the Wind Farms


Wind speed /Voltage rank of Bus j

Voltage Tangent Vector rank of Bus j

Interconnection cable length rank of Bus j

Wind farm placement distance from the Wind Bus

Wind Turbine/Wind Farm Index


Rotor Speed, Rotor Reference Speed

Wind Farm Placement Index of Bus j

Index of Grid connection of Bus j

Maximum Safe Instantaneous wind energy penetration limit.


Grid connected Wind Turbine Generators (WTGs) in large numbers can introduce unwanted conditions such as: loss of synchronism, voltage collapse, load shedding, large deviations in voltage and/or frequency , introducing flicker and harmonics in high transmission and distribution losses, over loading and increased power oscillation[1]. Among the various types of wind turbines available, DFIG is having lots of advantages such as the reactive power compensation and hence, DFIG has been used in this work. The Wind Power penetration, in a grid, is the ratio of wind power output to the load at an instant of time and has been termed as instantaneous penetration [2].

So far, the area of maximum wind penetration was based on stochastic analysis by taking into account the capacity credit.[3][4]. In the deregulated electricity market, authorities always under rate the Wind Acceptance Rejection factor for the sake of maximum grid stability and has been treated as constant. The calculation of the above factor has been the trade secret of the electricity authority and lots of rejections are taking place due to the wrong chosen of the factor.[5-8] Moreover the factor is quite time varying in nature and cannot be treated as constant. The proposed algorithm consisted of two stages; Identification of the suitable bus for wind farm placement [9] and secondly the calculation of the maximum instantaneous wind share possible in the grid by holding all the control and operational constraints within limits .

Wind Farm Modeling

The dynamic nature of the instantaneous wind penetration problem requires detailed dynamic modeling of power system components including wind and turbine generators as well. Wind has been modeled as a Weibull distribution by taking into account the composite nature of wind which includes average, ramp, gust and turbulence components and low pass filter has been used to smooth the wind speed variations. The turbine generator used is DFIG. The stator is directly connected and the rotor is connected to the grid through slip rings and lossless power electronic converter. The modeling is in compliance with IEEE 14 - bus dynamic model as given in Table I


Component Model Specifications

Power System Component



Synchronous ; Order V, Type 2

Turbine Governor

IEEE Type -1

AVR Model

IEEE Type -2


Constant PQ Model

Maximum Instantaneous WIND PENETRATION Problem

The reason for WTG interconnected operation is Fuel Displacement and for earning Capacity credit [14][15]. The quality of the interconnected operation has been assessed in terms of operational constraints and the normal operation presupposes that a number of constraint parameters are to be maintained with in predetermined limits of which the most significant ones are voltage and frequency. Only fundamental frequency based analysis has been considered and the analysis assumed suitable buffer energy storage to handle the unpredicted power level fluctuations in additional to the adequate spinning reserve.

A. Problem Formulation

1. Objective Function:

The objective of the penetration problem is to maximize the wind share in the grid. Accordingly, the objective function have been formulated for any time t as

2. Power Balance Constraints:

Equality constraints are a mainly nodal power equation which has to be satisfied in each time interval

3. Generator & System Operating Constraints:

Wind power constraint:

The wind power used for dispatch should not exceed the available wind power from the wind park:

Power System Stability Constraints:

The small signal stability model of the system with DFIG can be expressed as

, where A is the System State Matrix

where are power flow jacobian matrices

If the complex eigenvalues of the linearized system have negative real parts, then the power system can withstand small disturbances and is considered stable in the small-signal sense. The Eigen value stability analysis [11] is incorporated to the constraint by the expression.

Optimization Algorithm

Fitness function for the above problem has been formulated as

A. Wind Farm Placement

The bus to which the wind farm to be placed is identified by the calculation of wind farm placement index [13]

= 1; if ;= 2; if ;= 3; if

; For generator bus; Rank from high voltage to low voltage.

; Rank bus bars from higher value to lower.

; Rank bus bars from higher value to lower.

= 0; for major power system grid else = Number of buses in the small mesh of load buses getting connected to the single node of the major grid. The constants have been suitably chosen depending on the grid by giving suitable weight. Tangent vector of the node voltage determines the weakest bus.

B. Neuro Particle Swarm Optimization [10].

Neural network trained particle swarm algorithm has been used to identify the optimal loading pattern and thereby to determine the maximum safe instantaneous penetration

C. Methodology

Step 1: Input line data and bus data, wind data, voltage and line limits, PSO settings.

Step 2: Identify the best location for wind farm placement by the calculation of wind farm placement index and connect the wind farm to that particular bus.

Step 3: Calculate the base case power flow with the wind farm at the identified bus.

Step 4: Randomly generate an initial population (array) of particles with random positions and velocities on dimensions in the solution space. Set the iteration counter k = 0.

Step 5: For each particle, calculate and compare its objective function value with the individual best. If the objective value is

higher than Pbest, set this value as the current Pbest, and record the corresponding particle position.

Step 6: Choose the particle associated with the minimum individual best Pbest of all particles, and set the value of Pbest as the current overall Gbest.

Step 7: Update the velocity and position of particle using the velocity and position update equations

Step 8: If the iteration number reaches the maximum limit, go to step 9. Otherwise set iteration index k = k+1 and go back to step 5.

Step 9: Print out the optimal solution to the target problem. The best position include the maximum load in each load bus , the initial MVA , power angle settings of slack generators and the initial voltage settings of all the PV buses and the fitness value gives the maximum safe instantaneous wind penetration limit (ψ) .

Results & Discussions

The proposed methodology has been tested on IEEE 14 bus modified test system as given in figure 1 with the only modifications of load MVA rating have been reduced by 50% and the Wind Farm have been connected at Bus No: 2. Detailed dynamic modelings of the generator have been used and the loads are modeled as constant power loads (PQ load) and is solved by using Newton Raphson Power flow analysis routine. The Wind Bus is modeled as a Vɵ bus and the load sharing between the Wind Generators and the system generators is through the initial bus angle setting.

Fig. 1. IEEE 14 Bus Modified Test system

The program has been coded in an integrated PSAT/Matlab integrated environment [12] and is run for 250 iterations. The Wind Farm Placement Index Calculation identifies Bus-2 as the most suitable bus and accordingly Wind Farm of 600 MVA / 69kV capacity comprising of 30 Wind Turbines have been connected to the Bus-2 by assuming that wind farm is located at an equidistant point from all the buses and the constants have been chosen on trial and error basis with practical study on Thailand and practical power system

B. Maximum Penetration Calculation

The base case power flow results shows the active power generation of 1.86pu with an active power loss of 0.05pu.

The PSO optimization shows the maximum safe instantaneous wind share 44.07% with no positive eigen values and all voltages, line flows generations are all within permissible limits. The initial settings for maximum penetration have been given in Table II

The loading level and generation level at maximum penetration have been given in Fig-2. The additional loading is only an indication of the excess load capacity of the bus if incase required. The excitation of the voltage generator buses have to be set to a slightly higher excitation level for maximizing the penetration. For maximizing the penetration different control strategies as given in Table III have been formulated for comparison and the best can be chosen and adapted depending on the flexibility of the grid in terms Generator Capacities, AVR ratings, response characteristics, losses etc.

Fig. 2. Generation & Load Level during penetration


Maximum penetration in various control dimensions

Penetration in Various Control Strategies







V1 (V)






Slack Bus













Wind Bus



















PV Buses













Pw (pu)






Max Wind Share









A methodology for safe instantaneous wind energy penetration limit (has been formulated and tested by taking into account the operational and stability constraints.


The Wind Model


wind model parameters

Nominal Wind Speed


Air Density


Filter Time Constant/Sample Time


Weibull Constant C & K


Ramp Constants [ ]


Gust Constants [ ]


Turbulence Constants [ ]


DFIG Model


dfig parameters

[MVA,KV,Hz], kWs/kVA

[600 69 60], 3pu

[Rs,Xs] [Rr,Xr] Xm

[0.01 0.10] [0.01 0.08] 3.00pu

Kp, Tp, Kv, Te

[10pu 3s], 10pu, 0.01s

Pole, Gear Ratio

[4 1/89]

Blade Length and Number

[75.00m 3]

Pmax, Pmin; Qmax, Qmin

[1.00 0.00]pu; [0.7 -0.7]pu

No of generators