Simultaneous Optimization of Renewable Power at Transmission and Distribution Grid

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Procedia Technology 21 ( 2015 ) 24 – 32

ScienceDirect

Peer-review under responsibility of Amrita School of Engineering, Amrita Vishwa Vidyapeetham University doi: 10.1016/j.protcy.2015.10.005

SMART GRID Technologies, August 6-8, 2015

Simultaneous Optimization of Renewable Power at Transmission

and Distribution Grid

Sasidharan Sreedharan

a*

, Reza Ghorbani

a

, Saeed Sepasi

a

, Weerakorn Ongsakul

b

and

Jai Govind Singh

b

a_{Renewable energy design laboratory (REDLab), University of Hawaii at Manoa. Hawaii, USA}

b_{School of Environment Resources & Development, Energy Field of Study, Asian Institute of Technology, Bangkok Thailand}

Abstract

In this paper, the simultaneous optimization of transmission and distribution grid has been proposed. The dynamic model of the grid consists of turbine governors (TG), automatic voltage regulators (AVR) as well as wind turbines, solar power units and energy storage units. Grid stability is obtained by line stability and voltage stability indices and also by conducting eigenvalue analysis of the complete power system grid. Particle Swarm Optimization (PSO) algorithm adjusts the grid control settings (active and reactive power management) to maximize the renewable penetration at all layers of the grid. IEEE 14 bus system in conjunction with a micro grid is used as the test system. The results demonstrate that simultaneous reactive power management of transmission and distribution grid can maximize the renewable penetration at transmission and distribution layers of the grid. However different case studies with different renewable power pro-files at each layer of the grid are remained to be optimized, this study recommends that real-time management of reactive power at all layers of the grid can be a good candidate to deal with intermittency of renewable sources.

Peer-review under responsibility of Amrita School of Engineering, Amrita Vishwa Vidyapeetham University.

Keywords: Turbine governors; automatic voltage regulators and particle swarm optimization

1. Introduction

For rapid decarburization of the power sector and there by the society, renewable power generation is inevitable. Among the various available renewable energy sources, wind and solar generation are said to hit large integrations in future [1]; but as the renew-able share increases there arises lots of instability problems in the grid.

*Corresponding author. Tel.: +91 9447061365 E-mail address:[email protected]

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Large scale renewable integration may result in unwanted system conditions such as: loss of synchronism, voltage collapse, load shedding, large deviations in voltage and/or frequency, introducing flicker and harmonics, high transmission and distribution losses, over loading and increased power oscillation [2]. Some of the solutions to the above stated problems are to integrate the renewable farms to the most suitable buses and device a suitable grid control mechanism for maximizing renewable penetration. Among the various types of wind turbines available, Doubly-Fed Induction Generators (DFIGs) have lots of advantages [3] and hence DFIG has been used in this work .Moreover, solar PV systems have been used be-cause they are the most versatile, simplest to install and cheapest to maintain, and close to the point of use [4]. In this work to balance the intermittency in renewable power generation, storage systems have been used, as well. Instantaneous penetration in a grid with renewable sources is the ratio of total renewable power out-put to the load at any instant of time [5] which maximized in this work. Most of the works done in the area of maximum wind penetration were on stochastic analysis [6] by taking into account the seasonal variations by assuming a fixed wind absorption rejection factor. In the deregulated electricity market, utilities curtail the wind power to maximize the grid stability [7], thus understanding the wind power penetration limit is vital to grid operators. The literature [8] indicates clearly that integrated distributed generation (DG) could impact the voltage of the distribution grid. When the DG produces more power than the local demand, the net power will flow upstream (towards the substation) [9] which increase the voltage at the substation.

Nomenclature

E j Eigen value of the state Jacobian matrix Fx, Fy, Gy, Gx Power flow Jacobian matrices

k, nk Violated constraint index, No of Violated Constraints

MVAline Line MVA rating

Nb, M Total No of buses, Generators

P, Q Active power, Reactive power

Pfk, Uk Penalty factor & violation of constraint k

PD Total demand power

PW Total real power output of all the wind farms

PS Total real power output of all solar farms

PR Total real power output of all renewable farms

qe Per unit extracted capacity Rwj,RVj Wind speed /Voltage rank of Bus j RTVj Voltage tangent vector rank of Bus j Rlj Interconnection cable length rank of Bus j

Vθ Thermal potential

VD PN junction voltage in solar cell

Vi, Vj Voltage of the bus-i and j respectively

wt, wf Wind turbine/Wind farm index

wj Weight associated with constraint j

θ Ambient temperature

Iwpj Wind farm placement index of bus j

im Battery current

idc Current through low pass filter

igrid, j Index of grid connection of bus j

ψ Maximum safe instantaneous wind energy penetration limit

The proposed algorithm in this paper maximizes the renewable penetration at all layers of the grid by active and reactive power management at both transmission grid and distribution grid (storage). The paper is organized as

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follows; section 2 deals with the underlined methodology and modeling aspects. Maximum renewable penetration problem formulation has been explained in detail in section 3. Section 4 deals with the proposed methodology and results and discussions are given in section 5.

2. Proposed Methodology and Modeling

The proposed methodology consisted of development of a suitable control algorithm for maximizing renewable penetration as shown in the Fig. 1. The development of the algorithm requires detailed problem formulation with dynamic modeling of solar- PV, storage, and wind farm and power system. The purpose of the storage is to balance the adequacy during intermittency.

Fig. 1. Proposed Methodology for Maximum Renewable Penetration

2.1 Wind Farm Modelling

Wind has been modeled as a composite distribution by taking into account its composite nature by including average, ramp, gust and turbulence components [10]. The turbine generator used is DFIG whose stator is directly connected. And its rotor is connected through slip rings and lossless power electronic converter.

2.2 Solar photo voltaic cell

For describing the solar cell electrical circuit equations in [11] are used. This dynamic PV model is suitable for DG applications.

2.3 Battery energy system

A battery is a voltage source [12] that depends on the generated current and on the state of charge (SOC) of the battery itself [13-14]. For battery a dynamic, rechargeable model presented in [15-16] has been used.

Table 1. Component Model Specifications

Power System Component Model Details

Wind model Composite distribution

Wind turbine Doubly fed induction generator Battery energy storage system Li-ion cell

Generator Synchronous ; Order V, Type 2

Turbine governor IEEE Type -1

AVR IEEE Type -2

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2.4 Power system modelling

The power system dynamic modeling was in compliance with IEEE 14 - bus dynamic model as given in Table 1.

2.5 Fast voltage stability index (FVSI)

Fast voltage stability index, proposed by Musirin [17], has been utilized in this paper to assure the safe bus loading as given below:

(1) Where,

Z is the line impedance. X is the line reactance.

Qj is the reactive power at the receiving end.

Vi is the sending end voltage.

The line that exhibits FVSI closed to 1.00 implies that it is approaching its instability point. If FVSI goes beyond 1.00, one of the buses connected to the line will experience a sudden voltage drop leading to system collapse. FVSI index incorporation in the controller assures that no bus will collapse due to overloading.

2.6 Line stability factor (LQP)

(2) Line stability factor assures the controller that no line is overloaded under any grid conditions.

3. Maximum Renewable Penetration Problem Formulation

The quality of the operation has been assessed in terms of operational constraints and the normal operation presupposes that a number of constraint parameters are 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 and storage. The optimization is done on both transmission and distribution grid simultaneously to maximize the penetration of renewable at all layers of the grid. At distribution grid, two feeders are modeled and connected to the transformer at the substation. Feeder 1 has large load with no renewable penetration and feeder 2 has renewable power and battery. It is important to regulate the voltages of the transmission side in order to maximize the penetration of PV power at the distribution grid. This is due to the fact that on load tap changer of the substation cannot serve both the feeders at the same time during high PV and high load penetration.

3.1 Problem formulation

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

Maximize PR = PW + PS (3)

3.2 Power balance constraints

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3.3 Generator & System operating constraints

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3.4 Wind power constraint

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

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3.5 Power system stability constraints

The small signal stability model of the system with renewable power can be expressed as'x A'x

.

, where x is the state vector and A is the system state matrix equal to

F

_x

F

_y

G

_y1

G

_x. Where Fx,Fy,Gy,Gxare power flow

Jacobian matrices. If the complex eigen values of the linearized state equation have negative real parts, then the power system can withstand small disturbances and is considered stable in the small-signal sense. The Eigen value based stability analysis [18] is incorporated to the constraint by the expression.

Ej ( Fx, Fy, Gy, Gx) ≤ 0 (7) 4. Optimization Algorithm

Particle swarm optimization algorithm has been used to identify the optimal loading pattern and thereby to determine the maximum safe instantaneous penetration. Fitness function for the above problem is formulated as in eq (8).

Gn (8)

4.1. Wind farm placement

The bus for connecting the wind farm is identified by the calculation of wind farm placement index [20] as follows: (9) M 1 0dPDPL

¦

PGidPW ij ij 1 ij ij 1 Y cos ( ) Y sin ( ) b b N i Gi Di i j i j j N i Gi Di i j i j j P P P V V Q Q Q V V G G T G G T ½ _° ° ¾ ° °¿

¦

min max min max min , max Gi Gi Gi Gi Gi Gi i i i line line P P P Q Q Q V V V MVA MVA d d d d d d d max ½ ° ° ¾ ° ° ¿ , 1 1 1 ; 6 9 ; 2 ; 6 ; 3 ; 6

0; for generator bus; rank high voltage to low 1/abs (TV) ; 1/ wpj wj v Vj TVj lj grid j TV l wj j wj j wj j Vj TVj lj lj I R C R R R i C C R if W R if W R if W R R R R ½ _° ° d d ° °° d _¾ ° t ° ¿ ° ° °

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Where for major power system grid igrid,j= 0; else igrid,j= Number of buses in the small mesh of load buses getting

connected to the single node of the major grid. Constants have been suitably chosen depending on the grid by giving suitable weight. The weakest bus is determined by tangent vector of the node voltage.

5. Results and Discussions

The proposed methodology has been tested on a modified micro grid test system based on IEEE 14- bus system. The wind farm placement index calculation [19] identifies bus-3 as the most suitable bus and accordingly wind farm is connected to bus-3. The model study is conducted in Matlab-PSAT integrated environment and linked to optimization tool box of PSO.

5.1. Maximum Penetration Calculation

To achieve the maximum renewable penetration, the loads have been increased and this increase is shared by renewable generations. Slack bus is providing only dynamic balance of the grid under various loading conditions.

5.2. Comparison of Results

The bus generations are given in Fig. 2 and 3. Wind farm connected bus is bus No: 15. Solar farms are connected to buses No 26, 29 and 36. From the Fig. 2, it is clear that the wind farm shares a considerable part of the load in the system. The renewable mix at maximum penetration is given in the Table 2. From the table it is clear that there is an increase in renewable penetration by 0.98 pu.

Fig. 4 shows the bus voltage profile at maximum penetration. From the curve, it is clear that all voltage variations are within the specified limits of 0.9 to 1.1 pu. The change in voltage is achieved by the reactive power management of the grid. Figs. 5 and 6 show the load changes at various buses. It is clear that the loads in various buses have been increased by the action of controller. The active power flow changes by various methods are given in Fig. 7. From the figure, it can be identified that the most over loaded lines are the lines 20 and 36.

The lower order Eigen values at maximum penetration show that the system is stable in high degrees of renewable penetration. Only Eigen values from 0 to -1.5 have only been plotted and the higher order values are ignored due to clarity/space issue. The results are compared and consolidated for various methods of wind penetration as given in Table 3. Maximum renewable energy penetration limit is obtained as 41%.

Table 2. Renewable Mix

Solar (pu) Wind (pu)

Bus No 26 29 36 15

Base Case 0.005 0.01 0.0300 1.1999 Max Penetration 0.005 0.04 0.1128 2.0595

Table 3. Result Comparison at Maximum Renewable Penetration

Penetration Type IEEE 14 - Bus modified micro grid test system Total load (pu) Maximum solar share (pu) Wind (pu)

Base Case 3.6612 0.0450 1.25

Maximum renewable penetration (%) 34

Maximum Penetration 5.4041 0.1578 2.2

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Fig. 2. Real power generation in various methods of wind penetration (busses 1-18)

Fig. 3. Real power generation in various methods of wind penetration (Busses 19-36)

Fig. 4. Voltage profiles

0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Real p o w er g eneration (pu ) Bus no. Base Case

Maximum Renewable Penetration With Out Renewable

0.05 0.00 0.05 0.10 0.15 16 18 20 22 24 26 28 30 32 34 36 Real p o w er g eneration (pu ) Bus no. Base Case

Maximum Renewable Penetration With Out Renewable

0.90 0.95 1.00 1.05 1.10 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 B u s v o ltag e (pu ) Bus no. Base Case Maximum Renewable Penetration

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Fig. 5. Real power load (Busses 1-14)

Fig..6. Real power load (Busses 15-36) 6. Conclusion

In this paper, a new concept of integrated optimization of transmission and distribution grid has been proposed for maximizing renewable penetration. For modeling grid dynamics, TG, AVR, wind turbines, solar panels and energy storage units have been used. Grid stability is obtained by line stability and voltage stability indices and also by conducting eigen value analysis of the complete power system grid. A particle swarm optimization based algorithm has been used to obtain the maximum safe instantaneous wind penetration limit. This is done by adjusting the grid control settings (reactive power management) at all layers of the grid.

The results demonstrate that simultaneous reactive power management of transmission and distribution grid can maximize the renewable penetration at all layers of the grid. The algorithm also gives explicitly the maximum permissible loadings at each bus at higher degrees of renewable penetration. These results seem to be quite promising as tested on IEEE 14-bus modified micro grid system.

0.00 1.00 2.00 3.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 R eal pow er L o ad (pu ) Bus no. Base Case Maximum Penetration With Out Renewable

0.00 0.01 0.01 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 R eal pow er L o ad (pu ) Bus no. Base Case Maximum Penetration

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Fig. 7. Real power flow in various methods of wind penetration

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0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 R eal pow er fl ow (pu ) Line No.