Acausal modelling and dynamic simulation of a stand-alone PV-wind-battery plant applicable to optimal energy management strategies

1Edinburgh University, May, 2013

Acuasal modelling and dynamic simulation of a stand-alone PV-Wind-Battery plant applicable to

optimal energy management strategies

Arash M. DizqahSchool of Computing, engineering, and Information

Sciences

Northumbria University, UKMay, 2013

Institute for Energy Systems (IES), Edinburgh University

Dr. A. Maheri

Prof. K. Busawon


Hybrid wind and solar energy systems (HRES)

Constrained optimal control problems

Why it requires to model the HRES

mathematically?

Preface


Hybrid wind and solar energy systems

Climate changes caused by greenhouse effect

Renewable energy sources

Hybrid Renewable Energy System

(HRES)

More than one type of power resource

HRES Motivations

Renewable Energy System (RES)

Rise in price of fossil fuel

Fossil fuels are exhaustive

Energy security

Solar / Wind energy systems


Inverter Load

AC Load BusDC Bus

IPV

-

+VPV

IPV-DC

-

+VDC

(Optional)DC-DC converter and battery controller

-

+VBat

IBat

-

+VDC

IBat-DC

IDC

-

+VDC

ILoad

-

+VLoad

DC-DC converter

IW T

-

+VW T

IW T-DC

-

+VDCAC-DC

converter

Centralized EMS (Supervision) vs. Distributed EMS EMS manages the whole system to reach to the optimum operating point w.r.t. cost criteria such as battery life span and constraints such as boundaries.

Optimal energy management strategies (EMS)


0 1 2 3 4 5 6 7 8 9 1048

49

50

51

52

53

54

55

56

57

58

Tim e

Battery Voltage (V)

Battery voltage with and without optim al controller

No optim al controlEm ploying optim al control

BulckCharging

Absorption Float

Float Voltage

Gassing Voltage


For instance satisfying battery charging constraints vs. MPPT strategy:


OCP: Optimal Control Problem

NMPC: Nonlinear Model-based Predictive Controller

EMS Manages

the production

and consumption w.r.t.

cost criteria

and constraint

s

Optimization

Problem

Real-time dynamic optimizat

ion problem

OCP -- when the results are

applied to the system and there

is feedback

NMPC is a

realization that relies on the model-based

prediction

Mathematical

Modelling



OCP could be assumed as a general form of controllers NMPC is the most well-known implementation of OCP for

nonlinear systems

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uyxxxFx)(xx)(x

tosubject

TxduyxxLu

dcdcdc

dccddcc

Tt

tdcu

(.),(.)],,[ 0))(),((

0))(),(),(( 0))(),(),(),((

0))(),(),(),(),(( 00 00

:

))(())(),(),(),((infarg(.)

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0

(.)

Nonlinear MPC




The topology of the system in this study

An overview on the HRES mathematical and

electrical modelling

System modelling and simulation using Modelica

Analysis and discussion

Conclusion and future works

Outline


The PV, wind turbine, and the battery modules are nonlinear. The PV, wind turbine, load, and the battery modules introduce algebraic constraints. The battery module is hybrid and has at least two modes of operation, i.e., charging and discharging modes. The converter is also a hybrid system including a high frequency state transition, However, in this study an average model has been used for simplicity’s sake.

Standalone hybrid wind-solar energy systems

Load

DC Bus

IPV

-

+VPV

IPV-DC

-

+VDC

-+VBat

IBat

ILoad

-

+VLoadDC-DC

converter

IW T

-

+VW T

IW T-DC

-

+VDCDC-DC

converter

3-phase rectifier

Control signals

[β, D w, D s]β Dw

Ds

G enerator

The topology and componentsSystem overview


An overview on the mathematical/electrical modelling

The PV module equivalent electrical circuit and the I-V curve


The battery equivalent electrical circuit and operating modes

Controlled

voltage source



The boost-type converter electrical circuit and the average model



The combined/hybrid power generation plant


Load Lx

Non-manipulated variables (perturbations): [Sx, Tx, Ux, Lx]Manipulated variables:[β, Dw, Ds]

system being described by nonlinear HDAEs of Index-1

MIMO system

It is a...

ODE-DAE-HDAE summary

0);,,,,( :HDAEImplicit

0);,,,( :DAEImplicit

0);,,( :ODEImplicit

tuqzxxF

tuzxxF

tuxxF


Traditional causal modelling/simulation can be assumed as: Having several back-to-back connected blocks A simulator solves the first blocks for its inputs and

estimates the output of that block Then, it feeds the output of each block to the next block

as the input and so on. System is decomposed into ODEs – Basic Simulink or normal

programming

Block A

Block B

Block Z

..

.Input

sOutputs

Acausal modelling/simulation: Solving the mathematical model of the system as flat

HDAEs One of the challenges is the modelling language –

e.g. Modelica

Causal vs. Acausal modelling


Modelica -- Overview

A language for modeling of complex cyber physical systemsi.e., Modelica is not a tool

Declarative equation-based textual languageclass VanDerPol "Van der Pol oscillator model" Real x(start = 1) "Descriptive string for x”; Real y(start = 1) "y coordinate”; parameter Real lambda = 0.3;equation der(x) = y; der(y) = -x + lambda*(1 - x*x)*y; end VanDerPol;

Differential equations

Variabledeclarations

Hybrid modeling = continuous-time + discrete-time modeling

time

Continuous-timeDiscrete-time



Simulation and analysis

Being used in model-based controllers

The energy system needs to be

modelled for... System modelModelica

model

Object-oriented design

Providing a library of Modelica classes

Employed approach #1 ...

Flat HDAE modelMinimum number of equations

More suitable for model-based controllers

Employed approach # 2 ...


class HRES ...; discrete Boolean Mode_bat(start = true) ”true: charging”; Real soc(start = 0.6) ”State of charge of the battery”; RealInput Ux ”The wind speed (m/s)”; RealInput RL ”The load demand (ohm)”; RealInput beta ”The pitch angle (degree)”; RealInput Ds ”The boost converter duty-cycle [0,1]”; RealInput Dw ”The buck converter duty-cycle [0,1]”;equation Ipv = Iph - I0 * (exp((Ipv * rs Tc + Vpv) / a Tc) - 1) - (Ipv * rs Tc + Vpv) / rsh Tc Sx; Iph = (Npvp * ((Rsh + Rs) / Rsh * Isc stc + Ki * (Tc - Tc stc)) * Sx) / Sx stc; I0 = (Npvp * (Isc stc + Ki * (Tc - Tc stc))) / (exp(((Voc stc + Kv * (Tc - Tc stc)) * q) / (nD * Ns * K * Tc)) - 1); Vpv = Vbstack * (1 - Ds); Ipvdc = (1 - Ds) * iPV; Mode bat = if If 0 then true else false; der(If) = -1 / Ts * If + 1 / Ts * Ibat; der(Qact) = 1 / 3600 * Ibat; der(V exp) = if Mode bat then P2=3600 * abs(Ibat) *(P3 - Vexp) else -(P2 *abs(Ibat))/3600* Vexp; when change(Mode bat) and pre(Mode bat) then tmp = if not Mode bat then pre(Vbat) - V0 – R*pre(Ibat)- (P6*Cmax)/(Cmax-pre(Qact))*pre(Qact)- (P6*Cmax)/(pre(Qact) + 0.1*Cmax)*pre(If)

The Modelica model of the whole system else 0;

reinit(V exp; tmp); end when; soc = 1-charge/Cmax; Vbstack = if Mode bat then Nbat * (V0-R*Ibat-(P1*Cmax)/(Cmax-Qact)*Qact- (P1*Cmax)/(Qact + 0.1*Cmax)*If + Vexp) else Nbat * (V0-R*Ibat-(P1*Cmax)/(Cmax-Qact)*Qact- (P1*Cmax)/(Cmax-Qact)*If + Vexp); -Te * wr = Iwtdc * Vbstack; -Tm * wr = Cp_pu * (Ux / 12)ˆ3 * Pnom; der(wr) = (Te - Tm - F * wr) / J; Vwt = (1.35 * P * psi * sqrt(3) * wr) / sqrt(2) - (3 * Lst * P * wr * Iwt) / pi; lambda = (R * wr) / Ux; lambda i = 1/(1/(lambda+0.08*beta)-0.035/(betaˆ3+1)); Cp = (C1 * (C2 / lambda_i - C3 * beta - C4) * exp(-C5 / lambda_i) + C6 * lambda) / 0.48; Ipvdc + Ibat + Iwtdc = Vbstack / RL;end HRES;

Input variables

Discrete variable


The Modelica model (cont.)

Algebraic constraint

Reinitialization


The simulated I-V (solid-line) and P-V (dashed-line) curves of the KC200GT PV module and empirical points provided by the manufacturer (the circle markers)

The developed PV model has been simulated separately.The simulation results validated with the available data in manufacturer datasheet. It follows accurately the empirical data available by the manufacturer. The simulated MPP is matched to the empirical data provided by the manufacturer (26.3V, 7.61A).The datasheet of the PV module is available from www.kyocerasolar.com/assets/001/5195.pdf

Validating the PV module simulation

results

PV voltage (V)

PV c

urre

nt

(A)

PV pow

er (W)


http://www.kyocerasolar.com/assets/001/5195.pdf

http://www.kyocerasolar.com/assets/001/5195.pdf


The simulated (a) battery voltage, (b) battery current,

and (c) the SOC of the battery.

Validating the battery simulation resultsThe developed Modelica model

for Panasonic LC-R127R2PG battery has been simulated separately for all zones. The battery Modelica model validated with the available data in manufacturer datasheet. According to the simulation scenario, battery is charging for 100 minutes and then it is discharged. Discharging with the average current of 7.2A, it takes around 35 min to reach the cut-off voltage (10.2V). It matches perfectly with datasheet.The datasheet of the battery is available from www.farnell.com/datasheets/1624915.pdf

Batter

y cu

rren

t (A)

Batter

y vo

ltage

(V)

SOC

Time (minutes) (c)

Time (minutes) (b)

Time (minutes) (a)


http://www.farnell.com/datasheets/1624915.pdf

http://www.farnell.com/datasheets/1624915.pdf


The SOC and EFC of the batteries.

The values of the manipulated variables

Power generation and consumption

Sx = 1000 Wh/m², Ux = 12m/s, Tx=25°C At t=100sec, step change in load demand At t=350sec, step change in wind speed from 12 to 20m/s At t=500sec, a step change in Dw makes the share of the WT to zero

Simulation scenario



Simulation results



Analysis and discussionThe proposed model vs. the equivalent

SIMULINK/SimPowerSystem model for the optimal energy management problemsPerformance criteria* The equivalent SIMULINK/

SimPowerSystem modelThe proposed Modelica

model

Simulation time (with the step-size of 100 nsec)**

Around 10 hrs for 3 sec of simulation

Around 8 hours for 3 sec of simulation

Simulation time(for 3600 sec)

It is not easy to remove the PWM and make it fast.

Around 30 sec (with the step-size of 720 usec)

Flexibility*** It cannot be integrated into the collocation methodIt is not easy to be integrated into the multiple shooting method

It can be used for the OCP applications

* It is just a rough comparison for this specific application. It is not the results of a systematic comparison.** The equivalent SIMULINK model consists of PWM modules with the frequency of 100 KHz that causes it to be very slow and memory expensive. While for this application, it is not straightforward to replace the converters with the average model in SIMULINK, it has been done in the proposed Modelica model that make it much faster.*** For OCP applications


Conclusion and Future works


XxUuTttTxTxr

yxxhuyxxG

uyxxxFx)(xx)(x

tosubject

TxduyxxLu

dcdcdc

dccddcc

Tt

tdcu

(.),(.)],,[ 0))(),((

0))(),(),(( 0))(),(),(),((

0))(),(),(),(),(( 00 00

:

))(())(),(),(),((infarg(.)

0

0

(.)

Nonlinear MPC


Thank you for your

attention.

Acausal modelling and dynamic simulation of a stand-alone PV-wind-battery plant applicable to optimal energy management strategies

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