Formulae and Functions

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Formulae can be entered as substitutes for specific values into most fields in EMarket to control the derivation of variable values at run time. A formula can contain any combination of:

Constants

Constants can be:

  • Numbers: Integers or Reals (e.g. 1, 2.5, -3), they can also be entered in scientific notation e.g. '3E+10'.
  • Strings: Written inside double quotes e.g. "A Node"
  • Dates: Must be enclosed in single quotes e.g '1/3/2004' or '14 April 2005'

Warning: The format for entering dates should compatible with the computer's local date (locality) setting

Variables

Variables can be regarded as user-defined Entity.Traits which can be defined in the Volatility Matrix or in a Schedule. Previously defined variables can be used in formulae.

Note: EMarket provides a 'system' variable the user need not define: 'DateTime' which is of type 'Date' and gives the current simulation date as the model runs.

Special Variables

These variable names are automatically included in the schedule

Variable Name Definition
DateTime This returns the date/time of the current time step
TimeInterval This returns the duration, in half hours, of the current time step
Date Date of current Tick
TP TP number of current Tick
Version The number of the current version in the volatility matrix, numbered from zero
RandomSeed This variable is set up according to the 'Random Seed' option in the Run Resource. It allows the generation of random sequences to be

coordinated for all Random Functions within the run

Operators

Operators are all pre-defined in EMarket. Their purpose is to separate a formula into parts that are then combined to give a single value.

The following operators are shown in descending order of precedence.

Operator Meaning Example Parameter Type Return Type
\ Integer Division 3\2 = 1 Real; Int Int
% Modulus 7%5 = 2 Real; Int Int
/ Division 3/2 = 1.5 Real; Int Real
* Multiplication 5*4.2 = 21 Real; Int Real
- Subtraction 7-3.2 = 3.8 Real; Int Real
+ Addition 3.5+1.5 = 5 Real; Int Real

Functions

Functions provide a powerful mechanism for deriving field and variable data values from input parameters.

A function has the form FunctionName(Parameter1, Parameter2, ...)

An operator is used in a Function in the following form: <Parameter1>Operator<Parameter2>.

EMarket provides the following function types:

  • Arithmetic functions
  • Logic functions
  • Run information functions
  • Time functions
  • Other functions

Note: Logic operators and functions evaluate to one for a result that is true (for example 6 = 6), and zero for false.

Arithmetic Functions

The following table lists EMarket's Arithmetic functions:

Function Purpose Parameters Return Type Example Result
Sqrt Square root of a number Integer or Real Real Sqrt(546.94) 23.387
Abs Absolute value of a number Integer or Real Real Abs(-19.1) 19.1
Int Integer portion of a number Integer or Real Integer Int(45.786) 45
Sum Total value of numbers in an array Value Array (Exclude Value), Integer or Real Real Sum(Node.Price)
Max Maximum value of numbers in an array, optionally excluding values with value over an exclude value Value Array (Exclude Value), Integer or Real Real Max(Generator.Generation)
Min Minimum value of numbers in an array Value Array (Exclude Value), Integer or Real Real Min(Generator.Generation)
StdDev Standard deviation of numbers in an array Value Array (Exclude Value), Integer or Real Real StdDev(Generator.Generation)
Avg Average value of numbers in an array Value Array (Exclude Value), Integer or Real Real Avg(Generator.Generation)
WgtAvg Average of numbers in an array, weighted by numbers in another array Value Array (Weights Array), Integer or Real Real WgtAvg(Generator.Generation,Generator.Cost)
Choke Returns a collared value (i.e. the value of the referenced variable is returned if it falls within the specified range otherwise the relevant minimum or maximum value is returned) Integer or Real Real Choke(500,200,Generator.Generation)

Logic Functions

The following table lists EMarket3's Logic functions:

Operator Purpose Parameters Return Value Example Result
= Whether two numbers are Equal 2 numbers, Integer or Real 0 or 1 5 = 6 0
< Whether first number is less than the second 2 numbers, Integer or Real 0 or 1 -2 < 7 1
> Whether first number is Greater than the second 2 numbers, Integer or Real 0 or 1 9 > 7 1
AND Whether two numbers are both non-zero 2 numbers, Integer or Real 0 or 1 And(6=6,4<3) 0
OR Whether either of two numbers are non-zero 2 numbers, Integer or Real 0 or 1 OR(3<5, 2>3) 1
Between Whether a number is between two limits Number: lower limit; upper limit, Integer, real or date 0 or 1 Between(5.7,9.7) 0

Time Functions

The following table lists EMarket's Time functions:

Function Purpose Parameters Return Type Example Result
GetDate Converts a date to a day number Date/Time Integer GetDate('1/4/2004')
hh Gets the half hourly TP from a date Date/Time Integer hh(DateTime)
4h Gets the number of the block of 4 hourly trading periods for a given date (e.g. 1 = TP 1-8) Date/Time Integer 4h(DateTime)
6h Gets the number of the block of 6 hourly trading periods for a given date (e.g. 0 = TP 1-12) Date/Time Integer 6h(DateTime)
DOW Gets the weekday for a date, 0 = Sunday Date/Time Integer Dow('14/6/2004') 1
WO Whether a date is a week day rather than a weekend or holiday, 1 = Weekend; 0 = Weekday Date/Time 0 or 1 WO('13/6/2004') 1
WODN 0=Week Night(WN); 1=Week Day(WD); 2=Other Night(ON); 3=Other Day(OF) Date/Time 0 to 3 WODN('1/5/2004 22:00') 3
WODN6 0=Week Night(WN); 1=Week Day(WD); 2=Other Night(ON); 3=Other Day(OF). Using A night period running from Midnight to 6am (not to 8am as in WODN) Date/Time 0 to 3 WODN6('1/5/2004 22:00') 3
Month Gets the month from a date, 0 = January Date/Time 0 to 11 Month('1/5/2004') 4
WeekOfYear Gets the week from a date, 0 = 1st full week in April Date/Time 0 to 51 WeekOfYear('1/5/2004') 4
DateDiff Calculates the number of days between two date/times Date/Time, Date/Time Real DateDiff('1/5/2004', '5/5/004') 4
DateSeq Gets the position of a required date within a list of ordered dates Date/Time being looked up, List of Date/Time Integer DateSeq('5 / 4 / 2004', '1 / 4 / 2004', '2 / 4 / 2004', '3 / 4 / 2004', '4 / 4 / 2004', '5 / 4 / 2004') 5
TimeSeries Given a date ordered sequence of values, finds the value for a required date. Date format is Date:TimePeriod 'DD/MM/YYYY:TP' , if no TP then TP '01' is used List of (Initial value, first date and time period applies for value2, value2 , ....) Real TimeSeries(735 , '1/04/2004:24', 760 , ' 1/04/2005', 840)

Other Functions

The following table lists EMarket's other functions:

Function Purpose Parameters Return Type Example Result
LastVal Returns the value of the named variable in the last tick or, in the initial tick, a default value Variable Name, Default Value (Real or Integer) Real LastVal(Var, 100) 100 in the first tick, the previous value of 'Var' in following ticks
ArrayTable Uses two indices to retrieve a value from an array (matrix) Index1, Index2, Value array. May be real or Integer Real or Integer ArrayTable(p,q,m,n, V00, V01, V02, ...V0m, V10, V11, ... Vnm) where p,q represent the position of the array; m,n represent the numbers of columns and rows in the array; 0<= p < m and 0 <= q < n would return Vpq.
E.g. ArrayTable(1, 1, 2, 3, 4, 32.1, 6.3, 1.8, 31, 5). This defines a 2 * 3 matrix, and looks for the entry indexed by 1, 1. Note that if the indices are out of bounds no error will be given, and an indeterminate value will be returned.
31
Index Gets the number in given position (index) in a list of numbers. First number has position zero. 1 or more numbers, can be integers or real Real Index(p, V0, V1, V2, ... Vm) where p is the position (index) in a list of numbers.
E.g. Index(3, 4.5, 7, 8.9, -23.4)
-23.4
PieceWiseLinear Generates a value based on an extrapolation of existing data. Given a target value (p) and a set of x, y pairings defining a function, the PieceWiseLinear function will find the y value corresponding to p. This function is included primarily for use in defining Demand elasticity. Set of x,y value pairings, can be integers or real Real or Integer PieceWiseLinear(p, x1, y1, x2, y2, ...xn, yn) where p is the target value. Note that you can use internal model variables as the target value, as in this example:
PieceWiseLinear(HydroSystem:Waitaki.SystemMWV, 0, 1, 80, 1, 150, 0.8, 400, 0.64)
RunningAverage This function facilitates the smoothing of a value over time by applying a running average to the given value. The formula used is V = MV' + (1 - M)v, where V is the running average value, V' is the last value of the running average, v is the value being averaged. M is given by the formula: M = Exp(-Ln(2) * (D / H)) where D is the duration in days of the time step and H is the half-life parameter. On the first step M = 0. The current Date/Time, input value (Real or Integer), half-life days (Real or Integer) Real RunningAverage(DateTime, Generator:ABC.Generation, 7)
FileInput This function accesses a CSV file in the 'Misc' subdirectory of the data directory and returns values from this file. This file will a set of time dependent value series which are each given a series number (e.g. inflow years). The format of the input file can be found in Ancillary Files The file name string, the date for which a value is being looked up, the integer series number Real or Integer FileInput("MyGenCapacity.csv", DateTime, InflowYearNo)
CurrentInflowYear Returns the year of the inflow sequence being used given the starting inflow year and the current date/time Current Date/Time, Inflow Sequence (integer) Integer CurrentInflowYear(DateTime, InflowYear)

Random Functions

The following functions create a random sequence, the results of which depends on the seed given, the start date of the sequence and the order of definition and exact formula used to define the function. The RandomSeed variable should usually be used as the seed as this will ensure a unique sequence is generated based on the "Random Seed" option chosen for the run

Function Purpose Parameters Return Type Example
RandomBinaryState Returns values from a random sequence of values which are either 0 or 1 with the properties that proportion of the time spent in the zero state is a given proportion and the average length of time spent in the one state is a given number of days Seed for random sequence, Date/Time, Zero state proportion, Average One state length Real RandomBinaryState(Seed, DateTime, 0.95, 4), will return a random 0/1 series with 0.05 time spent in the one state and an average four day span of each one state
MRJD Returns a value that follows a mean reverting random walk on a logarithmic scale Seed for random sequence, Date/Time, Starting Value, Mean, Reversion Rate, Volatility[,ProportionalJump, JumpVolatility, JumpFrequency] Real MRJD(RandomSeed, DateTime, 5, 10, 11, 5), will return a random walk starting with the value 5 where the average log value is equal to log(10), reversion rate of 10 (half reversion in 1/10 year), volatility of 5 (two times diffusion in 1/5 year). The jump parameters are optional


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