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 |
| 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) |
Array Functions
The following table lists EMarket's array functions:
| Function | Purpose | Parameters | Return Type | Example |
|---|---|---|---|---|
| Sum | Total value of numbers in an array | Integer or Real Array, [Exclude Value] | Real | Sum(Node.Price) |
| Max | Maximum value of numbers in an array, optionally excluding values with value over an exclude value | Integer or Real Array, [Exclude Value] | Real | Max(Generator.Generation) |
| Min | Minimum value of numbers in an array | Integer or Real Array, [Exclude Value] | Real | Min(Generator.Generation) |
| StdDev | Standard deviation of numbers in an array | Integer or Real Array, [Exclude Value] | Real | StdDev(Generator.Generation) |
| Avg | Average value of numbers in an array | Integer or Real Array, [Exclude Value] | Real | Avg(Generator.Generation) |
| WgtAvg | Average of numbers in an array, weighted by numbers in another array | 2 x Integer or Real Array, (Values, Weights) | Real | WgtAvg(Generator.Generation,Generator.Cost) |
| ArrMult | Returns an array whose elements are the product of the elements in an array and a scalar value | Integer or Real Array, Integer or Real Value | Real Array | ArrMult(Node.Demand, Duration) |
| AddElements | Returns an array whose elements are the sum of the elements in two arrays (the arrays must be of the same size) | 2 x Integer or Real Arrays | Real Array | AddElements(Node.Demand, Node.Losses) |
| SubElements | Returns an array whose elements are the difference of the elements in two arrays (the arrays must be of the same size) | 2 x Integer or Real Arrays | Real Array | SubElements(Circuit.Flow, Circuit.Losses) |
| MultiplyElements | Returns an array whose elements are the product of the elements in two arrays (the arrays must be of the same size) | 2 x Integer or Real Arrays | Real Array | MultiplyElements(Node.Demand, Node.Price) |
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 |