6 Quantities and Units model

6.1 General

This model supplements the information of EngineeringUnit Properties, providing comprehensive ObjectTypes for quantities and units and their linkage. See 5.6.4 how EngineeringUnit Properties reference instances of these ObjectTypes. It is also possible to specify AlternativeUnits and the conversion factors.

Furthermore, the model provides a powerful way to relate quantities and units to established works of other organizations (see Syntax References in 6.3).

Figure 7 Illustrates the model.

6.2 Quantities entry point

Quantities is a standardized entry point to access all Quantities and their Units managed in the Server. It is formally defined in Table 37. All Objects of the QuantityType defined in clause 6.4.1, that are managed in the Server, shall be referenced directly from this Object with Organizes or a subtype of Organizes.

6.3 Syntax References

6.3.1 General

Syntax References represent established works of other organizations. Such works – among others – can define semantic information, topologies, a language for a code set, or dictionaries and facilitate the programmatic evaluation or the lookup of a quantity or unit e.g. in a dictionary or ontology. They can be publicly defined by standard bodies such as IEC or proprietary (e.g. vendor-specific dictionaries).

The Quantities and Unit Model provides a powerful way to relate quantities and units to such Syntax References using the Dictionary References model defined in OPC 10000-19.

Table 38 lists Syntax References that are applied in certain markets. This list can be extended in future versions. Vendors or organizations can also specify additional Syntax References.

An overview for each Syntax Reference in this table is provided in Annex C.

6.3.2 Using Dictionary References

HasDictionaryEntry is used to define the relationship to a Syntax Reference by referencing from quantity or unit Nodes to an instance of a SyntaxReferenceEntryType. Each quantity or unit instance can have zero, one or more such references.

Instances of SyntaxReferenceEntryType have a well-defined NodeId as defined in Table 39.

When calling the Browse Service for a Quantity or Unit Node, the response includes the HasDictionaryEntry Reference together with the well-defined NodeId for the SyntaxReferenceEntryType instance. The actual instance therefore is not required in the AddressSpace.

Figure 8 provides an example of References to external works.

6.3.3 Syntax Reference Identifier

Table 40 defines the identifiers for each Syntax Reference.

6.4 ObjectTypes

6.4.1 QuantityType ObjectType definition

The QuantityType defines a model for physical quantities. These are listed in the Quantites Folder. Each quantity has a ServerUnits Folder in which the units, referenced by EngineeringUnit Properties with HasEngineeringUnitDetails, are listed. Each ServerUnit can have a list of alternative units to which the Variable value can be converted.

It is illustrated in Figure 9 and formally defined in Table 41.

The DisplayName Attribute of each instance shall provide the name of the quantity, e.g. “acceleration”, “battery capacity” or “pressure in relation to volume flow rate”.

The Description Attribute should be used to expose a more verbose explanation of the QuantityType instance.

The Symbol Property is used for the symbol of the quantity (e.g. ‘l’ for length, ‘t’ for time, or ‘T’ for temperature).

Annotation allows naming annotations for a physical quantity. These Annotations are explanations of the physical quantity such as "relative" for a relative velocity. The AnnotationDataType is described in chapter 6.6.1.

For example, a V_{AC RMS} measurement is the quadratic mean measurement of an AC voltage. We are using two annotation elements to represent it. Its Instance would contain the following values:

ConversionService allows to name an external conversion service for the unit in which the client can have a conversion to a target unit performed.

Dimension describes the dimension of a physical quantity in power representation. Its DataType is described in chapter 6.6.4.

ServerUnits allows listing ServerUnits for a physical quantity. The ServerUnits are of ServerUnitType which is described in 6.4.2.

Syntax References: Instances of the QuantityType can identify the physical quantity in a specific external reference work using HasDictionaryEntry References – see 6.3.2.

The components of the QuantityType have additional subcomponents which are defined in Table 42.

6.4.2 UnitType and subtypes

6.4.2.1 General

The Units model describes the relations between UnitType, ServerUnitType and AlternativeUnitType.

The UnitType is the base class and defines details that are relevant of all derived types.

6.4.2.2 UnitType ObjectType Definition

It is formally defined in Table 43.

The DisplayName Attribute of each instance shall provide the name of the unit, e.g. “second”, “degree Celsius” or “square metre”. This matches the “description” field of the EUInformation structure (see 5.6.4.3).

The Description Attribute should be used to expose a more verbose explanation of the UnitType instance.

The Symbol Property is used for the symbol of the unit (e.g. "h" for hour or "m/s" for meter per second). If no symbol is defined for the unit, the DisplayName Attribute shall be used as symbol. Symbol matches the “displayName” field of the EUInformation structure (see 5.6.4.3).

The UnitSystem Property describes the system of units (e.g. ISQ) in which the unit is specified. If any of the well-known systems defined in Table 44 is used, the acronym in the column “UnitSystem” shall be used for the value of this Property.

Syntax References: Instances of the UnitType can identify the unit in a specific external reference work using HasDictionaryEntry References – see 6.3.2.

6.4.2.3 ServerUnitType ObjectType Definition

Instances of ServerUnitType define the units utilizes in the Server. They are assigned to the proper Quantities. EngineeringUnit Properties can refer to it. It is formally defined in Table 45.

The optional Object AlternativeUnits contains Objects of the AlternativeUnitsType. These explicitly specify the units into which the conversion can be made.

The mandatory Property ConversionLimit indicates whether the ServerUnit can be converted. A distinction is made between NO_CONVERSION, LIMITED and UNLIMITED.

UNLIMITED means the client can perform conversions based on the rules defined by the given UnitSystem.

LIMITED conversion means that a conversion can not be performed by simply applying the rules defined by the given UnitSystem. Either only the conversions mentioned in the AlternativeUnits are to be used or the client requires application specific know-how for a conversion on his own.

NO_CONVERSION means that no conversion is allowed (e.g. for statistical values).

The CoherentUnit of a value is a derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of base units, with the proportionality factor being one. Therefore it shall share the same UnitSystem as the ServerUnit.

The components of the ServerUnitType have additional subcomponents which are defined in Table 46.

6.4.2.4 AlternativeUnitType ObjectType Definition

The AlternativeUnitType describes alternative units to a ServerUnit. It is required to specify a conversion method for a value from the ServerUnit to this AlternativeUnit. It is formally defined in Table 47.

The use of conversions enables that a server and a client can work with different units and even in different systems of units. E.g. a server works with imperial units and a client uses metric units.

As a single server can distribute values to a number of clients with different needs the actual conversion has to be performed at client side.

The Server shall provide either a LinearConversion or a MathMLConversion together with a corresponding MathMLInverseConversion. It can provide Linear and MathML conversions in parallel.

The optional Property LinearConversion represents a simple conversion according to the following formula. The values (a, b, c, d) are given in a Structure as defined in the LinearConversionDataType in chapter 6.6.2. The value x is published by the Server in the named server unit and y is the value converted into the named alternative unit.

This also defines the inverse conversion to be used if a Client wants to write a value to the Server. The values (a, b, c, d) are given in a Structure as defined in the LinearConversionDataType in chapter 6.6.2. The value y¹ is the value that the Client wants to write to the Server in the named alternative unit and x¹ is the value the Client actually has to write to the Server instead

The optional Property MathMLConversion allows the specification of all kinds of conversion methods. The MathML syntax is used for this. Within the MathML expression X always stands for the value at the server side and Y for the value at the client side. An example (formula of the LinearConversion) looks as follows.

6.4.3 SyntaxReferenceEntryType ObjectType definition

The SyntaxReferenceEntryType defined in Table 48 is used to represent Syntax References that use Syntax Reference specific IDs as unique identifiers.

Because of their well-defined NodeIds (see 6.3.2), instances of this type are not required in the AddressSpace.

CommonName shall be the corresponding field in Table 38.

The namespace for the NodeId and the BrowseName Attributes of instances of the SyntaxReferenceEntryType shall be the URI of the Syntax Reference as defined in Table 38.

6.5 References

6.5.1 HasEngineeringUnitDetails

The HasEngineeringUnitDetails is a concrete ReferenceType and can be used directly. It is a subtype of NonHierarchicalReferences.

The semantics of this ReferenceType is to link a Variable with EUInformation DataType to its more detailed AddressSpace representation Instance of the ServerUnitType ObjectType.

The SourceNode of References of this type shall be a Variable with EUInformation DataType.

The TargetNode of this ReferenceType shall be an Instance of the ServerUnitType ObjectType.

The Reference has to change if the value (the concrete EngineeringUnit) is changing. Clients can subscribe to the value and, in case of change, should rebrowse.

The HasEngineeringUnitDetails is formally defined in Table 49.

6.5.2 HasQuantity

The HasQuantity is a concrete ReferenceType and can be used directly. It is a subtype of NonHierarchicalReferences.

The semantics of this ReferenceType is to link a Variable with EUInformation DataType to an Instance of the QuantityType ObjectType.

The SourceNode of References of this type shall be a Variable with EUInformation DataType (typically the EngineeringUnits Property).

The TargetNode of this ReferenceType shall be an Instance of the QuantityType ObjectType.

The HasQuantity is formally defined in Table 50.

6.6 DataTypes

6.6.1 AnnotationDataType DataType definition

This structure contains additions as explanation and specification of the physical quantity such as "relative" for a relative velocity. The structure is defined in Table 51.

Examples are given in Table 52.

Its representation in the AddressSpace is defined in Table 53.

6.6.2 LinearConversionDataType DataType definition

This structure contains a simple conversion according to the following formula. The factors (a = inititialAddend, b = multiplicand, c = divisor, d = finalAddend) are given in a Structure. X is the source value (in source unit) and f(x) the target value (in target unit). The structure is defined in Table 54.

The values of the structure can also be used for a simple inverse conversion. It can be used if a Client wants to write a value to the Server. The value y¹ is the value that the Client wants to write to the Server in the named alternative unit and x¹ is the value the Client actually has to write to the Server instead.

Its representation in the AddressSpace is defined in Table 53.

6.6.3 ConversionLimitEnum

ConversionLimitEnum indicates whether the ServerUnit can be converted. A distinction is made between NO_CONVERSION, LIMITED and UNLIMITED. NO_CONVERSION means that no conversion is allowed (e.g. for statistical values). LIMITED conversion means that either only the conversions mentioned in the AlternativeUnits are to be used or the client requires specific know-how for the conversion. UNLIMITED means the conversion is simple and possible if the client knows the UnitSystem. The enumeration is defined in Table 56.

Its representation in the AddressSpace is defined in Table 57.

6.6.4 QuantityDimension

The QuantityDimension Structure DataType describes the dimensionality of a kind of quantity in the context of a system of units. In the SI system of units, the dimensions of a kind of quantity are expressed as a product of the basic physical dimensions length (L), mass (M), time (T), current (I), absolute temperature (θ), amount of substance (N) and luminous intensity (J) as

.

The rational powers of the dimensional exponents (α, β, γ, δ, ε, η, v), are positive, negative, or zero.

An additional dimensionless exponent is used for countable things that have no physical quantity assigned.

The QuantityDimension elements are defined in Table 58.

Its representation in the AddressSpace is defined in Table 59.

For example, the dimension of the physical quantity kind

,

the dimension of the physical quantity kind force is

,

and the dimension of the physical quantity kind “things (e.g., screws) per time” is

.

The extended SI System of units includes derived units that are built as a product of base units. That makes it difficult to compare units as SI allows an unlimited number of “SI unit strings” to describe the same quantity.

All 3 are valid SI representations of the quantity “speed” and therefore share the same quantity dimensions. A specific representation of a unit is often used to express details how the unit was measured. The dimension structure makes it much easier to identify and compare the kind of quantity of EU values.