Merge branch 'dev' into ms/#53-upgrate-to-scala3

# Conflicts:
#	CHANGELOG.md
#	src/main/scala/edu/ie3/simona/agent/participant/ParticipantAgent.scala
#	src/main/scala/edu/ie3/simona/agent/participant/ParticipantAgentFundamentals.scala
#	src/main/scala/edu/ie3/simona/agent/participant/ServiceRegistration.scala
#	src/main/scala/edu/ie3/simona/agent/participant/data/Data.scala
#	src/main/scala/edu/ie3/simona/agent/participant/statedata/BaseStateData.scala
#	src/main/scala/edu/ie3/simona/agent/participant/statedata/DataCollectionStateData.scala
#	src/main/scala/edu/ie3/simona/agent/participant/statedata/ParticipantStateData.scala
#	src/main/scala/edu/ie3/simona/io/result/AccompaniedSimulationResult.scala
#	src/main/scala/edu/ie3/simona/model/participant/SystemParticipant.scala
#	src/test/scala/edu/ie3/simona/agent/em/EmAgentIT.scala
#	src/test/scala/edu/ie3/simona/event/listener/RuntimeEventListenerKafkaSpec.scala

Author: staudtMarius

CHANGELOG.md

@@ -46,6 +46,10 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Throw exception if the slack node is not directly conected to a transformer. [#525](https://github.com/ie3-institute/simona/issues/525)
 - Added support for topologies without transformers and slack grids with multiple nodes [#1099](https://github.com/ie3-institute/simona/issues/1099)
 - Checking the number of slack nodes [#1122](https://github.com/ie3-institute/simona/issues/1122)
+- Enhance exception message in case of InvalidGridException [#1124](https://github.com/ie3-institute/simona/issues/1124)
+- Integration test for thermal grids [#1145](https://github.com/ie3-institute/simona/issues/1145)
+- Added `VoltageLimits` [#1133](https://github.com/ie3-institute/simona/issues/1133)
+- Introducing new ParticipantAgent and ParticipantModel [#1134](https://github.com/ie3-institute/simona/issues/1134)
 
 ### Changed
 - Adapted to changed data source in PSDM [#435](https://github.com/ie3-institute/simona/issues/435)
@@ -118,6 +122,16 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Fixed SonarQube quality gate using the correct parameter '-Dsonar.qualitygate.wait=true' [#1072](https://github.com/ie3-institute/simona/issues/1072)
 - Updated `simonaAPI` to version `0.6.0` [#1080](https://github.com/ie3-institute/simona/issues/1080)
 - Enhanced title in `CITATION.cff` [#1088](https://github.com/ie3-institute/simona/issues/1088)
+- Refactor ThermalEnergyDemand definitions [#917](https://github.com/ie3-institute/simona/issues/917)
+- Rewrote PvModelIT from groovy to scala [#646](https://github.com/ie3-institute/simona/issues/646)
+- Fix negative required energy demand for thermalHouse [#1127](https://github.com/ie3-institute/simona/issues/1127)
+- Refactored EM messages [#1138](https://github.com/ie3-institute/simona/issues/1138)
+- `OperationInterval` should extend `RightOpenInterval` [#1142](https://github.com/ie3-institute/simona/issues/1142)
+- Enhance EmAggregate of SelfOpt to cope with other targetLimits [#1131](https://github.com/ie3-institute/simona/issues/1131)
+- Switched to `pureconfig` [#608](https://github.com/ie3-institute/simona/issues/608)
+- Removing generated methods and cleaning up in config [#1170](https://github.com/ie3-institute/simona/issues/1170)
+- Changed `pvInput` values in `PvInputTestData` to more realistic values [#1144](https://github.com/ie3-institute/simona/issues/1144)
+- Refactor `RuntimeConfig` [#1172](https://github.com/ie3-institute/simona/issues/1172)
 - Upgrated `scala2` to `scala3` [#53](https://github.com/ie3-institute/simona/issues/53)
 
 ### Fixed
@@ -163,6 +177,10 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Fixed SonarQube quality gate using the right link for PRs or Branches [#1061](https://github.com/ie3-institute/simona/issues/1061)
 - Fixed ignored EM strategy [#1091](https://github.com/ie3-institute/simona/issues/1091)
 - EM should output flex option results even if it has no parent [#1112](https://github.com/ie3-institute/simona/issues/1112)
+- Rename `PrimaryDataWithApparentPower` to `PrimaryDataWithComplexPower` [#1140](https://github.com/ie3-institute/simona/issues/1140)
+- Refactoring of `ThermalGrid.handleInfeed` to fix thermal storage recharge correctly when empty [#930](https://github.com/ie3-institute/simona/issues/930)
+- Move `ScheduleServiceActivation` out of `RegistrationResponseMessage` [#1143](https://github.com/ie3-institute/simona/issues/1143)
+- Check for runningHp when handling infeed to thermalGrid [#1167](https://github.com/ie3-institute/simona/issues/1167)
 
 ## [3.0.0] - 2023-08-07
 

Jenkinsfile

@@ -373,10 +373,9 @@ def determineDisplayName(String currentBranchName, String commitHash, String org
 
 def publishReports(String relativeProjectDir) {
   // publish test reports
-  publishHTML([allowMissing: true, alwaysLinkToLastBuild: true, escapeUnderscores: false, keepAll: true, reportDir: relativeProjectDir + '/build/reports/tests/allTests', reportFiles: 'index.html', reportName: "${relativeProjectDir}_java_tests_report", reportTitles: ''])
 
   // publish scalatest reports for main project only (currently the only one with scala sources!)
-  publishHTML([allowMissing: false, alwaysLinkToLastBuild: true, escapeUnderscores: false, keepAll: true, reportDir: relativeProjectDir + '/build/reports/tests/scalatest', reportFiles: 'index.html', reportName: "${relativeProjectDir}_scala_tests_report", reportTitles: ''])
+  publishHTML([allowMissing: false, alwaysLinkToLastBuild: true, escapeUnderscores: false, keepAll: true, reportDir: relativeProjectDir + '/build/reports/tests/test', reportFiles: 'index.html', reportName: "${relativeProjectDir}_scala_tests_report", reportTitles: ''])
 
   // publish scapegoat src report for main project only
   publishHTML([allowMissing: false, alwaysLinkToLastBuild: true, escapeUnderscores: false, keepAll: true, reportDir: relativeProjectDir + '/build/reports/scapegoat/src', reportFiles: 'scapegoat.html', reportName: "${relativeProjectDir}_scapegoat_src_report", reportTitles: ''])

build.gradle

@@ -1,7 +1,6 @@
 import com.github.jengelman.gradle.plugins.shadow.transformers.AppendingTransformer
 
 plugins {
-  id 'groovy' // groovy support
   id 'java' // java support
   id 'scala' // scala support
   id 'signing'
@@ -13,7 +12,6 @@ plugins {
   id "com.github.johnrengelman.shadow" version "8.1.1" // fat jar
   id "org.sonarqube" version "6.0.1.5171" // sonarqube
   id "org.scoverage" version "8.1" // scala code coverage scoverage
-  id "com.github.maiflai.scalatest" version "0.32" // run scalatest without specific spec task
   id 'org.hidetake.ssh' version '2.11.2'
   id 'net.thauvin.erik.gradle.semver' version '1.0.4' // semantic versioning
   id "application"
@@ -28,7 +26,6 @@ ext {
   pekkoVersion = '1.1.2'
   jtsVersion = '1.20.0'
   confluentKafkaVersion = '7.4.0'
-  tscfgVersion = '1.2.4'
   scapegoatVersion = '3.1.4'
 
   testContainerVersion = '0.41.8'
@@ -56,7 +53,6 @@ java {
 
 apply from: scriptsLocation + 'spotless.gradle'
 apply from: scriptsLocation + 'checkJavaVersion.gradle'
-apply from: scriptsLocation + 'tscfg.gradle' // config tasks
 apply from: scriptsLocation + 'documentation.gradle' // documentation tasks + configuration
 apply from: scriptsLocation + 'tests.gradle' // tasks for tests
 apply from: scriptsLocation + 'sonarqube.gradle' // sonarqube config
@@ -110,13 +106,18 @@ dependencies {
   implementation "ch.qos.logback:logback-classic:1.5.16"
 
   /* testing */
-  testImplementation 'org.spockframework:spock-core:2.3-groovy-4.0'
-  testImplementation 'org.scalatestplus:mockito-3-4_2.13:3.2.10.0'
-  testImplementation 'org.mockito:mockito-core:5.15.2' // mocking framework
+  // scalatest & junit
   testImplementation "org.scalatest:scalatest_${scalaVersion}:3.2.19"
-  testRuntimeOnly 'com.vladsch.flexmark:flexmark-all:0.64.8' //scalatest html output
-  testImplementation group: 'org.pegdown', name: 'pegdown', version: '1.6.0'
-  testImplementation "org.apache.pekko:pekko-testkit_${scalaVersion}:${pekkoVersion}" // pekko testkit
+  testImplementation "org.junit.platform:junit-platform-launcher:1.11.4"
+  testRuntimeOnly "org.junit.platform:junit-platform-engine:1.11.4"
+  testRuntimeOnly "org.scalatestplus:junit-5-11_${scalaVersion}:3.2.19.0"
+
+  // mocking framework
+  testImplementation 'org.mockito:mockito-core:5.15.2'
+  testImplementation "org.scalatestplus:mockito-3-4_${scalaVersion}:3.2.10.0"
+
+  // pekko
+  testImplementation "org.apache.pekko:pekko-testkit_${scalaVersion}:${pekkoVersion}"
   testImplementation "org.apache.pekko:pekko-actor-testkit-typed_${scalaVersion}:${pekkoVersion}"
 
   // testcontainers
@@ -135,8 +136,8 @@ dependencies {
 
   /* config */
   implementation 'com.typesafe:config:1.4.3'
-  implementation "com.github.carueda:tscfg_2.13:$tscfgVersion"
   implementation "com.github.scopt:scopt_${scalaVersion}:4.1.0" // cmd args parser
+  implementation "com.github.pureconfig:pureconfig_${scalaVersion}:0.17.8"
 
   // JTS
   implementation ("org.locationtech.jts:jts-core:${jtsVersion}"){
@@ -159,7 +160,7 @@ dependencies {
   implementation 'tech.units:indriya:2.2.2' // quantities
   implementation "org.typelevel:squants_${scalaVersion}:1.8.3"
   implementation 'org.apache.commons:commons-csv:1.13.0'
-  implementation 'org.scalanlp:breeze_2.13:2.1.0' // scientific calculations (http://www.scalanlp.org/)
+  implementation "org.scalanlp:breeze_${scalaVersion}:2.1.0" // scientific calculations (http://www.scalanlp.org/)
   implementation 'de.lmu.ifi.dbs.elki:elki:0.7.5' // Statistics (for random load model)
   implementation 'org.jgrapht:jgrapht-core:1.5.2'
 
@@ -210,6 +211,12 @@ tasks.withType(ScalaCompile) {
     "-P:scapegoat:disabledInspections:VariableShadowing",
     "-P:scapegoat:ignoredFiles:.*/SimonaConfig.scala" // see scapegoat-sbt page for this param
   ]
+  // increasing stack size required for our pureconfig configuration
+  // see: https://github.com/pureconfig/pureconfig/issues/481#issuecomment-647760554
+  scalaCompileOptions.forkOptions.jvmArgs = [
+    '-Xss2m',
+    '-XX:-UseGCOverheadLimit'
+  ]
 }
 
 // separate scapegoat report for test classes

docs/readthedocs/_static/bibliography/bibtexAll.bib

@@ -12,12 +12,6 @@ @Article{Maleki.2017
 DOI = {10.3390/en10010134}
 }
 
-@MISC{Itaca_Sun,
-author = {Itacanet},
-title = {The Sun As A Source Of Energy},
-howpublished={\url{https://www.itacanet.org/the-sun-as-a-source-of-energy/part-3-calculating-solar-angles/}}
-}
-
 @article{Spencer.1971,
   added-at = {2018-06-18T21:23:34.000+0200},
   author = {Spencer, J. W.},
@@ -73,7 +67,7 @@ @book{Quaschning.2013
  author = {Quaschning, Volker},
  year = {2013},
  title = {Regenerative Energiesysteme: Technologie; Berechnung; Simulation},
- url = {http://ebooks.ciando.com/book/index.cfm/bok_id/471802},
+ url = {https://www.hanser-elibrary.com/doi/book/10.3139/9783446435711},
  price = {39.99 EUR},
  address = {M{\"u}nchen},
  edition = {8., aktualisierte und erw. Aufl.},
@@ -92,7 +86,8 @@ @Inbook{Schoenberg.1929
 pages={1--280},
 abstract={Die ersten Versuche, Messungen der Lichtst{\"a}rke der Himmelsk{\"o}rper auszuf{\"u}hren, um auf diesem Wege Aufschl{\"u}sse {\"u}ber ihre Beschaffenheit zu erhalten, fallen in die Zeit jenes gewaltigen Aufschwungs, welchen die Optik durch die Arbeiten von Newton und Huygens am Ende des siebzehnten und zu Beginn des achtzehnten Jahrhunderts erfahren hatte. Schon Huygens1 selbst versuchte die Helligkeit des Sirius mit derjenigen der Sonne zu vergleichen, indem er das Sonnenlicht durch eine kleine {\"O}ffnung im verschlossenen Ende eines langen Rohres abschw{\"a}chte. Der schwedische Physiker Celsius2 suchte nach einem Gesetze der Lichtabnahme beleuchteter Fl{\"a}chen, doch waren seine Schlu{\ss}folgerungen, ebenso wie diejenigen von Huygens, infolge der Unzul{\"a}nglichkeit der angewandten Methoden nicht stichhaltig. Au{\ss}er der Formel der Lichtabnahme mit dem Quadrate der Entfernung besa{\ss} die Physik noch keinerlei R{\"u}stzeug an strengen Definitionen und Gesetzen und keinerlei Apparate zur Messung der Lichtst{\"a}rken. Buffon3 versuchte den Verlust zu bestimmen, den das Sonnenlicht bei Reflexion an gl{\"a}sernen Spiegeln erleidet. Aber erst die gro{\ss} angelegten Arbeiten von Pierre Bouguer4 5 (1698--1758) und Johann Heinrich Lambert (1728--1777) schufen die Grundlagen der Photometrie. In systematischer experimenteller Arbeit, die durch sinnreiche Theorien erl{\"a}utert wird, behandelt Bouguer ihre Hauptprobleme: die Absorption des Lichtes bei der Reflexion und beim Durchgang durch feste und fl{\"u}ssige K{\"o}rper sowie die diffuse Reflexion an matten Fl{\"a}chen und beim Durchgange durch tr{\"u}be Medien.},
 isbn={978-3-642-90703-6},
-doi={10.1007/978-3}
+doi={10.1007/978-3},
+url = {https://link.springer.com/chapter/10.1007/978-3-642-90703-6_1}
 }
 
 @MISC{WikiAirMass,
@@ -122,7 +117,7 @@ @book{Iqbal.1983
  author = {Iqbal, Muhammad},
  year = {1983},
  title = {An Introduction To Solar Radiation},
- url = {http://site.ebrary.com/lib/alltitles/docDetail.action?docID=10678925},
+ url = {https://books.google.de/books/about/An_Introduction_To_Solar_Radiation.html?id=3_qWce_mbPsC&redir_esc=y},
  address = {Oxford},
  publisher = {{Elsevier Science}},
  isbn = {9780123737502}
@@ -195,4 +190,19 @@ @MISC{Radiation_ECMWF
   author = {Robin Hogan},
   title = {Radiation Quantities in the ECMWF model and MARS},
   howpublished = {\url{https://www.ecmwf.int/sites/default/files/elibrary/2015/18490-radiation-quantities-ecmwf-model-and-mars.pdf}}
-}
+}
+
+@misc{EN_50160,
+    title = {EN 50160:2020-11, Voltage characteristics of electricity supplied by public electricity networks},
+    publisher = {CENELEC},
+    type = {NORM},
+    year = {2022},
+    date = {2022-12-01},
+}
+
+@online{EU_2017/1485,
+    author = {{The European Commission}},
+    title = {COMMISSION REGULATION (EU) 2017/1485 of 2 August 2017 establishing a guideline on electricity transmission system operation},
+    date = {2017-08-02},
+    url = {https://eur-lex.europa.eu/legal-content/DE/TXT/?uri=CELEX%3A32017R1485},
+}

docs/readthedocs/config.md

@@ -245,6 +245,7 @@ Tba:
 
 ## Grid configuration 
 
+### Reference System
 The reference system contains a list of voltage levels. Each element includes the nominal apparent power, the nominal 
 voltage and the separate configuration of each voltage level. The voltage level configuration is composed of the identifier 
 and the nominal voltage.
@@ -268,6 +269,32 @@ simona.gridConfig.refSystems = [
 Further typical voltage levels which can be used in the simulation and the configuration of individual reference systems
 are described in the documentation of [reference system](models/reference_system).
 
+### Voltage limits
+
+The voltage limits contains a list of voltage levels. Each element includes the minimal and maximal allowed voltage and
+the separate configuration of each voltage level. The voltage level configuration is composed of the identifier and the
+nominal voltage. 
+
+The configuration of a voltage limits is optional. If no configuration is provided by the user, the default
+[voltage limits](models/voltage_limits) that includes all common german voltage levels is used. For those users
+who need other voltage levels than the common german voltage levels or different voltage limits, they can configure
+their limits as shown below.
+
+The voltage limits can be configured as follows:
+
+```
+simona.gridConfig.voltageLimits = [
+  {vMin = 0.9, vMax = 1.1, voltLvls = [{id = "Lv", vNom = "0.4 kV"}]},
+  {vMin = 0.9, vMax = 1.1, voltLvls = [{id = "Mv", vNom = "20 kV"}]},
+  {vMin = 0.9, vMax = 1.1, voltLvls = [{id = "Hv", vNom = "110 kV"}]},
+  {vMin = 0.9, vMax = 1.05, voltLvls = [{id = "EHV", vNom = "380 kV"}]},
+]
+```
+
+Further typical voltage levels which can be used in the simulation and the configuration of individual voltage limits
+are described in the documentation of [voltage limits](models/voltage_limits).
+
+
 ## Power flow configuration 
 
 Maximum allowed deviation in power between two sweeps, before overall convergence is assumed:

docs/readthedocs/models.md

@@ -17,6 +17,7 @@ models/three_winding_transformer_model
 models/reference_system
 models/thermal_grid_model
 models/thermal_house_model
+models/voltage_limits
 ```
 
 ## System Participant Related Models

docs/readthedocs/models/pv_model.md

@@ -127,7 +127,7 @@ $$
 **References:**
 
 * {cite:cts}`Maleki.2017`
-* {cite:cts}`Itaca_Sun`
+* {cite:cts}`Duffie.2013` p. 17 (formula 1.6.10)
 
 
 ### Solar Altitude Angle
@@ -146,7 +146,7 @@ $$
 **References:**
 
 * {cite:cts}`Maleki.2017` p. 5
-* {cite:cts}`Itaca_Sun`
+* {cite:cts}`Duffie.2013` p. 15 (formula 1.6.5) with $\sin (\alpha_s) = \cos (\theta_z)$
 
 
 ### Zenith Angle
@@ -198,11 +198,11 @@ $$
 Calculating the air mass ratio by dividing the radius of the earth with approx. effective height of the atmosphere (each in kilometer)
 
 $$
-airmassratio = (\frac{6371 km}{9 km}) = 707.8\overline{8}
+\mathrm{airmassratio} = (\frac{6371 km}{9 km}) = 707.8\overline{8}
 $$
 
 $$
-airmass = \sqrt{(707.8\overline{8} \cdot \cos({\theta_z}))^2 +2 \cdot 707.8\overline{8} +1)} - 707.8\overline{8} \cdot \cos{(\theta_z)})
+\mathrm{airmass} = \sqrt{(707.8\overline{8} \cdot \cos({\theta_z}))^2 +2 \cdot 707.8\overline{8} +1)} - 707.8\overline{8} \cdot \cos{(\theta_z)})
 $$
 
 **References:**
@@ -234,6 +234,8 @@ $$
 
 * {cite:cts}`Zheng.2017` p. 53, formula 2.3b
 * {cite:cts}`Iqbal.1983`
+* {cite:cts}`Spencer.1971`
+* {cite:cts}`Duffie.2013` (the fifth ed. seems to have a typo in formula (1.4.1b): factor $0.000719$ is missing a zero)
 
 
 ### Beam Radiation on Sloped Surface
@@ -274,7 +276,7 @@ b = (\cos(\phi) \cdot \cos(\delta)) \cdot (\sin(\omega_{2}) - \sin(\omega_{1}))
 $$
 
 $$
-E_{beam,S} = E_{beam,H} \cdot \frac{a}{b}
+E_{\mathrm{beam},S} = E_{\mathrm{beam},H} \cdot \frac{a}{b}
 $$
 
 **Please note:** $\frac{1}{180}\pi$ is omitted from these formulas, as we are already working with data in *radians*.
@@ -286,7 +288,7 @@ $$
 **$\omega_1$** = hour angle $\omega$\
 **$\omega_2$** = hour angle $\omega$ + 1 hour\
 **$\alpha_e$** = surface azimuth angle\
-**$E_{beam,H}$** = beam radiation (horizontal surface)
+**$E_{\mathrm{beam},H}$** = beam radiation (horizontal surface)
 
 **Reference:**
 
@@ -300,13 +302,15 @@ The diffuse radiation is computed using the Perez model, which divides the radia
 A cloud index is defined by
 
 $$
-\epsilon = \frac{\frac{E_{dif,H} + E_{beam,H}}{E_{dif,H}} + 5.535 \cdot 10^{-6} \cdot \theta_{z}^3}{1 + 5.535 \cdot 10^{-6} \cdot \theta_{z}^3}
+\epsilon = \frac{\frac{E_{\mathrm{dif},H} + E_{\mathrm{beam},N}}{E_{\mathrm{dif},H}} + 5.535 \cdot 10^{-6} \cdot \theta_{z}^3}{1 + 5.535 \cdot 10^{-6} \cdot \theta_{z}^3}
 $$
 
+with angle $\theta_z$ values in **degrees** ({cite:cts}`Duffie.2013` p. 94) and $E_{\mathrm{beam},N} = \frac{E_{\mathrm{beam},H}}{\cos (\theta_z)}$ ({cite:cts}`Duffie.2013` p. 95).
+
 Calculating a brightness index
 
 $$
-\Delta = m \cdot \frac{E_{dif,H}}{I_{0}}
+\Delta = m \cdot \frac{E_{\mathrm{dif},H}}{I_{0}}
 $$
 
 **Perez Fij coefficients (Myers 2017):**
@@ -384,7 +388,7 @@ $$
 the diffuse radiation can be calculated:
 
 $$
-E_{dif,S} = E_{dif,H} \cdot (\frac{1}{2} \cdot (1 +
+E_{\mathrm{dif},S} = E_{\mathrm{dif},H} \cdot (\frac{1}{2} \cdot (1 +
 cos(\gamma_{e})) \cdot (1- F_{1}) + \frac{a}{b} \cdot F_{1} +
 F_{2} \cdot \sin(\gamma_{e}))
 $$
@@ -396,25 +400,27 @@ $$
 **$\gamma_{e}$** = slope angle of the surface\
 **$I_{0}$** = Extraterrestrial Radiation\
 **$m$** = air mass\
-**$E_{beam,H}$** = beam radiation (horizontal surface)\
-**$E_{dif,H}$** = diffuse radiation (horizontal surface)
+**$E_{\mathrm{beam},H}$** = beam radiation (horizontal surface)\
+**$E_{\mathrm{beam},N}$** = beam radiation (normal incidence, thus radiation on a plane normal to the direction of the beam)\
+**$E_{\mathrm{dif},H}$** = diffuse radiation (horizontal surface)
 
 **References:**
 
 * {cite:cts}`Perez.1987`
 * {cite:cts}`Perez.1990`
 * {cite:cts}`Myers.2017` p. 96f
+* {cite:cts}`Duffie.2013` p. 95f
 
 
 ### Reflected Radiation on Sloped Surface
 
 $$
-E_{ref,S} = E_{Ges,H} \cdot \frac{\rho}{2} \cdot (1-
+E_{\mathrm{ref},S} = E_{\mathrm{Ges},H} \cdot \frac{\rho}{2} \cdot (1-
 \cos(\gamma_{e}))
 $$
 
 *with*\
-**$E_{Ges,H}$** = total horizontal radiation ($E_{beam,H} + E_{dif,H})$\
+**$E_{\mathrm{Ges},H}$** = total horizontal radiation ($E_{\mathrm{beam},H} + E_{\mathrm{dif},H})$\
 **$\gamma_e$** = slope angle of the surface\
 **$\rho$** = albedo
 
@@ -428,13 +434,13 @@ $$
 Received energy is calculated as the sum of all three types of irradiation.
 
 $$
-E_{total} = E_{beam,S} + E_{dif,S} + E_{ref,S}
+E_{\mathrm{total}} = E_{\mathrm{beam},S} + E_{\mathrm{dif},S} + E_{\mathrm{ref},S}
 $$
 
 *with*\
-**$E_{beam,S}$** = Beam radiation\
-**$E_{dif,S}$** = Diffuse radiation\
-**$E_{ref,S}$** = Reflected radiation
+**$E_{\mathrm{beam},S}$** = Beam radiation\
+**$E_{\mathrm{dif},S}$** = Diffuse radiation\
+**$E_{\mathrm{ref},S}$** = Reflected radiation
 
 A generator correction factor (depending on month surface slope $\gamma_{e}$) and a temperature correction factor (depending on month) multiplied on top.