A Benchmark Model for Power System Restoration Studies

Benchmark restoration model Documentation Ljubljana, 2025 2 Restoration Document prepared by: dr. Tadej Škrjanc (UL FE) dr. Leopold Herman (UL FE) prof. dr. Rafael Mihalič (UL FE) ass. prof. dr. Urban Rudež (UL FE) Document reviewed by: Dawn Virginillo (EPFL) dr. Asja Derviškadič (Swissgrid) dr. Gilles Torresan (RTE) Mathilde Bongrain (CRESYM) Version: v1.0 Date: 14/10/2025 3 Restoration Table of content 1. Use case purpose and context ................................................................. 4 2. Network description ................................................................................ 4 3. Model description ................................................................................... 5 4. Input data ............................................................................................... 6 5. Scenarios ............................................................................................. 16 6. References ........................................................................................... 18 4 Restoration 1. Use case purpose and context The benchmark restoration model (BRM) represents an electrical power system under restoration conditions following a large-scale blackout. It provides a standardized test case for evaluating conventional and advanced restoration strategies, black start coordination, and network reenergization sequences. The BRM offers a flexible, practical platform for analysing restoration strategies and related dynamic phenomena. It includes key network components typically available in early restoration phases and supports scenario-based testing under various operating conditions, including those involving inverter-based resources such as battery energy storage systems (BESS). Designed for system operator back offices and researchers, the model supports the development and assessment of restoration plans and control strategies, rather than serving as a training or realtime decision-support tool. The BRM defines six scenarios representing a bottom-up restoration strategy, focusing on small network cells with limited inertia and short-circuit power where critical transients and dynamic interactions arise. By bridging research and practice, the model promotes more resilient and adaptive restoration strategies for future power systems. 2. Network description The network, illustrated in Figure 1, consists of four main sections interconnected through transmission lines and step-up transformers: • two restoration cells, • one supporting (non-black start) generation unit, and • one external source (interconnection). The external source enables the observation of synchronization between a restoration cell and a fully operational network. It also allows simulation of a top-down restoration strategy, where the external grid can be modelled either as a large equivalent synchronous generator or as a grid segment unaffected by the blackout. The supporting generation unit represents a non–black-start source, enabling analysis of its connection sequence and contribution to network expansion. The two restoration cells, together with their interconnecting lines, form the core of the benchmark model and allow detailed investigation of the following phenomena: • energization of cables, overhead lines, and transformers, • self-excitation of a synchronous generator, • local and remote (cold) load pick-up, • the role of pumped-storage hydro units used as ballast loads, black-start sources, or in combination with BESS for operational support, • the impact of distributed generation, and • synchronization between two restoration cells. 5 Restoration Figure 1: Benchmark restoration model diagram in DIgSILENT PowerFactory 3. Model description The BRM is designed to capture the key phenomena and operational strategies relevant to electrical power system (EPS) restoration. Its structure and components are based on the minimum configuration required to reproduce both the typical dynamic behaviours and the fundamental assets found in real-world restoration scenarios. The model was developed through an extensive literature review and further refined using practical experience and consultations with transmission system operators. This process ensures an effective balance between academic completeness and operational relevance. The BRM comprises the following components: • busbars at eight voltage levels: 10, 10.5, 18, 21, 27, 33, 220, and 400 kV, • four overhead lines (two of them mutually coupled), one cable, and six shunt reactors, • seven two-winding and two three-winding transformers, allowing future analysis of restoration sequences initiated at the low-voltage level through tertiary windings, • two thermal power plants (gas and coal); their generator controllers are implemented using standard IEEE dynamic models, with parameters obtained from published literature ([1], [2], [3]) and IEEE guidelines ([4], [5]), • a pumped-storage hydro (PSH) unit, • four distinct load types: induction motor (dynamic), auxiliary load, static load, and a load representing cold load pick-up, SM ~ SG ~ SG ~ SG ~ SG ~ MOT_psh GEN_psh CBa-pshLINE_3CB-psh TR_psh GEN_gas TR_gas CB-gas CB-ic LOAD_aux TR_aux DER TR2_bc TR1_bc LOAD_1a CB2-ld1 TR_ld1 CB1-ld1 SRb_ln1 SRa_ln1 GEN_ic TR_ic LOAD_ic LINE_ic CB1-bess TR1_bess GEN_coal LOAD_2a TR_ld2 CB2-ld2CB1-ld2 TR2_bess TR_coal CB2-bess CB-bess CB-coal SRb_cb POWER SOURCE SRa_cb LOAD_2b CBb-ln2-sr SRa_ln2 SRb_ln2 BUSc Line Couplings BUSb BUSa ONE OF POSSIBLE BESS LOCATIONS NON-BLACK START UNIT CELL #2 CELL #1 BESS INTERCONNECTION CB_aux CBb-cb CBb-ln1 CBb-ln2 CB1-cb CB2-cb CBb-cb-sr CBb-ln1-sr CABLE LINE_1 LINE_2 CBa-ln2-sr CBa-cb-sr CBa-ln1-sr CBa-cb CBa-ln1 CBa-ln2 6 Restoration • distributed energy resources (DERs) represented by the generic aggregated WECC DER_A model [6], which treats DER generation or storage as a single equivalent static generator, and • a neighbouring grid, consisting of a power source, power plant, static load, transformer, and transmission line. 4. Input data Each component has been selected for its relevance in reproducing restoration-related dynamics. The corresponding parameter values are provided in Table 1 – Table 21. Wherever possible, typical and realistic values were applied, complemented by data from the literature and the authors’ practical experience. Table 1: Data of synchronous motor mechanical loading and AVR settings Parameter Label Unit MOTpsh Excitation field base ratio efdBaseRatio - 1 Proportional factor mdmlp p.u. 0.125 Exponent mdmex - 3 Moment of inertia Jme kgm2 0 Gear ratio gratio - 1 Starting field resistance rf_st p.u. 0.01 Trigger excitation at speed speed_th p.u. 0.95 Constant field voltage ve_const p.u. 1 Table 2: Data of synchronous generators Parameter Label Unit GENgas GENpsh GENcoal GENic Rated apparent power sgn MVA 50 200 600 1560 Rated voltage ugn kV 10.5 18 21 27 Rated power factor cosn - 0.8 0.8 0.85 0.87 Inertia constant h s 5 4 5.22 8.439 Armature resistance rstr p.u. 0.002 0.002 0.001 0 Armature leakage reactance xl p.u. 0.135 0.1 0.224 0.15 Zero sequence reactance x0sy p.u. 0.1 0.1 0.1 0.1 Negative sequence reactance x2sy p.u. 0.2 0.2 0.2 0.2 d-axis synchronous reactance (unsaturated) xd p.u. 2.4 2 2.23 2.25 d-axis transient reactance (unsaturated) xds p.u. 0.31 0.3 0.365 0.4 d-axis subtransient reactance (unsaturated) xdss p.u. 0.24 0.2 0.268 0.17 q-axis synchronous reactance (unsaturated) xq p.u. 1.33 2 1.9 2.001 q-axis transient reactance (unsaturated) xqs p.u. 1.33 0.3 0.785 0.65 7 Restoration q-axis subtransient reactance (unsaturated) xqss p.u. 0.35 0.2 0.268 0.174 d-axis transient time constant (short-circuit) tds s 1.45 1 1.267 1.416667 d-axis subtransient time constant (short-circuit) tdss s 0.022 0.05 0.034 0.014875 q-axis transient time constant (short-circuit) tqs s 0.000001 1 1.15 0.406047 q-axis subtransient time constant (short-circuit) tqss s 0.0095 0.05 0.074 0.00936923 Table 3: URST5T controller parameters Parameter Label Unit GENgas Measurement time constant Tr s 0.01 Lag-time constant Tb1 s 12 Lead-time constant Tc1 s 1.2 Controller gain Kr p.u. 500 Lag-time constant Tb2 s 0.01 Lead-time constant Tc2 s 0.02 Controller time constant T1 s 0.01 Rectifier loading factor Kc p.u. 0.1 Voltage regulator minimum output Vrmin p.u. -6.5 Voltage regulator maximum output Vrmax p.u. 7.65 Table 4: ESST1A controller parameters Parameter Label Unit GENpsh Measurement delay Tr s 0.001 Filter first delay time constant Tb s 20 Filter first derivative time constant Tc s 0.01 Filter second delay time constant Tb1 s 0.1 Filter second derivative time constant Tc1 s 0.01 Controller gain Ka p.u. 55 Controller time constant Ta s 0.01 Current limiter factor Kc p.u. 0.01 Stabilization path gain Kf p.u. 0.1 Stabilization path time constant Tf s 0.31 Current input factor Klr p.u. 1 Current input reference Ilr p.u. 2 PSS input selector [1,2] Vos - 1 Uel input selector [1,2,3] Vel - 1 Controller input minimum Vimin p.u. -0.05 Controller minimum output Vamin p.u. -2.6 Exciter minimum output Vrmin p.u. -3.4 Controller input maximum Vimax p.u. 0.05 8 Restoration Controller maximum output Vamax p.u. 2.6 Exciter maximum output Vrmax p.u. 3.4 Table 5: IEEE ST7B controller parameters Parameter Label Unit GENcoal UEL router selector [1/3] UEL_flag - 1 OEL router selector [1/3] OEL_flag - 1 Feedback gain Kl p.u. 1 Feedback gain Kh p.u. 0 Voltage regulator gain Kpa p.u. 40 Input filter time constant Tr s 0 Voltage regulator lag time constant Tb s 1 Voltage regulator lead time constant Tc s 1 Voltage input lag time constant Tf s 1 Voltage input lead time constant Tg s 1 First order feedback gain Kia p.u. 1 First order feedback time constant Tia s 4 Voltage reference minimum limit Vmin p.u. 0.95 Voltage regulator minimum limit VRmin p.u. -4.655 Voltage reference maximum limit Vmax p.u. 1.05 Voltage regulator maximum limit VRmax p.u. 4.655 Table 6: GGOV1 governor parameters Parameter Label Unit GENgas Load limiter reference value Ldref p.u. 1 Turbine gain Kturb p.u. 2.005 No load fuel flow Wfnl p.u. 0.17 Load limiter proportional gain Kpload p.u. 0.15 Load limiter time constant Tfload s 0 Temperature detection lead time constant Tsa s 12 Temperature detection lag time constant Tsb s 15 Acceleration limiter gain Ka p.u./s 10 Acceleration limiter time constant Ta s 0.1 Power controller reset gain Kimw p.u. 0 Electrical power transducer time constant Tpelec s 1 Governor droop feedback signal selector Rselect - -2 Acceleration limiter setpoint Aset p.u./s 1 Permanent droop r p.u. 0.04 Speed governor deadband db p.u. 0.0002 Governor proportional gain Kpgov p.u. 3.2 Governor integral gain Kigov p.u. 1.8 Governor derivative gain Kdgov p.u. 0 Governor derivative controller time constant Tdgov s 1 Actuator time constant Tact s 0.2 9 Restoration Turbine rated power (=0→PN=Pgnn) Trate MW 0 Mechanical damping coefficient Dm p.u. 0 Switch for fuel source characteristic Flag - 0 Diesel engine transport time constant Teng s 0 Turbine lead time constant Tc s 0 Turbine lag time constant Tb s 0.1 Load limiter integral gain Kiload p.u. 0.075 Maximum rate of load limit decrease rdown p.u./s -1 Minimum speed error signal minerr p.u. -0.2 Minimum valve position limit Vmin p.u. 0.09 Maximum valve closing rate rclose p.u./s -3.3 Maximum rate of load limit increase rup p.u./s 1 Maximum speed error signal maxerr p.u. 0.2 Maximum valve position limit Vmax p.u. 0.669 Maximum valve opening rate ropen p.u./s 3.3 Table 7: HYGOV governor parameters Parameter Label Unit GENpsh Temporary droop r p.u. 0.36 Governor time constant Tr s 5.88 Filter time constant Tf s 0.08 Servo time constant Tg s 0.5 Water starting time Tw s 1.2 Turbine gain At p.u. 1 Frictional losses factor Dturb p.u. 0.5 No load flow qnl p.u. 0.05 Permanent droop R p.u. 0.04 Turbine rated power (=0→PN=Pgnn) PN MW 0 Minimum gate limit Gmin p.u. 0.01 Gate velocity limit Velm p.u. 0.2 Maximum gate limit Gmax p.u. 0.99 Table 8: IEEEG1 governor parameters Parameter Label Unit GENcoal Controller gain K p.u. 20 Governor time constant T1 s 0 Governor derivative time constant T2 s 0 Servo time constant T3 s 0.004 High pressure turbine factor K1 p.u. 0.275 High pressure turbine factor K2 p.u. 0 Intermediate pressure turbine time constant T5 s 15 Intermediate pressure turbine factor K3 p.u. 0 Intermediate pressure turbine factor K4 p.u. 0 Medium pressure turbine time constant T6 s 0.2 16 Restoration Series reactance Xseries % 20 Series resistance Rseries % 0 Angle detection time const. Tpll s 0.001 Freeze angle detection if voltage < ufreeze ufreeze p.u. 0 Table 21: Static generator model data Parameter Label Unit DER Rated apparent power sgn MVA 20 Rated power factor cosn - 0.95 Switch-off threshold umin p.u. 0.1 Switch-on threshold uonthr p.u. 0.15 Switch-on delay Tondelay s 0 Short circuit impedance of series reactor uk % 20 Copper losses of series reactor Pcu kW 0 d-axis proportional gain Kd - 1 d-axis integration time const. Td s 0.01 q-axis proportional gain Kq - 1 q-axis integration time const. Tq s 0.01 5. Scenarios The proposed BRM includes six scenarios, labelled "A" through "F". Since different phenomena occur over varying time scales and require different simulation methods, each scenario is further divided into multiple steps labelled "a" to "g", with step "0" representing the initial state. Steps are intended to be executed sequentially. Restoration typically begins with the energization of a black start unit, followed by either synchronizing additional generating units to increase the system’s short-circuit strength and inertia or reconnecting loads to enhance system damping and restore power to critical customers. Each of these actions is important, yet they do not determine the system’s stability identically. Scenario A Scenario A illustrates a broad range of key dynamic phenomena typically encountered during a standard restoration sequence. Its main objective is to demonstrate the step-by-step network expansion by progressively connecting generation units, lines, transformers, and loads, while observing the resulting impacts on system dynamics. The scenario comprises seven steps (a–g), where the following phenomena can be observed: • step 0 – Ferranti effect, • step a – cold load pick-up, • step c – switching over-voltage, • step d – inrush current, • step e – auxiliary load pick-up and series sympathetic inrush, 17 Restoration • step f – load pick-up (static + DER), • step g – parallel sympathetic inrush. Scenario B Unlike Scenario A, Scenario B prioritizes early load reconnection to improve black-start unit stability by increasing loading levels, emphasizing the need for careful, simultaneous energization of dynamic loads. It also illustrates how minor equipment failures, such as incorrect operation of shunt compensation, can impose significant operational challenges. In this case, a line is replaced by an underground cable to connect the black-start unit. Due to its short length, the Ferranti effect does not occur. The scenario comprises three steps (a–c), demonstrating the following phenomena: • step a – generator self-excitation, • step b – inrush currents, • step c – load pick-up (synchronous motor). Scenario C Scenario C also emphasizes early load reconnection but focuses on load-related dynamic phenomena, including cold load pick-up, transformer (sympathetic) inrush, cable energization effects, and the consequences of associated switching operations. The scenario proceeds through five steps (a–e), highlighting: • step a – series sympathetic inrush, • step b – cold load pick-up, • step c – switching over-voltage and missing zero-crossing, • step d – switching over-voltage, • step e – load pick-up (static + DER). Scenario D Scenario D examines early load reconnection with a pumped-storage hydro unit serving as the black-start source. Its purpose is to analyse local and remote load restoration dynamics before adding new generation, particularly under conditions involving transformer inrush, DER behaviour, and long-line energization. The scenario proceeds through four steps (a–d), showing: • step a – series sympathetic inrush, • step b – load pick-up (static + DER), • step c – Ferranti effect and switching over-voltage, • step d – cold load pick-up. Scenario E Scenario E investigates the sensitivity of inrush behaviour to line length, DER penetration, and system loading. It provides a foundation for analysing how load composition and network topology influence inrush dynamics in inverter-dominated systems. The scenario consists of three steps (a–c), illustrating: • step 0 – Ferranti effect, • step a – load pick-up (static + DER), • step b – switching over-voltage, • step c – parallel sympathetic inrush. 18 Restoration Scenario F Scenario F shares similarities with Scenario B but reverses the order of key actions to highlight the impact of early generation support. Its goal is to demonstrate how additional synchronous generation can increase short-circuit strength, enhance reactive power availability, improve voltage stability, and facilitate the successful start-up of large motor loads. The scenario proceeds through three steps (a–c), featuring: • step a – load pick-up (auxiliary), • step b – switching over-voltage and missing zero-crossing, • step c – load pick-up (synchronous motor). 6. References [1] “Dynamic models package ‘Standard-1’ - GMB dynamic models for PSS® software product suite.” Siemens, Oct. 2012. Accessed: Dec. 20, 2023. [Online]. Available: https://docplayer.net/23948599-Dynamic-models-package-standard-1.html [2] “Turbine-governor models - Standard dynamic turbine-governor systems in NEPLAN power system analysis tool.” NEPLAN AG. Accessed: Dec. 20, 2023. [Online]. Available: https://www.neplan.ch/wp-content/uploads/2015/08/Nep_TURBINES_GOV.pdf [3] “Exciter models - standard dynamic excitation systems in NEPLAN power system analysis tool.” NEPLAN AG. Accessed: Dec. 20, 2023. [Online]. Available: https://www.neplan.ch/wpcontent/uploads/2015/08/Nep_EXCITERS1.pdf [4] IEEE, “IEEE Recommended Practice for Excitation System Models for Power System Stability Studies,” IEEE Std 4215-2016 Revis. IEEE Std 4215-2005, pp. 1–207, Aug. 2016, doi: 10.1109/IEEESTD.2016.7553421. [5] Power System Dynamic Performance Committee, Power System Stability Subcommittee, Task Force on Turbine-Governor Modeling, “Dynamic Models for Turbine-Governors in Power System Studies,” IEEE PES, Technical Report PES-TR1, Jan. 2013. Accessed: Sep. 10, 2025. [Online]. Available: https://resourcecenter.ieee-pes.org/publications/technicalreports/pestr1 [6] The Electric Power Research Institute (EPRI), “The New Aggregated Distributed Energy Resources (der_a) Model for Transmission Planning Studies: 2019 Update,” EPRI, California, Technical Update 3002015320, Mar. 2019. Accessed: Jan. 03, 2025. [Online]. Available: https://www.epri.com/research/products/000000003002015320