Microgrids

The microgrids use case in GridLAB-D™ is implemented to allow islanded, smaller power system simulations. These simulations examine sub-second influences on parameters like frequency and voltage. The final capability allows the examination of transients in the voltage and frequency associated with microgrid operations.

Microgrids functionality in GridLAB-D™ is primarily an overall capability of the simulation engine. No specific microgrid module exists, but rather objects in several modules support transient-level time scales (~10 ms) and islanded operation.

Microgrids are typically operated in a manner that there is no strong, stiff source bus on the system. During microgrid operations, connections to the larger, bulk transmission system are disconnected and only local, smaller, often distributed, generation sources are utilized. Under such scenarios, the dynamics of the system are expected to play a more significant part in the stability of the power system.

Equations

The primary basis for the implementation of the microgrids capability involves modeling the relevant components with accurate equation models. At this time, these models are expected to operate down to a 1-millisecond time step.

Equations are taken from Reference 1 and 2 below. Equation notation follow:

Sub-second Implementation (Dynamic)

The GridLAB-D™ dynamic simulations represent electro-mechanic transients of unbalanced micro grid operation. The synchronous machines models are in fundamental frequency phasor representation considering unbalanced operation. The network and loads are represented with a full abc model. Additionally, diesel governor control and automatic voltage regulators are modeled. Figure 1 briefly presents the overall algorithm. Each model in the algorithm is explained in detail below.

Notation

The following variables and parameters are used in the dynamic model equations below.

Classic synchronous machine

The classic, synchronous machine is governed by several equations. For rotating machines, it is often useful to perform a space transformation from the \(abc\) plane to a \(dq0\) plane. This aligns the system with the rotor of the machine and makes inductance values fixed, rather than angle dependent. The transformation is given by:

with an inverse transform of

This transformation is also useful for voltages and currents on the machine. For traditional, transmission-level synchronous machine modeling, the \(S_0\) terms are assumed zero (balanced condition). For the unbalanced microgrid scenarios, all three components of the transformation need to be kept.

Despite the inclusion of the \(0\) terms, many assumptions go into the typical \(dq0\) representation that may not be valid for a microgrid scenario. To ensure these assumptions do not bias the distribution-level results, the \(dq0\) transformation is not used to explicitly solve for the stator voltages or flux values.

The equations for the three stator voltages are given by: [R1.2.1]

where the individual fluxes are defined as

The rotor voltage equations are governed by:

where the individual fluxes are defined as

Various components of these terms may be zeroed out, or omitted, for different models of the synchronous generator. These terms need to be handled appropriately to ensure the solver is stable.

The output power of the stator is defined as:

The mechanical components of the synchronous generator are governed by a series of equations relating the electrical and mechanical aspects of the generator. These are computed as:

and

Three-phase synchronous machine model

Unbalanced operation of three phase synchronous machines is modeled using a simplified fundamental frequency model in phasor representation according to [1, 2, 3, 4]. This simplification allows representing the machine in symmetrical components where the positive sequence represents the main electrical torque, and the negative sequence current produces a torque in opposition. The total electrical torque is constant, facilitating the solution and determination of equilibrium. However, the variation of electrical torque due to unbalanced operation reported in [5, 6] is ignored. In addition, typical assumptions for transient stability models are also made: ignoring sub-transient saliency, and neglecting the stator dynamics [7].

The machine electrical dynamic equations are:

The machine mechanical dynamic equations are:

Network solution: initial static power flow and network solution during dynamic simulations

The network and loads are represented in full abc coordinates. The abc representation allows a complete representation of line and load unbalances. The network solution is anextension the method proposed in [8].

To adequately initialize the dynamic simulation, the static power flow solution of three-phase synchronous generator buses should consider the symmetry built features of generators. In other words the phase voltage and power unbalance of the generator buses cannot be freely determined. Even though the phase powers and voltages can be still unbalanced, they are subject to a generator symmetry built constraint. The symmetry built constraint was first introduced in [9] for PQ generator buses in a distribution network power flow solution. In [10], the symmetry built constraint is also applied to slack and PV buses, allowing for an adequate initialization of dynamic simulation from the static power flow solution. The symmetry constraints are applied to the initial static power flow as follows.

The following equations describe the network solution model in compact form, for more details see [8].

Where the matrix \(\left[ Jac \right]\) is equal to the bus admittance matrix, except for the diagonal elements that have additional terms to represent ZIP loads [8]. The full generator admittances are incorporated to the bus admittance matrices to represent the machine characteristics. The generator admittance matrices are, according to [9]:

The symmetry constraint applied to generator buses in the initial static power flow solution is given by [9]:

Due to generator symmetry built, there are no negative and zero sequence current sources [9]:

The symmetry built constraint was applied to PQ generator buses in [9]. The application to Slack and PV generator buses in a micro grid setting is reported in [10]. The symmetry constraint is no longer applied during the dynamic simulations, where the symmetric generator’s current source injection depend on the dynamic states as explained in the following point.

Interface between machine model and network solution

The synchronous machine dynamic models are linked to the network solution by using Norton current source equivalents with shunt generator impedances, as suggested in [9, 11]. The current sources are symmetric balanced current injections to respect the generator symmetry built (windings symmetrically distributed in stator and rotor), and the generator impedances account for the effect of unbalanced terminal voltages. It is important to notice that the total generator current (current source minus current derived through generator shunt impedance) can also be unbalanced. The interface is formulated as:

Where \(\left[ E^{\prime\prime}_{a,b,c} \right]\) is a balanced voltage calculated by transforming \(E^{\prime\prime}_{di}\) and \(E^{\prime\prime}_{qi}\) to network reference frame and then to abc reference frame.

Synchronous machine controllers: governor and automatic voltage regulator

Generator control models are also defined in the GridLAB-D™ dynamic simulations. The generator control models are:

• Woodward diesel governor (DEGOV1) that modifies the mechanical power of the diesel generator proportionally to the generator speed deviation
• Simplified exciter system (SEXS) that modifies the generator field voltage (and hence its reactive power) to control the generator^\prime s terminal voltage (average voltage magnitude of all phases)

DEGOV1 and SEXS models are commonly used in power system industry-grade transient stability programs such as GE PSLF and PSS/E.Block diagrams for DEGOV1 and SEXS can be found here. DEGOV1 is on page 123 and SEXS is on page 88.

The simplified exciter system (SEXS) equations are:

The diesel governor DGOV1 equations are:

• Electric control box:

• Actuator:

• Diesel engine:

Traditional Transmission-level Implementation Comparison

Under traditional, positive-sequence, balanced implementation, the positive-sequence portion was often transferred into the \(dq0\) space for the solutions. As part of this transformation and derivation, the equations were based on the assumption that the system is balanced three-phase. With this assumption, many of the terms are considered identical. Machine parameters are based on phase \(A\) of the system, or a multiple of 3.0 of the phase \(A\) component. Dependent on the parameter, this balanced assumption may pose problems with voltages or currents of a microgrid system. The nature of this impact is unknown at this time.

With the ability to collapse the equations to balanced forms, and as a result ignore the \(i_0\) term of the \(dq0\) transformation, the equations for implementation become significantly reduced. Since everything is transferred to the \(dq0\) plane, much of the formulation occurs in that notation. Table 2 shows the positive-sequence version compared to the unbalanced three-phase version above. Equations may be simplified for space using notation from 1.

From the table, it is clear the unbalanced equations end up being a little more complicated. Simplifications and reductions associated with the \(dq0\) space and balanced voltage and current values allow the traditional model to collapse significantly. It is unclear at this time what the additional benefit the full three-phase unbalanced model brings over the assumed balanced model, so implementations may be altered to fit the "assumed balanced" model to reduce computational burdens.

Speed control

For the first implementation, simple speed control for the synchronous generator are be provided by two simple governor schemes. An isochronous and speed-droop governor are implemented for frequency and speed control on the initial microgrids test scenarios.

Isochronous governor

An isochronous governor is used to adjust a generator's power output to maintain a specific frequency. This type of governor is often used on single-generator systems, or when only a single generator responds to changing loads (e.g., the other generators are ungoverned). A basic isochronous governor equation would be

where \(K\) is an appropriate scalar between frequency deviation and power output. The integration operator is meant to reduce the isochronous governor's response to noise and momentary load changes.

Speed-droop governor

Speed-droop controls are necessary when more than one generator needs to correct for load changes. Each generator responds in a proportional manner to the frequency shift and adjusts its output. As a result, all generators (with the droop control) pick up a portion of the power output change. A simple droop governor equation is given by

As with the isochronous governor control, \(K\) is the scalar between frequency deviation and power output adjustments, while \(R\) represents the droop factor.[R1.2.2]

Exciters

The requirements call for the implementation of a simple DC exciter [R1.2.3]. A simple thyristor-rectifier exciter is also implemented to enable more feasible modeling of lower cost, modern diesel generators. Both exciter types support load compensation inputs through the voltage \(V_{Comp}\) 1. In both cases, this is defined as:

where \(\tilde{E}_{t}\) and \(\tilde{I}_{t}\) are the positive-sequence terminal voltage and current, respectively. The positive-sequence version is used as a rough indication for the excitation field adjustment since only one field exists for all three phases (only one rotor per generator).

DC Exciter

To properly model the synchronous machine, the field windings inside the rotor need to be excited. A simple self-excited DC exciter is modeled for the initial implementation. The modeled exciter is an IEEE type DC1A, diagrammed on page 363 of 1. The exciter is governed by the equations

where

The regulator output (\(V_R\)) can be further constrained by limiting values. These values, \(V_{RMAX}\) and \(V_{RMIN}\), are applied to the output of the regulator, if present.

Terminal voltage for the exciter control is taken as the magnitude of the positive sequence component of all connected voltage terminals.

This equation set represents an implementation where all possible components of the DC exciter are implemented (compensators, stabilizers, and amplifiers). These devices may not all always be present, so appropriate catches and checks need to be in place to "remove" unneeded portions of the equations (R1.2.3, R1.2.4).

Thyristor Rectifier Exciter

A simple thyristor rectifier exciter does not have a feedback loop, so it is a more simplistic implementation that a DC exciter. This implementation is also known as an IEEE type AC4A exciter. The exciter is represented by the equations derived from Figure 8.42 of 1 as:

where

The value of \(V_{in}\) can be constrained by limiting values of \(V_{IMIN}\) and \(V_{IMAX}\). The output can also be limited by values \(V_{RMIN}\) and \(V_{RMAX}-K_Ci_{fd}\). As with the DC exciter, the implementation includes all possible inputs (including PSS units), which may not always be present. Appropriate catches and processes need to be in place to ensure this does not cause any issues with the solver.

Solver

The key development for the microgrids capability in GridLAB-D™ is the inclusion of a power system dynamic solver that interfaces with the appropriate objects within the GridLAB-D™ environment. Initially, this is expected to be predominately the powerflow module.

Updates to voltage and frequency values should be made apparent for the next "quasi-steady-state" powerflow iteration. These values should be implemented in such a way that powerflow will not significantly override the control actions from the generator or load, with regards to voltage or frequency. An incremental powerflow solution is required at all dynamic timesteps to ensure the system is properly responding, so this incremental powerflow solution should coincide with the static solution at "quasi-steady-state" points (R3.4, R3.5).

The implemented solver shall be done as a modified Euler, predictor-corrector solution method1. This implementation provides the basic structure laid out in the Power System Toolbox (PST) for MATLAB 3. Utilizing the modified Euler method allows the flexibility of the different timestep sizes and progression outlined in the Solution Timesteps section below.

Interfacing Overview

To implement the dynamic equations to produce the frequency information, the microgrids implementation needs to be able to exchange several different pieces of information. These can be broken into simple inputs and outputs related to the solver. These inputs and outputs may be direct module-level interfaces, object-level inputs, as well as function-level interfaces for other objects.[R2] Interfacing with the static powerflow requires the implementation of PV-bus functionality into the Newton-Raphson solver.

Object inclusion

Inclusion in the microgrids-enabled dynamic solver capability is handled during GridLAB-D™'s normal object initialization routines. Objects contributing to the dynamics of the system will flag appropriately for inclusion by the solver during its initialization.[R1.1]

Solver published inputs

Most of the inputs to the microgrids capability are handled by the solver directly, with links to appropriate objects. One "extraneous" situation requires an external input into the dynamic solver. The input is:

If the system assumed to be connected to a much larger, higher inertia system with minimal impact on the frequency, the external_frequency variable is used to set the system synchronous frequency.

In cases of just being attached to a larger system, it is recommended than an over-sized generator be attached at the SWING node (high inertia and power values). This allows the dynamic influences of a larger-connected (but not explicitly modeled) system to be accounted for without having to use the external_frequency variable.

Solver published outputs

Most of the added capabilities are handled at the specific objects. However, a few global outputs are available from the dynamic solver. These include:

These values are published mainly for recorder objects to capture them for overall GridLAB-D™ data output. The nature of the dynamic solver requires the creation of a new, frequency-capable recorder-like capability to capture the transient effects on the system. These properties will be among those recorded.

Solver data structure

To facilitate data operations between the individual objects and the dynamic solver capability, a common data structure is used to pass information back and forth. This data structure should contain information and pointers to the following elements:

NULL fields will be ignored as "no equipment present" to the solver. The pointer for this data structure is passed to the dynamic solver capability during the solver's initialization routine (R2.1, R2.2).

Solver external functions

The nature of the microgrid capability and the dynamic solver will not initially require any external functions for devices. All relevant data passes and solver calls should be handled internal to the implementation.

Solver timing

The actual execution of the solver and how often it is called are key aspects of the proper integration of the dynamic solution capabilities within GridLAB-D™. Solver calls need to be properly timed with the powerflow solution, as well as the requirements of the individual dynamic components. To ensure proper dynamic transitions, a form of the steady state powerflow must be resolved at each timestep of the dynamic simulation for the "non-contributing" objects. Loads and devices not directly participating in the dynamic solver are assumed to maintain fixed load values over the sub-GridLAB-D™-standard timesteps. These devices may influence the magnitude and duration of the dynamic response, so they must be included in some form. Functionality for faster, dynamic loads will be in place for future implementations of microgrid devices. Through the continuous updates of the quasi-static powerflow, transitions at normal GridLAB-D™ timesteps should be minimized to be predominately non-dynamic state changes.

Solver Passes

The actual solver follows the modified Euler, predictor-corrector implementation of the MATLAB Power System Toolbox (PST)3. For the predictor steps, the solution proceeds as:

1. Solve base powerflow
2. Solve the network interface components (solve the loadflow - this may be a reduced loadflow)
   1. Solve for the generators and motors
   2. Solve for the exciters
   3. Solve for the governors
3. Solve the system dynamics components
   1. Solve for the generators and motors
   2. Solve for any PSS units present
   3. Solve for the exciters
   4. Solve for the governors

4. Apply the solutions as a predictor update This is followed by a similar process for the corrector step. The corrector step follows:

5. Solve the network interface components (solve the loadflow - this may be a reduced loadflow)

   1. Solve for the generators and motors
   2. Solve for any PSS units present
   3. Solve for the exciters
   4. Solve for the governors
6. Solve the system dynamics components
   1. Solve for the generators and motors
   2. Solve for any PSS units present
   3. Solve for the exciters
   4. Solve for the governors
7. Apply the solutions as a corrector update

After all "machine values" have been updated, a global frequency is estimated

1. Update frequency calculation

After these two steps complete, the simulation advances to the next timestep. This sequence repeats until the next GridLAB-D™ overall timestep is encountered. At that point, the changes are reflected into the quasi-steady state powerflow solution, and the process will repeat.

Solution Timesteps

Timestep progression is handled in a manner similar to GridLAB-D™'s core functionality. All objects requesting a dynamic solution update will request a time for recalculation. The minimum value will drive the simulation forward. The solver shall be implemented as a predictor-corrector solver, so larger timestep progression should be possible. A "maximum dynamic" timestep will also be specified to ensure any unexpected "passive" element (not requesting a timestep update) are handled.[R3.2]

The initial solver time resolution is 1 ms. Timestep updates occur in multiples of 1 ms, but are not allowed to be any less than 1 ms (R3, R3.1).

Solver Call Timing

Actual execution of the solver relies heavily on the interactions with the powerflow module. Dynamic quantity updates need to wait for a final powerflow solution before progressing forward. To ensure proper powerflow convergence, the dynamics capabilities must not interfere with the static powerflow. The use of the new Subsecond capabilities and postupdate calls are implemented to ensure this interaction does not occur. This ensures all "dynamic contribution" objects are ready to transition back to the static powerflow.

Testing and Validation

Testing and validation are conducted at various points along the programming to ensure the implementation is producing the correct results. Testing and validation is also performed against known IEEE test systems and against simple systems in other software packages. Due to the nature of the three-phase unbalanced powerflow, fully testing the system is difficult. The DigSilent Powerfactory software 4 is used as the primary validation software suite for the GridLAB-D™ microgrids capability.

A variety of test systems are needed to test the functionality of the microgrids capabilities. The expected models are:

• Single machine, infinite bus system
• Two machine, single line system
• Two machine, three line system
• Adapted IEEE 34-bus test feeder

Further validation could be accomplished with a model of real microgrids in operation on the United States grid. These are not necessary for final implementation success, but are useful validation systems:

• Oak Ridge National Laboratory microgrid
• San Diego Gas & Electric Beach Cities microgrid
• CERTS AEP microgrid

Validation using these real systems occurs against measured field data for those systems.

Single machine, infinite bus system

The classic single machine, infinite bus (SMIB) system provides an initial testing platform for the microgrids solver capabilities. The SMIB is utilized to test a balanced, three-phase system. With infinite inertia (via the infinite bus), the system frequency is fixed at 60 Hz. The system runs unfaulted. The system should run at a steady value and not produce any control actions.

The completion of this test gauges the numerical stability of the microgrids capability. The end results are also validated against the base SMIB equations, or a simulation of the SMIB in the DigSilent or PST software.

Two machine, single line system

The two machine, single line (TWSL) system (Figure 1) are used to test the simulation of actual dynamics on the system. All devices are full three-phase. Overhead lines connecting the two generators and the load follow the format of the IEEE 4-node test feeders 5. All test results are validated against a DigSilent PowerFactory simulation to ensure the three-phase, unbalanced power is being handled correctly.

The two machine, single line system are used in a variety of ways to test and validate the results. For all of the testing scenarios, Gen 1 and Gen 2 are assumed to be 100 MVA diesel generators. Unless otherwise specified, both generators are identical. Both incorporate DC exciters and droop-control governors with the following parameters:

The actual tests are defined as:

Successful completion of these tests, as well as the successful validation against DigSilent results, are required before attempting the Adapted 34-bus test feeder.

Two machine, three line system

The two machine, three line (TWTL) system (Figure 2) is used to test the simulation of actual dynamics on the system. Many parameters follow those of the TWSL system. All devices are full three-phase. Overhead lines connecting the two generators and the load follow the format of the IEEE 4-node test feeders 5. All test results are validated against a DigSilent PowerFactory simulation to ensure the three-phase, unbalanced power is being handled correctly.

The two machine, three line system are used in a variety of ways to test and validate the results. For all of the testing scenarios, Gen 1 and Gen 2 are assumed to be 100 MVA diesel generators. Both generators follow the exact same setup as the two machine, single line system tested previously.

The actual tests for the two machine, three line system is identical to those of the two machine, single line system. However, the extra interaction path is expected to change the numerical values and requires resimulation by the DigSilent PowerFactory software.

Adapted IEEE 34-bus test feeder

The adapted 34-bus test feeder (Figure 3) serves as the overall test and validation system for the initial microgrids implementation. Since wind turbine generators and energy storage are not part of the initial microgrids implementations, these devices are substituted with equivalent diesel generators. All simulation results are validated against values obtained for an equivalent model run in the DigSilent software.

References

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4. Makram, E. B., V. O. Zambrano, R. G. Harley, and Juan C. Balda. "Three-phase modeling for transient stability of large scale unbalanced distribution systems." Power Systems, IEEE Transactions on 4, no. 2 (1989): 487-493.
5. Salim, R. H., and R. A. Ramos. "A Model-Based Approach for Small-Signal Stability Assessment of Unbalanced Power Systems." IEEE Transactions on Power Systems, November 2012.
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8. Garcia, Paulo AN, Jose Luiz R. Pereira, Sandoval Carneiro Jr, Vander M. da Costa, and Nelson Martins. "Three-phase power flow calculations using the current injection method." Power Systems, IEEE Transactions on 15, no. 2 (2000): 508-514.
9. Chen, T-H., M-S. Chen, Toshio Inoue, Paul Kotas, and Elie A. Chebli. "Three-phase cogenerator and transformer models for distribution system analysis." Power Delivery, IEEE Transactions on 6, no. 4 (1991): 1671-1681.
10. Elizondo M, F Tuffner, K Schneider, “Network solution for initialization and simulation of transient stability model of unbalanced microgrid,” to be submitted
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Capabilities

Capabilities have slowly been evolving. This section documents what milestones certain features have been deployed, or are expected to be deployed.

Version 2.3 - Grizzly

• transient mode capabilities - ability to transition to simulation timesteps as small as one nanosecond, then transition back into traditional, event-driven GridLAB-D™ mode.
• Player capabilities - the ability to play in subsecond data to influence objects during transient mode execution.
• Recorder capabilities - the ability to record subsecond data during transient mode operations.
• Powerflow capabilities - basic support for three-phase, unbalanced powerflow operations in transient mode and in isolated operation
• Diesel_dg capabilities - Initial implementation of a three-phase, unbalanced dynamics-capable diesel generator

Version 3.0 - Hassayampa

• Various bug fixes

Version 3.1 - Hatwai (planned)

• Various bug fixes in time handling and transition
• Diesel_dg model validated against EMTP-type solver
• Inverter capabilities - Initial implementation of transient-level (~10 ms) dynamics of a three-phase inverter system
• Grid-connected dynamic support
• Assert capabilities - the ability to check values and execute unit testing in transient mode
• Powerflow integration - full support for transient mode operations by all powerflow objects
• Powerflow dynamics - transient-level impacts of line charging and transformer in-rush currents
• Frequency measurement - localized frequency measurements during transient mode
• Reliability capabilities - the ability to induce events at a subsecond time level (metrics not supported yet)

Version 4.0 - Jojoba

• Neutral-earth voltage (generic polyphase implementation) powerflow solver for protection modeling
• Protective device capabilities - initial models of protection devices for examining microgrid and distribution-level behavior
• Reliability update - changes to the reliability module to handle the new powerflow solver and protection capabilities

Super-second Implementation

TODO - Incomplete - Super-second implementation details will go here - AVR and Drooping

Related Concepts:

• User's manual
• Requirements
• Specifications