15.2.1 Needs of Coordination and Control in Microgrids

For good coordination and control of microgrids, the following attributes are needed (Colson and Nehrir, 2009; Kondoleon et al., 2002):

• New microsources are added to the system without modification of existing equipment.

• The microgrid connects and disconnects itself from the grid rapidly and seamlessly.

• Reactive and active power are independently controlled.

• System imbalances are handled within the microgrids.

• Microgrids can meet the grid’s dynamic load requirements.

In order to ensure these tasks, the microgrids use two control methods, gained through microsource power injections into it (Kondoleon et al., 2002):

1. The first physical control method is the voltage regulation through droop, where, as the reactive current generated by the microsource becomes more capacitive, the local voltage setpoint is reduced. Conversely, as the current becomes more inductive, the voltage setpoint is increased.

2. The second physical control method is the frequency regulation through droop (normally presented in isolated mode). When the microgrid separates from the grid, the voltage phase angles at each microsource in the microgrid change, resulting in a reduction in local frequency. This frequency reduction is coupled with a power increase, but the microsources have a maximum power rating.

Traditionally, these two control methods are coordinated by an architecture comprised of three main components: a microsource controller, a protection coordinator, and an energy manager (Kondoleon et al., 2002; Lasseter and Piagi, 2004).

The main functions of the microsource controller are: to regulate power flow on feeders, to regulate the voltage at the interface of each microsource, and to ensure that each microsource rapidly picks up its share of the load when the system islands. The protection coordinator must respond to both power system elements and microgrid faults (Kondoleon et al., 2002; Lasseter and Piagi, 2004). On the other hand, the 3 main functions of the Energy Manager are: (1) to provide the individual power and voltage setpoints for each microsource controller; (2) to ensure that heat and electrical loads are met; (3) to ensure that the microgrid satisfies operational contracts with the transmission system and maximizes the operational efficiency of the microsources (Kondoleon et al., 2002; Lasseter and Piagi, 2004).

These key functions must be coordinated within a single microgrid, as well as across multiple microgrids, while considering the associated components. This semiautonomous microgrid behavior can be achieved through a hierarchical control structure with three layers. These include a primary and secondary control, and a tertiary dispatch (Bidram and Davoudi, 2012; Vandoorn et al., 2011). The first two are often associated with the power system’s transient stability, while the latter is associated with inter-microgrid coordination.

15.2.2 Primary and Secondary Controls for Transient Stability

The primary and secondary control layers are largely responsible for the real-time transient stability of the power grid and have received significant attention in the industry (Saadat, 2004). Primary control operates on a real-time feedback control principle based on local measurements (Vandoorn et al., 2011).

Secondary control compensates for voltage and frequency deviations that may exist in spite of the primary control. It adjusts setpoints dynamically to achieve minimum and stable deviations, while the power system transits to new operating points (Bidram and Davoudi, 2012; Muzhikyan et al., 2013b).

This functionality is particularly important after large disturbances such as generator or load faults. Many approaches to microgrid transient stability control, such as turbine governors and automatic voltage regulators, have been borrowed from traditional power systems (Abdelhalim et al., 2013; Majumder, 2013). Microgrids, however, pose greater challenges because each generator or load makes up a comparatively large portion of the power flow. As a result, any individual disturbance can have a significantly larger impact on the power system’s stability. Similarly, further transient stability analysis is required to address disturbances originating within a microgrid that may impact neighboring microgrids under potentially different operational jurisdictions.

15.2.3 Secondary and Tertiary Coordination by Multi-Agent Systems

Tertiary coordination refers to the power system’s dispatch in order to restore secondary control reserves, manage line congestion, and bring frequency and voltage deviations back to their targets (Vandoorn et al., 2011). The secondary control and tertiary dispatch application to microgrids is limited for two reasons.

First, each individual microgrid may have only a few microsources to be dispatched, so reliability demands often overshadow economic optimization. Second, a multiple microgrid system may not necessarily have a centralized organization that can centrally optimize on its behalf.

In contrast, multi-agent system technology promises to address a number of specific multi-microgrid operational challenges in the power industry (Dimeas and Hatziargyriou, 2005; Rieger and Zhu, 2013; Rieger et al., 2013). These include:

• The micro-sources, either within a microgrid or across microgrids, may have different owners. Decentralized coordination facilitates each owner’s unique management interest.

• Each microgrid may operate in a liberalized market and hence should maintain a certain level of “intelligence” as it bids and participates.

• Each microgrid can operate autonomously in the absence of communication systems or cooperatively using potentially any available communication technologies.

• Each microgrid can dynamically and flexibly adapt to the activities occurring in neighboring microgrids and power systems.

Multi-agent systems achieve these challenges for simultaneous, geographically distributed and coordinated decision making with the control design of each agent. Collectively, they exhibit the following characteristics (Dimeas and Hatziargyriou, 2005; Colson and Nehrir, 2013):

• Each (virtual software) agent represents a physical entity so as to control its interactions with the rest of the environment.

• Each agent senses changes in the environment and can take action accordingly.

• Each agent can communicate with other agents in the power system with minimal data exchange and computational demands.

• Each agent exhibits a certain level of autonomy over the actions that it takes.

• Each agent has a minimally partial representation of the environment.

15.3.1 Differential Algebraic Equations and the Model Predictive Control Approach

The differential algebraic equations that describe the dynamics of the multiple microgrids are presented based upon the models given in Gomez Exposito et al. (2009). The differential equations describe the dynamics of the dispatchable generators and loads and are simply modeled as either a damped synchronous generator or motor, respectively (Gomez Exposito et al., 2009). Each synchronous machine i is described by Equation (15.1):

δi=ωi−ω0ω˙i=ω02Hi[Pmi−Pei(δ)−Diωi]$\begin{array}{l}{\delta }_i={\omega }_i-{\omega }_0\hfill \\ {\dot{\omega }}_i=\frac{{\omega }_0}{2H_i}\left[{\text{Pm}}_i-P{e}_i\left(\delta \right)-D_i{\omega }_i\right]\hfill \end{array}$$\begin{array}{l}{\delta }_i={\omega }_i-{\omega }_0\hfill \\ {\dot{\omega }}_i=\frac{{\omega }_0}{2H_i}\left[{\text{Pm}}_i-P{e}_i\left(\delta \right)-D_i{\omega }_i\right]\hfill \end{array}$

where δ_i is the machine phase angle, ω_i is the angular frequency, H_i is the mechanical inertia, D_i is the damping, Pm_i is the dispatchable power applied to the prime mover, and Pe_i is the electrical power at generator i, which is a nonlinear function of the machine phase angles. The dynamics of each synchronous machine are coupled by the power flows through the grid topologies, as shown in Equation (15.2):

$Pe=\mathfrak{R}\left[{\text{E}}^{\text{*}}\text{YE}\right]$

where E is the system bus voltage and Y is the system admittance matrix; detailed formulation is in Gomez Exposito et al. (2009). The stochastic generators (i.e., solar PV and wind) and noncontrollable loads are modeled as static power injections that affect the system admittance matrix (Gomez Exposito et al., 2009). These equations can be thought to apply to each microgrid when they are mutually disconnected or to the aggregation of microgrids when the admittance matrix has been manipulated to reflect their interconnectedness.

The microgrid agents dispatch their dispatchable elements autonomously with the dispatchMicroGrid method. In practice, this is implemented by calling an economic dispatch program written in the General Algebraic Modeling System (GAMS), RunGAMS class in Figure 15.3. In this control approach, each microgrid agent implements its own model predictive control (MPC), as an economic dispatch method, which is able to dispatch the mechanical power setpoints Pm_i for the synchronous machines within its control area. The MPC uses a time horizon of 4 time blocks of 15-second duration and dispatches Pm_i for the first time block in each generator. The MPC formulation is as follows:

$min{\displaystyle \sum }_{t=k}^K{\displaystyle \sum }_{i=1}^{N_G}\left(C_i^F+C_i^G{P}_{m_{i,t}}^G\right)$

$\text{s}.\text{t}.{\displaystyle \sum }_{i=1}^{N_G}{P}_{m_{i,t}}^G=P_{N{L}_t}$

$-R_i^{G,min}\le P_{m_{i,t}}^G-P_{m_{i,t-1}}^G\le R_i^{G,max}$

$-P_{m_i}^{G,\text{min}}\le P_{m_{i,t}}^G\le P_{m_i}^{G,\text{max}}$

where the following notations are used:

$\begin{array}{l}{C}_i^{\text{F}},C_i^{\text{G}}:\text{fixed and generation (fuel) costs of generator }i\\ P_{m_{i,s}}^G\text{: power output of generator }i\text{ at time }t\\ P_{{\text{NL}}_t}\text{:}\text{netload forecast at time }t\\ R_i^{G,max},R_i^{G,min}\text{:}max/min\text{ramping rate of generator }i\\ P_i^{G,max},P_i^{G,min}\text{:}max/min\text{power limits of generator }i\\ N_G\text{:}\text{number of generators}\end{array}$

15.3.2 Mutual Connection Coordination by Heuristics

The inter-microgrid coordination is achieved with a heuristic control–action behavior that is able to respond to events/disturbances. In such a way, each agent may interact and negotiate with other agents to achieve a coordinated and semiautonomous behavior. In order to demonstrate the coordination actions and the decentralized decision making, three kinds of events/disturbances are used: (i) net load high-variability time periods, (ii) net load ramp events, and (iii) net load changes during high load levels. When these events are forecast in the microgrids, the agents interact and negotiate with each other to change the topology of the microgrids.

Within this approach, the stochastic generators’ agents and noncontrollable loads agents read power-time series data. The data are sent to the microgrid agent which calculates the net load time series (P_NL) and evaluates two measures; the relative standard deviation $\overline{\sigma }=\sigma \left(P_{\text{NL}}\right)/{\overline{P}}_{\text{NL}}$ and the average ramp rate (R) over the four-block MPC time horizon. When either measure exceeds a previously determined critical value, a coordination control action u[t] is issued to mutually connect (u[t] = 1) or disconnect (u[t] = 0) the microgrids.

$u\left[t\right]=\left\{\begin{array}{ll}1,\hfill & \overline{\sigma }>{\overline{\sigma }}_{crit}\hfill \\ 1,\hfill & R>R_{\text{crit}}\text{where}{R}_{\text{crit}}=A*{\displaystyle \sum }_i{R}_i^{G,\text{max}}\hfill \\ 1,\hfill & P_{\text{NL}}>P_{\text{crit}}\text{where}{P}_{\text{crit}}=B*{\displaystyle \sum }_i{P}_{m_i}^{G,\text{max}}\hfill \\ 0,\hfill & \text{otherwise}\hfill \end{array}\right\}$

Notice that R_crit and P_crit correspond to Equations (15.5) and (15.6), respectively, in the MPC formulation.

In summary, the hybrid platform works along the following operating principle: (1) The MAS makes decentralized but coordinated decisions under events/disturbances through the MPC and the coordination behavior described by Equation (15.7); (2) The control signals are sent as reconfigurations and setpoint actions to the MATLAB power grid simulation through the facilitator agent / Matlabcontrol interface; (3) MATLAB executes a time domain simulation of the power grid transients; (4) The power system state variables are sent back to the MAS via the facilitator agent/Matlabcontrol interface.

15.4.1 Resilience Toward Net Load Variability

To understand the impact of net load variability on power system operation, the MAS transient stability platform is tested with different net load relative standard deviations. Figure 15.5 shows the time domain simulation of the generator angles and speeds for the three unconnected microgrids with a relatively low net load variability in each microgrid.

In this case, the relative standard deviation of the net load is less than 10% throughout and the net load change period is every 15 seconds. The generators’ phase angles find new equilibria in approximately 6.3 seconds after each net load change. Meanwhile, the generators’ speeds return to the nominal 60 Hz in approximately 7.5 seconds. The oscillations that occur during these times are generally considered acceptable for reliable operation.

In contrast, very different transient behavior is observed once the net load variability is increased. Figure 15.6 shows the time domain simulation of the generator angles and also the speeds for the same system but with a net load variability greater than 10%. Here, some generator speeds do not always return to the nominal 60 Hz and instead settle at lower speeds. As a result, the associated phase angle of these generators continually fall behind in angle relative to the reference bus.

In order to alleviate the shortcomings of this transient behavior, the multi-agent system’s coordination strategy seeks to take advantage of the combined inertia of the three microgrids during times of high net load variability. As before, Figure 15.7 shows the time domain simulation but with the additional markings of C and NC to reflect when the MAS has mutually connected (C) or disconnected (NC) the microgrids. As mentioned in Section 15.3, the MAS decides between a connected and disconnected topology on the basis of Equation (15.7).

Despite having the same net load variability as in Figure 15.6, Figure 15.7 shows a greatly improved system response that much more closely resembles that of Figure 15.5. Intuitively, the energy of the net load variability is “spread out” among the inertias of all of the generators, not just those of the local microgrid. In this case, the MAS coordination strategy has successfully allowed for the system phase angles to return to equilibria and the generator speeds to return to the nominal 60 Hz.

15.4.2 Resilience Toward Net Load Ramping

In order to understand the impact of net load ramping events on power system operation, the MAS transient stability platform is tested with a determined ramp event. Figure 15.8 shows the time domain simulation of the generator angles and speeds when microgrid 1 experiences a net load ramp event greater than 300 W/min (R_crit). Here, A = 0.6 in Equation (15.7), which means that the microgrid is well within its cumulative ramping capability constraint. In spite of this, the ramp event causes the generator speeds to fall well below the nominal 60 Hz and the associated phase angles of these generators continually fall behind in an angle relative to the reference bus. Interestingly, the simulation shows oscillations in the other microgrids by virtue of the choice of reference bus used in perturbed microgrid 1.

As in Section 15.4.1, in order to alleviate the shortcomings of this transient behavior, the multi-agent system’s coordination strategy seeks to take advantage of the combined inertia of the three microgrids during times of net load ramp events. In this case, the MAS coordination approach detects a forecast of ramp events, through the microgrid agents, and requests the network change its topology connecting the microgrids through the line agents that link the microgrids.

As before, Figure 15.9 shows the time domain simulation with the additional markings of C and NC to reflect when the MAS has mutually connected (C) or disconnected (NC) the microgrids. As mentioned in Section 1.3, the MAS decides between a connected and disconnected topology on the basis of Equation (15.7).

The system oscillates away from the equilibria points when a ramp event occurs, and then the system phase angles return to equilibria and the generator speeds return to the nominal 60 Hz. These peaks in the oscillations are acceptable for the system, and the recovery is in approximately 7.5 seconds for the phase angles and 8.4 seconds for the speeds after each ramp event. As in Section 15.4.1, the energy of the ramp events are “spread out” among the inertias of all of the generators, not just those of the local microgrid. Additionally, while the microgrids are connected as A → 1 during high net load ramps, this means that the microgrids could potentially share the ramping capability in the situation required.

15.4.3 Resilience Toward Net Load Changes during High Load Levels

In order to understand the impact of net load changes during high load levels on power system operation, the MAS transient stability platform is tested with net load levels near to the maximum power generations. Figure 15.10 shows the time domain simulation of the generator angles and speeds for the three unconnected microgrids with some high-level periods in each microgrid. In this case, P_crit is 1805 W, corresponding to B = 0.95 in Equation (15.7). In other words, as the net load approaches the maximum capacities of the dispatchable generators in the microgrid, the microgrid has increasingly less reserve capacity to respond to further deviations. Furthermore, the higher net load values weaken the electrical coupling between the generators, compromising their ability to maintain stability. This indeed occurs in Figure 15.10 because some generator speeds do not always return to the nominal 60 Hz and instead settle at lower or higher speeds. As a result, the associated phase angle of these generators continually fall behind in an angle relative to the reference bus.

As in Section 15.4.1, in order to alleviate the shortcomings of this transient behavior, the multi-agent system’s coordination strategy seeks to take advantage of the combined inertia of the three microgrids during times of net load changes in high-load levels. As before, Figure 15.11 shows the time domain simulation with the additional markings of C and NC to reflect when the MAS has mutually connected (C) or disconnected (NC) the microgrids. The MAS decides between a connected and disconnected topology on the basis of Equation (15.7).

The system oscillates away from the equilibria points when a net load change occurs, and then the system phase angles return to equilibria and the generator speeds return to the nominal 60 Hz. These peaks in the oscillations are acceptable for the system—the recovery is in approximately 9 seconds for the phase angles and 8.6 seconds for the speeds after each net load change. As in Section 15.4.1, the energy of the ramp events are “spread out” among the inertias of all of the generators, not just those of the local microgrid. Furthermore, the three mutually connected microgrids enhance the system impedance matrix and directly improve the system’s stability.