Cyber-resilient sliding mode consensus-based distributed control system for ac microgrids and method for operating same

A method for increasing the cyber-resiliency of an islanded alternating current microgrid comprising:

• (a) providing the microgrid, the microgrid comprising a plurality of distributed energy resources wherein the distributed energy resources are organized in a hierarchical multi-layered regulation scheme comprising:
• i. a primary level, comprising a plurality of local controllers for each distributed energy resource, wherein the local controllers are configured in a grid forming mode;
• ii. a secondary level, comprising a sliding mode consensus control scheme for each distributed energy resources;
• iii. a tertiary level;
• and
• iv. n nodes, comprising node i and node j;
• wherein the sliding mode consensus control scheme comprises:
• an intrusion impact module;
• an aggregate impact module;
• a hysteresis-based communication link quality observer;
• and
• a sliding mode switching control block;
• (b) assigning power set points for the local controllers in the secondary level;
• (c) establishing an adjacency matrix for the microgrid, comprising a plurality of matrix elements, represented by aij;
• wherein the adjacency matrix is of a size n×m;
• and
• wherein the adjacency matrix is represented by:
• A
• n
• ,
• n
• =
• [
• a
• 1
• ,
• 1
• a
• 1
• ,
• 2
• …
• a
• 1
• ,
• n
• a
• 2
• ,
• 1
• a
• 2
• ,
• 2
• …
• a
• 2
• ,
• n
• ⋮
• ⋮
• ⋱
• ⋮
• a
• n
• ,
• 1
• a
• n
• ,
• 2
• …
• a
• n
• ,
• n
• ]
• (d) establishing a consensus-based update rule on a variable x for node i as:
• x
• i
• .
• =
• -
• ∑
• j
• =
• 1
• n
• a
• ij
• (
• x
• i
• -
• x
• j
• )
• wherein the variable xi on node i converges to a weighted average of its neighbor values xij with the time constant of
• ∑
• j
• =
• 1
• n
• ⁢
• a
• ij
• .
• (e) determining a regulation set point for the secondary level;
• (f) determining the second layer frequency and voltage dependent control objectives;
• (g) selecting one or more sliding surfaces, comprising two complimentary terms, comprising:
• a first term, comprising functionality to perform first order dynamics to ensure convergence to reference values and minimizing any error terms;
• and
• a second term, comprising functionality to counteract any introduced offsets through applied flexible adjustments.
• (h) applying an exponential factor to each compensation term;
• (i) converging state variables towards the sliding surfaces;
• (j) retaining the state variables over the sliding surfaces;
• and
• (k) enforcing sliding over a specified manifolds using discontinuous control signals.