See Appendix Sample Clauses
The "See Appendix" clause directs readers to consult an appendix for additional information, details, or supporting documents related to the main agreement. In practice, this clause is used when the contract references complex data, technical specifications, or supplementary terms that are too lengthy or detailed to include in the main body. By incorporating appendices, the clause helps keep the main contract concise while ensuring all necessary information is accessible, thereby improving clarity and organization.
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See Appendix. Note that in case the controller at a node i ∈ I11 or i ∈ I21 does not have access to the desired output y∗, one can set ui to a constant, namely a nominal value, and incor- porate the node i in the subdynamics of (11) corresponding to the nodes indexed by I12 or I22, respectively. In Theorem 2, the control input u has been designed such that output agreement on a prescribed vector y∗ is achieved for the network. Observe that the “steady-state” control signal u¯ = ξ¯ is primarily determined by the initialization of the system/controller. Next, under the constraint of output agreement (6), we aim to minimize the following quadratic cost function 0 = (J11 − R11)∇H11(x¯11) min = 1 Σ u¯T Q u¯ (16) − G11(B11 ⊗ I)∇He(η¯) u¯ 2 i∈Ic + G11u¯11 + G11δ11 (13b) 0 = (J12 − R12)∇H12(x¯12) − G12(B12 ⊗ I)∇He(η¯) + G12δ12 (13c) 0 = (J21 − R21)∇H21(x¯21) − G21(B21 ⊗ I)∇He(η¯) (13d) + G21u¯21 + G21δ21 0 = (J22 − R22)∇H22(x¯22) − G22(B22 ⊗ I)∇He(η¯) + G22δ22 (13e) where Qi ∈ Rm × Rm is a positive definite matrix for each i, and Ic = I11 ∪ I21. Note that the optimization above determines the steady-state distribution of the control effort
See Appendix. Note that Theorem 1 implies that the network (4) reaches an output agreement providing that there exist constant vectors (x¯, η¯) ∈ (Ωn)N ×(Ωe)M satisfying (6), (7), and thus
See Appendix. Changing Shift
See Appendix the vectors and matrices MG, AG, θG, and uG, as MG = diag(Mi), AG = diag(Ai), θG = col(θi), uG = col(ui), and δG = col(δi) where i ∈ VG. The vectors and matrices AI , θI , and uI are defined as AI = diag(Ai), θI = col(θi), uI = col(ui), and δG = col(δi) with i ∈ VI . In addition, let AL = diag(Ai), θL = col(θi) and δL = col(δi) where i ∈ VL. Finally, let P = col(Pi), θ = col(θG, θI, θL), and sin(x) := col(sin(xi)) for a given vector x. Then, it is easy to observe that the dynamics of the synchronous generators, the inverters, and the loads can be written compactly as: MGθ¨G + AGθ˙G = −BGΓsin(B⊤θ) + uG − δG (26a)
IV. Case study We consider a (fairly) general heterogeneous microgrid which consists of synchronous generators, droop-controlled AI θ˙I ALθ˙L = −BI Γsin(B⊤θ) + uI = −BLΓsin(B⊤θ) + δL − δI (26b) (26c) inverters, and frequency dependent loads. We partition the buses, i.e. the nodes of G, into three sets, namely VG, VI , and VL, corresponding to the set of synchronous generators, inverters, and loads, respectively. The dynamics of each synchronous generator is governed by the so-called swing equation, and is given by: Miθ¨i = −Aiθ˙i + ui − Pi + δi, i ∈ VG, (22) Note that this is the same model as [8], see also [19]. By defining η = BT θ, ωG = θ˙G, ωI = θ˙I , ωL = θ˙L, and θ˙ = ω = col(ωG, ωI, ωL), the network dynamics (26), admits the following representation η˙ = BT ω (27a) MGω˙ G + AGωG = −BGΓsin(η) + uG + δG (27b) AIωI = −BI Γsin(η) + uI + δI (27c) where Pi = Σ Im(Yij)ViVj sin(θi − θj) (23) ALωL = −BLΓsin(η) + δL (27d) Now, let pG = MGωG, HG = 1 pT M −1pG, HI = 1 ωT ωI , {i,j}∈E HL = 1 wT wL, and He = −1T Γcos(η). Then, (27) can be is the active nodal injection at node i. Here, Mi > 0 is the moment of inertia, Ai > 0 is the damping constant, ui is the local controllable power generation, and δi is the local load at node i ∈ VG . The value of Yij ∈ C is equal to the admittance of the branch {i, j} ∈ E, and θi is the voltage angle at node i. Also, Vi is the voltage magnitude at node i, and is assumed to be constant. For the droop-controlled inverters, we consider the follow- ing first-order model
See Appendix the vectors and matrices MG, AG, θG, and uG, as MG = diag(Mi), AG = diag(Ai), θG = col(θi), uG = col(ui), and δG = col(δi) where i ∈ VG. The vectors and matrices AI , θI , and uI are defined as AI = diag(Ai), θI = col(θi), uI = col(ui), and δG = col(δi) with i ∈ VI . In addition, let AL = diag(Ai), θL = col(θi) and δL = col(δi) where i ∈ VL. Finally, let P = col(Pi), θ = col(θG, θI, θL), and sin(x) := col(sin(xi)) for a given vector x. Then, it is easy to observe that the dynamics of the synchronous generators, the inverters, and the loads can be written compactly as: MGθ¨G + AGθ˙G = −BGΓ sin(B⊤θ) + uG − δG (26a)
See Appendix. All Training and development opportunities for governors (school based and central courses) are via a credit scheme or PAYG, outlined in the centralised CPD brochure and on-lined at the Shropshire Learning Gateway.
See Appendix. It appears that contrary to the requirements of section 35.3 of the Commission’s regulations, 18 C.F.R. § 35.3 (2014), SPP failed to file the Agreement in a timely manner. SPP is reminded that it must submit filings on a timely basis or face possible sanctions by the Commission. Absent a strong showing of good cause, the Commission’s policy is to deny waiver of the notice requirement for rate increases.3 SPP has not made such a showing. For any revenues collected before the effective date, SPP must refund the time value of the difference between the increased rate and the existing rate actually collected for the time period during which the increased rate was charged without Commission authorization.4 Accordingly, SPP must make time value refunds within 30 days of the date of this letter order and file a refund report with the Commission within 30 days thereafter.5 Notices of the filings were issued on December 4, 2014, with comments, protests, or interventions due on or before December 26, 2014. Under 18 C.F.R. § 385.210, interventions are timely if made within the time prescribed by the Secretary. Under 18 C.F.R. § 385.214, the filing of a timely motion to intervene makes the movant a party to the proceeding, if no answer in opposition is filed within fifteen days. The filing of a timely notice of intervention makes a State Commission a party to the proceeding. No comments, protests or interventions were filed. This action does not constitute approval of any service, rate, charge, classification, or any rule, regulation, contract, or practice affecting such rate or service provided for in the filed documents; nor shall such action be deemed as recognition of any claimed contractual right or obligation affecting or relation to such service or rate; and such action is without prejudice to any findings or orders which have been or may hereafter be made by the Commission in any proceeding now pending or hereafter instituted by or against any of the applicant(s).
See Appendix. In year one of the contract, 2013-2014, the following will apply:
See Appendix. Lab Load - Establishing Eligibility. The Full-time Service Obligation (Load obligation) is thirty (30) teaching units of Calculated A Hours (CAHs) per Academic Year, averaging fifteen (15) Calculated A Hours (CAHs) per Semester, or the equivalent as defined herein.
See Appendix. A" The classifications and wage rates for the effective period of this Agreement shall be those attached hereto in Appendix "A".