ERCOT CIM16 Project Overview: Upgrading Network Models to CIM Standards
ERCOT is upgrading from CIM10 to CIM16 for producing network models in XML format. The Network Model Management System (NMMS) is being enhanced to natively produce CIM16 model files, reducing the need for legacy code. This project started execution in August 2024 and is expected to be completed by Q1 2027. Processes relying on files directly from NMMS must prepare for the updated schema, affecting various files such as MIS, TSP versions of CIM Network Models, and incremental CIM change requests. ERCOT will prioritize the delivery of CIM16 test models, with test files for TSPs and non-TSPs being provided in a recurring cadence leading up to the go-live of CIM16.
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INTEGRATION (ANTI-DERIVATIVES) Lecture Outline: Techniques of Integration Undoing a derivative (Differential equations) Definite integrals Application Area problems
Integrating (or anti-differentiating) ?(?) produces the integral (or anti-derivative) ? ? + ? We denote this by writing
Power rule for Integration + c n 1 1 n x = + n x dx + ? ??? ? ?? ? ???? ?????? 1 ? ?? = ?? + ?
Example Evaluate the following: a) ?3+ 4?2 6? + 5 ?? 13 2? 45+ 1 ?? b) ? a) ?3+ 4?2 6? + 5 ?? = ?4 4+4?3 3 6?2 2+ 5? + ?
45+ 1 ?? 13 2? ? 95 9 5 a= ac 43 4 3 2? = ? + ? + ? b b c 95 43 10? = 3? + ? + ? 4 9
Exercises Evaluate the following: a) 5?4+ 7?3 ? + 8 ?? 25 6? 3 ?? b) 4? ?) =5?5 +7?4 ?2 2+ 8? + ? 5 4 = ?5+7?4 4 ?2 2+ 8? + ?
25 6?3 ?? 4? 75 7 5 = 4? 6? 2 2+ ? 75 = 20? + 3? 2+ ? 7
Applications: Differential Equations Any equation involving a derivative function is called a differential equation. From the derived function, the original function needs to be obtained. Also an initial condition is given. This is used to solve for the constant c . ? ? = ? ? ??
Example If ? ? = ?? ? ,???? ? ? ?? ? ? = ? ? ? = ? ? ?? ? ? = 6? 2 ?? 6?2 2 2? + ? ? ? = ?(?) = 3?2 2? + ? Need to solve for c
?(2) = 3 ????? ??? ? = 2,?(?) = 3 ? ? = 3?2 2? + ? 3 = 3 22 2 2 + ? 3 = 8 + ? ? = 5 ? ? = 3?2 2? 5
Exercise The slope of the tangent to a curve at any point is given by 3?2+ 1. Determine the equation of the curve if it contains the point (1,4) Recap: Remember that only the ?? ?? or ? function gives slope equation of tangent line. ?? ??= 3?2+ 1 ? = ?? ?? ?? = 3?2+ 1 ?? ? =3?3 + ? + ? = ?3+ ? + ? 3
? = ?3+ ? + ? (1,4) ????? ?(1) = 4 4 = 13+ 1 + ? ? = 2 Answer: ? ? = ?3+ ? + 2
Example The marginal cost of producing x units of an item is given by = + 2 ( ' ) 1000 20 C x x x If the fixed cost of production is $9000, find the cost function?
?(?) is the derivative of ?(?) = + 2 ( ) 1000 20 C x x x dx 2 3 20 x x 3 = + + ( ) 1000 C x x k 2 Find k C(0) = 9000 , k= 9000 3 x = + + 2 ( ) 1000 10 9000 C x x x 3
Exercise It is believed that the population of mosquitoes which spreads malaria is changing at a rate of 450?2+ 2?3+ 5?4per month. If the current population is 2000, what will be the population size after 3 years? First find the population function. Derivative function = rate of change function
??? ?(?) ?? ?? ?????????? ?? ????????? ?? ???? ? ? ? = 450?2+ 2?3+ 5?4 ? ? = ? ? ?? ? ? = 450?2+ 2?3+ 5?4 ?? ? ? =450?3 ? ? = 150?3+ ?.??4+ ?5+ ? +2?4 +5?5 + ? 3 4 5
Determine the value of c Initial condition? ?(0) = 2000 2000= 150(0)3+0.5(0)4+(0)5+? ? = 2000 ? ? = 150?3+ 0.5?4+ ?5+ 2000 population size after 3 years? ? 36 = 68 306 384 mosquitoes
THE DEFINITE INTEGRAL By the fundamental Theorem of Calculus, the definite integral of a continuous function, ? from ? ?? ? is given by: b a = ( ) ( ) ( ) f x dx F b F a Where F(x) is the integral of f(x). ? is called the lower limit of integration and ? is called the upper limit of integration.
Example 4 1 + 2 3 2 1 x x dx Evaluate Answer: 75
Area Under the Curve Recall the two properties of Area from Form6. a) Area 0 b) If A and B are areas of two non-overlapping regions then the Total area = Area A + Area B
Definition Let ?(?) be a continuous function on a closed interval [a,b], where a<b , then the definite integral a b = ( ) Area f x dx gives the area under the graph of f(x) and above the x-axis between x=a and x=b.
Suppose a function f(x) is continuous on [a,b] but ?(?) < 0 , then; b dx x f Area ) ( a =
Exercise Find the area enclosed by ? = ?3, the x-axis between; a) ? = 2 ??? ? = 5 b) ? = 3 ??? ? = 1 c) ? = 2 ??? ? = 3
[2,5] 5 b ?3 ?? ? = a = ( ) A f x dx 2 = 156.25 4 = 152.25 ????2
[3,1] 1 ?3 ?? ? = b a = ( ) Area f x dx 3 4 4 ( ) 1 ( ) 3 = + + A C C 4 4 . 0 = = = 2 25 20 25 . [ 20 ] 20 A unit
[2,3] 3 A2 ?3 ?? ? A1 2 A = Area 1 + Area 2 0 ?3 ?? ?1 = 2 3 ?3 ?? ?2 = ?1 = 4 ??? ?2 = 20.25 [??????] 0 ????? ???? = 4 + 20.25 = 24.25 ????2
