The main thing I would recommend is to study the mathematical formulation in Chapter 4 of the MOST User’s Manual <http://www.pserc.cornell.edu/matpower/docs/MOST-manual-1.0.pdf>. See my responses below for more comments ...
> On May 20, 2018, at 5:43 PM, Shady Mamdouh > <[email protected]> wrote: > > Hello Dear, > Regarding the problem formulation in MOST program, I have these questions > that I am confused about. > > 1- Difference between zonal reserve and contingency reserve : I understand > that zonal reserve are some constant amount of reserve specified before the > solution, but what is the definition of "zone" and how can I specify zones? > and what is the difference between zone and area in bus data? And what is the > difference between zonal reserve and contingency reserve? See section 3.2 of the MOST User’s Manual <http://www.pserc.cornell.edu/matpower/docs/MOST-manual-1.0.pdf>, along with section 7.5.1 in the MATPOWER User’s Manual <http://www.pserc.cornell.edu/matpower/docs/MATPOWER-manual-6.0.pdf>. The BUS_AREA column of the bus matrix is used for area summaries in the pretty printed output of MATPOWER and also can be used by a few other functions such as scale_load() and apply_changes() to make area-wide modifications to a case. The ZONE column is a loss zone identifier originally from IEEE and/or PSS/E formats, but is not currently used at all by MATPOWER or MOST. > 2- Contingency reserves: what is meant by it? and how can this reserve > amount be determined or calculated? is its value determined after MOST > solution or pre-specified? See section 3.2 of the MOST User’s Manual <http://www.pserc.cornell.edu/matpower/docs/MOST-manual-1.0.pdf>. It is determined by the MOST solution and is defined as the maximum upward and downward deviations across all base and contingency dispatches from the reference dispatch. > 3-Difference between contingency reserve limits and physical ramping limits? Physical ramping limits are used to constrain all base dispatches in one period with respect to all base dispatches in adjacent periods. Contingency reserves are limited by both physical capabilities and offered reserve capacity and are determined by the optimization (and thus also depend on the cost) and they apply only within a given period to the deviations across base and contingency cases from the reference dispatch for that period. See also Figure 3-3. > 4- Difference between load following ramping (wear & tear) and load > following ramp reserves? See section 3.5 and Figure 3-6. Load following ramp is used to impose a probability-weighted quadratic cost on all base-case transitions. Load-following ramp reserve quantities are (like contingency reserves) outputs of the optimization determined by the cost of the maximum ramps from a base state in one period to a base state in the next and the quantity can be restricted by physical ramp limits as well as an offered ramping capacity. > 5-Active contract value "Pc": what does it mean? (Is this a contract between > consumers and utility or what?) > and how its value be determined? (After MOST solution or the user specifies > its value?) and what about the deviations from it ? > From my reading on the manual and the papers "Secure Planning and Operations > of Systems with Stochastic Sources, Energy Storage, and Active Demand" & > "Stochastically Optimized, Carbon-Reducing Dispatch of Storage, Generation, > and Loads", I understand that we have 2 stages, stage 1 determines the > contract value and stage 2 determines the deviations from this value as a > recourse action. MOST solves the problem with the formulation given in Chapter 4 of the manual. This can be used to implement a two stage market (e.g. day-ahead that determines the contract value and real-time that determines recourse deviations from the contract) by using it to solve separate problems for each stage, but any given run of MOST is simply solving a problem which is (potentially a subset) of the form given in Chapter 4. In this formulation, Pc only has meaning for stochastic problems where you have multiple base cases and/or contingencies. Pc is an optimization variable which is simply the reference dispatch from which upward and downward deviations are defined for inc/dec costs and contingency reserves. In a day ahead problem, for example, it could be used as the day-ahead contract quantity between the ISO and the generators, but this is a matter of market design. It’s value need not be used at all. The full range from Pc – downward contingency reserves to Pc + upward contingency reserves is required to be able to meet the contingencies. The value of Pc simply determines how much of the reserves are “upward” and how much are “downward” and, depending on the problem, may not even be well-defined. > 6- Details about the cost functions Cp(P), CR(r), Cδ(δ)….. : the form of the > equations ,is it a quadratic or what type? And the coefficient needed to > specify them? These are specified in the xGenData as described in Table 5-1. C_P() and C_R() are linear and C_∂() is quadratic. > 7-Confusion about the usage of probabilities in the objective functions: > ψα: probability of contingency used in cost of dispatch and redispatch > function f(p,p+,p-).(why it used in this cost function only?) Because the summations in this term are over all individual states, each of which has it’s own probability of occurring. Dispatch and deviation variables are per state. > ϒ: probability of making it to period 't' (what does "it" refer to here?) > and why this probability used in all objective functions except the cost of > dispatch & redispatch f(p,p+,p-)? Other cost terms are summed over period only, so the probability is of “making it to period t” or to put it another way “the probability of avoiding all contingencies before arriving at period t”. For example, reserve variables are per-period, not per-state, so there is no summation over the states in period t for reserve costs. The summations are only over period. > 8-When using the DC network model instead of nonlinear network network the > problem is converted from MINLP to MIQP, How does this happen? (Why not > converted to MILP problem?) MOST does not implement the AC network model case, so the choice is between a DC network or no network. With a DC network there are two cost terms that can be quadratic, one is the generator costs themselves and the other is the ramping wear-and-tear costs. This makes it a MIQP problem. If you don’t want to do unit commitment it turns into a QP. If you have linear generator costs and no ramping wear-and-tear costs it is an MILP. And with no UC, linear gen costs and no ramping wear-and-tear costs, it becomes a simple LP. > 9- What does "Nodal energy prices" mean? and what is the difference between > it and "shadow prices" and "marginal prices”? Shadow price is a general term referring to the Kuhn-Tucker/Lagrange multiplier on any given constraint. Nodal energy prices refers to the expected marginal prices of energy at a node and is the sum of the shadow prices on the power balance constraints for that node across the states in that period (adjusted by the probability of making it to that period). > 10- I understand that MOST is used to model transmission systems and one can > add wind and storage sources, but if I want to model a Microgrid, how can I > use MOST to model it? And what about adding PV generation? If a DC model is appropriate, there should be no difference. You could model PV as an uncertain source of generation, just like wind. > 11- What meant by transmission congestion and its effect on nodal energy > prices, storage, and min up&down times? Transmission congestion simply refers to binding branch flow constraints. The presence or absence of binding transmission flow limits can affect the entire solution, including all prices, dispatches and commitments. Hope this helps, Ray
