Correct mistake in handling of ramp wear & tear for Detla_T ~= 1

CHANGES.md

@@ -5,7 +5,7 @@ Change history for MOST
 since 1.2
 ---------
 
-#### 10/24/23
+#### 10/25/23
  - Fix [issue #39][10] in which the value of `mdi.Delta_T`, the number of
  hours represented by each period, was not being accounted for in most
  of the terms in the objective function.

docs/src/MOST-manual/MOST-manual.tex

@@ -1469,7 +1469,7 @@ \subsubsection{{\tt xgd} -- Extra Generator Data ({\tt xGenData})}
  \item [*] {All fields are $n_g \times 1$ vectors of per-generator values.}
  \item [\dag] {These are defaults provided by \code{loadxgendata}. If \code{gen} is provided, either directly or as the \code{gen} field of \mpc{}, then \code{P = gen(:, PG)}, \code{C = gen(:, GEN\_STATUS)} and \code{R = 2*(gen(:, PMAX) - MIN(0, gen(:, PMIN)))}, otherwise $\code{C}~=~1$, $\code{R}~=~0$ and no default is provided for \code{P} (corresponding field is not optional).}
  \item [\dag\dag] {Ramping costs/restrictions from the initial dispatch at $t=0$ are ignored for single-period problems.}
- \item [\ddag] {Each of these costs $C(\cdot)$ is presented in the formulation as a general function, but is implmented as a simple linear function of the form $C(x) = a x$, where the linear coefficient being supplied is $a$. The only exception is the ramping cost, which has the quadratic form $C_\delta^i(x) = a x^2$.}
+ \item [\ddag] {Each of these costs $C(\cdot)$ is presented in the formulation as a general function, but is implmented as a simple linear function of the form $C(x) = a x$, where the linear coefficient being supplied is $a$. The only exception is the ramping cost, which has the quadratic form $C_\delta^i(x) = \frac{1}{\Delta^2} a x^2$.}
  \item [\S] {Requires that \code{CommitKey} be present and non-empty.}
  \item [\P] {Sign is based on \code{C}\tnote{\dag}, i.e. $+\infty$ for \code{C} = 1, $-\infty$ for \code{C} = 0.}
 \end{tablenotes}
@@ -1722,7 +1722,7 @@ \subsubsection{Input Data}
 \code{mpc} & I & & base system data, standard \matpower{} case struct\tnote{\ddag}, with \baseMVA{}, \bus{}, \gen{}, \branch{} and \gencost{} fields \\
 \code{offer(t)} & I & & struct with offer data for period~$t$, see Table~\ref{tab:md_inputoffer} for details of sub-fields \\
 \code{OpenEnded} & I & 1 & ignore terminal dispatch ramp constraints, \emph{deprecated} \\
-\code{RampWearCostCoeff(i,t)} & I & 0 & $n_g \times n_t$, cost of ramping of generator~$i$ from period~$t-1$ to $t$, coefficient $C_\delta^i$ for square of dispatch difference in \eqref{eq:rampcost} \\
+\code{RampWearCostCoeff(i,t)} & I & 0 & $n_g \times n_t$, cost of ramping of generator~$i$ from period~$t-1$ to $t$, coefficient $C_\delta^i$ for square of dispatch difference in \eqref{eq:rampcost}\tnote{\S} \\
 \code{Storage} & B & & struct with parameters for storage units, see Table~\ref{tab:md_inputstorage} for the input fields \\
 \code{TerminalPg(i)} & I & & $n_g \times 1$, injection of generator~$i$ at $t = n_t$, \emph{deprecated, untested} \\
 \code{tstep(t)} & B & & $n_t \times 1$ struct of parameters related to period~$t$ \\
@@ -1736,6 +1736,7 @@ \subsubsection{Input Data}
  \item [*] {I = input, O = output, B = both, opt = taken from \matpower{} options.}
  \item [\dag] {See Section~\ref{sec:contab} for details. Note that, while \code{loadmd} assigns the same \code{contab} to all $t$ and $j$, it is possible to set different \code{contab} values manually and they will be respected by \code{most}.}
  \item [\ddag] {See Appendix~\ref{MUM-app:caseformat} in the \mum{} for details.}
+ \item [\S] {More precisely, $C_\delta^i(x) = \frac{1}{\Delta^2} a x^2$}, where $a$ is the corresponding value of \code{RampWearCostCoeff(i,t)}.
 \end{tablenotes}
 \end{threeparttable}
 \end{table}

lib/most.m

@@ -1722,19 +1722,19 @@
  om.init_indexed_name('qdc', 'RampWear', {nt+1, nj_max, nj_max});
  end
  for j = 1:mdi.idx.nj(1)
- w = mdi.tstep(1).TransMat(j,1); % the probability of going from initial state to jth
- Q = mdi.Delta_T * spdiags(w * baseMVA^2 * mdi.RampWearCostCoeff(:,1), 0, ng, ng);
- c = -mdi.Delta_T * w * baseMVA * mdi.RampWearCostCoeff(:,1) .* mdi.InitialPg;
- k0 = mdi.Delta_T * w * 0.5 * mdi.RampWearCostCoeff(:,1)' * mdi.InitialPg.^2;
+ w = mdi.Delta_T * mdi.tstep(1).TransMat(j,1); % the probability of going from initial state to jth
+ Q = spdiags(w * baseMVA^2 * mdi.RampWearCostCoeff(:,1) / mdi.Delta_T^2, 0, ng, ng);
+ c = -w * baseMVA * mdi.RampWearCostCoeff(:,1) .* mdi.InitialPg;
+ k0 = w * 0.5 * mdi.RampWearCostCoeff(:,1)' * mdi.InitialPg.^2;
  vs = struct('name', {'Pg'}, 'idx', {{1,j,1}});
  om.add_quad_cost('RampWear', {1,j,1}, Q, c, k0, vs);
  end
  % Then the remaining periods
  for t = 2:nt
  for j2 = 1:mdi.idx.nj(t)
  for j1 = 1:mdi.idx.nj(t-1)
- w = mdi.tstep(t).TransMat(j2,j1) * mdi.CostWeights(1, j1, t-1);
- h = mdi.Delta_T * w * baseMVA^2 * mdi.RampWearCostCoeff(:,t);
+ w = mdi.Delta_T * mdi.tstep(t).TransMat(j2,j1) * mdi.CostWeights(1, j1, t-1);
+ h = w * baseMVA^2 * mdi.RampWearCostCoeff(:,t) / mdi.Delta_T^2;
  i = (1:ng)';
  j = ng+(1:ng)';
  Q = sparse([i;j;i;j], [i;i;j;j], [h;-h;-h;h], 2*ng, 2*ng);
@@ -1749,10 +1749,10 @@
  % that makes sense for nt+1; all other fields in mdi.tstep(nt+1) can be empty.
  if ~mdi.OpenEnded
  for j = 1:mdi.idx.nj(nt)
- w = mdi.tstep(nt+1).TransMat(1, j) * mdi.CostWeights(1, j, nt);
- Q = mdi.Delta_T * spdiags(w * baseMVA^2 * mdi.RampWearCostCoeff(:,nt+1), 0, ng, ng);
- c = -mdi.Delta_T * w * baseMVA * mdi.RampWearCostCoeff(:,nt+1) .* mdi.TerminalPg;
- k0 = mdi.Delta_T * w * 0.5 * mdi.RampWearCostCoeff(:,nt+1)' * mdi.TerminalPg.^2;
+ w = mdi.Delta_T * mdi.tstep(nt+1).TransMat(1, j) * mdi.CostWeights(1, j, nt);
+ Q = spdiags(w * baseMVA^2 * mdi.RampWearCostCoeff(:,nt+1) / mdi.Delta_T^2, 0, ng, ng);
+ c = -w * baseMVA * mdi.RampWearCostCoeff(:,nt+1) .* mdi.TerminalPg;
+ k0 = w * 0.5 * mdi.RampWearCostCoeff(:,nt+1)' * mdi.TerminalPg.^2;
  vs = struct('name', {'Pg'}, 'idx', {{nt,j,1}});
  om.add_quad_cost('RampWear', {nt+1,j,1}, Q, c, k0, vs);
  end
@@ -1772,7 +1772,7 @@
  for t = 1:nt
  for j = 1:mdi.idx.nj(t)
  for k = 1:mdi.idx.nc(t,j)+1
- w = mdi.CostWeightsAdj(k,j,t);  %% NOTE (k,j,t) order !!!
+ w = mdi.Delta_T * mdi.CostWeightsAdj(k,j,t); %% NOTE (k,j,t) order !!!
 
  % weighted polynomial energy costs for committed units
  gc = mdi.flow(t,j,k).mpc.gencost;
@@ -1784,15 +1784,15 @@
  if ncost > 3
  error('most: polynomial generator costs of order higher than quadratic not supported');
  elseif ncost == 3
- Q = sparse(ipol, ipol, mdi.Delta_T * 2 * w * baseMVA^2*gc(ipol, COST), ng, ng);
+ Q = sparse(ipol, ipol, 2 * w * baseMVA^2*gc(ipol, COST), ng, ng);
  else
  Q = sparse(ng,ng);
  end
  c = zeros(ng, 1);
  if ncost >= 2
- c(ipol) = mdi.Delta_T * w * baseMVA*gc(ipol, COST+ncost-2);
+ c(ipol) = w * baseMVA*gc(ipol, COST+ncost-2);
  end
- k0 = mdi.Delta_T * w * sum(gc(ipol, COST+ncost-1));
+ k0 = w * sum(gc(ipol, COST+ncost-1));
  else %% non-uniform order of polynomials
  %% use a loop
  Q = sparse(ng,ng);
@@ -1802,12 +1802,12 @@
  if ncost > 3
  error('most: polynomial generator costs of order higher than quadratic not supported');
  elseif ncost == 3
- Q(i,i) = mdi.Delta_T * 2 * w * baseMVA^2*gc(i, COST);
+ Q(i,i) = 2 * w * baseMVA^2*gc(i, COST);
  end
  if ncost >= 2
- c(i) = mdi.Delta_T * w * baseMVA*gc(i, COST+ncost-2);
+ c(i) = w * baseMVA*gc(i, COST+ncost-2);
  end
- k0 = mdi.Delta_T * w * gc(i, COST+ncost-1);
+ k0 = w * gc(i, COST+ncost-1);
  end
  end
  vs = struct('name', {'Pg'}, 'idx', {{t,j,k}});
@@ -1817,22 +1817,22 @@
  % weighted y-variables for piecewise linear energy costs for committed units
  % ipwl = find( (mdi.flow(t,j,k).mpc.gen(:,GEN_STATUS) > 0) & (gc(:,MODEL) == PW_LINEAR));
  if mdi.idx.ny(t,j,k)
- c = mdi.Delta_T * w * ones(mdi.idx.ny(t,j,k),1);
+ c = w * ones(mdi.idx.ny(t,j,k),1);
  vs = struct('name', {'y'}, 'idx', {{t,j,k}});
  om.add_quad_cost('Cy', {t,j,k}, [], c, 0, vs);
  end
 
  % inc and dec offers for each flow
- c = mdi.Delta_T * w * baseMVA * mdi.offer(t).PositiveActiveDeltaPrice(:);
+ c = w * baseMVA * mdi.offer(t).PositiveActiveDeltaPrice(:);
  vs = struct('name', {'dPp'}, 'idx', {{t,j,k}});
  om.add_quad_cost('Cpp', {t,j,k}, [], c, 0, vs);
- c = mdi.Delta_T * w * baseMVA * mdi.offer(t).NegativeActiveDeltaPrice(:);
+ c = w * baseMVA * mdi.offer(t).NegativeActiveDeltaPrice(:);
  vs = struct('name', {'dPm'}, 'idx', {{t,j,k}});
  om.add_quad_cost('Cpm', {t,j,k}, [], c, 0, vs);
 
  % weighted fixed reserves cost
  if mdi.IncludeFixedReserves
- c = mdi.Delta_T * w * mdi.FixedReserves(t,j,k).cost(r.igr) * baseMVA;
+ c = w * mdi.FixedReserves(t,j,k).cost(r.igr) * baseMVA;
  vs = struct('name', {'R'}, 'idx', {{t,j,k}});
  om.add_quad_cost('Rcost', {t,j,k}, [], c, 0, vs);
  end

lib/mostver.m

@@ -19,7 +19,7 @@
 v = struct( 'Name', 'MOST', ...
  'Version', '1.2+', ...
  'Release', '', ...
- 'Date', '24-Oct-2023' );
+ 'Date', '25-Oct-2023' );
 if nargout > 0
  if nargin > 0
  rv = v;