Abstract
In conventional power system, multiple generators commonly coexist. In
the meantime, each of the generators has different characteristics in
terms of generation cost. Hence, it is necessary to consider them
coordinately and achieve the rational power generation mix. Furthermore,
in modern smart grids, the characteristics of the generators become even
complex, which requires further considerations of different generation
cost factors in order to fulfill the requirements of system optimal
operation. In this paper, different types of generation costs are
analyzed in detail, including starting cost, minimum power generation
cost, marginal cost, etc. At the same time, the simplified optimization
model is proposed to accelerate the solving rate and ensure that the
solution is a global optimal one. Numerical experiments are conducted to
validate the proposed method.
Keywords : Generator mix, marginal cost, generation cost
minimization
- 1.Introduction
In order to meet the requirements of ever growing electricity demands,
the coordinated characteristics of multiple generators should be
considered simultaneously so that coordination among various generation
units can be achieved and generation costs can be thereby reduced
[1]-[4]. Meanwhile, the overall system reliability can be also
enhanced by coordinating multiple generators in the same electric grids.
Conventional optimization approach and cost analysis are more suitable
for studying the characteristics of small-scale power systems. However,
for larger-scale power systems with large numbers of synchronous
generators (especially for modern smart grids with various generation
mix), the legacy approach may not be effective and the corresponding
cost optimization could be infeasible. The deployment of microgrids
could be a good solution to consolidate the dispersed generations into a
single unit with relatively larger generation capacity [5]-[8].
However, microgrids themselves may also induce operational issues
regarding power dispatch, electricity transactions, resource allocation,
etc. Additional discussions are needed to fully leverage the benefits of
microgrids in cost analysis and economic dispatch in modern electric
grids.
Economic operation is one of the critical requirements and criteria in
the operation and management of modern power systems. Especially for
today’s electric grids, the particular requirements can be detailed in
the following aspects:
1) The generation costs follow the basic hourly generation cost rate,
which determines the particular hourly generation cost of each
individual generator;
2) Frequency start-up and shut-down procedures should be avoided, so
that the additional cost during the start process can be eliminated,
which thereby reduced the overall generation cost;
3) The minimum output power of each generator should be taken into
account during the analysis, which is induced by the physical limit of
each generator.
4) When the output power of each generator is controlled to be larger
than its minimum limit, an additional hourly rate should be considered,
which is called marginal cost. Marginal cost is used to represent the
overall cost increase induced by the additional power generation of each
particular generator.
In order to optimally combine the generation costs from multiple
generators (i.e., to minimize the overall system cost), the above cost
categories should be comprehensively considered. Hence, the overall cost
equation can be derived. Meanwhile, various operational constraints
should be considered during the combination of multiple generators,
including system topology constraints, maximum power generation
constraints, minimum power generation constraints, etc.
For unit commitment and combination of multiple generators, the
computational efficiency should be always taken care of. It is necessary
to ensure the required computational efficiency and minimize model
complexity. In order to solve the above issues, the conventional way of
solving the problem is focused on the solving mode, i.e., to improve the
original problem solving efficiency and accuracy by altering the solving
modes. Particularly, the traditional approaches mainly focus on
heuristic methods [9], which is relied on continuously changing the
decision variables and gradually approaching the optimal solution. These
methods feature lower complexity and less model dependency. However,
there could still be some issues regarding convergence. In other words,
the algorithm may not converge at the desired and optimal operation
points due to the continuous changing and perturbation in the system. In
some cases, the optimization problem may lead to sub-optimal other than
global optimal due to the inherent issues of heuristic methods.
In this paper, we focus on the improvement of original models, rather
than changing the solving methods. In particular, we first adjust the
decision variables based on the understanding of physical systems. The
purpose of this step is to reduce the numbers of decision variables.
Meanwhile, by involving sign signals, the unnecessary procedures or
unrealistic unit commitment can be eliminated. Hence, the feasible range
is simplified and minimized, and the solving efficiency is thereby
enhanced.
Based on the practical and given system model, all the generation costs
are listed and analyzed, and the overall cost equation is derived based
on the coordination among multiple generation units. After that, in
order to minimize the overall generation cost, the optimization model is
simplified and the modified model is presented for following analysis.
The proposed model can be used to enhance the solving efficiency of the
corresponding optimization problem, and the computational efficiency can
be enhanced. Meanwhile, it can be guaranteed that the obtained results
are the global optimal other than sub-optimal. Finally, the proposed
mathematical model is derived in numerical experiment and the proposed
optimization problem is thereby analyzed. The related results are given
to validate the proposed model and method.