Therefore, we choose the MO-GOMEA to tackle the multi-objective dynamic DNEP problem.
6.1.4. Our contributions
In this chapter, we consider the dynamic DNEP problem with multiple objectives (MO-DNEP). We incorporate the future options for DSM as an additional invest-ment action for DNOs. We present efficient trade-off solutions for this MO-DNEP problem and discuss their implications on DNEP decision making. We will show that MO-GOMEA can be employed to assist DNOs in designing effective expansion plans regarding the upcoming introductions of smart grid technologies (e.g., DSM or storage systems) into the existing traditional electricity networks.
The remainder of this chapter is organized as follows. Section 6.2 proposes how the DSM can be modeled into the DNEP problem. Section 6.3 formulates the MO-DNEP problem and introduces various objectives of interest. Section 6.4 presents the benchmark networks and experiment setup for the solver MO-GOMEA. Section 6.5 shows and discusses the experimental results on the benchmark networks. Finally, Section 6.6 concludes the chapter.
6.2. Expansion options
We assume that two categories of planning options are available to DNOs when solving DNEP: physical asset investment and DSM options. Asset investments (i.e., installing new facilities, upgrading existing equipment, or changing network topology) can increase the physical capacity of the distribution network. On the other hand, DSM policy contributions can be seen as improving the efficiency of network usage. DSM helps decrease the peak loads so that the current network capacity suffices to handle the corresponding power flow. In this section, we describe how these two options can be modeled together into the DNEP problem.
6.2.1. Network facilities (assets)
To represent the network assets of a candidate expansion plan for the multi-objective dynamic DNEP problem, we can employ the same encoding scheme that was pro-posed in Chapter 5 for the single-objective case. Let l be the total number of branches that can be considered for expansion planning, i.e., both existing cables and potential cable connections. A network configuration in the horizon year thorizon
can be presented as a vector x of l integer elements:
x= (x1, x2, . . . , xl), |xk| ∈ Ω(k) ∪ {0}, k ∈ {1, 2, . . . , l} (6.1) where Ω(k) is the set of cable types that can be installed at the k-th branch. The value of xk indicates the status and the type of cable installed:
• xk = ID > 0: A cable of type ID ∈ Ω(k) is installed.
• xk = 0: No cable is installed at the kthbranch.
• xk = −ID < 0: This is a normally-open point (NOP): a cable of type ID ∈ Ω(k) is installed but is out of normal operation. NOPs can be used to reconfigure the network during network failures.
While electric cables have very long lifetimes of about 30 years, planning periods longer than 30 years can be considered as impractical since there are many uncer-tainties at such distant horizons. Therefore, during a practical planning period, a network branch is normally reinforced at most once. A vector x of the network con-figuration in the horizon year suffices to represent an expansion plan (of 30 years).
If x0= (x01, x02, . . . , x0l) encodes the currently existing network, element-wise differ-ences between x and x0 indicate which new assets should be installed to transform x0 to x. To determine the installation year of each new asset for a feasible candi-date solution, we employ the decomposition heuristic, that was proposed in Chapter 5), which can be summarized as follows. First, based on the forecast annual peak load growth rate, we determine the year tX when the currently existing network becomes infeasible. Second, we create a base schedule by assuming that all new assets are installed in the same year tX and evaluate this base schedule. Next, we loop through all these new assets in a random order and try to postpone each instal-lation by one year if such delay yields a better expansion plan. This postponement checking is continued until further other delay is possible. Note that, in Chapter 5 regarding single-objective DNEP problems, an expansion plan can be considered as better than another plan in terms of a single objective (i.e., the investment cost or the total cost). For MO-DNEP problems, where multiple conflicting objectives are involved, the quality of expansion plans must be evaluated in terms of Pareto domination (see Section 6.3).
6.2.2. Demand side management (policies)
Parts of the power consumption from the network are flexible loads, such as the use of dishwashers, washing machines, tumble dryers, or charging electric vehicles.
DSM policies can motivate consumers to shift these flexible loads to different times out of the daily peak power consumption hours by giving consumers, for example, financial compensations [27]. We assume that DNOs, as a stakeholder in energy markets, might be allowed (or required) to contribute parts of those compensations.
In this study, we assume that the flexible loads account for 10% of the peak loads at the beginning of a planning period, and linearly grow to 30% of peak loads at the end of the planning period. This assumption is based on the fact that the emergence of smart household appliances gradually enlarges the magnitude of flexible loads.
We also assume that DNOs can contribute to DSM policies through a financial means in EUR/year for each peak power consumption reduction of 1 kW on an MV node in the whole year. Note that the numbers that we use here are simplified to set up a demonstration case. Different and more fine-grained scenarios can be created by customizing these assumptions as input data. In this study, we take into account only the peak shaving effects of DSM because this is the most important aspect to DNEP while other related details, such as the actual mechanism of DSM, who administers DSM, and how consumers are incentivized to participate in DSM, are abstracted away.
6.2. Expansion options
Demand side management representation
Unlike (long lifetime) physical assets, DSM options can be seen as operational poli-cies which can be changed from year to year during the planning period. In principle, in order to represent a DSM policy for a planning period of multiple years, we need a DSM decision variable for each year. However, in this study, we use a DSM strategy which applies peak-shaving and only when it is necessary to prevent bottlenecks.
Therefore, we only need DSM decision variables for the years from the first infeasible year tX until (and including) thorizon. We have nd= thorizon− tX+ 1 is the number of years in a DSM policy. We represent a DSM policy over nd years as a vector of nd non-negative integer elements.
y= (y1, y2, . . . , ynd), yt∈ D, t = 1, 2, . . . , nd (6.2) where D is the set of DSM option levels that are available to implement. The value of ytindicates the chosen DSM level in year t. For the sake of simplicity in making decisions, DNOs are assumed to decide the amount of DSM contribution (i.e., corre-sponding with the desired amount of flexible load reduction) in discrete DSM levels, namely 0 (no DSM is needed), 1 (25% flexible load reduction), 2 (50% flexible load reduction), 3 (75% flexible load reduction) and 4 (100% flexible load reduction). We then have D = {0, 1, 2, 3, 4}. Here, we take a holistic approach in which a single DSM level ytis applied to all network nodes (i.e., MV/LV substations and MV cus-tomer stations) in each year t of the planning period. Our formulation can be easily extended to support a more fine-grained approach in which each suitable network node i has its own DSM level per year yitas in the case of battery storage systems considered in Chapter 5.
Effects of DSM on peak loads
Let ftdenote the percentage of flexible loads in peak power consumption in a year t. We assume that f0 = 10% in the beginning year and fhorizon = 30% in the end year of the planning period. The values of ft’s, 0 < t < thorizon can be calculated by linear interpolation.
For an MV-D network of n nodes, assuming that no DSM policy is used, the vector of peak active power demand at each node in year t is:
Pt,0= (P1t,0, P2t,0, . . . , Pnt,0) (6.3) The accompanying vector of peak reactive power is:
Qt,0= (Qt,01 , Qt,02 , . . . , Qt,0n ) (6.4) In that year t, if we use a DSM policy at a level yt> 0, yt= 1, 2, 3, 4, then the vector of new peak active power demands will be
Pt,yt = (P1t,yt, P2t,yt, . . . , Pnt,yt) (6.5) where Pit,yt = Pit,0∗ (1 − (yt/4) ∗ ft), so that yt= 1, 2, 3, 4 corresponds to 25%, 50%, 75%, 100% flexible load reduction, respectively. And the corresponding vector of peak reactive power will be:
Qt,yt= (Qt,y1 t, Qt,y2 t, . . . , Qt,yn t) (6.6) where Qt,yi t = Qt,0i ∗ (1 − (yt/4) ∗ ft). Then, Pt,yt and Qt,yt form the new load due to the peak shaving effect of the DSM level ytin the year t.
The total reduction in peak active power demands corresponds with employing the DSM level y in year t is:
Ptotalt,yt =
n
X
i=1
(Pit,0− Pit,yt) (6.7)
6.2.3. Solution representation
A solution s of the DNEP problem for a network over a planning period consists of the network configuration xhorizon at the end of the planning period and the DSM policy y (i.e., the list of DSM levels that are applied on the network in each year).
For the sake of convenience in representation, we shorten xhorizon as x.
s= (x, y) = (x1, x2, . . . , xnl, y1, y2, . . . , ynd) (6.8) The total number of decision variables is then nl+ nd. An installation schedule of new physical assets in x is determined by our installation decomposition approach (see Section 6.2.1). The DSM policy y indicates the DSM levels that affect the peak load profile Pt,yt and Qt,yt in each year t (see section 6.2.2), and will be used to verify constraint violations of the corresponding network configuration in year t.