# Fast Constraint Screening for Multi-Interval Unit Commitment

Xuan He1, Jiayu Tian2, Yufan Zhang3, Honglin Wen4 and Yize Chen1 1 Hong Kong
University of Science and Technology (Guangzhou<EMAIL_ADDRESS>gz.edu.cn<EMAIL_ADDRESS>2 Sun Yat-Sen University,
<EMAIL_ADDRESS>University of California, San Diego,
<EMAIL_ADDRESS>Shanghai Jiaotong University<EMAIL_ADDRESS>
###### Abstract

Power systems Unit Commitment (UC) problem determines the generator commitment
schedule and dispatch decisions for power networks based on forecasted
electricity demand. However, with the increasing penetration of renewables and
stochastic demand behaviors, it becomes challenging to solve the large-scale,
multi-interval UC problem in an efficient manner. The main objective of this
paper is to propose a fast and reliable scheme to eliminate a set of redundant
or inactive physical constraints in the high-dimensional, multi-interval,
mixed-integer UC problem, while the reduced problem is equivalent to the
original full problem in terms of commitment decisions. Our key insights lie
on pre-screening the constraints based on the load distribution and
considering the physical feasibility regions of multi-interval UC problem. For
the multi-step UC formulation, we overcome screening conservativeness by
utilizing the multi-step ramping relationships, and can reliably screen out
more constraints compared to current practice. Extensive simulations on both
specific load samples and load regions validate the proposed technique can
screen out more than 80% constraints while preserving the feasibility of
multi-interval UC problem.

##  I Introduction

Obtaining accurate solutions for unit commitment in an efficient manner is
crucial for ensuring reliable generation dispatch [1]. For transmission grid
operations, Unit commitment (UC) problems are typically formulated as mixed
integer programming (MIP) problems involving both discrete variables for
generator statuses and continuous variables for dispatch levels. In
particular, for the multi-interval UC problems, temporal constraints, such as
ramping constraints, are incorporated to regulate the capacity at which
generators can adjust their output levels in response to dynamic changes of
electricity demand and system conditions. However, due to the NP-hard nature
of such nonconvex MIP problems, the solution process can be exceedingly time-
consuming [2, 3]. Such computation complexity can be further increased by the
existence of numerous network constraints such as line flow limits [4, 5].

The need to accelerate the unit commitment (UC) solution process has prompted
research into developing a surrogate UC model with fewer line flow limits
while maintaining the solution equivalence of the resulting UC problem and the
original UC problem. Such technique is backed up by the observation that only
a subset of security constraints is binding in the real world systems. The
process to identify the appropriate subset of line flow limits is termed
_constraint screening_ [6, 7]. [6] proposes to eliminate the constraints whose
line flow cannot reach the boundary given load inputs and show that the
feasible region will be the same as the original UC problem.

However, for the standard screening model [6, 8], screening strategies can be
conservative, while many redundant or inactive constraints are still kept
rather than screened out. [9] and [10] propose the cost-driven screening
models to utilize the operating cost constraint to limit the line flow value
range further. Yet most of the literature focus on single-step formulation of
UC constraint screening, while ignoring the impact of temporal constraints
such as generation ramping constraints on the feasible region of screening
problems. On the other hand, relaxed binary variables of generator commitment
schedule in the standard screening model for a load sample also enlarge the
line flow value range [11]. The strong representation capability by machine
learning (ML) models [12, 13] can be utilized to predict the value of the
binary variables, i.e., the decisions of generator states, which shows
potential for further integrating the predictions to the screening model to
handle the loose line flow range issue.

Another concern is the computation costs in standard constraint screening
setup, which come from solving the optimization-based screening problem for
each network constraint and each electricity load instance. For the former,
the ML models [14, 15, 16, 17, 18] directly use ML predictions to classify if
a network constraint is redundant, while there is no guarantee the reduced UC
is equivalent to the original one. For the latter, in fact, empirical evidence
shows that the samples belonging to some typical load regions can have the
same set of redundant constraints in their corresponding UC problems [11]. It
is then sufficient to implement screening on the load region rather than
working on individual load sample [19, 20].

To address such challenges, we develop one of the first multi-interval UC
constraint screening models to narrow down the search space of line flow
constraints reliably, leading to screening strategy with more efficient
performance. Our key insights lie on integrating the temporal constraints,
i.e., the ramping constraints to the standard screening model, and such
approach can be applied for either given load region or individual load
sample. The potential of utilizing the ML predictions of generator states to
improve the screening efficiency is also explored. Specifically, we formulate
a tractable linear programming problem for multi-interval UC, and prove that
more inactive constraints can be eliminated without changing the feasible
region of original UC problem. Moreover, our method can be flexibly integrated
to screen constraints for either one specific load vector, or to achieve
solver warm-start (offline constraint screening beforehand to get the reduced
problem which can be later used for real-time operation problem) for a given
load region. We term these two cases as _sample-aware_ [6] and _sample-
agnostic_ [11] constraint screening respectively. Specially, for the _sample-
aware_ case, we further propose to make use of ML prediction on commitment
schedule to better limit the search space of the constraint screening problem.
In the sample-aware case on IEEE 39-bus system, our proposed method with
ground truth generator states can achieve 95.3% screening rate, achieving a
boost compared to the standard constraint screening [6] (82%). With partial
predictions, the feasible rate of our method reach 84% while the solution gap
is only 0.32%. In the sample-agnostic case on 118-bus, our procedure can also
find the most compact form of UC problem after the more efficient screening
process.

Figure 1: Illustration of the inactive constraints corresponding to the
different feasible region. By using our technique, it is possible to screen
more constraints (line in red) compared to standard single timestep screening
method.

##  II Multi-Interval UC Problem Formulation

In this paper, we assume the system operators need to decide both the ON/OFF
statuses (the commitment schedule) as well as dispatch level for all
generators. Herein we consider the day-ahead UC problem taking ramp
constraints into consideration. For the $T$ timesteps UC problem with $n$
generators involved, the problem is formulated as

$\displaystyle\min_{\mathbf{u},\mathbf{x},\mathbf{f}}\quad$
$\displaystyle\sum_{t=1}^{T}\sum_{i=1}^{n}c_{i}x_{i}(t)$ (1a) s.t.
$\displaystyle u_{i}\underline{x}_{i}\leq x_{i}(t)\leq
u_{i}\bar{x}_{i},\quad\forall i,t$ (1b)
$\displaystyle-\overline{\mathbf{f}}\leq\mathbf{Kf(t)}\leq\overline{\mathbf{f}},\quad\forall
t$ (1c)
$\displaystyle\mathbf{x(t)}+\mathbf{A}\mathbf{f(t)}=\bm{\ell}(t),\;\forall t$
(1d) $\displaystyle u_{i}(t)\in\\{0,1\\},\quad\forall i,t$ (1e) $\displaystyle
x_{i}(t)-x_{i}(t-1)\leq\text{R}^{up}_{i}u_{i}(t-1)$
$\displaystyle+\text{R}^{su}_{i}(u_{i}(t)-u_{i}(t-1))+\bar{x}_{i}(1-u_{i}(t))\;\forall
i,t$ (1f) $\displaystyle x_{i}(t-1)-x_{i}(t)\leq\text{R}^{dn}_{i}u_{i}(t)$
$\displaystyle+\text{R}^{sd}_{i}(u_{i}(t-1)-u_{i}(t))+\bar{x}_{i}(1-u_{i}(t-1))\;\forall
i,t.$ (1g)

In the UC problem, we optimize over the generator statuses $\mathbf{u}$, the
generator dispatch $\mathbf{x}$ and the line power flow $\mathbf{f}$ to find
the least-cost solutions with cost defined in the objective function (1a).
$c_{i}$ denotes the cost coefficient. Constraint (1b), (1c) and (1d) denotes
the generation bound, the flow bound and the nodal power balance respectively.
Note that the power flows are modeled as a DC approximation, while the phase
angles are absorbed into the fundamental flows $\mathbf{f}\in\mathbb{R}^{n-1}$
[21, 22]; $K$ and $\mathbf{A}$ map such fundamental flows to flow constraints
and nodal power balance respectively. (1e) enforces the binary constraint of
generator statuses, where $u_{i}=1$ indicates the generator is on. (1f) and
(1f) are the ramping constraints to enforce limitations on the speed at which
generators are able to modify their output levels in response to fluctuations
in demand or system conditions. $R^{up}_{i},R^{su}_{i},R^{dn}_{i},R^{sd}_{i}$
are the upward limits, downward, start-up and shut-down capacity.

For the power system with numerous generators and networks, (1) can be a
large-scale MILP problem, which is intractable to solve efficiently so as to
satisfy the computation requirement of finding generation dispatch decisions.
Meanwhile, there is a large number of inactive constraints, especially the
inactive network constraints, giving the potential to simplify (1) by
screening out such inactive constraints. Then it is possible to solve a
reduced UC problem with fewer engineering constraints.

##  III Multi-Interval Constraint Screening Model

###  III-A Modeling of Inactive Constraints

In this work, we follow the definition of inactive constraint firstly
formulated by [6]. One constraint can be treated as inactive if it has no
influence on the feasible region of the multi-interval UC problem, and can
thus be eliminated as illustrated in Fig. 1. For the constraint screening
problem, it is thus of interest to correctly screen out as many inactive
constraints as possible. And ultimately, we want to tighten the feasible
region and make it close to the original UC problem, so constraints like those
marked in red in Fig. 1 can be screened out.

To formulate the feasible region mathematically, we use $P$ to denote the
feasible region defined by a constraint set $C^{P}$. $C^{P}$ is a subset of
the original UC problem’s constraint set. Then the actual feasible region of
the original problem defined by (1b)-(1g) can be naturally a subregion of $P$.

_Definition 1:_ A network constraint
$\mathbf{K}_{j}\mathbf{f(t)}\leq\overline{\mathbf{f}}$ or
$\mathbf{K}_{j}\mathbf{f(t)}\geq-\overline{\mathbf{f}}$ is defined inactive to
$P$ if and only if,

$\displaystyle P\supseteq P^{-\\{j\\}};$ (2)

where $P^{-\\{j\\}}$ is the region defined by the constraint set $C^{P}$
eliminating $\mathbf{K}_{j}\mathbf{f(t)}\leq\overline{\mathbf{f}}_{j}$ or
$\mathbf{K}_{j}\mathbf{f(t)}\geq-\overline{\mathbf{f}}_{j}$, and we denote
this set as $C^{P/j}$.

###  III-B Single-Step Constraint Screening

To identify each inactive flow constraint, the standard optimization-based
screening model[6] tries to evaluate whether the line $j$ will be binding
given the load input. In (3) we describe such formulation, which can be used
to conduct the _sample-aware constraint screening_ for the $j$-th line at time
step $k$.

$\displaystyle\max_{\mathbf{u_{k}},\mathbf{x_{k}},\mathbf{f_{k}}}/\min_{\mathbf{u_{k}},\mathbf{x_{k}},\mathbf{f_{k}}}\quad$
$\displaystyle\mathbf{K}_{j}\mathbf{f}(k)$ (3a) s.t. $\displaystyle
u_{i}\underline{x}_{i}\leq x_{i}(k)\leq u_{i}\bar{x}_{i},\quad i=1,...,n$ (3b)
$\displaystyle-\overline{\mathbf{f}}_{\mathcal{F}/j}\leq\mathbf{K}_{\mathcal{F}/j}\hat{\mathbf{f}}(k)\leq\overline{\mathbf{f}}_{\mathcal{F}/j}$
(3c) $\displaystyle\mathbf{x(k)}+\mathbf{A}\mathbf{f(k)}=\bm{\ell}(k)$ (3d)
$\displaystyle 0\leq u_{i}(k)\leq 1.\quad i=1,...,n;$ (3e)

where $\bm{\ell}$ is a known load vector for UC problem. Note that this
formulation can be extended to eliminate some inactive constraints for multi-
interval UC problem in [6], where
$C^{P/j}={\eqref{Screening2:gen}-\eqref{Screening2:balance}}\cup\\{u_{i}(t)\in\\{0,1\\}\\}$.
Note that (3e) relaxes $u$ as the continuous variables and thus (3) can be
solved as a linear programming problem. However, the feasible region $P$
considered by this model ignore the impact of the ramping constraints, leading
to a more relaxed screened region $P^{-\\{j\\}}$. This means more constraints
can be identified as active for the screened region, while actually they are
inactive for the feasible region of original UC problem, as shown in Fig. 1.

###  III-C Multi-Step Constraint Screening

In practice, multi-period UC is adopted for day-ahead scheduling. Yet in such
multi-period problem, the existence of ramping constraints complicate both the
solution procedure and also the analysis for constraint screening. Thus there
are fewer previous literature working on this more realistic setup.
Intuitively, ramping constraints can limit the generation range level and
further limit the line flow regions. Naturally, the ramping constraints can
also influence the constraint screening process, and to illustrate this,
consider the three-node network depicted in Fig. 2.

Figure 2: Illustrative example of the three-node network.

####  III-C1 Influence of the ramping constraints on screening

Assume that we are screening $f_{1}(t+1)$ and considering the impact of a
ramping-down constraint. Suppose we have load $l_{3}(t)=60\text{MW}$,
$l_{3}(t+1)=35\text{MW}$, and we assume the upper bound of $f_{1}$ is $30$MW.
Assume at timestep $t$, we know the dispatch solution
$x_{1}(t)=30\text{MW},x_{2}(t)=30\text{MW}$. Regarding the screening models
maximizing the line flow of $f_{1}(t)$ we have: For the single-step screening,
$x_{1}(t+1)=35\text{MW},x_{2}(t+1)=0\text{MW},f_{1}(t+1)=30\text{MW}$, then
the upper bound of $f_{1}(t+1)$ is identified as active. For the multi-step
screening,
$x_{1}(t+1)=20\text{MW},x_{2}(t+1)=15\text{MW},f_{1}(t+1)=20\text{MW}$, then
the upper bound of $f_{1}(t+1)$ is identified as inactive.

The above example illustrates that considering the ramping constraints in the
screening can identify more inactive constraints, and such constraints can be
eliminated from the original problem. Thus, we formulate the multi-step
constraint screening model with ramping limits, and further prove that it can
screen more constraints safely than the single-step screening.

####  III-C2 Model formulation

Without sacrificing generality, we first analyze the screening model (4) for
the upper bounds of the line limits, i.e.,
$\mathbf{K}_{j}\mathbf{f(t)}\leq\overline{\mathbf{f}}_{j}$, and the analysis
for the lower bound can be achieved in the same manner.

_Theorem 1:_ Consider the following screening model for $j$-th line at time
step $k$:

$\displaystyle
S_{j}^{*}(k)=\max_{\mathbf{u}_{k},\mathbf{x}_{k},\mathbf{f}_{k}}$
$\displaystyle\mathbf{K}_{j}\mathbf{f}(k)$ (4a) s.t.
$\displaystyle\mathbf{u}_{k},\mathbf{x}_{k},\mathbf{f}_{k}\in P^{-\\{j\\}}$
(4b)

A constraint $\mathbf{K}_{j}\mathbf{f}(k)\leq\overline{\mathbf{f}}_{j}$ is
inactive to $P$ if and only if $S_{j}^{*}(k)\leq\overline{\mathbf{f}}_{j}$.

See proof in Appendix -A. Built upon on this theorem, we can define $C^{P/j}$
for the multi-step constraint screening model considering ramping constraints
as follows,

$\displaystyle u_{i}(t)\underline{x}_{i}\leq x_{i}(t)\leq
u_{i}(t)\bar{x}_{i},\quad\forall i\in I,t\leq k$ (5a)
$\displaystyle-\overline{\mathbf{f}}\leq\mathbf{K}_{\mathcal{F}/j}\mathbf{f(t)}\leq\overline{\mathbf{f}},\quad
t\leq k$ (5b)
$\displaystyle\mathbf{x(t)}+\mathbf{A}\mathbf{f(t)}=\bm{\ell}(t),\quad t\leq
k$ (5c) $\displaystyle u_{i}(t)\in\\{0,1\\},\quad\forall i\in I,\;t\leq k$
(5d) $\displaystyle\scriptstyle
x_{i}(t)-x_{i}(t-1)\leq\text{R}^{up}_{i}u_{i}(t-1)+\text{R}^{su}_{i}(u_{i}(t)-u_{i}(t-1))$
$\displaystyle\scriptstyle+\bar{x}_{i}(1-u_{i}(t))\quad\forall i\in I,\;t\leq
k,$ (5e) $\displaystyle\scriptstyle
x_{i}(t-1)-x_{i}(t)\leq\text{R}^{dn}_{i}u_{i}(t)+\text{R}^{sd}_{i}(u_{i}(t-1)-u_{i}(t))$
$\displaystyle\scriptstyle+\bar{x}_{i}(1-u_{i}(t-1))\quad\forall i\in
I,\;t\leq k$ (5f)

where $I$ denotes the bus index set. We denote the set (5a)-(5f) as
$C^{P/j}_{m}$ and corresponding feasible region as $P^{-\\{j\\}}_{m}$. By
integrating $C^{P/j}_{m}$ to (4), we can get a multi-step screening model that
can screen out inactive constraints reliably.

###  III-D Comparison of Single-Step and Multi-Step Screening

One of our key insights come from including temporal relations (5e) and (5f)
into the multi-interval constraint screening process. The constraint set of
single-step screening (3) is a subset of $C^{P/j}_{m}$, then the feasible
region of (3) covers that of $C^{P/j}_{m}$. This means that a constraint can
be active for the feasible region of single-period problem (3), while it is
inactive for the feasible regions of $C^{P/j}_{m}$ and the original UC
problem. Thus, it can be proved that the screening model derived by Theorem 1
can screen more inactive constraints for the original UC problem than the
single-step screening reliably.

##  IV Improved model formulations for multi-step constraint screening

Note that the multi-step screening model described in Section III is still not
tractable to solve due to the existence of binary variables, the cumbersome
constraints and the regular fluctuation of load samples. To improve the
screening efficiency and develop realistic multi-step screening methods, in
this section we further develop more efficient and reliable screening models.

###  IV-A Sample-Aware Screening with Generator States

Here _sample-aware_ means we implement constraint screening for a known load
instance. As the binary variables make the basic screening model a MILP
problem, we first consider relaxing the value of binary variables to
$u\in[0,1]$. Then, to further lower the model complexity, we replace the nodal
balance constraints (5c) with the load balance constraints (6d) and (6e), and
reduce the network constraints (5b) to (6c), as described in the following
formulation (6).

_Corollary 1:_ Consider the following multi-step screening model with the
relaxation of the binary variables, part of nodal balance constraints and
network constraints:

$\displaystyle S_{aware_{j}}^{*}(k)=$
$\displaystyle\max_{\mathbf{u}_{k},\mathbf{x}_{k},\mathbf{f}_{k}}\;\mathbf{K}_{j}\mathbf{f}(k)$
(6a) s.t.
$\displaystyle\mathbf{\underline{x}}\leq\mathbf{x(t)}\leq\mathbf{\bar{x}},\quad
t\leq k,$ (6b)
$\displaystyle-\overline{\mathbf{f}}_{\mathcal{F}/j}\leq\mathbf{K}_{\mathcal{F}/j}\mathbf{f(k)}\leq\overline{\mathbf{f}}_{\mathcal{F}/j},\quad
t=k,$ (6c)
$\displaystyle\mathbf{x(k)}+\mathbf{A}\mathbf{f(t)}=\bm{\ell}(t),\quad t=k,$
(6d) $\displaystyle\sum{x(t)}=\sum{l(t)},\quad t\leq k,$ (6e)
$\displaystyle\eqref{UC_con:ramping_up}-\eqref{UC_con:ramping_down}.$

If $S_{aware_{j}}^{*}(k)\leq\overline{\mathbf{f}}_{j}$, then constraint
$\mathbf{K}_{j}\mathbf{f}(k)\leq\overline{\mathbf{f}}_{j}$ is inactive to
$P_{m}$, and thus is inactive to original UC problem.

###### Proof.

With relaxing the binary variables, the nodal balance constraints, and the
network constraints, the feasible region of (6) denoted as
$P^{-\\{j\\}}_{aware}$ will cover $P^{-\\{j\\}}_{m}$, then naturally
$S_{j}^{*}(k)\leq S_{aware_{j}}^{*}(k)$. Thus,
$S_{aware_{j}}^{*}(k)\leq\overline{\mathbf{f}}_{j}$ implies that
$S_{j}^{*}(k)\leq\overline{\mathbf{f}}_{j}$ and based on Theorem 1 the
constraint $\mathbf{K}_{j}\mathbf{f}(k)\leq\overline{\mathbf{f}}_{j}$ will be
inactive to $P_{m}$. ∎

Nevertheless, the relaxation of the binary variables can enlarge the screened
feasible region, and thus line flow value range can be increased a lot. Then,
more inactive constraints in the feasible region of the original problem are
identified as active. Thus, it is of significance to limit the value of binary
variables to narrow the screened feasible region. The recently emerging works
on predicting the decisions of generator states, i.e., the binary variables
using ML model [12, 13] give the potential that utilizing the ML predictions
to aid the constraint screening. We denote the ground truth and the prediction
of $\mathbf{u(t)}$ as $\mathbf{u}^{*}(t)$ and $\mathbf{\hat{u}}(t)$
respectively. The constraint set $C^{P/j}_{m}$ with $\hat{u}(t)$ is denoted as
$C^{P/j}_{m,\hat{u}}$, and the corresponding feasible region is denoted as
$P^{-\\{j\\}}_{m,\hat{u}}$.

_Corollary 2:_ When $\mathbf{\hat{u}}(t)=\mathbf{u}^{*}(t)$ holds for all time
steps, consider the following screening model.

$\displaystyle S_{truth_{j}}^{*}(k)=$
$\displaystyle\max_{\mathbf{x}_{k},\mathbf{f}_{k}}\mathbf{K}_{j}\mathbf{f}(k)$
(7a) s.t. $\displaystyle\hat{u}_{i}(t)\underline{x}_{i}\leq
x_{i}(t)\leq\hat{u}_{i}(t)\bar{x}_{i},\forall i\in I,t\leq k,$ (7b)
$\displaystyle\eqref{UC_con:ramping_up}-\eqref{UC_con:ramping_down},\eqref{UC_AW:flow}-\eqref{UC_AW:balance}.$

If $S_{truth_{j}}^{*}(k)\leq\overline{\mathbf{f}}_{j}$, then the constraint
$\mathbf{K}_{j}\mathbf{f}(k)\leq\overline{\mathbf{f}}_{j}$ is inactive to
$P_{m,\hat{u}}$, and thus is inactive to original UC problem with
$\hat{u}(t)$.

###### Proof.

$C^{P/j}_{m,\hat{u}}$ is obviously still $C^{P/j}$ corresponding to
$C^{P}_{m}$ with $\hat{u}(t)$. Let $P^{-\\{j\\}}=P^{-\\{j\\}}_{m,\hat{u}}$ in
(4), then if $S_{j}^{*}(k)\leq\overline{\mathbf{f}}_{j}$, according to Theorem
1 $\mathbf{K}_{j}\mathbf{f}(k)\leq\overline{\mathbf{f}}_{j}$ is inactive to
$P_{m,\hat{u}}$, and thus is inactive to original UC problem with
$\hat{u}(t)$. Further, as the feasible region of (7) covers $P_{m,\hat{u}}$,
then we have $S_{j}^{*}(k)\leq S_{truth_{j}}^{*}(k)$. Thus,
$S_{truth_{j}}^{*}(k)\leq\overline{\mathbf{f}}_{j}$ can imply
$S_{j}^{*}(k)\leq\overline{\mathbf{f}}_{j}$ so as to identify the inactive
constraint. ∎

Actually, the ML predictions are not always reliable, which means
$\mathbf{\hat{u}}(t)=\mathbf{u}^{*}(t)$ may not hold. Then, the predictions
$\mathbf{\hat{u}}_{k}=\\{\mathbf{\hat{u}}(1),\mathbf{\hat{u}}(2),...,\mathbf{\hat{u}(k)}\\}$
can cause the infeasible cases for both the original UC model and the
screening model. Thus, we consider only replacing a part of binary variables
with accurate ML predictions 111This is achievable for some critical nodes or
timesteps by learning the UC binary decisions of a reduced problem., such as
for specified time steps $t\in T_{pre}$, we give the predictions
$\hat{u}_{i}(t)={u}^{*}_{i}(t),\forall i\in I$ as shown in (8b). As long as
the inserted predictions are accurate, the feasible solutions
$\mathbf{u}^{orig}_{T}=\mathbf{u}^{*}$ for (1) and $\mathbf{u}^{scre}_{k}$ for
(8) can be found. Specifically, with the mixed decision vectors
$\mathbf{u}_{T}$ to solve the original UC problem (1) and $\mathbf{u}_{k}$ to
solve the screening problem (8), we can get the corresponding solutions
involving the value of generator states and the generations, where the rest
solutions of ${u}_{i}(t),\forall i\in I,t\notin T_{pre}$ are determined. Let
$\mathbf{u}^{orig}_{k}=\\{\mathbf{u}^{orig}(1),\mathbf{u}^{orig}(2),...,\mathbf{u}^{orig}(k)\\}$,
the case that $\mathbf{u}^{orig}_{k}\neq\mathbf{u}^{scre}_{k}$ may occur due
to the different objective functions. The next Corollary states that under
such case, our screening model can still promise effectiveness to identify the
inactive constraints correctly.

_Corollary 3:_ Consider the following screening model with partial ML
predictions:

$\displaystyle S_{partial_{j}}^{*}(k)=$
$\displaystyle\max_{\mathbf{x}_{k},\mathbf{f}_{k},\mathbf{u}_{k}}\mathbf{K}_{j}\mathbf{f}(k)$
(8a) s.t. $\displaystyle{u}_{i}(t)=\hat{u}_{i}(t),i\in I,\quad t\in T_{pre},$
(8b) $\displaystyle{u}_{i}(t)\underline{x}_{i}\leq x_{i}(t)\leq
u_{i}(t)\bar{x}_{i},\forall i\in I,\quad t\leq k,$ (8c)
$\displaystyle\eqref{UC_con:ramping_up}-\eqref{UC_GUP},\eqref{UC_AW:flow}-\eqref{UC_AW:balance}.$

If $S_{partial_{j}}^{*}(k)\leq\overline{\mathbf{f}}_{j}$, the constraint
$\mathbf{K}_{j}\mathbf{f}(k)\leq\overline{\mathbf{f}}_{j}$ is inactive to
$P_{m,u^{c}_{f}(k)}$, and thus is inactive to the original UC problem with
$\mathbf{u}^{orig}_{k}$.

###### Proof.

If $S_{partial_{j}}^{*}(k)\leq\overline{\mathbf{f}}_{j}$, then the value of
$S_{partial_{j}}(k)$ corresponding to $\mathbf{u}^{orig}_{k}$ will always
satisfy $S_{partial_{j}}^{*}(k)\leq
S_{partial_{j}}^{*}(k)\leq\overline{\mathbf{f}}_{j}$. Thus, the constraint
$\mathbf{K}_{j}\mathbf{f}(k)\leq\overline{\mathbf{f}}_{j}$ is inactive to the
original UC problem with $\mathbf{u}^{orig}_{k}$. ∎

Therefore, with the accurate and partial predictions of $u(t)$, we can still
eliminate the inactive constraints identified by (8) safely. Note that
Corollary 2 and Corollary 3 can also be extended easily to other screening
models with the different definitions of $P$, e.g., the cost-driven screening
model proposed by [9].

###  IV-B Sample-Agnostic Screening with Typical Load Region

In practice, the group of active constraints tend to remain the same across
different realizations of load samples for given power grid, motivating
methods that identify a collection of active constraints with varying load
data. Our framework can also be extended to such setup, and we term it as
_sample-agnostic screening_. We define a load region $\mathcal{L}$, and we
assume that all the possibly upcoming load samples $\bm{\ell}\in\mathcal{L}$,
while in the screening model the load sample is transformed to
$\bm{\ell}^{r}$.

_Corollary 4:_ Consider the following multi-step screening model for a
specified load region:

$\displaystyle S_{R_{j}}^{*}(k)=$
$\displaystyle\max_{\mathbf{u}_{k},\mathbf{x}_{k},\mathbf{f}_{k},\mathbf{l}^{r}_{k}}\mathbf{K}_{j}\mathbf{f}(k)$
(9a) s.t.
$\displaystyle\mathbf{\underline{x}}\leq\mathbf{x(t)}\leq\mathbf{\bar{x}},\quad
t\leq k,$ (9b)
$\displaystyle-\overline{\mathbf{f}}_{\mathcal{F}/j}\leq\mathbf{K}_{\mathcal{F}/j}\mathbf{f(t)}\leq\overline{\mathbf{f}}_{\mathcal{F}/j},\quad
t=k,$ (9c)
$\displaystyle\mathbf{x(t)}+\mathbf{A}\mathbf{f(t)}=\bm{\ell}^{r}(t),\quad
t=k,$ (9d) $\displaystyle\sum{x(t)}=\sum{l^{r}(t)},\quad t\leq k,$ (9e)
$\displaystyle\bm{\ell}^{r}\in\mathcal{L},$ (9f)
$\displaystyle\eqref{UC_con:ramping_up}-\eqref{UC_con:ramping_down}.$

If $S_{region_{j}}^{*}(k)\leq\overline{\mathbf{f}}_{j}$, then constraint
$\mathbf{K}_{j}\mathbf{f}(k)\leq\overline{\mathbf{f}}_{j}$ is inactive to
$P_{m}$, and thus is inactive to original UC problem.

###### Proof.

With relaxing the binary variables and load value, the feasible region of (9)
denoted will cover $P^{-\\{j\\}}_{m}$, then naturally $S_{j}^{*}(k)\leq
S_{region_{j}}^{*}(k)$. Thus,
$S_{region_{j}}^{*}(k)\leq\overline{\mathbf{f}}_{j}$ implies that
$S_{j}^{*}(k)\leq\overline{\mathbf{f}}_{j}$ and based on Theorem 1 the
constraint $\mathbf{K}_{j}\mathbf{f}(k)\leq\overline{\mathbf{f}}_{j}$ will be
inactive to $P_{m}$. ∎

Figure 3: The schematic of the solution process of the improved models.

##  V Solution for the improved models

As we describe in the previous sections, proposed screening model can be
treated as a pre-processing step that needs to be solved before the
optimization process of UC problem. In this paper, we will solve the
optimization models derived by Corollary 2-Corollary 4, and the solution
process of the improved models is shown in Fig. 3. This process is conducted
for each time step $t=1,2,...,T$, and the optimization horizon is equal to the
current time step $k$, making the solution process a rolling problem.

###  V-A Solution for Sample-Aware Screening

For the sample-aware case, the solution process involves the prediction part
as illustrated in Fig. 3 by the yellow blocks which represent the predictions
of generator states $\mathbf{\hat{u}}(t)$. Regarding the solution process with
ground truth, we get the ground truth by solving the original multi-interval
UC problem and record the generator states $\mathbf{{u}}^{*}(t)$. Then, we let
$\mathbf{\hat{u}}(t)=\mathbf{{u}}^{*}(t),t\leq k$ and solve the model (7) with
the optimization horizon equal to $k$.

Regarding the solution process with partial predictions, here we use k-Nearest
Neighbor (KNN) method to get the predictions due to its simplicity,
interpretability, and flexibility [15]. KNN calculates the distance between
the incoming load sample and the historical load samples, and then predicts
the ON/OFF states of generator according to the plurality vote of its closet K
neighbors. Once the prediction $\mathbf{\hat{u}}(t)$ is obtained, we have
$\mathbf{\hat{u}}(t)=\mathbf{{u}}^{*}(t),t\in T_{pre}$ and solve the model (8)
with the optimization horizon equal to $k$.

###  V-B Solution for Sample-Agnostic Screening

In this case, without the prediction part, we solve the screening model (9)
for a load region which needs to be formulated firstly. Herein, we define a
load range denoted as $r$, centered around the nominal load
$\overline{\bm{\ell}}_{t}$, then the load region $\mathcal{L}$ can be given as
follows,

$(1-r)\overline{\bm{\ell}}(t)\leq\bm{\ell}^{r}(t)\leq(1+r)\overline{\bm{\ell}}(t).$
(10)

Then, we can replace (9f) with (10) and solve the sample-agnostic screening
model (9) with the optimization horizon equal to $k$.

Note that the models for the lower bound of line limits will be solved
identically. Once the screening models are solved, we can get the binding
situation for each line limit at each time step of the original multi-interval
UC problem. Then, by eliminating the constraints identified as inactive, we
can get to the reduced multi-interval UC problem.

##  VI Case study

In this Section, we evaluate the performance of the proposed multi-step
constraint screening models, and compare the number of remaining constraints
and solution time with those of the original problem and the single-step
models. We demonstrate the proposed multi-step screening procedure is both
effective and reliable.

###  VI-A Simulation Setup

In our experiment, we conduct numerical simulations on IEEE 39-bus and IEEE
118-bus power systems to evaluate the effectiveness of our proposed method on
both small-scale and larger-scale system. Specifically, we test $r$ taking
values of 20%, 50%, 80%, and the nominal load profiles are coming from real
24-hour load dataset.

For the sample-aware screening with prediction, we take KNN as the prediction
model. To generate samples for training and validating KNN model, we use the
uniform distribution to get random ${\bm{\ell}_{t}}$ with $r=50\%$ and then
solve (1) for all generated loads. The states of each generator for 24 hours
are recorded. 2,500 samples of 39-bus system are solved for KNN training.
Moreover, when evaluating the screening performance of the multi-step and
single-step method, we use the same validation data and consider 50 samples
for each validation case.

To achieve the screening with partial predictions, we first evaluate the KNN
model’s performance in Table I. Based on the prediction accuracy and the
feasibility of the original problem, we find K$=$5 and Interval$=$4 to be an
appropriate choice so as to get as many feasible solutions as possible.

TABLE I: Parameter Selection of with
Available ML Model’s Partial Prediction

K1 | 2 | 5 | 10 | 20 | 40
---|---|---|---|---|---
Error2 | 6.44% | 5.10% | 4.87% | 4.70% | 4.65%
Feasible | 49% | 84% | 68% | 77% | 79%
Interval3 | 2 | 3 | 4 | 5 | 6
Feasible | 45% | 78% | 84% | 85% | 45%

  * •

1\. The number of nearest neighbours in KNN (Fixed Interval=4)

  * •

2\. The classcification error of generator states

  * •

3\. The interval at which the knn prediction is inserted (Fixed K=5)

TABLE II: Number of Remaining
Constraints after Sample-Aware Screening

Load Range | 20% | 50% | 80% | Average | Decline
---|---|---|---|---|---
Line Constraint1 | 483 | 478 | 472 | 478 | -78.36%
Line Constraint2 | 419 | 417 | 412 | 416 | -81.16%

  * •

1\. Remaining constraints after single-step screening

  * •

2\. Remaining constraints after multi-step screening

TABLE III: CPU Time for Solving
Original Problem after Sample-Aware Screening Load Range | 20% | 50% | 80% | Average | Speed-up
---|---|---|---|---|---
Original Problem | 2.04 | 2.20 | 1.95 | 2.06 | -
Single-step | 1.86 | 1.92 | 1.80 | 1.86 | 1.107
Multi-step | 1.84 | 1.88 | 1.79 | 1.84 | 1.124
TABLE IV: Result of Sample
Aware Screening with Partial Prediction

Method | Line Constraints | CPU Time | Speed-up
---|---|---|---
Original Problem | 2280 | 2.20 | -
Single-step | 478 | 1.98 | 1.108
Multi-step | 416 | 1.92 | 1.143
Single-step* | 414 | 1.17 | 1.873
Multi-step* | 287 | 1.06 | 2.065

  * •

* Insert KNN prediction every 4 hours

TABLE V: Number of Remaining
Constraints after Sample Agnostic Screening Scale Region | Multi-step Method | Single-step Method
---|---|---
20% | 50% | 80% | 20% | 50% | 80%
39-bus | 494 | 623 | 716 | 558 | 691 | 767
118-bus | 2283 | 2655 | 2978 | 2393 | 2744 | 3057

###  VI-B Simulation Results

_Sample-aware screening tasks_ : We consider three scenarios: i) without
generator statuses predictions, ii) with partial predictions, and iii) with
ground truth are considered to verify the effectiveness of the proposed
method. When there is no generator statuses predictions, our multi-step method
reduces 81.16% of line limits as shown in Table.II. With partial predictions,
the number of remaining constraints of multi-step is only 69% of single-step
method, and the CPU time solving the original problem is 1.103 times faster
than single-step method according to Table IV. It can be seen that multi-step
method can always eliminate more inactive constraints, and thus taking less
time to solve the reduced UC problem. Besides, the infeasible rate of the
original problem is only 16%, and the gap of objective value between the
reduced and the original UC problem is only 0.32%. Note that the bias between
the solution of binary variables obtained by the screening model and the UC
problem does not cause the infeasible case due to the line limits
misidentification, which verifies Corollary 3. According to Fig. 4, the case
with the ground truth can eliminate the most inactive constraints, while with
the partial predictions the remaining constraints can still be sufficiently
reduced compared to the case without prediction.

_Sample-agnostic screening tasks_ : In this setting, the cases both on 39-bus
and 118-bus systems with 20%, 50%, and 80% load variations are considered to
verify the scalability of the proposed method. As shown in Fig. 5, the number
of remaining constraints decrease by 60 and 100 for 39-bus and 118-bus system
over three load ranges respectively. It can be seen that with larger load
region, the number of remaining constraints increases. This may be due to the
increasing patterns of inactive constraints with wider load variation range,
i.e., the percentage of the inactive constraints decreases when widening the
load variation. Results above validate that the proposed multi-step screening
models can help boost screening performance accurately in both sample-aware
and sample-agnostic settings. This demonstrates both the possibility and the
necessity of including the practical multi-step ramping information into the
screening problem.

Figure 4: The Comparison among Sample Aware
Screening under Different Settings Figure 5: The Number of Remaining
Constraints
after Sample Agnostic Screening in (a). IEEE 39-Bus and (b). 118-Bus systems.

##  VII Conclusion

In this paper, we develop a unified framework which includes the basic and the
improved multi-step screening models with theoretical guarantees. The temporal
constraints and the ML predictions of generator states are incorporated into
the screening models, tightening the searching space of constraint screening
sufficiently. The flexibility of screening for a load region further improves
the efficiency of the proposed models. As we only consider the influence on
the searching space from the explicit constraints of UC problem, in the future
work we would like to seek theoretical understandings about the implicit
decision spaces impacting the screening and final UC solution results.

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###  -A Proof of Theorem 1

Our proof is inspired by the proof given in [6], but since the definition of
$P$ in this paper differs from that of [6], so we rewrite the proof and fit it
to our setup here.

###### Proof.

1) Sufficiency If $S_{j}^{*}(k)\leq\overline{\mathbf{f}}_{j}$, then any
feasible solution of (4) in $P^{-\\{j\\}}$, the following equation holds,

$\displaystyle\mathbf{K}_{j}\mathbf{f}(k)\leq
S_{j}^{*}(k)\leq\overline{\mathbf{f}}_{j}$ (11)

Then, (11) means any feasible solution to $P^{-\\{j\\}}$ is also a feasible
solution to $P$, i.e.,

$\displaystyle P\supseteq P^{-\\{j\\}}$ (12)

Thus, the constraint
$\mathbf{K}_{j}\mathbf{f}(k)\leq\overline{\mathbf{f}}_{j}$ is inactive to $P$
according to Definition 1, and this can imply that the constraint is also
inactive to the original UC problem as illustrated in Fig. 1.

2) Necessity If the constraint
$\mathbf{K}_{j}\mathbf{f}(k)\leq\overline{\mathbf{f}}_{j}$ is inactive, (2)
holds. The inactive constraint implies that
$\mathbf{K}_{j}\mathbf{f}(k)\leq\overline{\mathbf{f}}_{j}$ is always satisfied
for any feasible solution in $P$, which means
$\mathbf{K}_{j}\mathbf{f}(k)\leq\overline{\mathbf{f}}_{j}$ always holds for
the feasible solution in $P^{-\\{j\\}}$. Thus,
$S_{j}^{*}(k)\leq\overline{\mathbf{f}}_{j}$ is satisfied. ∎

Figure 6: IEEE 39-Bus System

###  -B A Brief Illustration to Constraint Screening

To better illustrate the result of constraint screening, we choose IEEE 39-bus
as an example in Fig.6. In the original UC problem, it has 46 power lines, and
the power flow of each line has lower bound and upper bound at each time step.
Actually, not all such constraints are active in the original problem,
motivating the research of constraint screening.

We take a specific sample from our simulation for demonstrating the case,
where the real binding lower bound of the power line for current step are Line
24[15-16]*, 36[22-35], and the active constraints in our multi-step method are
Line 3[2-25], 24[15-16], 26[16-19], 34[21-22], 36[22-35], 38[23-36].
Meanwhile, single-step method remains ten more inactive constraints than our
method. By eliminating theses inactive constraints, we can take less time to
solve the reduced UC problem.

* Line $x$[$i$-$j$]: the $x$-th line is from the $i$-th bus to the $j$-th bus in IEEE 39-bus system.


# Blockchain and 6G: The Future of Secure and Ubiquitous Communication

Ali Hussain Khan, Naveed UL Hassan, Chau Yuen, Jun Zhao, Dusit Niyato, Yan
Zhang and H. Vincent Poor A. H. Khan and N. U. Hassan are with the Department
of Electrical Engineering at Lahore University of Management Sciences (LUMS),
Lahore, Pakistan 54792. (Emails<EMAIL_ADDRESS>naveed.hassan@lums.edu.pk).C. Yuen is with the Engineering Product Development
at the Singapore University of Technology and Design (SUTD), 8 Somapah Road,
Singapore 487372. (Email: yuenchau@sutd.edu.sg).J. Zhao and D. Niyato are with
the School of Computer Science and Engineering at Nanyang Technological
University, Singapore 639798. (Emails<EMAIL_ADDRESS>dniyato@ntu.edu.sg).Y. Zhang is with the Department of Informatics at
University of Oslo, Oslo, Norway 0315. (Email: yanzhang@ifi.uio.no).H. V. Poor
is with the Department of Electrical and Computer Engineering at Princeton
University, NJ 08544. (Email:poor@princeton.edu).This work was supported in
part by LUMS Faculty Initiative Fund (FIF), in part by the U.S. National
Science Foundation under Grants CCF-1908308 and ECCS-2039716, in part by
WASP/NTU grant M4082187 (4080) and Singapore Ministry of Education (MOE) Tier
1 (RG16/20), and in part by A*STAR under its RIE2020 Advanced Manufacturing
and Engineering (AME) Industry Alignment Fund – Pre Positioning (IAF-PP)
(Grant No. A19D6a0053). Any opinions, findings and conclusions or
recommendations expressed in this material are those of the author(s) and do
not reflect the views of A*STAR.Copyright (c) 20xx IEEE. Personal use of this
material is permitted. However, permission to use this material for any other
purposes must be obtained from the IEEE by sending a request to pubs-
<EMAIL_ADDRESS>
###### Abstract

The future communication will be characterized by ubiquitous connectivity and
security. These features will be essential requirements for the efficient
functioning of the futuristic applications. In this paper, in order to
highlight the impact of blockchain and 6G on the future communication systems,
we categorize these application requirements into two broad groups. In the
first category, called Requirement Group I (RG-I), we include the performance-
related needs on data rates, latency, reliability and massive connectivity,
while in the second category, called Requirement Group II (RG-II), we include
the security-related needs on data integrity, non-repudiability, and
auditability. With blockchain and 6G, the network decentralization and
resource sharing would minimize resource under-utilization thereby
facilitating RG-I targets. Furthermore, through appropriate selection of
blockchain type and consensus algorithms, RG-II needs of 6G applications can
also be readily addressed. Through this study, the combination of blockchain
and 6G emerges as an elegant solution for secure and ubiquitous future
communication.

##  I Introduction

As 5G is approaching commercial readiness, 6G vision papers have started to
appear in the literature [1, 2, 3, 4, 5]. These papers identify some key 6G
applications and services such as, Human Bond Communication (HBC), Multi-
sensory eXtended Reality Applications (XR), Wearable Technology based
Futuristic Applications (WTech), Large-scale connected autonomous systems (LS-
CAS), and greater support for several vertical domains. These applications
have very stringent requirements of data rate, latency and reliability. The
nature of data collected by several 6G applications will be increasingly
sensitive and critical. The successful adoption of 6G applications by the
users would therefore require strict data security guarantees. Blockchain is a
distributed ledger technology where cryptography and hash functions are used
to form a chain of data blocks, created when an event occurs and verified in a
decentralized way using consensus algorithms [6]. Blockchain, initially only
used in cryptocurrencies is now being used in other application domains like
smart grid, connected vehicles, and Internet of Things. [7, 8, 9, 10].

Blockchain is believed to be a key technology in the 6G applications [2, 1,
4]. The stringent network performance requirements of these applications will
require support of technologies like Reconfigurable Intelligent Surafaces
(RIS), TeraHertz (THz) communication, Artificial Intelligence (AI) and small
cell networks. To enable efficient combination of these technologies for the
provisions of resources to achieve the performance requirements, collaboration
and coordination in a transparent and trustless environment is needed. These
technologies also require dense network deployments which will lead to more
infrastructure and complicated network deployment. Network decentralization
will be needed to simplify the network deployment. Blockchain will provide the
desired transparency and trustlessness in the decentralized network.
Blockchain will also provide the strict security requirements of the future
communication systems because of its in-built security features.

Based on the application requirements, the decentralization, security and
scalability of blockchain can be fine tuned by selection of appropriate
blockchain components. Consensus is an important property in blockchain
systems which ensures that all the nodes agree on the network state. By a
careful consideration of consensus algorithms and protocols, blockchain can
attain superior and diverse security features such as data integrity, non-
repudiation, and auditability [11, 7]. Appropriate selection of communication
network can have an impact on the decentralization and scalability of the
system. For example, if latency is not an issue but decentralization and
scalability are required, Proof-of-Work (PoW) can be used. If the system is
required to converge in a very short time, 6G can be used with communication-
intensive mechanisms like Practical Byzantine Fault Tolerance (PBFT).

We divide 6G application requirements into two broad categories with the
objective of making the blockchain and 6G combination easier to understand. In
the first category, called Requirement Group I (RG-I), we include the
performance-related needs on data rates, latency, reliability and massive
connectivity. These performance requirements will help enable ubiquitous
communication. In the second category, called Requirement Group II (RG-II), we
include the security-related needs on data integrity, non-repudiability, and
auditability. The major contributions of this paper are as follows:

  * •

We identify the requirements for optimal performance of 6G applications. We
divide these requirements into two groups based on traditional and security
requirements.

  * •

We discuss the combination of blockchain and 6G for these application
requirements. The decentralization & trustlessness and the security features
of blockchain will cater to both types of application requirements.

  * •

We consider the blockchain employment in an LS-CAS scenario. We derive the
time required to detect malicious miners in a blockchain system. By simulation
results, we show that blockchain will help detect malicious miners and 6G will
help accelerate this detection.

##  II 6G applications and their requirements

In this section, we discuss some futuristic 6G applications as shown in Figure
1 and discuss their requirements.

Figure 1: 6G Applications.

###  II-A 6G Applications

####  II-A1 Human Bond Communication

This application is concerned with data from all five human senses to allow
more expressive, realistic and holistic information exchange between humans
and machines. This application would require strict security guarantees
because a lot of intimate data would be transmitted.

####  II-A2 Multi-sensory eXtended Reality Applications

By combining information from human senses, human gestures, surrounding
environment, and multiple data sources, XR applications can provide fully-
immersive user experiences. Data integrity is required for this application
because any data attack by a malicious entity could change the entire user
experience.

####  II-A3 Wearable Technology based Futuristic Applications

Another key area is wearable technology (implantable sensors, wearable
clothing, brain-computer-interface (BCI)), which requires ultra-reliability
for reliable data exchange. Existing 5G systems fall short in leveraging the
numerous potential opportunities beyond traditional healthcare scenarios.

####  II-A4 Large-scale connected autonomous systems

Another area where 6G can find potential applications is connected robotics
and autonomous systems, which include drone-delivery systems, autonomous cars,
autonomous drone swarms, vehicle platoons, and autonomous robotics [1]. These
applications simultaneously demand all three 5G service classes, and network
slicing in 5G may not be the ideal way to achieve the requirements of such
applications.

####  II-A5 Greater Support for Vertical Domains

For vertical industries in which similar products or services are developed,
produced, and provided (e.g., manufacturing, energy, health, automation), 3GPP
has defined multiple key performance indicators (KPIs) for several core and
secondary quality of service (QoS) parameters. 5G massive machine type
communication (mMTC) will not be able to cope up with increasing number of
connected devices in vertical industries.

###  II-B 6G Application Requirements

We divide 6G application requirements into two broad categories with the
objective of making it easier to understand blockchain utility. In the first
category, we group those requirements that have always remained a major
consideration in all the previous generations of wireless communication
systems. These traditional requirements include ultra-reliability, low-
latency, enhanced data rates, and massive connectivity. We refer to these as
‘Requirement-Group-I’ (RG-I). 6G applications will demand several orders of
magnitude improvements in RG-I values. In the second category, we include
privacy & confidentiality, data integrity, non-repudiability, and auditability
requirements. We refer to these, mostly security-related requirements, as
‘Requirement-Group-II’ (RG-II). 6G applications are envisioned to use and
manipulate large amount of data produced by human senses/organs, and
autonomous agents that necessitate the inclusion of both types of requirements
as inherent and necessary components/features.

In 6G vision papers, we find a lot of discussion on various technologies that
can help in the further improvements in RG-I values. Some of these front-
runner 6G technologies include THz communication, RIS [1, 4, 2] and AI [3,
12]. We anticipate that the advancements in these new technologies and new
network architectures will enable ultra-reliable, low-latency, and enhanced
broadband connectivity for massive number of devices in 6G communication
systems. On the other hand, in 6G literature, there is not much discussion
about RG-II. This is due to several reasons. The exact definition and scope of
security-related requirements may vary in different application scenarios due
to the nature of involved entities such as operators, equipment, and machines,
and assigning responsibility for the fulfillment of these requirements is also
not straightforward. As the application and use-case landscape in future 6G
applications becomes more and more complex, fixing RG-II values also becomes
challenging.

##  III Blockchain and 6G

In this section, we first discuss blockchain followed by the combination of
blockchain and 6G from RG-I and RG-II perspective.

###  III-A Blockchain

Blockchain is a distributed ledger in which information is stored as a chain
of data blocks. Blockchain is an amalgamation of several technologies for
network, consensus and automation management. All these technologies have to
be carefully combined and selected to attain the desired security features
required for the underlying application scenario. As the use cases of
blockchain are expanding, so are the number of available options to build a
blockchain. With respect to administrative control, blockchain can be either
public, consortium or private. Any node can join, leave, read or write on the
public blockchain and it is completely decentralized. In consortium and
private blockchains, the write access is owned respectively by a group of
organizations and a single organization. PoW algorithms provide the greatest
amount of security features in terms of data immutability but their use on
resource-constrained nodes becomes challenging. PoS variants like dPoS, on the
other hand, can be made more secure by engaging large number of verifiers in
the network which increases the communication overhead and the time required
for reaching consensus. Automation on blockchain is managed through smart
contracts which are computer programs stored on the blockchain to define the
contractual obligations and enable the automatic transfer of assets between
peers when the required conditions are met.

###  III-B Blockchain and 6G RG-I

For RG-I targets, 6G is expected to be 3D integrated with infrastructure
elements being present in all three dimensions. The management of this
infrastructure and asset will be a challenging task. The spectrum, storage and
computation sharing models will also become more complex. AI will be an
essential part for resource optimization. The management of trained models
will become complex. Blockchain will provide the essential trustless
environment and security required for the resource and AI management.

Table I: Blockchain Based Resource and AI model parameter management for RG-I in 6G applications. Category |  Sub-Category |  Description |  Blockchain Based Solution
---|---|---|---
Resource Management Solutions) |  Spectrum Management |  Spectrum owners can coordinate with each other to provide spectrum resource for high data rates |  Spectrum usage information can be stored on blockchain
|  Infrastructure & Asset Management |  3D communication infrastructure is mobile, dense and diverse with complex ownership models. Its management is a challenging task for one entity |  Infrastructure location, ownership information, usage information, maintenance requirements, and useful life data can be stored on blockchain
|  Computing Power & Data Storage Management |  Un-utilized computing power or storage space anywhere in the network can shared to reduce battery drainage, decrease task latency, balance resources, and improve performance |  Computing power and data space shared information can be stored on blockchain
AI Model Parameter Management |  AI |  AI models can be trained for complex operational and environmental optimization tasks |  Hard trained AI model parameters are securely stored on and retrieved from blockchain

####  III-B1 Resource Management Solutions

6G applications would demand a large amount of spectrum, computing power, and
other available resources and infrastructure.

Spectrum Management: High data rate requirements of 6G applications can be
aided by spectrum sharing as data rate is directly proportional to the
available bandwidth. To maximize spectrum utilization, licensed spectrum
owners as well as unlicensed spectrum operators in any band can coordinate and
cooperate with each other under different terms and conditions automated
through smart contracts which are deployed on a blockchain. Spectrum sharing
framework described in [13] for 5G can be applied. In this framework, when a
user requests the desired bandwidth, the primary operator (operator which has
the registration information of the user) checks to see if it has the desired
resources. If not, it requests the secondary operator regarding the resource
availability. Once confirmed, the primary operator sends the user’s
information to secondary operator, which sends a service level agreement (SLA)
to the primary operator and provides the required permission to use the
spectrum. The authorized node verifies the transaction and adds it to the
blockchain. This framework can be made more secure for 6G by choosing a
consortium blockchain along with appropriate consensus algorithms. In such an
improved framework, a transaction containing both the operator identities,
user identity, and start and end time of spectrum usage is added to current
block which is verified by the network. Once verified, the new block
containing the spectrum sharing transaction is added to the blockchain.

Infrastructure & Asset Management: Dense deployment of communication devices
in all the three spatial dimensions owned by multiple operators or some
specialized asset service providers (SASPs) (e.g., specializing in
communication drones, HAPs, submarines) in 6G would be critical for RG-I
targets. At the same time, maximum utilization of all the available resources
would ensure the quality of service (QoS) of 6G users and would also maximize
the revenues of network operators and SASPs. We explain the utility of
blockchain through an example of a user wanting to decrease the communication
latency by finding the best communication relays provided by the SASPs. In a
blockchain-assisted infrastructure and asset management system, an
authenticated and registered user will search for the nearest communication
relays. The relays check the registration information of the user and its
network from the blockchain and then provide the desired connectivity to the
user according to the SLAs available in the smart contract for that network.
The transaction is recorded on the blockchain after verification through an
appropriate consensus algorithm.

Computing Power & Data Storage Management: Many 6G applications would require
a large amount of data from a very large number of sensors and nodes. For
example, to provide fully immersive XR experiences, thousands (if not
millions) of extremely small sensors may be required. Processing all this data
into meaningful rich information will require a huge amount of computing
power. However, even with future enhancements in battery technologies, such
intensive applications will severely deplete the battery and storage of mobile
devices and computing and storage resources might also be inadequate. For
compute power and storage management, authenticated users could use a public
blockchain. We can assume a double auction market model where some users in
need of computing power or storage space would submit their asks (required
resources and price) while others with spare computing power or storage space
can place their bids (available resources and price). In every such market
round, bids and asks are matched and market clearing price is determined. The
double auction algorithm is automated through a smart contract. The
transactions are added to new blocks which are verified through consensus and
added to the blockchain.

####  III-B2 AI Model Parameter Management Solutions

Operational and environmental intelligence may be achieved in 6G networks with
the help of AI. With network densification, novel RIS-based channel models,
multiple conflicting objectives, and extremely large number of variables,
optimization problems in 6G networks would become NP-hard. Instead of applying
traditional optimization, deep learning techniques will mostly be used for
efficient optimization of network resources in rapidly changing operational
and environmental conditions. AI models are difficult to train but very
efficient to use and produce results in no time. In this context, blockchain
may be used to safely store the hard-found AI model training parameters.

###  III-C Blockchain and 6G RG-II

In the following, we provide definitions of data integrity, non-repudiation
and auditability. These are essential security features for 6G applications
and have not been clearly defined previously in that context.

Data Integrity: Data integrity refers to the detection of unauthorized changes
in data. Data integrity attacks deliberately modify the original information
to corrupt communication system for some malicious gains. Data integrity
breaches may create safety issues in several control applications in vertical
domains and LS-CAS applications.

Non-repudiation: Non-repudiation refers to the availability of irrefutable
proof of who performed a certain action even if the nodes in the network are
not cooperating. As AI is becoming commonplace, we anticipate a very large
number of machine-type nodes in 6G applications to mimic some form of human
intelligence. In this context, non-repudiation will become an important
requirement in several 6G applications.

Auditability: Auditability is concerned with the ability to reconstruct
complete history of certain event or action from the historical records. In
many LS-CAS applications where critical decision making is involved,
auditability would be required to fix liability in case of malfunctions,
conflicts, or to safeguard commercial and financial interests.

With these definitions and in order to better understand the advantages
provided by blockchain for RG-II targets of 6G applications, we present a
brief discussion of security related options available in 4G and 5G systems.
The legacy authentication mechanisms in previous generations of communication
systems mostly employ symmetric-key cryptography where the same key is used
for encryption and decryption of data [14]. Up to 4G communication systems,
Authenticated key agreement protocol (AKA) and Extensible Authentication
Protocols (EAP) frameworks are largely used. AKA is a challenge-and-response
based authentication protocol, while in EAP, the user provides an identity to
the eNodeB which is then authenticated by the authentication server. On the
other hand, in 5G communication systems, asymmetric public-key-infrastructure
(PKI) based cryptography, which provides stronger security properties than
symmetric key cryptography, is used [15]. There is no protection in 4G
communication systems for user data integrity. In 5G communication systems,
protection of user data integrity is mandatory over the air interface.
Integrity protection is resource demanding, therefore, the maximum data rate
for integrity protected data traffic in 5G is limited to 64kbps. 4G
communication systems have no provision for non-repudiation because of
symmetric key cryptography, while non-repudiation protection is provided by 5G
due to PKI based cryptography. In both 4G and 5G communication systems, there
is no defined mechanism for auditability of data.

Integration of blockchain in 6G would not only help but also control RG-II
targets. Through appropriate selection of network, consensus, and automation
management algorithms, blockchain can provide desired levels of data
integrity, non-repudiation and auditability. Blockchain allows asymmetric PKI
based cryptography and the inclusion of privacy preservation frameworks for
greater data privacy & confidentiality. Blockchain accepts new blocks only
after verification through a consensus mechanism among multiple P2P nodes.
Every block is linked to its parent block (previous block in the chain) by a
cryptographic hash function. This allows auditability and makes it possible to
verify data all the way back to the genesis block. Data integrity in any block
can be easily verified simply by checking the hash-trees. Moreover, as the
blockchain size increases, data tampering becomes even more difficult because
of the linkage between all the chained blocks.

In addition to that, some state-of-the-art security technologies in practical
communication systems are used in 5G. The encryption system used in 5G is
128-NIA1 which provides a 128 bit security level, i.e., equivalent to that of
AES 128. Blockchain utilizes two different levels of security where, for data
verification, the data is encrypted. For data storage, the hash of the block
is cascaded into the next block. For privacy, 5G uses the Elliptic Curve
Integrated Encryption System (ECIES). Here the International Mobile Subscriber
Identity (IMSI) of the user is encrypted multiple times to generate different
identities every time. In blockchain, privacy is ensured by generating a
different key pair for every transaction to avoid linking of transactions. The
control plane of 5G is logically centralized using SDN and NFV. This
highlights an obvious vulnerability related to availability. Blockchain, being
a decentralized network, provides better availability.

##  IV Case Study and Simulation Results

In this section, we present a case study to show how blockchain and 6G
combined can provide a fast and secure communication system. We consider an
LS-CAS example which is a data- and machine-centric application and large
amount of critical data is automatically generated and shared between
autonomous nodes. Such applications are already been discussed in 4G and 5G
communication systems. However, we will demonstrate that combining blockchain
and 4G or blockchain and 5G cannot achieve the same level of synergy that we
can obtain with blockahin and 6G. This is because of the fact that superior
security features of blockchain require resource-intensive consensus
algorithms and superior communication networks. Therefore, when 6G speeds are
combined with blockhain security we achieve the desired goal of truly fast and
secure communication.

###  IV-A LS-CAS Scenario

Our LS-CAS scenario consists of autonomous vehicles & delivery drones
(collectively referred to as User Equipments (UE)) and Road Side Units (RSU).
We assume that some RSUs are fixed while others are drone-mounted. In this
application, we have U2U (user equipment to user equipment), U2I (user
equipment to infrastructure) and I2I (infrastructure to infrastructure)
communications. UEs and RSUs together form a large-scale wireless-connected
distributed autonomous system. We assume UEs are equipped with several sensors
and state-of-the art camera systems. The data generated by UEs might represent
real-time road maps, location information, infotainment, RSU reputation
information, sensor readings, or any other information related to UE safety,
transportation or entertainment needs. This data should be shared in the
network with low latency while ensuring data integrity which is important for
safe navigation and other reasons. In a scenario where this system is under
attack from some malicious actors (RSUs and colluding vehicles) inside the
network who can tamper data for their advantage, we need a mechanism to detect
data tampering and also to recognize malicious actors. With the introduction
of blockchain and its features, such data integrity attacks and bad actors can
be easily recognized.

###  IV-B Secure Enhanced dPoS Algorithm for LS-CAS

We consider a blockchain-based setup similar to [8]. This blockchain uses a
secure and enahnced dPoS alogrithm and there are numerous safegaurds for the
protection of shared data. We assume RSUs have the necessary resources to
implement and store the blockchain. The data shared among the UEs is sent to
the RSUs, which run a dPoS consensus algorithm for block mining. We assume
that RSUs are not fully trusted and can get compromised. Additionally, some
UEs can also collude with the compromised RSUs. Therefore, miner reputations
are updated after a complete round of data exchange and the record is uploaded
to the blockchain. In the following, we explain one round of block creation
and reputation updates. This process is also depicted in Figure 2.

Figure 2: Blockchain-based reputation and dPoS Implementation for LS-CAS
Application.

  1. 1.

First, the stakeholders (vehicles/drones) participate in a voting process to
determine active and standby miners according to the reputation scores. Active
miners are a pre-defined number of higher reputation miners from all the
miners, and they act as block managers in a round-robin fashion for the
following rounds. Real-time data is shared among UEs and the data sharing
record is shared with the nearest available RSU. UEs also upload recently
calculated reputation scores to the nearest RSU. RSUs route this data to the
block manager of that round.

  2. 2.

Active and standby miners are split into different types based on their
reputation scores. The block manager designs a smart contract for each type
and broadcast the unverified data block along with the different smart
contracts. Smart contracts are designed such that a verifier gets maximum
utility only if it attempts the respective smart contract. The block is
verified and the verification results are audited by the local neighborhood
after which, the block is sent back to the block manager.

  3. 3.

Block manager receives the verification reports and creates a new data block
based on 2/3 majority consensus basis. After consensus, the block manager
broadcasts new block and the RSUs add this block to their local blockchain
copies.

  4. 4.

UEs download the latest data block from their nearest RSU, check the accuracy
of their previous transactions, and accordingly update the reputation score of
the RSU for the next round.

There are numerous safeguards in this dPoS scheme to allow for the detection
of malicious actors and collusion attacks. However, it is also obvious that
the detection of any malicious activity largely depends on the amount of time
required to complete different tasks in each round. We can divide the latency
of different steps in each round into transmission latency, computational
latency and information diffusion latency. Due to the availability of
relatively fast processors in vehicles and RSUs, we neglect the computational
latency and thus the time for one round of this step will depend on the
network speeds and network scale.

###  IV-C The role of Communication Network

To show the role of communication networks (4G/5G/6G) we perform some
simulations. In these simulations, we assume a total area of 150km2. UE
positions are randomly initialized and RSUs are uniformly deployed across the
network. The positions and the range of RSUs are set according to the density
of network deployment. The weight of positive and negative interactions is set
as 0.4 and 0.6 respectively. The probability of successful message
transmission is 0.7. These parameters are derived from [8]. The adjustment
factor for number of hops is set to be 0.75. The reputation scores are
computed using multi-weight subjective logic (MWSL) model [8]. We consider
four different network scales, i.e., small-scale, medium scale, large-scale,
and very-large-scale. Different parameters required in the simulation (e.g.,
average number of hops to block manager, types of verifiers, number of RSUs
with UE records) are adjusted according to the network scale. In these
simulations, we consider an attack scenario where a miner starts to behave
maliciously after 20 rounds. The malicious miner also colludes with 25%, 33%
and 50% UEs in order to get high reputation scores. We consider the ability of
the blockchain-based scheme to detect the malicious miner in 4G, 5G and 6G
networks. Important simulation parameters are given in Table II.

In Figure 3, we plot the amount of time required to detect malicious miner for
different network sizes in 4G/5G/6G for different attack scenarios. As we
increase the network size, the amount of time required for the detection of
malicious miners increases. Similarly, for the same network size, as we
increase the percentage of colluding UEs, the amount of time required to
detect a malicious miner also increases. The performance of 4G network is only
adequate in small and medium-scale network where at 50% collusion it is able
to detect the malicious miner respectively in 15s and 340s respectively. In
large and very-large-scale networks, at 50% collusion, 5G network requires
681s and 1826s respectively to detect a malicious miner. On the other hand, 6G
network only requires 25s and 53s respectively in large and very-large-scale
networks to detect a malicious miner at 50% collusion.

Table II: Parameters and their values Parameter |  Small-Scale Network |  Medium-Scale Network |  Large-Scale Network |  Very-Large-Scale Network
---|---|---|---|---
Total number of active and standby miners |  100 |  1000 |  10000 |  20000
Total number of vehicular and drone users |  100 |  1000 |  10000 |  20000
Vote Size |  1KB |  10KB |  100KB |  200KB
UEs and RSUs download and upload speeds |  10Mbps(4G), 500Mbps(5G), 100Gbps(6G) |  10Mbps(4G), 500Mbps(5G), 100Gbps(6G) |  10Mbps(4G), 500Mbps(5G), 100Gbps(6G) |  10Mbps(4G), 500Mbps(5G), 100Gbps(6G)
Data block size before verification |  10KB |  100KB |  5MB |  10MB
Reputation block size before verification |  1.5KB |  15KB |  150KB |  300KB
Size of smart contract |  2KB |  15KB |  150KB |  200KB
Types of Verifiers |  10 |  10 |  10 |  10
Number of active miners |  15 |  41 |  199 |  255
Number of RSUs with UE data record |  [10, 40] |  [100, 400] |  [1000, 4000] |  [1500, 6000]
Maximum end to end number of hops |  8 |  23 |  71 |  100
Figure 3: Time Required to Detect Malicious Miner for Different Collusion
Rates in Different Sized Networks.

In order to clarify the importance of blockchain in this scenario, we consider
an adversary, which behaves honestly for 20 interactions and then switches
between malicious and honest behavior for 15 and 5 interactions alternatively.
We use the blockchain with MWSL model as well as blockchain with beta and
sigmoid reputation models. In beta reputation model, beta probability density
function is used to combine feedback and derive reputation. In sigmoid model,
reputation is calculated as a sigmoid function of an overall impact of honest
and malicious behavior. Using appropriate parameters and considering 33%
network collusion, we observe that some blockchains are able to detect
malicious miners, while others are not as shown in Figure 4. Even using 6G
will not help in those cases. Using the latency results of 6G, we will see
that malicious miners are detected the earliest when used 6G with an
appropriate blockchain model. This result shows that in LS-CAS, appropriate
selection of blockchain structure is necessary for detecting malicious
activity and therefore, improve the system integrity. Along with blockchain,
6G is the most appropriate technology that will facilitate timely detection.
In that sense, blockchain and 6G will form an ideal combination for the
application used i.e., LS-CAS.

Figure 4: Update sensitivity of different reputation schemes.

These simulation results are very promising and suggest the use of more secure
blockchain implementations in 6G are possible as both complement each other.
Secure consensus algorithms enhance security of 6G applications while 6G
enables their implementation through its faster speeds. At the same time, the
creation of a trustless environment in 6G by more secure blockchain
implementations would benefit RG-I by eliminating under-utilization of
critical resources deployed under complex ownership and sharing models. Some
challenges for wider blockchain implementations in 6G would require further
research in the following directions:

  * •

Sharding and sub-blockchain techniques could be utilized for further reduction
in convergence times in very large blockchain networks.

  * •

Smart contracts optimization techniques are necessary for decreasing block
size and consensus latency. Smart contracts should also be written extremely
carefully to make them less vulnerable to hackers.

  * •

Larger network sizes translate to larger storage requirements. Off-chain
storage can be used and a signature associated with the block can be stored on
the chain.

  * •

Without compromising the security features, there is a clear need for less
resource intensive consensus algorithms.

##  V Conclusion

In this paper, we have discussed the potential of blockchain and 6G for future
communication and highlighted a synergy between them. We have divided 6G
application requirements into performance related (RG-I) and security related
(RG-II) groups with the objective of making the synergy more understandable.
We have shown that the trustless nature of blockchain would make it easier to
manage and audit 3D network resources and AI model parameters in 6G networks
with complex ownership models. This flexible use of increasingly large and
complex network resources in 6G with the help of blockchain would
significantly facilitate RG-I targets. Furthermore, through appropriate
selection of blockchain type and consensus algorithms, RG-II needs of 6G
applications could also be readily addressed. Therefore, blockchain and 6G
combined can provide secure and ubiquitous communication.

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